TSTP Solution File: ALG148+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG148+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:37:51 EDT 2023
% Result : Unsatisfiable 20.49s 3.52s
% Output : Proof 171.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : ALG148+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.08 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.07/0.26 % Computer : n032.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Aug 28 02:48:15 EDT 2023
% 0.07/0.26 % CPUTime :
% 0.10/0.49 ________ _____
% 0.10/0.49 ___ __ \_________(_)________________________________
% 0.10/0.49 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.10/0.49 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.10/0.49 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.10/0.49
% 0.10/0.49 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.10/0.49 (2023-06-19)
% 0.10/0.49
% 0.10/0.49 (c) Philipp Rümmer, 2009-2023
% 0.10/0.49 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.10/0.49 Amanda Stjerna.
% 0.10/0.49 Free software under BSD-3-Clause.
% 0.10/0.49
% 0.10/0.49 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.10/0.49
% 0.10/0.49 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.10/0.50 Running up to 7 provers in parallel.
% 0.10/0.51 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.10/0.51 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.10/0.51 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.10/0.51 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.10/0.51 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.10/0.51 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.10/0.51 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.30/1.35 Prover 1: Preprocessing ...
% 4.30/1.36 Prover 4: Preprocessing ...
% 4.30/1.39 Prover 0: Preprocessing ...
% 4.30/1.39 Prover 3: Preprocessing ...
% 4.30/1.39 Prover 6: Preprocessing ...
% 4.30/1.39 Prover 2: Preprocessing ...
% 4.30/1.39 Prover 5: Preprocessing ...
% 9.28/1.93 Prover 3: Constructing countermodel ...
% 9.28/1.93 Prover 2: Constructing countermodel ...
% 9.28/1.96 Prover 0: Constructing countermodel ...
% 9.28/1.97 Prover 6: Constructing countermodel ...
% 9.28/1.97 Prover 1: Constructing countermodel ...
% 9.28/1.98 Prover 4: Constructing countermodel ...
% 11.70/2.29 Prover 5: Constructing countermodel ...
% 20.49/3.52 Prover 6: proved (3004ms)
% 20.49/3.52
% 20.49/3.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 20.49/3.52
% 20.49/3.52 Prover 3: stopped
% 20.49/3.52 Prover 2: stopped
% 20.49/3.52 Prover 5: stopped
% 20.49/3.52 Prover 0: stopped
% 20.49/3.53 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 20.49/3.53 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 20.49/3.53 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 20.49/3.53 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.49/3.54 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 21.47/3.79 Prover 7: Preprocessing ...
% 23.03/3.86 Prover 10: Preprocessing ...
% 23.03/3.86 Prover 8: Preprocessing ...
% 23.03/3.88 Prover 11: Preprocessing ...
% 23.57/3.90 Prover 13: Preprocessing ...
% 24.62/4.05 Prover 8: Constructing countermodel ...
% 25.25/4.11 Prover 7: Constructing countermodel ...
% 25.25/4.16 Prover 10: Constructing countermodel ...
% 25.25/4.17 Prover 13: Constructing countermodel ...
% 25.80/4.18 Prover 11: Constructing countermodel ...
% 63.80/9.18 Prover 13: stopped
% 63.80/9.20 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 65.02/9.34 Prover 16: Preprocessing ...
% 66.15/9.56 Prover 16: Constructing countermodel ...
% 108.78/15.10 Prover 16: stopped
% 108.78/15.12 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 110.09/15.28 Prover 19: Preprocessing ...
% 110.37/15.40 Prover 19: Constructing countermodel ...
% 114.35/15.85 Prover 1: stopped
% 136.93/18.90 Prover 19: stopped
% 159.28/22.75 Prover 10: Found proof (size 768064)
% 159.28/22.75 Prover 10: proved (19228ms)
% 159.28/22.75 Prover 7: stopped
% 159.28/22.75 Prover 11: stopped
% 159.28/22.75 Prover 4: stopped
% 159.28/22.75 Prover 8: stopped
% 159.28/22.75
% 159.28/22.75 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 159.28/22.75
% 161.03/23.23 % SZS output start Proof for theBenchmark
% 161.17/23.31 Assumptions after simplification:
% 161.17/23.31 ---------------------------------
% 161.17/23.31
% 161.17/23.32 (ax1)
% 161.43/23.40 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.43/23.40 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 161.43/23.40 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 161.43/23.40 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 161.43/23.40 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 161.43/23.40 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 161.43/23.40 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 161.43/23.40 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 161.43/23.40 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 161.43/23.40 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 161.43/23.40 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 161.43/23.40 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 161.43/23.40 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 161.43/23.40 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 161.43/23.40 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 161.43/23.40 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 161.43/23.40 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 161.43/23.40 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 161.43/23.40 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 161.43/23.40
% 161.58/23.41 (ax10)
% 161.58/23.41 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.41 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 161.58/23.41 op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 &
% 161.58/23.41 $i(v1))))
% 161.58/23.41
% 161.58/23.41 (ax11)
% 161.58/23.41 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.41 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 161.58/23.41 op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 &
% 161.58/23.42 $i(v1))))
% 161.58/23.42
% 161.58/23.42 (ax12)
% 161.58/23.42 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.42 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 161.58/23.42 op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 &
% 161.58/23.42 $i(v1))))
% 161.58/23.42
% 161.58/23.42 (ax13)
% 161.58/23.42 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.42 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 161.58/23.42 op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 &
% 161.58/23.42 $i(v1))))
% 161.58/23.42
% 161.58/23.42 (ax14)
% 161.58/23.42 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.42 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 161.58/23.42 op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 &
% 161.58/23.42 $i(v1))))
% 161.58/23.42
% 161.58/23.42 (ax15)
% 161.58/23.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.43 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 161.58/23.43 op(e1, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 &
% 161.58/23.43 $i(v1))))
% 161.58/23.43
% 161.58/23.43 (ax16)
% 161.58/23.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.43 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 161.58/23.43 op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 &
% 161.58/23.43 $i(v1))))
% 161.58/23.43
% 161.58/23.43 (ax17)
% 161.58/23.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.43 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 161.58/23.43 op(e1, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 &
% 161.58/23.43 $i(v1))))
% 161.58/23.43
% 161.58/23.43 (ax18)
% 161.58/23.43 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.43 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 161.58/23.43 op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 &
% 161.58/23.43 $i(v1))))
% 161.58/23.43
% 161.58/23.43 (ax19)
% 161.58/23.44 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.44 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 161.58/23.44 op(e2, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 &
% 161.58/23.44 $i(v1))))
% 161.58/23.44
% 161.58/23.44 (ax2)
% 161.58/23.47 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.47 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 161.58/23.47 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 161.58/23.47 $i] : ? [v14: $i] : ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 =
% 161.58/23.47 e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3,
% 161.58/23.47 e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 161.58/23.47 e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15
% 161.58/23.47 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 &
% 161.58/23.47 op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3,
% 161.58/23.47 e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2)
% 161.58/23.47 | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1
% 161.58/23.47 & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3,
% 161.58/23.47 e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) =
% 161.58/23.47 e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15
% 161.58/23.47 = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 161.58/23.47 op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3,
% 161.58/23.47 e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0)
% 161.58/23.47 | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3
% 161.58/23.47 & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2)
% 161.58/23.47 = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 161.58/23.47 (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 161.58/23.47 op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2)
% 161.58/23.47 = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) |
% 161.58/23.47 (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 &
% 161.58/23.47 op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2,
% 161.58/23.47 e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) =
% 161.58/23.47 e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 161.58/23.47 (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 161.58/23.47 op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1)
% 161.58/23.47 = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) |
% 161.58/23.47 (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 &
% 161.58/23.47 op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2,
% 161.58/23.47 e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3))
% 161.58/23.47 & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 161.58/23.47 op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3,
% 161.58/23.47 e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1)
% 161.58/23.47 | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0
% 161.58/23.47 & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1)
% 161.58/23.47 = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) |
% 161.58/23.47 (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 161.58/23.47 op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) =
% 161.58/23.47 e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8
% 161.58/23.47 = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 &
% 161.58/23.48 op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2)
% 161.58/23.48 = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) &
% 161.58/23.48 ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 161.58/23.48 op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0)
% 161.58/23.48 = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0
% 161.58/23.48 = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 &
% 161.58/23.48 op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) =
% 161.58/23.48 e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1
% 161.58/23.48 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 161.58/23.48 op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) =
% 161.58/23.48 e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2
% 161.58/23.48 = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 &
% 161.58/23.48 op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3,
% 161.58/23.48 e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) =
% 161.58/23.48 e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) |
% 161.58/23.48 (v1 = e0 & op(e0, e1) = e0)))))
% 161.58/23.48
% 161.58/23.48 (ax20)
% 161.58/23.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.48 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 161.58/23.48 op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 &
% 161.58/23.48 $i(v1))))
% 161.58/23.48
% 161.58/23.48 (ax21)
% 161.58/23.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.48 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 161.58/23.48 op(e2, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 &
% 161.58/23.48 $i(v1))))
% 161.58/23.48
% 161.58/23.48 (ax22)
% 161.58/23.48 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.48 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 161.58/23.48 op(e2, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 &
% 161.58/23.48 $i(v1))))
% 161.58/23.48
% 161.58/23.48 (ax23)
% 161.58/23.49 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.49 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 161.58/23.49 op(e2, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 &
% 161.58/23.49 $i(v1))))
% 161.58/23.49
% 161.58/23.49 (ax24)
% 161.58/23.49 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.49 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 161.58/23.49 op(e3, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 &
% 161.58/23.49 $i(v1))))
% 161.58/23.49
% 161.58/23.49 (ax25)
% 161.58/23.49 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.49 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 161.58/23.49 op(e3, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 &
% 161.58/23.49 $i(v1))))
% 161.58/23.49
% 161.58/23.49 (ax26)
% 161.58/23.49 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.49 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 161.58/23.49 op(e3, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 &
% 161.58/23.49 $i(v1))))
% 161.58/23.49
% 161.58/23.49 (ax27)
% 161.58/23.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.50 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 161.58/23.50 op(e3, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 &
% 161.58/23.50 $i(v1))))
% 161.58/23.50
% 161.58/23.50 (ax28)
% 161.58/23.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.50 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 161.58/23.50 op(e3, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 &
% 161.58/23.50 $i(v1))))
% 161.58/23.50
% 161.58/23.50 (ax29)
% 161.58/23.50 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.50 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 161.58/23.50 op(e3, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 &
% 161.58/23.50 $i(v1))))
% 161.58/23.50
% 161.58/23.50 (ax3)
% 161.58/23.51 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.51 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 161.58/23.51 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 161.58/23.51 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~
% 161.58/23.51 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 =
% 161.58/23.51 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) &
% 161.58/23.51 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 =
% 161.58/23.51 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~
% 161.58/23.51 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) &
% 161.58/23.51 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) &
% 161.58/23.51 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) &
% 161.58/23.51 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~
% 161.58/23.51 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~
% 161.58/23.51 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 161.58/23.51 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 161.58/23.51 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 161.58/23.51 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 161.58/23.51 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 161.58/23.51 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 161.58/23.51 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 161.58/23.51
% 161.58/23.51 (ax4)
% 161.58/23.51 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~
% 161.58/23.51 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 161.58/23.51
% 161.58/23.51 (ax5)
% 161.58/23.54 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.54 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 161.58/23.54 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 161.58/23.54 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v5 & op(e2, e2) = v3 &
% 161.58/23.54 op(e1, e1) = v1 & op(e0, e0) = v0 & $i(v5) & $i(v3) & $i(v1) & $i(v0) & ( ~
% 161.58/23.54 (v5 = e2) | (v14 = e3 & op(e3, e2) = e3)) & ( ~ (v5 = e1) | (v11 = e3 &
% 161.58/23.54 op(e3, e1) = e3)) & ( ~ (v5 = e0) | (v6 = e3 & op(e3, e0) = e3)) & ( ~
% 161.58/23.54 (v3 = e3) | (v15 = e2 & op(e2, e3) = e2)) & ( ~ (v3 = e1) | (v10 = e2 &
% 161.58/23.54 op(e2, e1) = e2)) & ( ~ (v3 = e0) | (v4 = e2 & op(e2, e0) = e2)) & ( ~
% 161.58/23.54 (v1 = e3) | (v13 = e1 & op(e1, e3) = e1)) & ( ~ (v1 = e2) | (v12 = e1 &
% 161.58/23.54 op(e1, e2) = e1)) & ( ~ (v1 = e0) | (v2 = e1 & op(e1, e0) = e1)) & ( ~
% 161.58/23.54 (v0 = e3) | (v9 = e0 & op(e0, e3) = e0)) & ( ~ (v0 = e2) | (v8 = e0 &
% 161.58/23.54 op(e0, e2) = e0)) & ( ~ (v0 = e1) | (v7 = e0 & op(e0, e1) = e0)) & (v5 =
% 161.58/23.54 e3 | v3 = e2 | v1 = e1 | v0 = e0) & ((v15 = e3 & ~ (v3 = e2) & op(e2, e3)
% 161.58/23.54 = e3 & ( ~ (v5 = e2) | ( ~ (v14 = e3) & op(e3, e2) = v14 & $i(v14))) & (
% 161.58/23.54 ~ (v1 = e2) | ( ~ (v12 = e1) & op(e1, e2) = v12 & $i(v12))) & ( ~ (v0
% 161.58/23.54 = e2) | ( ~ (v8 = e0) & op(e0, e2) = v8 & $i(v8)))) | (v14 = e2 & ~
% 161.58/23.54 (v5 = e3) & op(e3, e2) = e2 & ( ~ (v3 = e3) | ( ~ (v15 = e2) & op(e2,
% 161.58/23.54 e3) = v15 & $i(v15))) & ( ~ (v1 = e3) | ( ~ (v13 = e1) & op(e1,
% 161.58/23.54 e3) = v13 & $i(v13))) & ( ~ (v0 = e3) | ( ~ (v9 = e0) & op(e0, e3)
% 161.58/23.54 = v9 & $i(v9)))) | (v13 = e3 & ~ (v1 = e1) & op(e1, e3) = e3 & ( ~
% 161.58/23.54 (v5 = e1) | ( ~ (v11 = e3) & op(e3, e1) = v11 & $i(v11))) & ( ~ (v3 =
% 161.58/23.54 e1) | ( ~ (v10 = e2) & op(e2, e1) = v10 & $i(v10))) & ( ~ (v0 = e1)
% 161.58/23.54 | ( ~ (v7 = e0) & op(e0, e1) = v7 & $i(v7)))) | (v12 = e2 & ~ (v1 =
% 161.58/23.54 e1) & op(e1, e2) = e2 & ( ~ (v5 = e1) | ( ~ (v11 = e3) & op(e3, e1) =
% 161.58/23.54 v11 & $i(v11))) & ( ~ (v3 = e1) | ( ~ (v10 = e2) & op(e2, e1) = v10
% 161.58/23.54 & $i(v10))) & ( ~ (v0 = e1) | ( ~ (v7 = e0) & op(e0, e1) = v7 &
% 161.58/23.54 $i(v7)))) | (v11 = e1 & ~ (v5 = e3) & op(e3, e1) = e1 & ( ~ (v3 =
% 161.58/23.54 e3) | ( ~ (v15 = e2) & op(e2, e3) = v15 & $i(v15))) & ( ~ (v1 = e3)
% 161.58/23.54 | ( ~ (v13 = e1) & op(e1, e3) = v13 & $i(v13))) & ( ~ (v0 = e3) | ( ~
% 161.58/23.54 (v9 = e0) & op(e0, e3) = v9 & $i(v9)))) | (v10 = e1 & ~ (v3 = e2) &
% 161.58/23.54 op(e2, e1) = e1 & ( ~ (v5 = e2) | ( ~ (v14 = e3) & op(e3, e2) = v14 &
% 161.58/23.54 $i(v14))) & ( ~ (v1 = e2) | ( ~ (v12 = e1) & op(e1, e2) = v12 &
% 161.58/23.54 $i(v12))) & ( ~ (v0 = e2) | ( ~ (v8 = e0) & op(e0, e2) = v8 &
% 161.58/23.54 $i(v8)))) | (v6 = e0 & ~ (v5 = e3) & op(e3, e0) = e0 & ( ~ (v3 =
% 161.58/23.54 e3) | ( ~ (v15 = e2) & op(e2, e3) = v15 & $i(v15))) & ( ~ (v1 = e3)
% 161.58/23.54 | ( ~ (v13 = e1) & op(e1, e3) = v13 & $i(v13))) & ( ~ (v0 = e3) | ( ~
% 161.58/23.54 (v9 = e0) & op(e0, e3) = v9 & $i(v9)))) | (v4 = e0 & ~ (v3 = e2) &
% 161.58/23.54 op(e2, e0) = e0 & ( ~ (v5 = e2) | ( ~ (v14 = e3) & op(e3, e2) = v14 &
% 161.58/23.54 $i(v14))) & ( ~ (v1 = e2) | ( ~ (v12 = e1) & op(e1, e2) = v12 &
% 161.58/23.54 $i(v12))) & ( ~ (v0 = e2) | ( ~ (v8 = e0) & op(e0, e2) = v8 &
% 161.58/23.54 $i(v8)))) | (v2 = e0 & ~ (v1 = e1) & op(e1, e0) = e0 & ( ~ (v5 =
% 161.58/23.54 e1) | ( ~ (v11 = e3) & op(e3, e1) = v11 & $i(v11))) & ( ~ (v3 = e1)
% 161.58/23.54 | ( ~ (v10 = e2) & op(e2, e1) = v10 & $i(v10))) & ( ~ (v0 = e1) | ( ~
% 161.58/23.54 (v7 = e0) & op(e0, e1) = v7 & $i(v7)))) | ( ~ (v0 = e0) & ( ~ (v5 =
% 161.58/23.54 e0) | ( ~ (v6 = e3) & op(e3, e0) = v6 & $i(v6))) & ( ~ (v3 = e0) | (
% 161.58/23.54 ~ (v4 = e2) & op(e2, e0) = v4 & $i(v4))) & ( ~ (v1 = e0) | ( ~ (v2 =
% 161.58/23.54 e1) & op(e1, e0) = v2 & $i(v2))) & ((v9 = e3 & op(e0, e3) = e3) |
% 161.58/23.54 (v8 = e2 & op(e0, e2) = e2) | (v7 = e1 & op(e0, e1) = e1)))))
% 161.58/23.54
% 161.58/23.54 (ax6)
% 161.58/23.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.55 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 161.58/23.55 op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 &
% 161.58/23.55 $i(v1))))
% 161.58/23.55
% 161.58/23.55 (ax7)
% 161.58/23.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.55 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 161.58/23.55 op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 &
% 161.58/23.55 $i(v1))))
% 161.58/23.55
% 161.58/23.55 (ax8)
% 161.58/23.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.55 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 161.58/23.55 op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 &
% 161.58/23.55 $i(v1))))
% 161.58/23.55
% 161.58/23.55 (ax9)
% 161.58/23.55 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 161.58/23.55 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 161.58/23.55 op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 &
% 161.58/23.55 $i(v1))))
% 161.58/23.55
% 161.58/23.55 (function-axioms)
% 161.58/23.55 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3,
% 161.58/23.55 v2) = v1) | ~ (op(v3, v2) = v0))
% 161.58/23.55
% 161.58/23.55 Those formulas are unsatisfiable:
% 161.58/23.55 ---------------------------------
% 161.58/23.55
% 161.58/23.55 Begin of proof
% 161.58/23.56 |
% 161.58/23.56 | ALPHA: (ax1) implies:
% 161.58/23.57 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 161.58/23.57 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 161.58/23.57 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 161.58/23.57 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 161.58/23.57 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 161.58/23.57 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 161.58/23.57 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 161.58/23.57 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 161.58/23.57 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 161.58/23.57 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 161.58/23.57 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 161.58/23.57 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 161.58/23.57 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 161.58/23.57 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 161.58/23.57 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 161.58/23.57 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 161.58/23.57 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 161.58/23.57 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 161.58/23.57 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 161.58/23.57 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 161.58/23.57 | = e0))
% 161.58/23.57 |
% 161.58/23.57 | ALPHA: (ax2) implies:
% 161.58/23.59 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 161.58/23.59 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 161.58/23.59 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 161.58/23.59 | ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & op(e3, e2)
% 161.58/23.59 | = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, e0) =
% 161.58/23.59 | e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 161.58/23.59 | e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3))
% 161.58/23.59 | & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11
% 161.58/23.59 | = e2 & op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 =
% 161.58/23.59 | e2 & op(e3, e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 &
% 161.58/23.59 | op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 &
% 161.58/23.59 | op(e3, e3) = e1) | (v14 = e1 & op(e3, e2) = e1) | (v11 = e1 &
% 161.58/23.59 | op(e3, e1) = e1) | (v6 = e1 & op(e3, e0) = e1)) & ((v15 = e1 &
% 161.58/23.59 | op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = e1) | (v9 = e1 &
% 161.58/23.59 | op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 = e0 &
% 161.58/23.59 | op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 161.58/23.59 | op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 &
% 161.58/23.59 | op(e3, e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 &
% 161.58/23.59 | op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 &
% 161.58/23.59 | op(e3, e2) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v8 = e3 &
% 161.58/23.59 | op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v14 = e2 &
% 161.58/23.59 | op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v8 = e2 &
% 161.58/23.59 | op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 161.58/23.59 | op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 &
% 161.58/23.59 | op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 &
% 161.58/23.59 | op(e3, e2) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 &
% 161.58/23.59 | op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v13 = e3 &
% 161.58/23.59 | op(e2, e3) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v10 = e3 &
% 161.58/23.59 | op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = e3)) & ((v13 = e2 &
% 161.58/23.59 | op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v10 = e2 &
% 161.58/23.59 | op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 161.58/23.59 | op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 &
% 161.58/23.59 | op(e2, e1) = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 &
% 161.58/23.59 | op(e2, e3) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 &
% 161.58/23.59 | op(e2, e1) = e0) | (v5 = e0 & op(e2, e0) = e0)) & ((v11 = e3 &
% 161.58/23.59 | op(e3, e1) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v7 = e3 &
% 161.87/23.60 | op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v11 = e2 &
% 161.87/23.60 | op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 161.87/23.60 | op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 &
% 161.87/23.60 | op(e3, e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 &
% 161.87/23.60 | op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 &
% 161.87/23.60 | op(e3, e1) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v7 = e0 &
% 161.87/23.60 | op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v9 = e3 &
% 161.87/23.60 | op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v7 = e3 &
% 161.87/23.60 | op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 161.87/23.60 | op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 &
% 161.87/23.60 | op(e1, e1) = e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 &
% 161.87/23.60 | op(e1, e3) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v7 = e1 &
% 161.87/23.60 | op(e1, e1) = e1) | (v4 = e1 & op(e1, e0) = e1)) & ((v9 = e0 &
% 161.87/23.60 | op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v7 = e0 &
% 161.87/23.60 | op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v6 = e3 &
% 161.87/23.60 | op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 161.87/23.60 | op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 &
% 161.87/23.60 | op(e3, e0) = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 &
% 161.87/23.60 | op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v6 = e1 &
% 161.87/23.60 | op(e3, e0) = e1) | (v5 = e1 & op(e2, e0) = e1) | (v4 = e1 &
% 161.87/23.60 | op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v3 = e3 &
% 161.87/23.60 | op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 &
% 161.87/23.60 | op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 161.87/23.60 | op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 &
% 161.87/23.60 | op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 &
% 161.87/23.60 | op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 &
% 161.87/23.60 | op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 &
% 161.87/23.60 | op(e0, e0) = e0) | (((v6 = e0 & op(e3, e0) = e0) | (v5 = e0 &
% 161.87/23.60 | op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v3 = e0 &
% 161.87/23.60 | op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 &
% 161.87/23.60 | op(e0, e1) = e0)))))
% 161.87/23.60 |
% 161.87/23.60 | ALPHA: (ax3) implies:
% 161.87/23.61 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 161.87/23.61 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 161.87/23.61 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 161.87/23.61 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~
% 161.87/23.61 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~
% 161.87/23.61 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~
% 161.87/23.61 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12
% 161.87/23.61 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 =
% 161.87/23.61 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9)
% 161.87/23.61 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~
% 161.87/23.61 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6)
% 161.87/23.61 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6
% 161.87/23.61 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) &
% 161.87/23.61 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 =
% 161.87/23.61 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 161.87/23.61 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 161.87/23.61 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 161.87/23.61 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 161.87/23.61 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 161.87/23.61 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 161.87/23.61 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 161.87/23.61 |
% 161.87/23.61 | ALPHA: (ax4) implies:
% 161.87/23.61 | (4) ~ (e1 = e0)
% 161.87/23.61 | (5) ~ (e2 = e0)
% 161.87/23.61 | (6) ~ (e2 = e1)
% 161.87/23.61 | (7) ~ (e3 = e0)
% 161.87/23.61 | (8) ~ (e3 = e1)
% 161.87/23.61 | (9) ~ (e3 = e2)
% 161.87/23.61 |
% 161.87/23.61 | ALPHA: (ax5) implies:
% 161.87/23.63 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 161.87/23.63 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 161.87/23.63 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 161.87/23.63 | $i] : ? [v15: $i] : (op(e3, e3) = v5 & op(e2, e2) = v3 & op(e1, e1)
% 161.87/23.63 | = v1 & op(e0, e0) = v0 & $i(v5) & $i(v3) & $i(v1) & $i(v0) & ( ~ (v5
% 161.87/23.63 | = e2) | (v14 = e3 & op(e3, e2) = e3)) & ( ~ (v5 = e1) | (v11 =
% 161.87/23.63 | e3 & op(e3, e1) = e3)) & ( ~ (v5 = e0) | (v6 = e3 & op(e3, e0) =
% 161.87/23.63 | e3)) & ( ~ (v3 = e3) | (v15 = e2 & op(e2, e3) = e2)) & ( ~ (v3 =
% 161.87/23.63 | e1) | (v10 = e2 & op(e2, e1) = e2)) & ( ~ (v3 = e0) | (v4 = e2 &
% 161.87/23.63 | op(e2, e0) = e2)) & ( ~ (v1 = e3) | (v13 = e1 & op(e1, e3) =
% 161.87/23.63 | e1)) & ( ~ (v1 = e2) | (v12 = e1 & op(e1, e2) = e1)) & ( ~ (v1 =
% 161.87/23.63 | e0) | (v2 = e1 & op(e1, e0) = e1)) & ( ~ (v0 = e3) | (v9 = e0 &
% 161.87/23.63 | op(e0, e3) = e0)) & ( ~ (v0 = e2) | (v8 = e0 & op(e0, e2) = e0))
% 161.87/23.63 | & ( ~ (v0 = e1) | (v7 = e0 & op(e0, e1) = e0)) & (v5 = e3 | v3 = e2
% 161.87/23.63 | | v1 = e1 | v0 = e0) & ((v15 = e3 & ~ (v3 = e2) & op(e2, e3) = e3
% 161.87/23.63 | & ( ~ (v5 = e2) | ( ~ (v14 = e3) & op(e3, e2) = v14 & $i(v14)))
% 161.87/23.63 | & ( ~ (v1 = e2) | ( ~ (v12 = e1) & op(e1, e2) = v12 & $i(v12)))
% 161.87/23.63 | & ( ~ (v0 = e2) | ( ~ (v8 = e0) & op(e0, e2) = v8 & $i(v8)))) |
% 161.87/23.63 | (v14 = e2 & ~ (v5 = e3) & op(e3, e2) = e2 & ( ~ (v3 = e3) | ( ~
% 161.87/23.63 | (v15 = e2) & op(e2, e3) = v15 & $i(v15))) & ( ~ (v1 = e3) |
% 161.87/23.63 | ( ~ (v13 = e1) & op(e1, e3) = v13 & $i(v13))) & ( ~ (v0 = e3)
% 161.87/23.63 | | ( ~ (v9 = e0) & op(e0, e3) = v9 & $i(v9)))) | (v13 = e3 & ~
% 161.87/23.63 | (v1 = e1) & op(e1, e3) = e3 & ( ~ (v5 = e1) | ( ~ (v11 = e3) &
% 161.87/23.63 | op(e3, e1) = v11 & $i(v11))) & ( ~ (v3 = e1) | ( ~ (v10 =
% 161.87/23.63 | e2) & op(e2, e1) = v10 & $i(v10))) & ( ~ (v0 = e1) | ( ~
% 161.87/23.63 | (v7 = e0) & op(e0, e1) = v7 & $i(v7)))) | (v12 = e2 & ~ (v1
% 161.87/23.63 | = e1) & op(e1, e2) = e2 & ( ~ (v5 = e1) | ( ~ (v11 = e3) &
% 161.87/23.63 | op(e3, e1) = v11 & $i(v11))) & ( ~ (v3 = e1) | ( ~ (v10 =
% 161.87/23.63 | e2) & op(e2, e1) = v10 & $i(v10))) & ( ~ (v0 = e1) | ( ~
% 161.87/23.63 | (v7 = e0) & op(e0, e1) = v7 & $i(v7)))) | (v11 = e1 & ~ (v5
% 161.87/23.63 | = e3) & op(e3, e1) = e1 & ( ~ (v3 = e3) | ( ~ (v15 = e2) &
% 161.87/23.63 | op(e2, e3) = v15 & $i(v15))) & ( ~ (v1 = e3) | ( ~ (v13 =
% 161.87/23.63 | e1) & op(e1, e3) = v13 & $i(v13))) & ( ~ (v0 = e3) | ( ~
% 161.87/23.63 | (v9 = e0) & op(e0, e3) = v9 & $i(v9)))) | (v10 = e1 & ~ (v3
% 161.87/23.63 | = e2) & op(e2, e1) = e1 & ( ~ (v5 = e2) | ( ~ (v14 = e3) &
% 161.87/23.63 | op(e3, e2) = v14 & $i(v14))) & ( ~ (v1 = e2) | ( ~ (v12 =
% 161.87/23.63 | e1) & op(e1, e2) = v12 & $i(v12))) & ( ~ (v0 = e2) | ( ~
% 161.87/23.63 | (v8 = e0) & op(e0, e2) = v8 & $i(v8)))) | (v6 = e0 & ~ (v5
% 161.87/23.63 | = e3) & op(e3, e0) = e0 & ( ~ (v3 = e3) | ( ~ (v15 = e2) &
% 161.87/23.63 | op(e2, e3) = v15 & $i(v15))) & ( ~ (v1 = e3) | ( ~ (v13 =
% 161.87/23.63 | e1) & op(e1, e3) = v13 & $i(v13))) & ( ~ (v0 = e3) | ( ~
% 161.87/23.63 | (v9 = e0) & op(e0, e3) = v9 & $i(v9)))) | (v4 = e0 & ~ (v3
% 161.87/23.63 | = e2) & op(e2, e0) = e0 & ( ~ (v5 = e2) | ( ~ (v14 = e3) &
% 161.87/23.63 | op(e3, e2) = v14 & $i(v14))) & ( ~ (v1 = e2) | ( ~ (v12 =
% 161.87/23.63 | e1) & op(e1, e2) = v12 & $i(v12))) & ( ~ (v0 = e2) | ( ~
% 161.87/23.63 | (v8 = e0) & op(e0, e2) = v8 & $i(v8)))) | (v2 = e0 & ~ (v1
% 161.87/23.63 | = e1) & op(e1, e0) = e0 & ( ~ (v5 = e1) | ( ~ (v11 = e3) &
% 161.87/23.63 | op(e3, e1) = v11 & $i(v11))) & ( ~ (v3 = e1) | ( ~ (v10 =
% 161.87/23.63 | e2) & op(e2, e1) = v10 & $i(v10))) & ( ~ (v0 = e1) | ( ~
% 161.87/23.63 | (v7 = e0) & op(e0, e1) = v7 & $i(v7)))) | ( ~ (v0 = e0) & (
% 161.87/23.63 | ~ (v5 = e0) | ( ~ (v6 = e3) & op(e3, e0) = v6 & $i(v6))) & ( ~
% 161.87/23.63 | (v3 = e0) | ( ~ (v4 = e2) & op(e2, e0) = v4 & $i(v4))) & ( ~
% 161.87/23.63 | (v1 = e0) | ( ~ (v2 = e1) & op(e1, e0) = v2 & $i(v2))) & ((v9
% 161.87/23.63 | = e3 & op(e0, e3) = e3) | (v8 = e2 & op(e0, e2) = e2) | (v7
% 161.87/23.63 | = e1 & op(e0, e1) = e1)))))
% 161.87/23.63 |
% 161.87/23.63 | ALPHA: (ax6) implies:
% 161.87/23.63 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 161.87/23.63 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e0, e3) = v1 &
% 161.87/23.63 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 & $i(v1))))
% 161.87/23.63 |
% 161.87/23.63 | ALPHA: (ax7) implies:
% 161.87/23.63 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 161.87/23.63 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e0, e2) = v1 &
% 161.87/23.63 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 & $i(v1))))
% 161.87/23.63 |
% 161.87/23.63 | ALPHA: (ax8) implies:
% 161.87/23.63 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 161.87/23.63 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e0, e3) = v1 &
% 161.87/23.63 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 & $i(v1))))
% 161.87/23.63 |
% 161.87/23.63 | ALPHA: (ax9) implies:
% 161.87/23.63 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 161.87/23.63 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e0, e1) = v1 &
% 161.87/23.63 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 & $i(v1))))
% 161.87/23.63 |
% 161.87/23.63 | ALPHA: (ax10) implies:
% 161.87/23.63 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 161.87/23.63 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e0, e2) = v1 &
% 161.87/23.63 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 & $i(v1))))
% 161.87/23.63 |
% 161.87/23.63 | ALPHA: (ax11) implies:
% 161.87/23.63 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 161.87/23.64 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e0, e1) = v1 &
% 161.87/23.64 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 & $i(v1))))
% 161.87/23.64 |
% 161.87/23.64 | ALPHA: (ax12) implies:
% 161.87/23.64 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 161.87/23.64 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e1, e3) = v1 &
% 161.87/23.64 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 & $i(v1))))
% 161.87/23.64 |
% 161.87/23.64 | ALPHA: (ax13) implies:
% 161.87/23.64 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 161.87/23.64 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e1, e2) = v1 &
% 161.87/23.64 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 & $i(v1))))
% 161.87/23.64 |
% 161.87/23.64 | ALPHA: (ax14) implies:
% 161.87/23.64 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 161.87/23.64 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e1, e3) = v1 &
% 161.87/23.64 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 & $i(v1))))
% 161.87/23.64 |
% 161.87/23.64 | ALPHA: (ax15) implies:
% 161.87/23.64 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 161.87/23.64 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e1, e0) = v1 &
% 161.87/23.64 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 & $i(v1))))
% 161.87/23.64 |
% 161.87/23.64 | ALPHA: (ax16) implies:
% 161.87/23.64 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 161.87/23.64 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e1, e2) = v1 &
% 161.87/23.64 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 & $i(v1))))
% 161.87/23.64 |
% 161.87/23.64 | ALPHA: (ax17) implies:
% 161.87/23.64 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 161.87/23.64 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e1, e0) = v1 &
% 161.87/23.64 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 & $i(v1))))
% 161.87/23.64 |
% 161.87/23.64 | ALPHA: (ax18) implies:
% 161.87/23.64 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 161.87/23.64 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e2, e3) = v1 &
% 161.87/23.64 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 & $i(v1))))
% 161.87/23.64 |
% 161.87/23.64 | ALPHA: (ax19) implies:
% 161.87/23.65 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 161.87/23.65 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e2, e1) = v1 &
% 161.87/23.65 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 & $i(v1))))
% 161.87/23.65 |
% 161.87/23.65 | ALPHA: (ax20) implies:
% 161.87/23.65 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 161.87/23.65 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e2, e3) = v1 &
% 161.87/23.65 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 & $i(v1))))
% 161.87/23.65 |
% 161.87/23.65 | ALPHA: (ax21) implies:
% 161.87/23.65 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 161.87/23.65 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e2, e0) = v1 &
% 161.87/23.65 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 & $i(v1))))
% 161.87/23.65 |
% 161.87/23.65 | ALPHA: (ax22) implies:
% 161.87/23.65 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 161.87/23.65 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e2, e1) = v1 &
% 161.87/23.65 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 & $i(v1))))
% 161.87/23.65 |
% 161.87/23.65 | ALPHA: (ax23) implies:
% 161.87/23.65 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 161.87/23.65 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e2, e0) = v1 &
% 161.87/23.65 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 & $i(v1))))
% 161.87/23.65 |
% 161.87/23.65 | ALPHA: (ax24) implies:
% 161.87/23.65 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 161.87/23.65 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e3, e2) = v1 &
% 161.87/23.65 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 & $i(v1))))
% 161.87/23.65 |
% 161.87/23.65 | ALPHA: (ax25) implies:
% 161.87/23.65 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 161.87/23.65 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e3, e1) = v1 &
% 161.87/23.65 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 & $i(v1))))
% 161.87/23.65 |
% 161.87/23.65 | ALPHA: (ax26) implies:
% 161.87/23.65 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 161.87/23.65 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e3, e2) = v1 &
% 161.87/23.65 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 & $i(v1))))
% 161.87/23.65 |
% 161.87/23.65 | ALPHA: (ax27) implies:
% 161.87/23.66 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 161.87/23.66 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e3, e0) = v1 &
% 161.87/23.66 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 & $i(v1))))
% 161.87/23.66 |
% 161.87/23.66 | ALPHA: (ax28) implies:
% 161.87/23.66 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 161.87/23.66 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e3, e1) = v1 &
% 161.87/23.66 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 & $i(v1))))
% 161.87/23.66 |
% 161.87/23.66 | ALPHA: (ax29) implies:
% 161.87/23.66 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 161.87/23.66 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e3, e0) = v1 &
% 161.87/23.66 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 & $i(v1))))
% 161.87/23.66 |
% 161.87/23.66 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 161.87/23.66 | (35) op(e0, e0) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e1) | ( ~ (all_4_0
% 161.87/23.66 | = e2) & op(all_4_1, e0) = all_4_0 & op(e1, e0) = all_4_1 &
% 161.87/23.66 | $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e1, e0) =
% 161.87/23.66 | all_4_1 & $i(all_4_1)))
% 161.87/23.66 |
% 161.87/23.66 | ALPHA: (35) implies:
% 161.87/23.66 | (36) op(e0, e0) = all_4_2
% 161.87/23.66 | (37) ~ (all_4_2 = e1) | ( ~ (all_4_0 = e2) & op(all_4_1, e0) = all_4_0 &
% 161.87/23.66 | op(e1, e0) = all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 =
% 161.87/23.66 | e3) & op(e1, e0) = all_4_1 & $i(all_4_1))
% 161.87/23.66 |
% 161.87/23.66 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 161.87/23.66 | (38) op(e1, e1) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e2) | ( ~ (all_6_0
% 161.87/23.66 | = e3) & op(all_6_1, e1) = all_6_0 & op(e2, e1) = all_6_1 &
% 161.87/23.66 | $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e2, e1) =
% 161.87/23.66 | all_6_1 & $i(all_6_1)))
% 161.87/23.66 |
% 161.87/23.66 | ALPHA: (38) implies:
% 161.87/23.66 | (39) op(e1, e1) = all_6_2
% 161.87/23.66 | (40) ~ (all_6_2 = e2) | ( ~ (all_6_0 = e3) & op(all_6_1, e1) = all_6_0 &
% 161.87/23.66 | op(e2, e1) = all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 =
% 161.87/23.66 | e0) & op(e2, e1) = all_6_1 & $i(all_6_1))
% 161.87/23.66 |
% 161.87/23.66 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 161.87/23.66 | (41) op(e2, e2) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e1) | ( ~ (all_8_0
% 161.87/23.66 | = e3) & op(all_8_1, e2) = all_8_0 & op(e1, e2) = all_8_1 &
% 161.87/23.66 | $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e1, e2) =
% 161.87/23.66 | all_8_1 & $i(all_8_1)))
% 161.87/23.66 |
% 161.87/23.66 | ALPHA: (41) implies:
% 161.87/23.66 | (42) op(e2, e2) = all_8_2
% 161.87/23.67 | (43) ~ (all_8_2 = e1) | ( ~ (all_8_0 = e3) & op(all_8_1, e2) = all_8_0 &
% 161.87/23.67 | op(e1, e2) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 =
% 161.87/23.67 | e0) & op(e1, e2) = all_8_1 & $i(all_8_1))
% 161.87/23.67 |
% 161.87/23.67 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 161.87/23.67 | gives:
% 161.87/23.67 | (44) op(e3, e3) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e0) | ( ~
% 161.87/23.67 | (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 & op(e0, e3) =
% 161.87/23.67 | all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) &
% 161.87/23.67 | op(e0, e3) = all_10_1 & $i(all_10_1)))
% 161.87/23.67 |
% 161.87/23.67 | ALPHA: (44) implies:
% 161.87/23.67 | (45) op(e3, e3) = all_10_2
% 161.87/23.67 | (46) ~ (all_10_2 = e0) | ( ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0
% 161.87/23.67 | & op(e0, e3) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 161.87/23.67 | (all_10_1 = e2) & op(e0, e3) = all_10_1 & $i(all_10_1))
% 161.87/23.67 |
% 161.87/23.67 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 161.87/23.67 | gives:
% 161.87/23.67 | (47) op(e0, e0) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e1) | ( ~
% 161.87/23.67 | (all_12_0 = e3) & op(all_12_1, e0) = all_12_0 & op(e1, e0) =
% 161.87/23.67 | all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) &
% 161.87/23.67 | op(e1, e0) = all_12_1 & $i(all_12_1)))
% 161.87/23.67 |
% 161.87/23.67 | ALPHA: (47) implies:
% 161.87/23.67 | (48) op(e0, e0) = all_12_2
% 161.87/23.67 | (49) ~ (all_12_2 = e1) | ( ~ (all_12_0 = e3) & op(all_12_1, e0) = all_12_0
% 161.87/23.67 | & op(e1, e0) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 161.87/23.67 | (all_12_1 = e2) & op(e1, e0) = all_12_1 & $i(all_12_1))
% 161.87/23.67 |
% 161.87/23.67 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 161.87/23.67 | gives:
% 161.87/23.67 | (50) op(e2, e2) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e3) | ( ~
% 161.87/23.67 | (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 161.87/23.67 | all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) &
% 161.87/23.67 | op(e3, e2) = all_14_1 & $i(all_14_1)))
% 161.87/23.67 |
% 161.87/23.67 | ALPHA: (50) implies:
% 161.87/23.67 | (51) op(e2, e2) = all_14_2
% 161.87/23.67 | (52) ~ (all_14_2 = e3) | ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0
% 161.87/23.67 | & op(e3, e2) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 161.87/23.67 | (all_14_1 = e1) & op(e3, e2) = all_14_1 & $i(all_14_1))
% 161.87/23.67 |
% 161.87/23.67 | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2
% 161.87/23.67 | gives:
% 161.87/23.67 | (53) op(e3, e3) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e2) | ( ~
% 161.87/23.67 | (all_16_0 = e0) & op(all_16_1, e3) = all_16_0 & op(e2, e3) =
% 161.87/23.67 | all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) &
% 161.87/23.67 | op(e2, e3) = all_16_1 & $i(all_16_1)))
% 161.87/23.67 |
% 161.87/23.67 | ALPHA: (53) implies:
% 161.87/23.67 | (54) op(e3, e3) = all_16_2
% 161.87/23.67 | (55) ~ (all_16_2 = e2) | ( ~ (all_16_0 = e0) & op(all_16_1, e3) = all_16_0
% 161.87/23.67 | & op(e2, e3) = all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~
% 161.87/23.67 | (all_16_1 = e1) & op(e2, e3) = all_16_1 & $i(all_16_1))
% 161.87/23.67 |
% 161.87/23.67 | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2
% 161.87/23.67 | gives:
% 161.87/23.67 | (56) op(e1, e1) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e2) | ( ~
% 161.87/23.67 | (all_18_0 = e0) & op(all_18_1, e1) = all_18_0 & op(e2, e1) =
% 161.87/23.67 | all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) &
% 161.87/23.67 | op(e2, e1) = all_18_1 & $i(all_18_1)))
% 161.87/23.67 |
% 161.87/23.67 | ALPHA: (56) implies:
% 161.87/23.67 | (57) op(e1, e1) = all_18_2
% 161.87/23.67 | (58) ~ (all_18_2 = e2) | ( ~ (all_18_0 = e0) & op(all_18_1, e1) = all_18_0
% 161.87/23.67 | & op(e2, e1) = all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~
% 161.87/23.67 | (all_18_1 = e3) & op(e2, e1) = all_18_1 & $i(all_18_1))
% 161.87/23.67 |
% 161.87/23.67 | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2
% 161.87/23.68 | gives:
% 161.87/23.68 | (59) op(e0, e0) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e2) | ( ~
% 161.87/23.68 | (all_20_0 = e1) & op(all_20_1, e0) = all_20_0 & op(e2, e0) =
% 161.87/23.68 | all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) &
% 161.87/23.68 | op(e2, e0) = all_20_1 & $i(all_20_1)))
% 161.87/23.68 |
% 161.87/23.68 | ALPHA: (59) implies:
% 161.87/23.68 | (60) op(e0, e0) = all_20_2
% 161.87/23.68 | (61) ~ (all_20_2 = e2) | ( ~ (all_20_0 = e1) & op(all_20_1, e0) = all_20_0
% 161.87/23.68 | & op(e2, e0) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~
% 161.87/23.68 | (all_20_1 = e3) & op(e2, e0) = all_20_1 & $i(all_20_1))
% 161.87/23.68 |
% 161.87/23.68 | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2
% 161.87/23.68 | gives:
% 161.87/23.68 | (62) op(e2, e2) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e3) | ( ~
% 161.87/23.68 | (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 161.87/23.68 | all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) &
% 161.87/23.68 | op(e3, e2) = all_22_1 & $i(all_22_1)))
% 161.87/23.68 |
% 161.87/23.68 | ALPHA: (62) implies:
% 161.87/23.68 | (63) op(e2, e2) = all_22_2
% 161.87/23.68 | (64) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0
% 161.87/23.68 | & op(e3, e2) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 161.87/23.68 | (all_22_1 = e0) & op(e3, e2) = all_22_1 & $i(all_22_1))
% 161.87/23.68 |
% 161.87/23.68 | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2
% 161.87/23.68 | gives:
% 161.87/23.68 | (65) op(e3, e3) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e0) | ( ~
% 161.87/23.68 | (all_24_0 = e2) & op(all_24_1, e3) = all_24_0 & op(e0, e3) =
% 161.87/23.68 | all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) &
% 161.87/23.68 | op(e0, e3) = all_24_1 & $i(all_24_1)))
% 161.87/23.68 |
% 161.87/23.68 | ALPHA: (65) implies:
% 161.87/23.68 | (66) op(e3, e3) = all_24_2
% 161.87/23.68 | (67) ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0
% 161.87/23.68 | & op(e0, e3) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 161.87/23.68 | (all_24_1 = e1) & op(e0, e3) = all_24_1 & $i(all_24_1))
% 161.87/23.68 |
% 161.87/23.68 | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2
% 161.87/23.68 | gives:
% 161.87/23.68 | (68) op(e0, e0) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e2) | ( ~
% 161.87/23.68 | (all_26_0 = e3) & op(all_26_1, e0) = all_26_0 & op(e2, e0) =
% 161.87/23.68 | all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) &
% 161.87/23.68 | op(e2, e0) = all_26_1 & $i(all_26_1)))
% 161.87/23.68 |
% 161.87/23.68 | ALPHA: (68) implies:
% 161.87/23.68 | (69) op(e0, e0) = all_26_2
% 161.87/23.68 | (70) ~ (all_26_2 = e2) | ( ~ (all_26_0 = e3) & op(all_26_1, e0) = all_26_0
% 161.87/23.68 | & op(e2, e0) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 161.87/23.68 | (all_26_1 = e1) & op(e2, e0) = all_26_1 & $i(all_26_1))
% 161.87/23.68 |
% 161.87/23.68 | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2
% 161.87/23.68 | gives:
% 161.87/23.68 | (71) op(e1, e1) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e3) | ( ~
% 161.87/23.68 | (all_28_0 = e0) & op(all_28_1, e1) = all_28_0 & op(e3, e1) =
% 161.87/23.68 | all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) &
% 161.87/23.68 | op(e3, e1) = all_28_1 & $i(all_28_1)))
% 161.87/23.68 |
% 161.87/23.68 | ALPHA: (71) implies:
% 161.87/23.68 | (72) op(e1, e1) = all_28_2
% 161.87/23.68 | (73) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e0) & op(all_28_1, e1) = all_28_0
% 161.87/23.68 | & op(e3, e1) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 161.87/23.68 | (all_28_1 = e2) & op(e3, e1) = all_28_1 & $i(all_28_1))
% 161.87/23.68 |
% 161.87/23.68 | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2
% 161.87/23.68 | gives:
% 161.87/23.68 | (74) op(e2, e2) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e0) | ( ~
% 161.87/23.68 | (all_30_0 = e1) & op(all_30_1, e2) = all_30_0 & op(e0, e2) =
% 161.87/23.68 | all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) &
% 161.87/23.68 | op(e0, e2) = all_30_1 & $i(all_30_1)))
% 161.87/23.68 |
% 161.87/23.68 | ALPHA: (74) implies:
% 161.87/23.69 | (75) op(e2, e2) = all_30_2
% 161.87/23.69 | (76) ~ (all_30_2 = e0) | ( ~ (all_30_0 = e1) & op(all_30_1, e2) = all_30_0
% 161.87/23.69 | & op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~
% 161.87/23.69 | (all_30_1 = e3) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 161.87/23.69 |
% 161.87/23.69 | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2
% 161.87/23.69 | gives:
% 161.87/23.69 | (77) op(e3, e3) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e1) | ( ~
% 161.87/23.69 | (all_32_0 = e2) & op(all_32_1, e3) = all_32_0 & op(e1, e3) =
% 161.87/23.69 | all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) &
% 161.87/23.69 | op(e1, e3) = all_32_1 & $i(all_32_1)))
% 161.87/23.69 |
% 161.87/23.69 | ALPHA: (77) implies:
% 161.87/23.69 | (78) op(e3, e3) = all_32_2
% 161.87/23.69 | (79) ~ (all_32_2 = e1) | ( ~ (all_32_0 = e2) & op(all_32_1, e3) = all_32_0
% 161.87/23.69 | & op(e1, e3) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~
% 161.87/23.69 | (all_32_1 = e0) & op(e1, e3) = all_32_1 & $i(all_32_1))
% 161.87/23.69 |
% 161.87/23.69 | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2
% 161.87/23.69 | gives:
% 161.87/23.69 | (80) op(e0, e0) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e3) | ( ~
% 161.87/23.69 | (all_34_0 = e1) & op(all_34_1, e0) = all_34_0 & op(e3, e0) =
% 161.87/23.69 | all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) &
% 161.87/23.69 | op(e3, e0) = all_34_1 & $i(all_34_1)))
% 161.87/23.69 |
% 161.87/23.69 | ALPHA: (80) implies:
% 161.87/23.69 | (81) op(e0, e0) = all_34_2
% 162.88/23.69 | (82) ~ (all_34_2 = e3) | ( ~ (all_34_0 = e1) & op(all_34_1, e0) = all_34_0
% 162.88/23.69 | & op(e3, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~
% 162.88/23.69 | (all_34_1 = e2) & op(e3, e0) = all_34_1 & $i(all_34_1))
% 162.88/23.69 |
% 162.88/23.69 | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2
% 162.88/23.69 | gives:
% 162.88/23.69 | (83) op(e1, e1) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e3) | ( ~
% 162.88/23.69 | (all_36_0 = e2) & op(all_36_1, e1) = all_36_0 & op(e3, e1) =
% 162.88/23.69 | all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) &
% 162.88/23.69 | op(e3, e1) = all_36_1 & $i(all_36_1)))
% 162.88/23.69 |
% 162.88/23.69 | ALPHA: (83) implies:
% 162.88/23.69 | (84) op(e1, e1) = all_36_2
% 162.88/23.69 | (85) ~ (all_36_2 = e3) | ( ~ (all_36_0 = e2) & op(all_36_1, e1) = all_36_0
% 162.88/23.69 | & op(e3, e1) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~
% 162.88/23.69 | (all_36_1 = e0) & op(e3, e1) = all_36_1 & $i(all_36_1))
% 162.88/23.69 |
% 162.88/23.69 | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2
% 162.88/23.69 | gives:
% 162.88/23.69 | (86) op(e3, e3) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e2) | ( ~
% 162.88/23.69 | (all_38_0 = e1) & op(all_38_1, e3) = all_38_0 & op(e2, e3) =
% 162.88/23.69 | all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) &
% 162.88/23.69 | op(e2, e3) = all_38_1 & $i(all_38_1)))
% 162.88/23.69 |
% 162.88/23.69 | ALPHA: (86) implies:
% 162.88/23.69 | (87) op(e3, e3) = all_38_2
% 162.88/23.69 | (88) ~ (all_38_2 = e2) | ( ~ (all_38_0 = e1) & op(all_38_1, e3) = all_38_0
% 162.88/23.69 | & op(e2, e3) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 162.88/23.69 | (all_38_1 = e0) & op(e2, e3) = all_38_1 & $i(all_38_1))
% 162.88/23.69 |
% 162.88/23.69 | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2
% 162.88/23.69 | gives:
% 162.88/23.69 | (89) op(e1, e1) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e0) | ( ~
% 162.88/23.69 | (all_40_0 = e2) & op(all_40_1, e1) = all_40_0 & op(e0, e1) =
% 162.88/23.69 | all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) &
% 162.88/23.69 | op(e0, e1) = all_40_1 & $i(all_40_1)))
% 162.88/23.69 |
% 162.88/23.69 | ALPHA: (89) implies:
% 162.88/23.69 | (90) op(e1, e1) = all_40_2
% 162.88/23.69 |
% 162.88/23.69 | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2
% 162.88/23.69 | gives:
% 162.88/23.69 | (91) op(e2, e2) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e0) | ( ~
% 162.88/23.69 | (all_42_0 = e3) & op(all_42_1, e2) = all_42_0 & op(e0, e2) =
% 162.88/23.69 | all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) &
% 162.88/23.69 | op(e0, e2) = all_42_1 & $i(all_42_1)))
% 162.88/23.69 |
% 162.88/23.70 | ALPHA: (91) implies:
% 162.88/23.70 | (92) op(e2, e2) = all_42_2
% 162.88/23.70 | (93) ~ (all_42_2 = e0) | ( ~ (all_42_0 = e3) & op(all_42_1, e2) = all_42_0
% 162.88/23.70 | & op(e0, e2) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 162.88/23.70 | (all_42_1 = e1) & op(e0, e2) = all_42_1 & $i(all_42_1))
% 162.88/23.70 |
% 162.88/23.70 | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2
% 162.88/23.70 | gives:
% 162.88/23.70 | (94) op(e0, e0) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e3) | ( ~
% 162.88/23.70 | (all_44_0 = e2) & op(all_44_1, e0) = all_44_0 & op(e3, e0) =
% 162.88/23.70 | all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) &
% 162.88/23.70 | op(e3, e0) = all_44_1 & $i(all_44_1)))
% 162.88/23.70 |
% 162.88/23.70 | ALPHA: (94) implies:
% 162.88/23.70 | (95) op(e0, e0) = all_44_2
% 162.88/23.70 | (96) ~ (all_44_2 = e3) | ( ~ (all_44_0 = e2) & op(all_44_1, e0) = all_44_0
% 162.88/23.70 | & op(e3, e0) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~
% 162.88/23.70 | (all_44_1 = e1) & op(e3, e0) = all_44_1 & $i(all_44_1))
% 162.88/23.70 |
% 162.88/23.70 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 162.88/23.70 | gives:
% 162.88/23.70 | (97) op(e1, e1) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e0) | ( ~
% 162.88/23.70 | (all_46_0 = e3) & op(all_46_1, e1) = all_46_0 & op(e0, e1) =
% 162.88/23.70 | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) &
% 162.88/23.70 | op(e0, e1) = all_46_1 & $i(all_46_1)))
% 162.88/23.70 |
% 162.88/23.70 | ALPHA: (97) implies:
% 162.88/23.70 | (98) op(e1, e1) = all_46_2
% 162.88/23.70 | (99) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e3) & op(all_46_1, e1) = all_46_0
% 162.88/23.70 | & op(e0, e1) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 162.88/23.70 | (all_46_1 = e2) & op(e0, e1) = all_46_1 & $i(all_46_1))
% 162.88/23.70 |
% 162.88/23.70 | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2
% 162.88/23.70 | gives:
% 162.88/23.70 | (100) op(e2, e2) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e1) | ( ~
% 162.88/23.70 | (all_48_0 = e0) & op(all_48_1, e2) = all_48_0 & op(e1, e2) =
% 162.88/23.70 | all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) &
% 162.88/23.70 | op(e1, e2) = all_48_1 & $i(all_48_1)))
% 162.88/23.70 |
% 162.88/23.70 | ALPHA: (100) implies:
% 162.88/23.70 | (101) op(e2, e2) = all_48_2
% 162.88/23.70 | (102) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e0) & op(all_48_1, e2) =
% 162.88/23.70 | all_48_0 & op(e1, e2) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | (
% 162.88/23.70 | ~ (all_48_1 = e3) & op(e1, e2) = all_48_1 & $i(all_48_1))
% 162.88/23.70 |
% 162.88/23.70 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2
% 162.88/23.70 | gives:
% 162.88/23.70 | (103) op(e3, e3) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e1) | ( ~
% 162.88/23.70 | (all_50_0 = e0) & op(all_50_1, e3) = all_50_0 & op(e1, e3) =
% 162.88/23.70 | all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) &
% 162.88/23.70 | op(e1, e3) = all_50_1 & $i(all_50_1)))
% 162.88/23.70 |
% 162.88/23.70 | ALPHA: (103) implies:
% 162.88/23.70 | (104) op(e3, e3) = all_50_2
% 162.88/23.70 | (105) ~ (all_50_2 = e1) | ( ~ (all_50_0 = e0) & op(all_50_1, e3) =
% 162.88/23.70 | all_50_0 & op(e1, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | (
% 162.88/23.70 | ~ (all_50_1 = e2) & op(e1, e3) = all_50_1 & $i(all_50_1))
% 162.88/23.70 |
% 162.88/23.70 | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2,
% 162.88/23.70 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 162.88/23.70 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives:
% 162.88/23.71 | (106) ~ (all_52_0 = all_52_1) & ~ (all_52_0 = all_52_2) & ~ (all_52_0 =
% 162.88/23.71 | all_52_3) & ~ (all_52_0 = all_52_4) & ~ (all_52_0 = all_52_8) &
% 162.88/23.71 | ~ (all_52_0 = all_52_12) & ~ (all_52_1 = all_52_2) & ~ (all_52_1 =
% 162.88/23.71 | all_52_3) & ~ (all_52_1 = all_52_5) & ~ (all_52_1 = all_52_9) &
% 162.88/23.71 | ~ (all_52_1 = all_52_13) & ~ (all_52_2 = all_52_3) & ~ (all_52_2 =
% 162.88/23.71 | all_52_6) & ~ (all_52_2 = all_52_10) & ~ (all_52_2 = all_52_14) &
% 162.88/23.71 | ~ (all_52_3 = all_52_7) & ~ (all_52_3 = all_52_11) & ~ (all_52_3 =
% 162.88/23.71 | all_52_15) & ~ (all_52_4 = all_52_5) & ~ (all_52_4 = all_52_6) &
% 162.88/23.71 | ~ (all_52_4 = all_52_7) & ~ (all_52_4 = all_52_8) & ~ (all_52_4 =
% 162.88/23.71 | all_52_12) & ~ (all_52_5 = all_52_6) & ~ (all_52_5 = all_52_7) &
% 162.88/23.71 | ~ (all_52_5 = all_52_9) & ~ (all_52_5 = all_52_13) & ~ (all_52_6 =
% 162.88/23.71 | all_52_7) & ~ (all_52_6 = all_52_10) & ~ (all_52_6 = all_52_14) &
% 162.88/23.71 | ~ (all_52_7 = all_52_11) & ~ (all_52_7 = all_52_15) & ~ (all_52_8
% 162.88/23.71 | = all_52_9) & ~ (all_52_8 = all_52_10) & ~ (all_52_8 = all_52_11)
% 162.88/23.71 | & ~ (all_52_8 = all_52_12) & ~ (all_52_9 = all_52_10) & ~
% 162.88/23.71 | (all_52_9 = all_52_11) & ~ (all_52_9 = all_52_13) & ~ (all_52_10 =
% 162.88/23.71 | all_52_11) & ~ (all_52_10 = all_52_14) & ~ (all_52_11 =
% 162.88/23.71 | all_52_15) & ~ (all_52_12 = all_52_13) & ~ (all_52_12 =
% 162.88/23.71 | all_52_14) & ~ (all_52_12 = all_52_15) & ~ (all_52_13 =
% 162.88/23.71 | all_52_14) & ~ (all_52_13 = all_52_15) & ~ (all_52_14 =
% 162.88/23.71 | all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3,
% 162.88/23.71 | e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 &
% 162.88/23.71 | op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) =
% 162.88/23.71 | all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1,
% 162.88/23.71 | e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 &
% 162.88/23.71 | op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) =
% 162.88/23.71 | all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3)
% 162.88/23.71 | & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) &
% 162.88/23.71 | $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) &
% 162.88/23.71 | $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15)
% 162.88/23.71 |
% 162.88/23.71 | ALPHA: (106) implies:
% 162.88/23.71 | (107) ~ (all_52_14 = all_52_15)
% 162.88/23.71 | (108) ~ (all_52_13 = all_52_15)
% 162.88/23.71 | (109) ~ (all_52_13 = all_52_14)
% 162.88/23.71 | (110) ~ (all_52_12 = all_52_15)
% 162.88/23.71 | (111) ~ (all_52_12 = all_52_14)
% 162.88/23.71 | (112) ~ (all_52_12 = all_52_13)
% 162.88/23.71 | (113) ~ (all_52_11 = all_52_15)
% 162.88/23.71 | (114) ~ (all_52_10 = all_52_14)
% 162.88/23.71 | (115) ~ (all_52_10 = all_52_11)
% 162.88/23.71 | (116) ~ (all_52_9 = all_52_13)
% 162.88/23.71 | (117) ~ (all_52_9 = all_52_11)
% 162.88/23.71 | (118) ~ (all_52_9 = all_52_10)
% 162.88/23.71 | (119) ~ (all_52_8 = all_52_12)
% 162.88/23.71 | (120) ~ (all_52_8 = all_52_11)
% 162.88/23.71 | (121) ~ (all_52_8 = all_52_10)
% 162.88/23.71 | (122) ~ (all_52_8 = all_52_9)
% 162.88/23.71 | (123) ~ (all_52_7 = all_52_15)
% 162.88/23.71 | (124) ~ (all_52_7 = all_52_11)
% 162.88/23.71 | (125) ~ (all_52_6 = all_52_14)
% 162.88/23.71 | (126) ~ (all_52_6 = all_52_10)
% 162.88/23.71 | (127) ~ (all_52_6 = all_52_7)
% 162.88/23.71 | (128) ~ (all_52_5 = all_52_13)
% 162.88/23.71 | (129) ~ (all_52_5 = all_52_9)
% 162.88/23.71 | (130) ~ (all_52_5 = all_52_7)
% 162.88/23.71 | (131) ~ (all_52_5 = all_52_6)
% 162.88/23.71 | (132) ~ (all_52_4 = all_52_12)
% 162.88/23.71 | (133) ~ (all_52_4 = all_52_8)
% 162.88/23.71 | (134) ~ (all_52_4 = all_52_7)
% 162.88/23.71 | (135) ~ (all_52_4 = all_52_6)
% 162.88/23.71 | (136) ~ (all_52_4 = all_52_5)
% 162.88/23.71 | (137) ~ (all_52_3 = all_52_15)
% 162.88/23.71 | (138) ~ (all_52_3 = all_52_11)
% 162.88/23.71 | (139) ~ (all_52_3 = all_52_7)
% 162.88/23.71 | (140) ~ (all_52_2 = all_52_14)
% 162.88/23.71 | (141) ~ (all_52_2 = all_52_10)
% 162.88/23.71 | (142) ~ (all_52_2 = all_52_6)
% 162.88/23.71 | (143) ~ (all_52_2 = all_52_3)
% 162.88/23.71 | (144) ~ (all_52_1 = all_52_13)
% 162.88/23.71 | (145) ~ (all_52_1 = all_52_9)
% 162.88/23.71 | (146) ~ (all_52_1 = all_52_5)
% 162.88/23.71 | (147) ~ (all_52_1 = all_52_3)
% 162.88/23.71 | (148) ~ (all_52_1 = all_52_2)
% 162.88/23.71 | (149) ~ (all_52_0 = all_52_12)
% 162.88/23.71 | (150) ~ (all_52_0 = all_52_8)
% 162.88/23.71 | (151) ~ (all_52_0 = all_52_4)
% 162.88/23.71 | (152) ~ (all_52_0 = all_52_3)
% 162.88/23.71 | (153) ~ (all_52_0 = all_52_2)
% 162.88/23.71 | (154) ~ (all_52_0 = all_52_1)
% 162.88/23.71 | (155) op(e0, e0) = all_52_15
% 162.88/23.71 | (156) op(e0, e1) = all_52_11
% 162.88/23.71 | (157) op(e0, e2) = all_52_7
% 162.88/23.71 | (158) op(e0, e3) = all_52_3
% 162.88/23.71 | (159) op(e1, e0) = all_52_14
% 162.88/23.71 | (160) op(e1, e1) = all_52_10
% 162.88/23.71 | (161) op(e1, e2) = all_52_6
% 162.88/23.71 | (162) op(e1, e3) = all_52_2
% 162.88/23.71 | (163) op(e2, e0) = all_52_13
% 162.88/23.71 | (164) op(e2, e1) = all_52_9
% 162.88/23.71 | (165) op(e2, e2) = all_52_5
% 162.88/23.72 | (166) op(e2, e3) = all_52_1
% 162.88/23.72 | (167) op(e3, e0) = all_52_12
% 162.88/23.72 | (168) op(e3, e1) = all_52_8
% 162.88/23.72 | (169) op(e3, e2) = all_52_4
% 162.88/23.72 | (170) op(e3, e3) = all_52_0
% 162.88/23.72 |
% 162.88/23.72 | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2,
% 162.88/23.72 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 162.88/23.72 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 162.88/23.72 | (171) op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2
% 162.88/23.72 | & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) =
% 162.88/23.72 | all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3)
% 162.88/23.72 | = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1,
% 162.88/23.72 | e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 &
% 162.88/23.72 | op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) &
% 162.88/23.72 | $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) &
% 162.88/23.72 | $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) &
% 162.88/23.72 | $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) &
% 162.88/23.72 | $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 |
% 162.88/23.72 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 |
% 162.88/23.72 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 |
% 162.88/23.72 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 |
% 162.88/23.72 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 |
% 162.88/23.72 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 |
% 162.88/23.72 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 |
% 162.88/23.72 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 |
% 162.88/23.72 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 |
% 162.88/23.72 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 |
% 162.88/23.72 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 |
% 162.88/23.72 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3
% 162.88/23.72 | | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 =
% 162.88/23.72 | e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13
% 162.88/23.72 | = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) &
% 162.88/23.72 | (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) &
% 162.88/23.72 | (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0)
% 162.88/23.72 |
% 162.88/23.72 | ALPHA: (171) implies:
% 162.88/23.72 | (172) op(e0, e0) = all_54_15
% 162.88/23.72 | (173) op(e0, e1) = all_54_14
% 162.88/23.72 | (174) op(e0, e2) = all_54_13
% 162.88/23.72 | (175) op(e0, e3) = all_54_12
% 162.88/23.72 | (176) op(e1, e0) = all_54_11
% 162.88/23.72 | (177) op(e1, e1) = all_54_10
% 162.88/23.72 | (178) op(e1, e2) = all_54_9
% 162.88/23.72 | (179) op(e1, e3) = all_54_8
% 162.88/23.72 | (180) op(e2, e0) = all_54_7
% 162.88/23.72 | (181) op(e2, e1) = all_54_6
% 162.88/23.72 | (182) op(e2, e2) = all_54_5
% 162.88/23.72 | (183) op(e2, e3) = all_54_4
% 162.88/23.72 | (184) op(e3, e0) = all_54_3
% 162.88/23.72 | (185) op(e3, e1) = all_54_2
% 162.88/23.72 | (186) op(e3, e2) = all_54_1
% 162.88/23.72 | (187) op(e3, e3) = all_54_0
% 162.88/23.72 | (188) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 162.88/23.72 | (189) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 162.88/23.72 | (190) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 162.88/23.72 | (191) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 162.88/23.73 | (192) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 162.88/23.73 | (193) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 162.88/23.73 | (194) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 162.88/23.73 | (195) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 162.88/23.73 | (196) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 162.88/23.73 | (197) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 162.88/23.73 | (198) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 162.88/23.73 | (199) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 162.88/23.73 | (200) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 162.88/23.73 | (201) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 162.88/23.73 | (202) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 162.88/23.73 | (203) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 162.88/23.73 |
% 162.88/23.73 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2,
% 162.88/23.73 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 162.88/23.73 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives:
% 162.88/23.74 | (204) op(e3, e3) = all_56_10 & op(e2, e2) = all_56_12 & op(e1, e1) =
% 162.88/23.74 | all_56_14 & op(e0, e0) = all_56_15 & $i(all_56_10) & $i(all_56_12) &
% 162.88/23.74 | $i(all_56_14) & $i(all_56_15) & ( ~ (all_56_10 = e2) | (all_56_1 = e3
% 162.88/23.74 | & op(e3, e2) = e3)) & ( ~ (all_56_10 = e1) | (all_56_4 = e3 &
% 162.88/23.74 | op(e3, e1) = e3)) & ( ~ (all_56_10 = e0) | (all_56_9 = e3 &
% 162.88/23.74 | op(e3, e0) = e3)) & ( ~ (all_56_12 = e3) | (all_56_0 = e2 &
% 162.88/23.74 | op(e2, e3) = e2)) & ( ~ (all_56_12 = e1) | (all_56_5 = e2 &
% 162.88/23.74 | op(e2, e1) = e2)) & ( ~ (all_56_12 = e0) | (all_56_11 = e2 &
% 162.88/23.74 | op(e2, e0) = e2)) & ( ~ (all_56_14 = e3) | (all_56_2 = e1 &
% 162.88/23.74 | op(e1, e3) = e1)) & ( ~ (all_56_14 = e2) | (all_56_3 = e1 &
% 162.88/23.74 | op(e1, e2) = e1)) & ( ~ (all_56_14 = e0) | (all_56_13 = e1 &
% 162.88/23.74 | op(e1, e0) = e1)) & ( ~ (all_56_15 = e3) | (all_56_6 = e0 &
% 162.88/23.74 | op(e0, e3) = e0)) & ( ~ (all_56_15 = e2) | (all_56_7 = e0 &
% 162.88/23.74 | op(e0, e2) = e0)) & ( ~ (all_56_15 = e1) | (all_56_8 = e0 &
% 162.88/23.74 | op(e0, e1) = e0)) & (all_56_10 = e3 | all_56_12 = e2 | all_56_14
% 162.88/23.74 | = e1 | all_56_15 = e0) & ((all_56_0 = e3 & ~ (all_56_12 = e2) &
% 162.88/23.74 | op(e2, e3) = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 162.88/23.74 | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~ (all_56_14 = e2)
% 162.88/23.74 | | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 & $i(all_56_3)))
% 162.88/23.74 | & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0, e2) =
% 162.88/23.74 | all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~ (all_56_10 =
% 162.88/23.74 | e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 162.88/23.74 | e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 162.88/23.74 | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2
% 162.88/23.74 | & $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0)
% 162.88/23.74 | & op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 &
% 162.88/23.74 | ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 162.88/23.74 | (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & (
% 162.88/23.74 | ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) =
% 162.88/23.74 | all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 162.88/23.74 | (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 162.88/23.74 | (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 162.88/23.74 | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4
% 162.88/23.74 | & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2)
% 162.88/23.74 | & op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 =
% 162.88/23.74 | e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 162.88/23.74 | $i(all_56_8)))) | (all_56_4 = e1 & ~ (all_56_10 = e3) &
% 162.88/23.74 | op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 162.88/23.74 | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~ (all_56_14 = e3)
% 162.88/23.74 | | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 & $i(all_56_2)))
% 162.88/23.74 | & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0, e3) =
% 162.88/23.74 | all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~ (all_56_12 =
% 162.88/23.74 | e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 162.88/23.74 | e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 162.88/23.74 | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3
% 162.88/23.74 | & $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0)
% 162.88/23.74 | & op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 &
% 162.88/23.74 | ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 162.88/23.74 | (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & (
% 162.88/23.74 | ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) =
% 162.88/23.74 | all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 162.88/23.74 | (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 162.88/23.74 | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) = e0 & ( ~
% 162.88/23.74 | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1
% 162.88/23.74 | & $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1)
% 162.88/23.74 | & op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 =
% 162.88/23.74 | e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 162.88/23.74 | $i(all_56_7)))) | (all_56_13 = e0 & ~ (all_56_14 = e1) &
% 162.88/23.74 | op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 162.88/23.74 | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~ (all_56_12 = e1)
% 162.88/23.74 | | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 & $i(all_56_5)))
% 162.88/23.74 | & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) =
% 162.88/23.74 | all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 162.88/23.74 | (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9
% 162.88/23.74 | & $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 =
% 162.88/23.74 | e2) & op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~
% 162.88/23.74 | (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) =
% 162.88/23.74 | all_56_13 & $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) =
% 162.88/23.74 | e3) | (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 162.88/23.74 | op(e0, e1) = e1))))
% 162.88/23.74 |
% 162.88/23.74 | ALPHA: (204) implies:
% 162.88/23.74 | (205) op(e0, e0) = all_56_15
% 162.88/23.74 | (206) op(e1, e1) = all_56_14
% 162.88/23.74 | (207) op(e2, e2) = all_56_12
% 162.88/23.74 | (208) op(e3, e3) = all_56_10
% 162.88/23.75 | (209) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 162.88/23.75 | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 162.88/23.75 | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 162.88/23.75 | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) |
% 162.88/23.75 | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))) |
% 162.88/23.75 | (all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 162.88/23.75 | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 162.88/23.75 | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 162.88/23.75 | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) |
% 162.88/23.75 | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 162.88/23.75 | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 162.88/23.75 | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 162.88/23.75 | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 162.88/23.75 | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) |
% 162.88/23.75 | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 162.88/23.75 | (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 162.88/23.75 | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 162.88/23.75 | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 162.88/23.75 | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) |
% 162.88/23.75 | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 162.88/23.75 | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 162.88/23.75 | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 162.88/23.75 | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 162.88/23.75 | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) |
% 162.88/23.75 | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 162.88/23.75 | (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~
% 162.88/23.75 | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 162.88/23.75 | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 162.88/23.75 | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) |
% 162.88/23.75 | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))) |
% 162.88/23.75 | (all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 162.88/23.75 | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 162.88/23.75 | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 162.88/23.75 | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) |
% 162.88/23.75 | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 162.88/23.75 | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) = e0 & ( ~
% 162.88/23.75 | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 162.88/23.75 | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 162.88/23.75 | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) |
% 162.88/23.75 | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))) |
% 162.88/23.75 | (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 162.88/23.75 | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 162.88/23.75 | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 162.88/23.75 | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) |
% 162.88/23.75 | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 162.88/23.75 | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 162.88/23.75 | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) |
% 162.88/23.75 | ( ~ (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11))) &
% 162.88/23.75 | ( ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) =
% 162.88/23.75 | all_56_13 & $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) =
% 162.88/23.75 | e3) | (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 162.88/23.75 | op(e0, e1) = e1)))
% 162.88/23.75 | (210) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 162.88/23.75 | (211) ~ (all_56_15 = e1) | (all_56_8 = e0 & op(e0, e1) = e0)
% 162.88/23.75 | (212) ~ (all_56_15 = e2) | (all_56_7 = e0 & op(e0, e2) = e0)
% 162.88/23.75 | (213) ~ (all_56_15 = e3) | (all_56_6 = e0 & op(e0, e3) = e0)
% 162.88/23.75 | (214) ~ (all_56_14 = e0) | (all_56_13 = e1 & op(e1, e0) = e1)
% 162.88/23.75 | (215) ~ (all_56_14 = e2) | (all_56_3 = e1 & op(e1, e2) = e1)
% 162.88/23.75 | (216) ~ (all_56_14 = e3) | (all_56_2 = e1 & op(e1, e3) = e1)
% 162.88/23.75 | (217) ~ (all_56_12 = e0) | (all_56_11 = e2 & op(e2, e0) = e2)
% 162.88/23.75 | (218) ~ (all_56_12 = e1) | (all_56_5 = e2 & op(e2, e1) = e2)
% 162.88/23.75 | (219) ~ (all_56_12 = e3) | (all_56_0 = e2 & op(e2, e3) = e2)
% 162.88/23.75 | (220) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 162.88/23.75 | (221) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 162.88/23.75 | (222) ~ (all_56_10 = e2) | (all_56_1 = e3 & op(e3, e2) = e3)
% 162.88/23.75 |
% 162.88/23.75 | DELTA: instantiating (2) with fresh symbols all_58_0, all_58_1, all_58_2,
% 162.88/23.75 | all_58_3, all_58_4, all_58_5, all_58_6, all_58_7, all_58_8, all_58_9,
% 162.88/23.75 | all_58_10, all_58_11, all_58_12, all_58_13, all_58_14, all_58_15 gives:
% 163.22/23.77 | (223) ((all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 163.22/23.77 | e3) | (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 163.22/23.77 | e0) = e3)) & ((all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 =
% 163.22/23.77 | e3 & op(e2, e3) = e3) | (all_58_6 = e3 & op(e1, e3) = e3) |
% 163.22/23.77 | (all_58_12 = e3 & op(e0, e3) = e3)) & ((all_58_0 = e2 & op(e3, e3)
% 163.22/23.77 | = e2) | (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_4 = e2 &
% 163.22/23.77 | op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)) &
% 163.22/23.77 | ((all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 163.22/23.77 | e2) | (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 163.22/23.77 | op(e0, e3) = e2)) & ((all_58_0 = e1 & op(e3, e3) = e1) |
% 163.22/23.77 | (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_4 = e1 & op(e3, e1) =
% 163.22/23.77 | e1) | (all_58_9 = e1 & op(e3, e0) = e1)) & ((all_58_0 = e1 &
% 163.22/23.77 | op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_6
% 163.22/23.77 | = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)) &
% 163.22/23.77 | ((all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 163.22/23.77 | e0) | (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 163.22/23.77 | e0) = e0)) & ((all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 =
% 163.22/23.77 | e0 & op(e2, e3) = e0) | (all_58_6 = e0 & op(e1, e3) = e0) |
% 163.22/23.77 | (all_58_12 = e0 & op(e0, e3) = e0)) & ((all_58_1 = e3 & op(e3, e2)
% 163.22/23.77 | = e3) | (all_58_3 = e3 & op(e2, e2) = e3) | (all_58_7 = e3 &
% 163.22/23.77 | op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)) &
% 163.22/23.77 | ((all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 163.22/23.77 | e2) | (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 &
% 163.22/23.77 | op(e0, e2) = e2)) & ((all_58_1 = e1 & op(e3, e2) = e1) |
% 163.22/23.77 | (all_58_3 = e1 & op(e2, e2) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 163.22/23.77 | e1) | (all_58_13 = e1 & op(e0, e2) = e1)) & ((all_58_1 = e0 &
% 163.22/23.77 | op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) | (all_58_7
% 163.22/23.77 | = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)) &
% 163.22/23.77 | ((all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 163.22/23.77 | e3) | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 &
% 163.22/23.77 | op(e2, e0) = e3)) & ((all_58_2 = e2 & op(e2, e3) = e2) |
% 163.22/23.77 | (all_58_3 = e2 & op(e2, e2) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 163.22/23.77 | e2) | (all_58_10 = e2 & op(e2, e0) = e2)) & ((all_58_2 = e1 &
% 163.22/23.77 | op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) | (all_58_5
% 163.22/23.77 | = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)) &
% 163.22/23.77 | ((all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 163.22/23.77 | e0) | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 163.22/23.77 | op(e2, e0) = e0)) & ((all_58_4 = e3 & op(e3, e1) = e3) |
% 163.22/23.77 | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_8 = e3 & op(e1, e1) =
% 163.22/23.77 | e3) | (all_58_14 = e3 & op(e0, e1) = e3)) & ((all_58_4 = e2 &
% 163.22/23.77 | op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_8
% 163.22/23.77 | = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)) &
% 163.22/23.77 | ((all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 163.22/23.77 | e1) | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 163.22/23.77 | op(e0, e1) = e1)) & ((all_58_4 = e0 & op(e3, e1) = e0) |
% 163.22/23.77 | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_8 = e0 & op(e1, e1) =
% 163.22/23.77 | e0) | (all_58_14 = e0 & op(e0, e1) = e0)) & ((all_58_6 = e3 &
% 163.22/23.77 | op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_8
% 163.22/23.77 | = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)) &
% 163.22/23.77 | ((all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 163.22/23.77 | e2) | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 163.22/23.77 | op(e1, e0) = e2)) & ((all_58_6 = e1 & op(e1, e3) = e1) |
% 163.22/23.77 | (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_8 = e1 & op(e1, e1) =
% 163.22/23.77 | e1) | (all_58_11 = e1 & op(e1, e0) = e1)) & ((all_58_6 = e0 &
% 163.22/23.77 | op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_8
% 163.22/23.77 | = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 163.22/23.77 | ((all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 163.22/23.77 | e3) | (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 163.22/23.77 | op(e0, e0) = e3)) & ((all_58_9 = e2 & op(e3, e0) = e2) |
% 163.22/23.77 | (all_58_10 = e2 & op(e2, e0) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 163.22/23.77 | e2) | (all_58_15 = e2 & op(e0, e0) = e2)) & ((all_58_9 = e1 &
% 163.22/23.77 | op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 163.22/23.77 | (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 163.22/23.77 | e1)) & ((all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 163.22/23.77 | op(e0, e2) = e3) | (all_58_14 = e3 & op(e0, e1) = e3) |
% 163.22/23.77 | (all_58_15 = e3 & op(e0, e0) = e3)) & ((all_58_12 = e2 & op(e0, e3)
% 163.22/23.77 | = e2) | (all_58_13 = e2 & op(e0, e2) = e2) | (all_58_14 = e2 &
% 163.22/23.77 | op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)) &
% 163.22/23.77 | ((all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 163.22/23.77 | e1) | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 163.22/23.77 | op(e0, e0) = e1)) & ((all_58_15 = e0 & op(e0, e0) = e0) |
% 163.22/23.77 | (((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 163.22/23.77 | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 =
% 163.22/23.77 | e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 163.22/23.77 | (all_58_14 = e0 & op(e0, e1) = e0))))
% 163.22/23.77 |
% 163.22/23.77 | ALPHA: (223) implies:
% 163.22/23.77 | (224) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 163.22/23.77 | e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 163.22/23.77 | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 163.22/23.77 | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 163.22/23.77 | = e0)))
% 163.22/23.77 | (225) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 163.22/23.77 | e1) | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0,
% 163.22/23.77 | e0) = e1)
% 163.22/23.77 | (226) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 163.22/23.77 | e2) | (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 163.22/23.77 | e0) = e2)
% 163.22/23.77 | (227) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 163.22/23.77 | e3) | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 163.22/23.77 | e0) = e3)
% 163.22/23.77 | (228) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 163.22/23.77 | e1) | (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 163.22/23.77 | e0) = e1)
% 163.22/23.77 | (229) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 163.22/23.77 | e2) | (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 163.22/23.77 | e0) = e2)
% 163.22/23.78 | (230) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 163.22/23.78 | e3) | (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 163.22/23.78 | e0) = e3)
% 163.22/23.78 | (231) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 163.22/23.78 | | (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 163.22/23.78 | e0)
% 163.22/23.78 | (232) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 163.22/23.78 | | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 163.22/23.78 | e1)
% 163.22/23.78 | (233) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 163.22/23.78 | | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 163.22/23.78 | e2)
% 163.22/23.78 | (234) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 163.22/23.78 | | (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 163.22/23.78 | e3)
% 163.22/23.78 | (235) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 163.22/23.78 | | (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 163.22/23.78 | e0)
% 163.22/23.78 | (236) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 163.22/23.78 | | (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 163.22/23.78 | e1)
% 163.22/23.78 | (237) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 163.22/23.78 | | (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 163.22/23.78 | e2)
% 163.22/23.78 | (238) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 163.22/23.78 | | (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 163.22/23.78 | e3)
% 163.22/23.78 | (239) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 163.22/23.78 | | (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 163.22/23.78 | e0)
% 163.22/23.78 | (240) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 163.22/23.78 | | (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 163.22/23.78 | e1)
% 163.22/23.78 | (241) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 163.22/23.78 | | (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 163.22/23.78 | e2)
% 163.22/23.78 | (242) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 163.22/23.78 | | (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 163.22/23.78 | e3)
% 163.22/23.78 | (243) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 163.22/23.78 | | (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 163.22/23.78 | e0)
% 163.22/23.78 | (244) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 163.22/23.78 | | (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 163.22/23.78 | e1)
% 163.22/23.79 | (245) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 163.22/23.79 | | (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 163.22/23.79 | e2)
% 163.22/23.79 | (246) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 163.22/23.79 | | (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 163.22/23.79 | e3)
% 163.22/23.79 | (247) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 163.22/23.79 | | (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 163.22/23.79 | e0)
% 163.22/23.79 | (248) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 163.22/23.79 | | (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 163.22/23.79 | e0)
% 163.22/23.79 | (249) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 163.22/23.79 | | (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 163.22/23.79 | e1)
% 163.22/23.79 | (250) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 163.22/23.79 | | (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 163.22/23.79 | e1)
% 163.22/23.79 | (251) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 163.22/23.79 | | (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 163.22/23.79 | e2)
% 163.22/23.79 | (252) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 163.22/23.79 | | (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 163.22/23.79 | e2)
% 163.22/23.79 | (253) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 163.22/23.79 | | (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 163.22/23.79 | e3)
% 163.22/23.79 | (254) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 163.22/23.79 | | (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 163.22/23.79 | e3)
% 163.22/23.79 |
% 163.22/23.79 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_20_2, e0, e0,
% 163.22/23.79 | simplifying with (48), (60) gives:
% 163.22/23.79 | (255) all_20_2 = all_12_2
% 163.22/23.79 |
% 163.22/23.79 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_34_2, e0, e0,
% 163.22/23.79 | simplifying with (69), (81) gives:
% 163.22/23.79 | (256) all_34_2 = all_26_2
% 163.22/23.79 |
% 163.22/23.79 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_34_2, e0, e0,
% 163.22/23.79 | simplifying with (60), (81) gives:
% 163.22/23.79 | (257) all_34_2 = all_20_2
% 163.22/23.79 |
% 163.22/23.79 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_44_2, e0, e0,
% 163.22/23.79 | simplifying with (81), (95) gives:
% 163.22/23.79 | (258) all_44_2 = all_34_2
% 163.22/23.79 |
% 163.22/23.79 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_52_15, e0, e0,
% 163.22/23.79 | simplifying with (95), (155) gives:
% 163.22/23.79 | (259) all_52_15 = all_44_2
% 163.22/23.79 |
% 163.22/23.79 | GROUND_INST: instantiating (function-axioms) with all_52_15, all_54_15, e0,
% 163.22/23.79 | e0, simplifying with (155), (172) gives:
% 163.22/23.79 | (260) all_54_15 = all_52_15
% 163.22/23.79 |
% 163.22/23.79 | GROUND_INST: instantiating (function-axioms) with all_54_15, all_56_15, e0,
% 163.22/23.79 | e0, simplifying with (172), (205) gives:
% 163.22/23.79 | (261) all_56_15 = all_54_15
% 163.22/23.79 |
% 163.22/23.79 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_56_15, e0, e0,
% 163.22/23.79 | simplifying with (36), (205) gives:
% 163.22/23.79 | (262) all_56_15 = all_4_2
% 163.22/23.79 |
% 163.22/23.79 | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_14, e1,
% 163.22/23.79 | e0, simplifying with (156), (173) gives:
% 163.22/23.79 | (263) all_54_14 = all_52_11
% 163.22/23.79 |
% 163.22/23.79 | GROUND_INST: instantiating (function-axioms) with all_52_7, all_54_13, e2, e0,
% 163.22/23.79 | simplifying with (157), (174) gives:
% 163.22/23.80 | (264) all_54_13 = all_52_7
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_54_12, e3, e0,
% 163.22/23.80 | simplifying with (158), (175) gives:
% 163.22/23.80 | (265) all_54_12 = all_52_3
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_14, all_54_11, e0,
% 163.22/23.80 | e1, simplifying with (159), (176) gives:
% 163.22/23.80 | (266) all_54_11 = all_52_14
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_28_2, e1, e1,
% 163.22/23.80 | simplifying with (57), (72) gives:
% 163.22/23.80 | (267) all_28_2 = all_18_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_36_2, e1, e1,
% 163.22/23.80 | simplifying with (72), (84) gives:
% 163.22/23.80 | (268) all_36_2 = all_28_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_52_10, e1, e1,
% 163.22/23.80 | simplifying with (98), (160) gives:
% 163.22/23.80 | (269) all_52_10 = all_46_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_52_10, e1, e1,
% 163.22/23.80 | simplifying with (90), (160) gives:
% 163.22/23.80 | (270) all_52_10 = all_40_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_52_10, e1, e1,
% 163.22/23.80 | simplifying with (84), (160) gives:
% 163.22/23.80 | (271) all_52_10 = all_36_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_54_10, e1, e1,
% 163.22/23.80 | simplifying with (98), (177) gives:
% 163.22/23.80 | (272) all_54_10 = all_46_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_54_10, all_56_14, e1,
% 163.22/23.80 | e1, simplifying with (177), (206) gives:
% 163.22/23.80 | (273) all_56_14 = all_54_10
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_56_14, e1, e1,
% 163.22/23.80 | simplifying with (39), (206) gives:
% 163.22/23.80 | (274) all_56_14 = all_6_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_6, all_54_9, e2, e1,
% 163.22/23.80 | simplifying with (161), (178) gives:
% 163.22/23.80 | (275) all_54_9 = all_52_6
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_54_8, e3, e1,
% 163.22/23.80 | simplifying with (162), (179) gives:
% 163.22/23.80 | (276) all_54_8 = all_52_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_13, all_54_7, e0, e2,
% 163.22/23.80 | simplifying with (163), (180) gives:
% 163.22/23.80 | (277) all_54_7 = all_52_13
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_9, all_54_6, e1, e2,
% 163.22/23.80 | simplifying with (164), (181) gives:
% 163.22/23.80 | (278) all_54_6 = all_52_9
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_30_2, e2, e2,
% 163.22/23.80 | simplifying with (63), (75) gives:
% 163.22/23.80 | (279) all_30_2 = all_22_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_30_2, e2, e2,
% 163.22/23.80 | simplifying with (51), (75) gives:
% 163.22/23.80 | (280) all_30_2 = all_14_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_42_2, e2, e2,
% 163.22/23.80 | simplifying with (63), (92) gives:
% 163.22/23.80 | (281) all_42_2 = all_22_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_5, all_54_5, e2, e2,
% 163.22/23.80 | simplifying with (165), (182) gives:
% 163.22/23.80 | (282) all_54_5 = all_52_5
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_54_5, e2, e2,
% 163.22/23.80 | simplifying with (42), (182) gives:
% 163.22/23.80 | (283) all_54_5 = all_8_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_5, all_56_12, e2, e2,
% 163.22/23.80 | simplifying with (165), (207) gives:
% 163.22/23.80 | (284) all_56_12 = all_52_5
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_56_12, e2, e2,
% 163.22/23.80 | simplifying with (101), (207) gives:
% 163.22/23.80 | (285) all_56_12 = all_48_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_56_12, e2, e2,
% 163.22/23.80 | simplifying with (92), (207) gives:
% 163.22/23.80 | (286) all_56_12 = all_42_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_54_4, e3, e2,
% 163.22/23.80 | simplifying with (166), (183) gives:
% 163.22/23.80 | (287) all_54_4 = all_52_1
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_12, all_54_3, e0, e3,
% 163.22/23.80 | simplifying with (167), (184) gives:
% 163.22/23.80 | (288) all_54_3 = all_52_12
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_8, all_54_2, e1, e3,
% 163.22/23.80 | simplifying with (168), (185) gives:
% 163.22/23.80 | (289) all_54_2 = all_52_8
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_52_4, all_54_1, e2, e3,
% 163.22/23.80 | simplifying with (169), (186) gives:
% 163.22/23.80 | (290) all_54_1 = all_52_4
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_32_2, e3, e3,
% 163.22/23.80 | simplifying with (66), (78) gives:
% 163.22/23.80 | (291) all_32_2 = all_24_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_38_2, e3, e3,
% 163.22/23.80 | simplifying with (78), (87) gives:
% 163.22/23.80 | (292) all_38_2 = all_32_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_50_2, e3, e3,
% 163.22/23.80 | simplifying with (87), (104) gives:
% 163.22/23.80 | (293) all_50_2 = all_38_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_52_0, e3, e3,
% 163.22/23.80 | simplifying with (104), (170) gives:
% 163.22/23.80 | (294) all_52_0 = all_50_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_52_0, e3, e3,
% 163.22/23.80 | simplifying with (54), (170) gives:
% 163.22/23.80 | (295) all_52_0 = all_16_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_54_0, e3, e3,
% 163.22/23.80 | simplifying with (66), (187) gives:
% 163.22/23.80 | (296) all_54_0 = all_24_2
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_54_0, all_56_10, e3, e3,
% 163.22/23.80 | simplifying with (187), (208) gives:
% 163.22/23.80 | (297) all_56_10 = all_54_0
% 163.22/23.80 |
% 163.22/23.80 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_56_10, e3, e3,
% 163.22/23.80 | simplifying with (45), (208) gives:
% 163.22/23.80 | (298) all_56_10 = all_10_2
% 163.22/23.80 |
% 163.22/23.80 | COMBINE_EQS: (297), (298) imply:
% 163.22/23.80 | (299) all_54_0 = all_10_2
% 163.22/23.80 |
% 163.22/23.80 | SIMP: (299) implies:
% 163.22/23.80 | (300) all_54_0 = all_10_2
% 163.22/23.80 |
% 163.38/23.81 | COMBINE_EQS: (284), (285) imply:
% 163.38/23.81 | (301) all_52_5 = all_48_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (301) implies:
% 163.38/23.81 | (302) all_52_5 = all_48_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (285), (286) imply:
% 163.38/23.81 | (303) all_48_2 = all_42_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (273), (274) imply:
% 163.38/23.81 | (304) all_54_10 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (304) implies:
% 163.38/23.81 | (305) all_54_10 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (261), (262) imply:
% 163.38/23.81 | (306) all_54_15 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (306) implies:
% 163.38/23.81 | (307) all_54_15 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (296), (300) imply:
% 163.38/23.81 | (308) all_24_2 = all_10_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (308) implies:
% 163.38/23.81 | (309) all_24_2 = all_10_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (282), (283) imply:
% 163.38/23.81 | (310) all_52_5 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (310) implies:
% 163.38/23.81 | (311) all_52_5 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (272), (305) imply:
% 163.38/23.81 | (312) all_46_2 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (312) implies:
% 163.38/23.81 | (313) all_46_2 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (260), (307) imply:
% 163.38/23.81 | (314) all_52_15 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (314) implies:
% 163.38/23.81 | (315) all_52_15 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (294), (295) imply:
% 163.38/23.81 | (316) all_50_2 = all_16_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (316) implies:
% 163.38/23.81 | (317) all_50_2 = all_16_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (302), (311) imply:
% 163.38/23.81 | (318) all_48_2 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (318) implies:
% 163.38/23.81 | (319) all_48_2 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (269), (270) imply:
% 163.38/23.81 | (320) all_46_2 = all_40_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (320) implies:
% 163.38/23.81 | (321) all_46_2 = all_40_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (270), (271) imply:
% 163.38/23.81 | (322) all_40_2 = all_36_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (259), (315) imply:
% 163.38/23.81 | (323) all_44_2 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (323) implies:
% 163.38/23.81 | (324) all_44_2 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (293), (317) imply:
% 163.38/23.81 | (325) all_38_2 = all_16_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (325) implies:
% 163.38/23.81 | (326) all_38_2 = all_16_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (303), (319) imply:
% 163.38/23.81 | (327) all_42_2 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (327) implies:
% 163.38/23.81 | (328) all_42_2 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (313), (321) imply:
% 163.38/23.81 | (329) all_40_2 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (329) implies:
% 163.38/23.81 | (330) all_40_2 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (258), (324) imply:
% 163.38/23.81 | (331) all_34_2 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (331) implies:
% 163.38/23.81 | (332) all_34_2 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (281), (328) imply:
% 163.38/23.81 | (333) all_22_2 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (333) implies:
% 163.38/23.81 | (334) all_22_2 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (322), (330) imply:
% 163.38/23.81 | (335) all_36_2 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (335) implies:
% 163.38/23.81 | (336) all_36_2 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (292), (326) imply:
% 163.38/23.81 | (337) all_32_2 = all_16_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (337) implies:
% 163.38/23.81 | (338) all_32_2 = all_16_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (268), (336) imply:
% 163.38/23.81 | (339) all_28_2 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (339) implies:
% 163.38/23.81 | (340) all_28_2 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (256), (257) imply:
% 163.38/23.81 | (341) all_26_2 = all_20_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (256), (332) imply:
% 163.38/23.81 | (342) all_26_2 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (291), (338) imply:
% 163.38/23.81 | (343) all_24_2 = all_16_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (343) implies:
% 163.38/23.81 | (344) all_24_2 = all_16_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (279), (280) imply:
% 163.38/23.81 | (345) all_22_2 = all_14_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (345) implies:
% 163.38/23.81 | (346) all_22_2 = all_14_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (267), (340) imply:
% 163.38/23.81 | (347) all_18_2 = all_6_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (341), (342) imply:
% 163.38/23.81 | (348) all_20_2 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (348) implies:
% 163.38/23.81 | (349) all_20_2 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (309), (344) imply:
% 163.38/23.81 | (350) all_16_2 = all_10_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (334), (346) imply:
% 163.38/23.81 | (351) all_14_2 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (351) implies:
% 163.38/23.81 | (352) all_14_2 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (255), (349) imply:
% 163.38/23.81 | (353) all_12_2 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | SIMP: (353) implies:
% 163.38/23.81 | (354) all_12_2 = all_4_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (280), (352) imply:
% 163.38/23.81 | (355) all_30_2 = all_8_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (338), (350) imply:
% 163.38/23.81 | (356) all_32_2 = all_10_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (326), (350) imply:
% 163.38/23.81 | (357) all_38_2 = all_10_2
% 163.38/23.81 |
% 163.38/23.81 | COMBINE_EQS: (317), (350) imply:
% 163.38/23.81 | (358) all_50_2 = all_10_2
% 163.38/23.82 |
% 163.38/23.82 | COMBINE_EQS: (270), (330) imply:
% 163.38/23.82 | (359) all_52_10 = all_6_2
% 163.38/23.82 |
% 163.38/23.82 | COMBINE_EQS: (295), (350) imply:
% 163.38/23.82 | (360) all_52_0 = all_10_2
% 163.38/23.82 |
% 163.38/23.82 | COMBINE_EQS: (285), (319) imply:
% 163.38/23.82 | (361) all_56_12 = all_8_2
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (154), (360) imply:
% 163.38/23.82 | (362) ~ (all_52_1 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (362) implies:
% 163.38/23.82 | (363) ~ (all_52_1 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (153), (360) imply:
% 163.38/23.82 | (364) ~ (all_52_2 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (364) implies:
% 163.38/23.82 | (365) ~ (all_52_2 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (152), (360) imply:
% 163.38/23.82 | (366) ~ (all_52_3 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (366) implies:
% 163.38/23.82 | (367) ~ (all_52_3 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (151), (360) imply:
% 163.38/23.82 | (368) ~ (all_52_4 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (368) implies:
% 163.38/23.82 | (369) ~ (all_52_4 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (150), (360) imply:
% 163.38/23.82 | (370) ~ (all_52_8 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (370) implies:
% 163.38/23.82 | (371) ~ (all_52_8 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (149), (360) imply:
% 163.38/23.82 | (372) ~ (all_52_12 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (372) implies:
% 163.38/23.82 | (373) ~ (all_52_12 = all_10_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (146), (311) imply:
% 163.38/23.82 | (374) ~ (all_52_1 = all_8_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (141), (359) imply:
% 163.38/23.82 | (375) ~ (all_52_2 = all_6_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (137), (315) imply:
% 163.38/23.82 | (376) ~ (all_52_3 = all_4_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (136), (311) imply:
% 163.38/23.82 | (377) ~ (all_52_4 = all_8_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (131), (311) imply:
% 163.38/23.82 | (378) ~ (all_52_6 = all_8_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (378) implies:
% 163.38/23.82 | (379) ~ (all_52_6 = all_8_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (130), (311) imply:
% 163.38/23.82 | (380) ~ (all_52_7 = all_8_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (380) implies:
% 163.38/23.82 | (381) ~ (all_52_7 = all_8_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (129), (311) imply:
% 163.38/23.82 | (382) ~ (all_52_9 = all_8_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (382) implies:
% 163.38/23.82 | (383) ~ (all_52_9 = all_8_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (128), (311) imply:
% 163.38/23.82 | (384) ~ (all_52_13 = all_8_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (384) implies:
% 163.38/23.82 | (385) ~ (all_52_13 = all_8_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (126), (359) imply:
% 163.38/23.82 | (386) ~ (all_52_6 = all_6_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (123), (315) imply:
% 163.38/23.82 | (387) ~ (all_52_7 = all_4_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (121), (359) imply:
% 163.38/23.82 | (388) ~ (all_52_8 = all_6_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (118), (359) imply:
% 163.38/23.82 | (389) ~ (all_52_9 = all_6_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (115), (359) imply:
% 163.38/23.82 | (390) ~ (all_52_11 = all_6_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (390) implies:
% 163.38/23.82 | (391) ~ (all_52_11 = all_6_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (114), (359) imply:
% 163.38/23.82 | (392) ~ (all_52_14 = all_6_2)
% 163.38/23.82 |
% 163.38/23.82 | SIMP: (392) implies:
% 163.38/23.82 | (393) ~ (all_52_14 = all_6_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (113), (315) imply:
% 163.38/23.82 | (394) ~ (all_52_11 = all_4_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (110), (315) imply:
% 163.38/23.82 | (395) ~ (all_52_12 = all_4_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (108), (315) imply:
% 163.38/23.82 | (396) ~ (all_52_13 = all_4_2)
% 163.38/23.82 |
% 163.38/23.82 | REDUCE: (107), (315) imply:
% 163.38/23.82 | (397) ~ (all_52_14 = all_4_2)
% 163.38/23.82 |
% 163.38/23.82 | BETA: splitting (37) gives:
% 163.38/23.82 |
% 163.38/23.82 | Case 1:
% 163.38/23.82 | |
% 163.38/23.82 | | (398) ~ (all_4_2 = e1)
% 163.38/23.82 | |
% 163.38/23.82 | | BETA: splitting (40) gives:
% 163.38/23.82 | |
% 163.38/23.82 | | Case 1:
% 163.38/23.82 | | |
% 163.38/23.82 | | | (399) ~ (all_6_2 = e2)
% 163.38/23.82 | | |
% 163.38/23.82 | | | BETA: splitting (43) gives:
% 163.38/23.83 | | |
% 163.38/23.83 | | | Case 1:
% 163.38/23.83 | | | |
% 163.38/23.83 | | | | (400) ~ (all_8_2 = e1)
% 163.38/23.83 | | | |
% 163.38/23.83 | | | | BETA: splitting (46) gives:
% 163.38/23.83 | | | |
% 163.38/23.83 | | | | Case 1:
% 163.38/23.83 | | | | |
% 163.38/23.83 | | | | | (401) ~ (all_10_2 = e0)
% 163.38/23.83 | | | | |
% 163.38/23.83 | | | | | BETA: splitting (52) gives:
% 163.38/23.83 | | | | |
% 163.38/23.83 | | | | | Case 1:
% 163.38/23.83 | | | | | |
% 163.38/23.83 | | | | | | (402) ~ (all_14_2 = e3)
% 163.38/23.83 | | | | | |
% 163.38/23.83 | | | | | | REDUCE: (352), (402) imply:
% 163.38/23.83 | | | | | | (403) ~ (all_8_2 = e3)
% 163.38/23.83 | | | | | |
% 163.38/23.83 | | | | | | BETA: splitting (55) gives:
% 163.38/23.83 | | | | | |
% 163.38/23.83 | | | | | | Case 1:
% 163.38/23.83 | | | | | | |
% 163.38/23.83 | | | | | | | (404) ~ (all_16_2 = e2)
% 163.38/23.83 | | | | | | |
% 163.38/23.83 | | | | | | | REDUCE: (350), (404) imply:
% 163.38/23.83 | | | | | | | (405) ~ (all_10_2 = e2)
% 163.38/23.83 | | | | | | |
% 163.38/23.83 | | | | | | | BETA: splitting (61) gives:
% 163.38/23.83 | | | | | | |
% 163.38/23.83 | | | | | | | Case 1:
% 163.38/23.83 | | | | | | | |
% 163.38/23.83 | | | | | | | | (406) ~ (all_20_2 = e2)
% 163.38/23.83 | | | | | | | |
% 163.38/23.83 | | | | | | | | REDUCE: (349), (406) imply:
% 163.38/23.83 | | | | | | | | (407) ~ (all_4_2 = e2)
% 163.38/23.83 | | | | | | | |
% 163.38/23.83 | | | | | | | | BETA: splitting (73) gives:
% 163.38/23.83 | | | | | | | |
% 163.38/23.83 | | | | | | | | Case 1:
% 163.38/23.83 | | | | | | | | |
% 163.38/23.83 | | | | | | | | | (408) ~ (all_28_2 = e3)
% 163.38/23.83 | | | | | | | | |
% 163.38/23.83 | | | | | | | | | REDUCE: (340), (408) imply:
% 163.38/23.83 | | | | | | | | | (409) ~ (all_6_2 = e3)
% 163.38/23.83 | | | | | | | | |
% 163.38/23.83 | | | | | | | | | BETA: splitting (76) gives:
% 163.38/23.83 | | | | | | | | |
% 163.38/23.83 | | | | | | | | | Case 1:
% 163.38/23.83 | | | | | | | | | |
% 163.38/23.83 | | | | | | | | | | (410) ~ (all_30_2 = e0)
% 163.38/23.83 | | | | | | | | | |
% 163.38/23.83 | | | | | | | | | | REDUCE: (355), (410) imply:
% 163.38/23.83 | | | | | | | | | | (411) ~ (all_8_2 = e0)
% 163.38/23.83 | | | | | | | | | |
% 163.38/23.83 | | | | | | | | | | BETA: splitting (198) gives:
% 163.38/23.83 | | | | | | | | | |
% 163.38/23.83 | | | | | | | | | | Case 1:
% 163.38/23.83 | | | | | | | | | | |
% 163.38/23.83 | | | | | | | | | | | (412) all_54_5 = e3
% 163.38/23.83 | | | | | | | | | | |
% 163.38/23.83 | | | | | | | | | | | COMBINE_EQS: (283), (412) imply:
% 163.38/23.83 | | | | | | | | | | | (413) all_8_2 = e3
% 163.38/23.83 | | | | | | | | | | |
% 163.38/23.83 | | | | | | | | | | | REDUCE: (403), (413) imply:
% 163.38/23.83 | | | | | | | | | | | (414) $false
% 163.38/23.84 | | | | | | | | | | |
% 163.38/23.84 | | | | | | | | | | | CLOSE: (414) is inconsistent.
% 163.38/23.84 | | | | | | | | | | |
% 163.38/23.84 | | | | | | | | | | Case 2:
% 163.38/23.84 | | | | | | | | | | |
% 163.38/23.84 | | | | | | | | | | | (415) ~ (all_54_5 = e3)
% 163.38/23.84 | | | | | | | | | | | (416) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 163.38/23.84 | | | | | | | | | | |
% 163.38/23.84 | | | | | | | | | | | BETA: splitting (416) gives:
% 163.38/23.84 | | | | | | | | | | |
% 163.38/23.84 | | | | | | | | | | | Case 1:
% 163.38/23.84 | | | | | | | | | | | |
% 163.38/23.84 | | | | | | | | | | | | (417) all_54_5 = e2
% 163.38/23.84 | | | | | | | | | | | |
% 163.38/23.84 | | | | | | | | | | | | COMBINE_EQS: (283), (417) imply:
% 163.52/23.84 | | | | | | | | | | | | (418) all_8_2 = e2
% 163.52/23.84 | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | COMBINE_EQS: (361), (418) imply:
% 163.52/23.84 | | | | | | | | | | | | (419) all_56_12 = e2
% 163.52/23.84 | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | REDUCE: (377), (418) imply:
% 163.52/23.84 | | | | | | | | | | | | (420) ~ (all_52_4 = e2)
% 163.52/23.84 | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | REDUCE: (379), (418) imply:
% 163.52/23.84 | | | | | | | | | | | | (421) ~ (all_52_6 = e2)
% 163.52/23.84 | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | REDUCE: (381), (418) imply:
% 163.52/23.84 | | | | | | | | | | | | (422) ~ (all_52_7 = e2)
% 163.52/23.84 | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | REDUCE: (403), (418) imply:
% 163.52/23.84 | | | | | | | | | | | | (423) ~ (e3 = e2)
% 163.52/23.84 | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | BETA: splitting (245) gives:
% 163.52/23.84 | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | Case 1:
% 163.52/23.84 | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | (424) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 163.52/23.84 | | | | | | | | | | | | | & op(e2, e2) = e2)
% 163.52/23.84 | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | BETA: splitting (424) gives:
% 163.52/23.84 | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | Case 1:
% 163.52/23.84 | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | (425) all_58_1 = e2 & op(e3, e2) = e2
% 163.52/23.84 | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | ALPHA: (425) implies:
% 163.52/23.84 | | | | | | | | | | | | | | (426) op(e3, e2) = e2
% 163.52/23.84 | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | REF_CLOSE: (169), (420), (426), (function-axioms) are
% 163.52/23.84 | | | | | | | | | | | | | | inconsistent by sub-proof #993.
% 163.52/23.84 | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | Case 2:
% 163.52/23.84 | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | (427) all_58_3 = e2 & op(e2, e2) = e2
% 163.52/23.84 | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | ALPHA: (427) implies:
% 163.52/23.84 | | | | | | | | | | | | | | (428) all_58_3 = e2
% 163.52/23.84 | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 163.52/23.84 | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | Case 1:
% 163.52/23.84 | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | (429) ~ (all_32_2 = e1)
% 163.52/23.84 | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | REDUCE: (356), (429) imply:
% 163.52/23.84 | | | | | | | | | | | | | | | (430) ~ (all_10_2 = e1)
% 163.52/23.84 | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 163.52/23.84 | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | Case 1:
% 163.52/23.84 | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | (431) all_54_0 = e3
% 163.52/23.84 | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (431) imply:
% 163.52/23.84 | | | | | | | | | | | | | | | | (432) all_10_2 = e3
% 163.52/23.84 | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (432) imply:
% 163.52/23.84 | | | | | | | | | | | | | | | | (433) all_56_10 = e3
% 163.52/23.84 | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | REDUCE: (363), (432) imply:
% 163.52/23.84 | | | | | | | | | | | | | | | | (434) ~ (all_52_1 = e3)
% 163.52/23.84 | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | REDUCE: (365), (432) imply:
% 163.52/23.84 | | | | | | | | | | | | | | | | (435) ~ (all_52_2 = e3)
% 163.52/23.84 | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | REDUCE: (369), (432) imply:
% 163.52/23.84 | | | | | | | | | | | | | | | | (436) ~ (all_52_4 = e3)
% 163.52/23.84 | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | REDUCE: (371), (432) imply:
% 163.52/23.84 | | | | | | | | | | | | | | | | (437) ~ (all_52_8 = e3)
% 163.52/23.84 | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 163.52/23.84 | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.84 | | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | | (438) ~ (all_34_2 = e3)
% 163.52/23.84 | | | | | | | | | | | | | | | | |
% 163.52/23.84 | | | | | | | | | | | | | | | | | REDUCE: (332), (438) imply:
% 163.52/23.85 | | | | | | | | | | | | | | | | | (439) ~ (all_4_2 = e3)
% 163.52/23.85 | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 163.52/23.85 | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.85 | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | (440) all_54_15 = e3
% 163.52/23.85 | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | REF_CLOSE: (307), (439), (440) are inconsistent by sub-proof
% 163.52/23.85 | | | | | | | | | | | | | | | | | | #992.
% 163.52/23.85 | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.85 | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | (441) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 163.52/23.85 | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | BETA: splitting (441) gives:
% 163.52/23.85 | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | (442) all_54_15 = e2
% 163.52/23.85 | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (307), (407), (442) are inconsistent by sub-proof
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | #991.
% 163.52/23.85 | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | (443) all_54_15 = e1 | all_54_15 = e0
% 163.52/23.85 | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | BETA: splitting (443) gives:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | (444) all_54_15 = e1
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (307), (398), (444) are inconsistent by sub-proof
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | #990.
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | (445) all_54_15 = e0
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (445) imply:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | (446) all_4_2 = e0
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | SIMP: (446) implies:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | (447) all_4_2 = e0
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (447) imply:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | (448) all_56_15 = e0
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (447) imply:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | (449) ~ (e1 = e0)
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (450) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (162), (166), (421), (433), (434), (435),
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | (450), (function-axioms) are inconsistent by
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | | sub-proof #984.
% 163.52/23.85 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (451) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (451) gives:
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | (452) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (419), (433), (452) are inconsistent by sub-proof
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | | #983.
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.86 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | (453) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (453) gives:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | (454) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (454) implies:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | (455) ~ (all_56_12 = e2)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (455) imply:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | (456) $false
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (456) is inconsistent.
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | (457) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (458) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (458) implies:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (459) all_56_13 = e0
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (460) ~ (all_56_14 = e1)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (460) imply:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (461) ~ (all_6_2 = e1)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (193), (214), (274), (305), (399), (409),
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (459), (461) are inconsistent by sub-proof #976.
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (462) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (463) ~ (all_56_15 = e0)
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (448), (463) imply:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | (464) $false
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (464) is inconsistent.
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.87 | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.87 | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | End of split
% 163.52/23.87 | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.87 | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | (465) all_34_2 = e3
% 163.52/23.87 | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (465) imply:
% 163.52/23.87 | | | | | | | | | | | | | | | | | (466) all_4_2 = e3
% 163.52/23.87 | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | SIMP: (466) implies:
% 163.52/23.87 | | | | | | | | | | | | | | | | | (467) all_4_2 = e3
% 163.52/23.87 | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (467) imply:
% 163.52/23.87 | | | | | | | | | | | | | | | | | (468) all_56_15 = e3
% 163.52/23.87 | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | REDUCE: (376), (467) imply:
% 163.52/23.87 | | | | | | | | | | | | | | | | | (469) ~ (all_52_3 = e3)
% 163.52/23.87 | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | REDUCE: (387), (467) imply:
% 163.52/23.87 | | | | | | | | | | | | | | | | | (470) ~ (all_52_7 = e3)
% 163.52/23.87 | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | REDUCE: (394), (467) imply:
% 163.52/23.87 | | | | | | | | | | | | | | | | | (471) ~ (all_52_11 = e3)
% 163.52/23.87 | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 163.52/23.87 | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.87 | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | (472) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 163.52/23.87 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 163.52/23.87 | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | BETA: splitting (472) gives:
% 163.52/23.87 | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | (473) all_58_4 = e3 & op(e3, e1) = e3
% 163.52/23.87 | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | ALPHA: (473) implies:
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | (474) op(e3, e1) = e3
% 163.52/23.87 | | | | | | | | | | | | | | | | | | |
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (437), (474), (function-axioms) are
% 163.52/23.87 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #975.
% 163.52/23.87 | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | (475) all_58_5 = e3 & op(e2, e1) = e3
% 163.52/23.88 | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | ALPHA: (475) implies:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | (476) op(e2, e1) = e3
% 163.52/23.88 | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | (477) ~ (all_56_15 = e3)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | REDUCE: (468), (477) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | (478) $false
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | CLOSE: (478) is inconsistent.
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | (479) all_56_6 = e0 & op(e0, e3) = e0
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | ALPHA: (479) implies:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | (480) all_56_6 = e0
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | (481) op(e0, e3) = e0
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | (482) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (169), (403), (436), (482),
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | #972.
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | (483) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (483) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (484) all_58_7 = e3 & op(e1, e2) = e3
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (485) op(e1, e2) = e3
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (158), (481) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (486) all_52_3 = e0
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (161), (485) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (487) all_52_6 = e3
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (164), (476) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (488) all_52_9 = e3
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (486) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (489) ~ (all_52_7 = e0)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | SIMP: (489) implies:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (490) ~ (all_52_7 = e0)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (486) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (491) ~ (all_52_11 = e0)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | SIMP: (491) implies:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (492) ~ (all_52_11 = e0)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (469), (486) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (493) ~ (e3 = e0)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (487) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (494) ~ (all_52_7 = e3)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (488) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (495) ~ (all_52_11 = e3)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (389), (488) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | (496) ~ (all_6_2 = e3)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | (497) all_54_13 = e3
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (470), (497) are inconsistent by sub-proof
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | #971.
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | (498) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (498) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | (499) all_54_13 = e2
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (422), (499) are inconsistent by sub-proof
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | #970.
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | (500) all_54_13 = e1 | all_54_13 = e0
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (500) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | (501) all_54_13 = e1
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (501) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_52_7 = e1
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (502) implies:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_52_7 = e1
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (503) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | (504) ~ (all_52_11 = e1)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (504) implies:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | (505) ~ (all_52_11 = e1)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (503) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | (506) op(e0, e2) = e1
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (507) all_54_14 = e3
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (471), (507) are inconsistent by sub-proof
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | #969.
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (508) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_54_14 = e2
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (509) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) all_52_11 = e2
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (510) implies:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) all_52_11 = e2
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (511) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) ~ (all_6_2 = e2)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (511) imply:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) op(e0, e1) = e2
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (162), (166), (421), (433), (434), (435),
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514), (function-axioms) are inconsistent by
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #984.
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (515) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (515) gives:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (516) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (419), (433), (516) are inconsistent by sub-proof
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #983.
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (517) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (517) gives:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (518) implies:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (519) ~ (all_56_12 = e2)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (519) imply:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (520) $false
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (520) is inconsistent.
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (521) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (521) gives:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (522) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (522) implies:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523) all_56_13 = e0
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (524) ~ (all_56_14 = e1)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (524) imply:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (525) ~ (all_6_2 = e1)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (193), (214), (274), (305), (399), (409),
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (523), (525) are inconsistent by sub-proof #976.
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (526) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (526) implies:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (527) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1)
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (480), (506), (513), (527),
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #966.
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | (528) all_54_14 = e1 | all_54_14 = e0
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (492), (505), (528) are inconsistent by
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #964.
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | (529) all_54_13 = e0
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (490), (529) are inconsistent by sub-proof
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | | #963.
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | (530) all_58_13 = e3 & op(e0, e2) = e3
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (470), (530), (function-axioms) are
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #962.
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.89 | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | (531) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 163.52/23.89 | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 163.52/23.89 | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | BETA: splitting (531) gives:
% 163.52/23.89 | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | (532) all_58_8 = e3 & op(e1, e1) = e3
% 163.52/23.89 | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (409), (532), (function-axioms) are
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 163.52/23.89 | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.89 | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | (533) all_58_14 = e3 & op(e0, e1) = e3
% 163.52/23.89 | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (471), (533), (function-axioms) are
% 163.52/23.89 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #960.
% 163.52/23.89 | | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | | End of split
% 163.52/23.89 | | | | | | | | | | | | | | | |
% 163.52/23.89 | | | | | | | | | | | | | | | Case 2:
% 163.52/23.89 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | (534) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | REF_CLOSE: (300), (401), (405), (430), (534) are inconsistent
% 163.52/23.90 | | | | | | | | | | | | | | | | by sub-proof #958.
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | End of split
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | (535) all_32_2 = e1
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | COMBINE_EQS: (356), (535) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | (536) all_10_2 = e1
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | SIMP: (536) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | (537) all_10_2 = e1
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | COMBINE_EQS: (298), (537) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | (538) all_56_10 = e1
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | REDUCE: (369), (537) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | (539) ~ (all_52_4 = e1)
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | REDUCE: (371), (537) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | (540) ~ (all_52_8 = e1)
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | REDUCE: (405), (537) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | (541) ~ (e2 = e1)
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | REDUCE: (45), (537) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | (542) op(e3, e3) = e1
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 163.52/23.90 | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | (543) ~ (all_56_10 = e1)
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | REDUCE: (538), (543) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | (544) $false
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | CLOSE: (544) is inconsistent.
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | (545) all_56_4 = e3 & op(e3, e1) = e3
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | ALPHA: (545) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | (546) all_56_4 = e3
% 163.52/23.90 | | | | | | | | | | | | | | | | (547) op(e3, e1) = e3
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 163.52/23.90 | | | | | | | | | | | | | | | | e1, e3, simplifying with (168), (547) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | (548) all_52_8 = e3
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | REDUCE: (133), (548) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | (549) ~ (all_52_4 = e3)
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | REDUCE: (122), (548) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | (550) ~ (all_52_9 = e3)
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | SIMP: (550) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | (551) ~ (all_52_9 = e3)
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | REDUCE: (120), (548) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | (552) ~ (all_52_11 = e3)
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | SIMP: (552) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | (553) ~ (all_52_11 = e3)
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | REDUCE: (388), (548) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | (554) ~ (all_6_2 = e3)
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | (555) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 163.52/23.90 | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | BETA: splitting (555) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | (556) all_58_0 = e2 & op(e3, e3) = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | ALPHA: (556) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | (557) op(e3, e3) = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (542), (557), (function-axioms) are
% 163.52/23.90 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #957.
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | (558) all_58_1 = e2 & op(e3, e2) = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | ALPHA: (558) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | (559) op(e3, e2) = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | (560) all_54_1 = e3
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (290), (549), (560) are inconsistent by sub-proof
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | #956.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | (561) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (561) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (562) all_54_1 = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (290), (420), (562) are inconsistent by sub-proof
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | #955.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (563) ~ (all_54_1 = e2)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (564) all_54_1 = e1 | all_54_1 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (564) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (565) all_54_1 = e1
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (290), (539), (565) are inconsistent by sub-proof
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | #954.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (566) all_54_1 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (566) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (567) all_52_4 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | SIMP: (567) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (568) all_52_4 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (420), (568) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (569) ~ (e2 = e0)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (568) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (570) op(e3, e2) = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (559), (570), (function-axioms) are
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #953.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | End of split
% 163.52/23.90 | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | (571) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 163.52/23.90 | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | BETA: splitting (571) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | (572) all_58_4 = e2 & op(e3, e1) = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | ALPHA: (572) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | (573) all_58_4 = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | (574) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (574) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (575) all_58_4 = e3 & op(e3, e1) = e3
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (573), (575) are inconsistent by sub-proof
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | #952.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (576) all_58_5 = e3 & op(e2, e1) = e3
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (576) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (577) op(e2, e1) = e3
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (551), (577), (function-axioms) are
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #951.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | (578) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (578) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (579) all_58_8 = e3 & op(e1, e1) = e3
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (409), (579), (function-axioms) are
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (580) all_58_14 = e3 & op(e0, e1) = e3
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (553), (580), (function-axioms) are
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #960.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | (581) all_58_9 = e2 & op(e3, e0) = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | ALPHA: (581) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | (582) all_58_9 = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | | (583) op(e3, e0) = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | (584) all_54_1 = e3
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (290), (549), (584) are inconsistent by sub-proof
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | #956.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | (585) ~ (all_54_1 = e3)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | (586) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (587) all_54_1 = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (290), (420), (587) are inconsistent by sub-proof
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | #955.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (588) ~ (all_54_1 = e2)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | (589) all_54_1 = e1 | all_54_1 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (589) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (590) all_54_1 = e1
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (290), (539), (590) are inconsistent by sub-proof
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | #954.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (591) all_54_1 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (591) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (592) all_52_4 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | SIMP: (592) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (593) all_52_4 = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (593) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (594) ~ (all_52_7 = e0)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | SIMP: (594) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (595) ~ (all_52_7 = e0)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (549), (593) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (596) ~ (e3 = e0)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (420), (593) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (597) ~ (e2 = e0)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (539), (593) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (598) ~ (e1 = e0)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (593) imply:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | (599) op(e3, e2) = e0
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | (600) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (600) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | (601) all_58_4 = e2 & op(e3, e1) = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (601) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | (602) all_58_4 = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (248), (250),
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | (254), (549), (582), (602), (function-axioms) are
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #939.
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | (603) all_58_5 = e2 & op(e2, e1) = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (603) implies:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | (604) all_58_5 = e2
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | (605) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (605) gives:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | (606) all_58_2 = e3 & op(e2, e3) = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (606) implies:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | (607) all_58_2 = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (608) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (608) gives:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (609) all_58_2 = e1 & op(e2, e3) = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (609) implies:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (610) all_58_2 = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (42), (239), (242),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (428), (604), (610), (function-axioms) are
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #930.
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (611) all_58_3 = e1 & op(e2, e2) = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (611) implies:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_58_3 = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (428), (612) imply:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (613) e2 = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (582), (613) imply:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (614) all_58_9 = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (168), (169), (221), (224), (225), (226),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (239), (240), (241), (242), (243),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (246), (248), (250), (251), (252), (254),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (399), (403), (407), (409), (428), (538), (539),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (614), (function-axioms) are inconsistent
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #799.
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (615) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (615) gives:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) all_58_5 = e1 & op(e2, e1) = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (616) implies:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_58_5 = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (604), (617) imply:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) e2 = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (618) implies:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) e2 = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (582), (619) imply:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) all_58_9 = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (168), (169), (221), (224), (225), (226),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (239), (240), (241), (242), (243),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (246), (248), (250), (251), (252), (254),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (399), (403), (407), (409), (428), (538), (539),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (620), (function-axioms) are inconsistent
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #799.
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) all_58_10 = e1 & op(e2, e0) = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (621) implies:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) op(e2, e0) = e1
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (239), (428), (604), (607), (622),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | #797.
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | (623) all_58_3 = e3 & op(e2, e2) = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (403), (623), (function-axioms) are
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | (624) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (624) gives:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | (625) all_58_5 = e3 & op(e2, e1) = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (625) implies:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | (626) op(e2, e1) = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (551), (626), (function-axioms) are
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #951.
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | (627) all_58_10 = e3 & op(e2, e0) = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (627) implies:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | (628) all_58_10 = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (239), (240), (428),
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | (604), (628) are inconsistent by sub-proof #850.
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | (629) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (629) gives:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | (630) all_58_8 = e2 & op(e1, e1) = e2
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (630), (function-axioms) are
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | (631) all_58_14 = e2 & op(e0, e1) = e2
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | (632) op(e0, e1) = e2
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | (633) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (633) gives:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | (634) all_58_4 = e3 & op(e3, e1) = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (634) implies:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_58_4 = e3
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (636) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (636) gives:
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (419), (599), (637), (function-axioms) are
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #796.
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (638) gives:
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (639) implies:
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (546), (640) are inconsistent by sub-proof
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #795.
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (641) gives:
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (642) implies:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (546), (643) are inconsistent by sub-proof
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #795.
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (644) implies:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) all_56_4 = e1
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) op(e3, e1) = e1
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (546), (645) imply:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) e3 = e1
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (635), (647) imply:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) all_58_4 = e1
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (649) gives:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_58_0 = e1 & op(e3, e3) = e1
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (650) implies:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) all_58_0 = e1
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (248), (254), (542),
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582), (648), (651), (function-axioms) are
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #788.
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) all_58_2 = e1 & op(e2, e3) = e1
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (652) implies:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) all_58_2 = e1
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.52/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (654) gives:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) all_58_4 = e2 & op(e3, e1) = e2
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (221), (248),
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (538), (542), (582), (648), (655),
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #787.
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) all_58_5 = e2 & op(e2, e1) = e2
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (656) implies:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) all_58_5 = e2
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (42), (239), (242),
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (428), (653), (657), (function-axioms) are
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #930.
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (629) gives:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) all_58_8 = e2 & op(e1, e1) = e2
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (658), (function-axioms) are
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_58_14 = e2
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (660) gives:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) all_58_12 = e1 & op(e0, e3) = e1
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (661) implies:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) all_58_12 = e1
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (166), (168), (169), (221), (224), (225),
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (228), (229), (230), (231), (232), (233),
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (235), (237), (238), (239), (240), (241),
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (243), (244), (246), (247), (248), (249),
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (251), (252), (254), (399), (403), (407),
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409), (428), (538), (539), (542), (582), (646),
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648), (659), (662), (function-axioms) are
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #765.
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) all_58_13 = e1 & op(e0, e2) = e1
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (663) implies:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_58_13 = e1
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (665) gives:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_58_0 = e3 & op(e3, e3) = e3
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (666) implies:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) all_58_0 = e3
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) ~ (all_56_10 = e1)
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (538), (668) imply:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) $false
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (669) is inconsistent.
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (670) gives:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) all_58_0 = e0 & op(e3, e3) = e0
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (671) implies:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) op(e3, e3) = e0
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (542), (672), (function-axioms) are
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #907.
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) all_58_1 = e0 & op(e3, e2) = e0
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (673) implies:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) all_58_1 = e0
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (633) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (248), (254), (542),
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582), (634), (648), (667), (function-axioms) are
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #764.
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) all_58_5 = e3 & op(e2, e1) = e3
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (675) implies:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) all_58_5 = e3
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (428), (653), (677) are inconsistent by
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #763.
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (678) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) all_58_5 = e0 & op(e2, e1) = e0
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (679) implies:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) all_58_5 = e0
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (676), (680) imply:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) e3 = e0
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (254), (582), (648), (667), (674),
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) are inconsistent by sub-proof #761.
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) all_58_10 = e0 & op(e2, e0) = e0
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (682) implies:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) all_58_10 = e0
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) op(e2, e0) = e0
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (685) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) all_58_1 = e3 & op(e3, e2) = e3
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (248), (542), (582), (648), (686),
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #791.
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) all_58_3 = e3 & op(e2, e2) = e3
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (403), (687), (function-axioms) are
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (688) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) all_58_7 = e3 & op(e1, e2) = e3
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (689) implies:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) all_58_7 = e3
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (691) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) all_58_9 = e1 & op(e3, e0) = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (692) implies:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_58_9 = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (168), (169), (221), (224), (225), (226),
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (239), (240), (241), (242), (243),
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (246), (248), (250), (251), (252), (254),
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399), (403), (407), (409), (428), (538), (539),
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (693), (function-axioms) are inconsistent
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #799.
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) all_58_10 = e1 & op(e2, e0) = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (694) implies:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) op(e2, e0) = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (684), (695), (function-axioms) are
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #849.
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (696) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) all_58_11 = e1 & op(e1, e0) = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (697) implies:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) all_58_11 = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (699) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) all_58_6 = e2 & op(e1, e3) = e2
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (700) implies:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) all_58_6 = e2
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (702) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_58_1 = e1 & op(e3, e2) = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (539), (703), (function-axioms) are
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #863.
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) all_58_3 = e1 & op(e2, e2) = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (704) implies:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) all_58_3 = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (428), (705) imply:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) e2 = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (582), (706) imply:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) all_58_9 = e1
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (708) gives:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (582), (707) are inconsistent by sub-proof
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #942.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) all_58_10 = e2 & op(e2, e0) = e2
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (683), (709) are inconsistent by sub-proof
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #760.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (710) gives:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) all_58_11 = e2 & op(e1, e0) = e2
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (711) implies:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) all_58_11 = e2
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (231), (232),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (234), (399), (690), (701), (712),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #816.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) all_58_15 = e2 & op(e0, e0) = e2
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (407), (713), (function-axioms) are
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (714) gives:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) all_58_7 = e1 & op(e1, e2) = e1
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (715) implies:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) all_58_7 = e1
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (647), (667) imply:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_58_0 = e1
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (248), (254), (542),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582), (648), (717), (function-axioms) are
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #788.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (168), (646) gives:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) all_52_8 = e1
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (168), (248), (254),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (547), (582), (648), (667), (718),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #759.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) all_58_7 = e2 & op(e1, e2) = e2
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (719) implies:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) op(e1, e2) = e2
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (421), (720), (function-axioms) are
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (721) gives:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) all_58_8 = e2 & op(e1, e1) = e2
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (722), (function-axioms) are
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) all_58_11 = e2 & op(e1, e0) = e2
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (723) implies:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_58_11 = e2
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (698), (724) imply:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) e2 = e1
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (725) implies:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) e2 = e1
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (582), (726) imply:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) all_58_9 = e1
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (168), (169), (221), (224), (225), (226),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (239), (240), (241), (242), (243),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (246), (248), (250), (251), (252), (254),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399), (403), (407), (409), (428), (538), (539),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (727), (function-axioms) are inconsistent
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #799.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) all_58_15 = e1 & op(e0, e0) = e1
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (728) implies:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) all_58_15 = e1
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (730) gives:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) all_58_4 = e0 & op(e3, e1) = e0
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (648), (731) are inconsistent by sub-proof
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #793.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) all_58_5 = e0 & op(e2, e1) = e0
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (732) implies:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_58_5 = e0
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (676), (733) imply:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) e3 = e0
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (254), (582), (648), (667), (674),
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) are inconsistent by sub-proof #761.
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (735) gives:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) all_58_8 = e0 & op(e1, e1) = e0
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (736) implies:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) all_58_8 = e0
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (42), (239), (242),
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (403), (428), (582), (648), (653), (667),
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674), (676), (683), (738), (function-axioms) are
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #758.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (232), (233),
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (254), (399), (542), (582), (648), (667),
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690), (729), (737), (739), (function-axioms) are
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #751.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) all_58_14 = e0 & op(e0, e1) = e0
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (740) implies:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) all_58_14 = e0
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (659), (741) are inconsistent by sub-proof
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #806.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) all_58_13 = e3 & op(e0, e2) = e3
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (742) implies:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) all_58_13 = e3
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (664), (743) imply:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) e3 = e1
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (647), (667) imply:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) all_58_0 = e1
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (248), (254), (542),
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582), (648), (745), (function-axioms) are
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #788.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (409), (659), (746), (function-axioms)
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #805.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (582), (648), (747) are inconsistent by
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #792.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) all_58_1 = e3 & op(e3, e2) = e3
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (248), (542), (582), (648), (748),
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #791.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (582), (648), (749) are inconsistent by
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #789.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (750) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (750) gives:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (751) all_58_14 = e1 & op(e0, e1) = e1
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (751) implies:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (752) op(e0, e1) = e1
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (632), (752), (function-axioms) are
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #967.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (753) all_58_15 = e1 & op(e0, e0) = e1
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (753) implies:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (754) all_58_15 = e1
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (755) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (755) gives:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (756) all_58_0 = e3 & op(e3, e3) = e3
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (756) implies:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (757) all_58_0 = e3
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (758) ~ (all_56_10 = e1)
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (538), (758) imply:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (759) $false
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (759) is inconsistent.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (760) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (760) gives:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (761) all_58_0 = e0 & op(e3, e3) = e0
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (761) implies:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (762) op(e3, e3) = e0
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (542), (762), (function-axioms) are
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #907.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (763) all_58_1 = e0 & op(e3, e2) = e0
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (763) implies:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764) all_58_1 = e0
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (633) gives:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (248), (254), (542),
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582), (634), (648), (757), (function-axioms) are
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #764.
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (765) all_58_5 = e3 & op(e2, e1) = e3
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (765) implies:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766) all_58_5 = e3
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (767) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (428), (653), (767) are inconsistent by
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #763.
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (768) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (768) gives:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (769) all_58_5 = e0 & op(e2, e1) = e0
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (769) implies:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (770) all_58_5 = e0
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (766), (770) imply:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) e3 = e0
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (254), (582), (648), (757), (764),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (771) are inconsistent by sub-proof #761.
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (772) all_58_10 = e0 & op(e2, e0) = e0
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (772) implies:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (773) all_58_10 = e0
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (774) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (42), (239), (242),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (403), (428), (582), (648), (653), (757),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (764), (766), (773), (774), (function-axioms) are
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #758.
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (775) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (775) gives:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (776) all_58_11 = e3 & op(e1, e0) = e3
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (776) implies:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777) all_58_11 = e3
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (778) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (778) gives:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (779) all_58_6 = e2 & op(e1, e3) = e2
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (779) implies:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (780) all_58_6 = e2
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (781) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (781) gives:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (782) all_58_6 = e1 & op(e1, e3) = e1
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (782) implies:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (783) all_58_6 = e1
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (784) op(e1, e3) = e1
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (116), (117), (124), (125), (127), (138),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (140), (142), (143), (144), (145), (148),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (161), (162), (163), (166), (168), (169),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188), (189), (191), (192), (194), (197), (198),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199), (221), (224), (225), (226), (227), (228),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (232), (233), (234), (237),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (239), (240), (241), (242), (243), (244),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (247), (248), (250), (251), (252), (254),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263), (265), (266), (275), (278), (283), (287),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307), (374), (376), (379), (383), (385), (394),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396), (397), (398), (399), (400), (403), (407),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409), (421), (428), (538), (539), (542), (582),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648), (659), (783), (784), (function-axioms) are
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (785) all_58_7 = e1 & op(e1, e2) = e1
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (785) implies:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786) all_58_7 = e1
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (787) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (787) gives:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (168), (646) gives:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (788) all_52_8 = e1
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (168), (248), (254),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (547), (582), (648), (757), (788),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #759.
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (789) all_58_10 = e2 & op(e2, e0) = e2
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (789) implies:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (790) all_58_10 = e2
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (239), (240),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (403), (428), (653), (790),
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #915.
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (791) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (791) gives:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (792) all_58_11 = e2 & op(e1, e0) = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (792) implies:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (793) all_58_11 = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (231), (234), (780),
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (786), (793) are inconsistent by sub-proof #726.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (794) all_58_15 = e2 & op(e0, e0) = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (794) implies:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (795) all_58_15 = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (224), (228), (582),
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (777), (795), (function-axioms) are inconsistent
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #719.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (796) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (796) gives:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (797) all_58_8 = e1 & op(e1, e1) = e1
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (797) implies:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (798) all_58_8 = e1
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (235), (648), (659), (766), (798)
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #717.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (799) all_58_11 = e1 & op(e1, e0) = e1
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (799) implies:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (800) all_58_11 = e1
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (777), (800) imply:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (801) e3 = e1
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (647), (757) imply:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (802) all_58_0 = e1
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (248), (254), (542),
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582), (648), (802), (function-axioms) are
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #788.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (803) all_58_7 = e2 & op(e1, e2) = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (803) implies:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (804) op(e1, e2) = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (421), (804), (function-axioms) are
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (805) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (805) gives:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (806) all_58_8 = e2 & op(e1, e1) = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (806), (function-axioms) are
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (807) all_58_11 = e2 & op(e1, e0) = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (807) implies:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (808) all_58_11 = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (777), (808) imply:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (809) e3 = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (766), (809) imply:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (810) all_58_5 = e2
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (42), (239), (242),
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (428), (653), (810), (function-axioms) are
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #930.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_58_15 = e3 & op(e0, e0) = e3
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (248), (254), (542),
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582), (648), (754), (757), (811),
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #752.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (812) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (812) gives:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (813) all_58_8 = e3 & op(e1, e1) = e3
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (409), (813), (function-axioms) are
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (814) all_58_14 = e3 & op(e0, e1) = e3
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (659), (814) are inconsistent by sub-proof
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #809.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (815) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (582), (648), (815) are inconsistent by
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #792.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (816) all_58_1 = e3 & op(e3, e2) = e3
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (248), (542), (582), (648), (816),
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #791.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (582), (648), (817) are inconsistent by
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #789.
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (818) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (818) gives:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (819) all_58_6 = e1 & op(e1, e3) = e1
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (819) implies:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (820) all_58_6 = e1
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (821) op(e1, e3) = e1
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (822) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (822) gives:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (823) all_58_4 = e2 & op(e3, e1) = e2
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (221), (248),
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (538), (542), (582), (648), (823),
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #787.
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (824) all_58_5 = e2 & op(e2, e1) = e2
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (824) implies:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) all_58_5 = e2
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (826) gives:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) all_58_0 = e3 & op(e3, e3) = e3
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (827) implies:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) op(e3, e3) = e3
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 163.91/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (166), (239), (240), (428),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (825), (828), (829), (function-axioms) are
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #716.
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (830) gives:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) all_58_6 = e2 & op(e1, e3) = e2
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (820), (831) are inconsistent by sub-proof
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #715.
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) all_58_12 = e2 & op(e0, e3) = e2
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (832) implies:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) all_58_12 = e2
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (239), (240),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (403), (428), (542), (825), (834),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #714.
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (162), (821), (833), (835),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #713.
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) all_58_1 = e3 & op(e3, e2) = e3
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (248), (542), (582), (648), (836),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #791.
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (582), (648), (837) are inconsistent by
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #766.
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (629) gives:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) all_58_8 = e2 & op(e1, e1) = e2
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (838), (function-axioms) are
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) all_58_14 = e2
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (116), (117), (124), (125), (127), (138),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (140), (142), (143), (144), (145), (148),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (161), (162), (163), (166), (168), (169),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (188), (189), (191), (192), (194), (197), (198),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199), (221), (224), (225), (226), (227), (228),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (232), (233), (234), (237),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (239), (240), (241), (242), (243), (244),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (247), (248), (250), (251), (252), (254),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263), (265), (266), (275), (278), (283), (287),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307), (374), (376), (379), (383), (385), (394),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (396), (397), (398), (399), (400), (403), (407),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409), (421), (428), (538), (539), (542), (582),
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648), (820), (821), (839), (function-axioms) are
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) all_58_12 = e1 & op(e0, e3) = e1
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (840) implies:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) all_58_12 = e1
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/23.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (842) gives:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) all_58_12 = e2 & op(e0, e3) = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (843) implies:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) all_58_12 = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (841), (844) imply:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) e2 = e1
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (845) implies:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) e2 = e1
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (582), (846) imply:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) all_58_9 = e1
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (168), (169), (221), (224), (225), (226),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (239), (240), (241), (242), (243),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (246), (248), (250), (251), (252), (254),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399), (403), (407), (409), (428), (538), (539),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (847), (function-axioms) are inconsistent
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #799.
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) all_58_13 = e2 & op(e0, e2) = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (848) implies:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) all_58_13 = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (850) gives:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) all_58_0 = e3 & op(e3, e3) = e3
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (851) implies:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) all_58_0 = e3
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) op(e3, e3) = e3
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (854) gives:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) all_58_4 = e2 & op(e3, e1) = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (855) implies:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) all_58_4 = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (248), (250), (582),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852), (853), (856), (function-axioms) are
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #941.
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) all_58_5 = e2 & op(e2, e1) = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (857) implies:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) all_58_5 = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (166), (239), (240), (428),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853), (858), (859), (function-axioms) are
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #716.
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (860) gives:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) all_58_6 = e2 & op(e1, e3) = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (861) implies:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) all_58_6 = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (239), (240),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (403), (428), (542), (858), (863),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #714.
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (864) gives:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_58_6 = e0 & op(e1, e3) = e0
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (862), (865) are inconsistent by sub-proof
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #712.
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) all_58_12 = e0 & op(e0, e3) = e0
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (866) implies:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) all_58_12 = e0
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (841), (867) are inconsistent by sub-proof
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #873.
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) all_58_12 = e2 & op(e0, e3) = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (168), (169), (221), (224), (225), (226),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (239), (240), (241), (242), (243),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (246), (248), (250), (251), (252), (254),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399), (403), (407), (409), (428), (538), (539),
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542), (582), (841), (868), (function-axioms) are
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #768.
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (629) gives:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) all_58_8 = e2 & op(e1, e1) = e2
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (869), (function-axioms) are
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) all_58_14 = e2
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (871) gives:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) all_58_12 = e3 & op(e0, e3) = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (872) implies:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) all_58_12 = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (647), (852) imply:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) all_58_0 = e1
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (248), (254), (542),
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582), (648), (874), (function-axioms) are
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #788.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_58_13 = e3 & op(e0, e2) = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (875) implies:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) all_58_13 = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (849), (876) imply:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) e3 = e2
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (852), (877) imply:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) all_58_0 = e2
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (850) gives:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (852), (878) imply:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) e3 = e2
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (877) imply:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) $false
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (880) is inconsistent.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) all_58_1 = e3 & op(e3, e2) = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (881) implies:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) all_58_1 = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (243), (244), (428),
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876), (882) are inconsistent by sub-proof #707.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (883) gives:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (248), (250), (582),
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635), (878) are inconsistent by sub-proof #700.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_58_9 = e3 & op(e3, e0) = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (884) implies:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) all_58_9 = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (582), (885) are inconsistent by sub-proof
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #790.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (886) gives:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) all_58_14 = e3 & op(e0, e1) = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (887) implies:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) all_58_14 = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (870), (888) are inconsistent by sub-proof
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #855.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) all_58_15 = e3 & op(e0, e0) = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (889) implies:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) all_58_15 = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) all_58_15 = e0 & op(e0, e0) = e0
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (890), (891) are inconsistent by sub-proof
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #887.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (892) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (892) implies:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (893) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (893) gives:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (894) all_58_12 = e0 & op(e0, e3) = e0
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (894) implies:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (895) all_58_12 = e0
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (841), (895) are inconsistent by sub-proof
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #873.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (896) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (896) gives:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (897) all_58_13 = e0 & op(e0, e2) = e0
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (849), (897) are inconsistent by sub-proof
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #872.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (898) all_58_14 = e0 & op(e0, e1) = e0
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (870), (898) are inconsistent by sub-proof
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #858.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (899) all_58_1 = e3 & op(e3, e2) = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (248), (542), (582), (648), (899),
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #791.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (900) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (582), (648), (900) are inconsistent by
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #766.
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (901) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (901) gives:
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (631) implies:
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (902) all_58_14 = e2
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (166), (168), (169), (221), (224), (225),
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (228), (229), (230), (231), (232), (233),
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (235), (237), (238), (239), (240), (241),
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (243), (244), (246), (247), (248), (249),
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (251), (252), (254), (399), (403), (407),
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (409), (428), (538), (539), (542), (582), (646),
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648), (841), (902), (function-axioms) are
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #765.
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (903) all_58_15 = e2 & op(e0, e0) = e2
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (407), (903), (function-axioms) are
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (904) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (904) gives:
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (905) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (905) gives:
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (906) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (906) implies:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (907) ~ (all_56_12 = e2)
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (907) imply:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (908) $false
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (908) is inconsistent.
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (909) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (909) implies:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (910) op(e3, e0) = e0
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (583), (910), (function-axioms) are
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #699.
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (911) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (911) gives:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (912) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (912) implies:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (913) ~ (all_56_12 = e2)
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (419), (913) imply:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (914) $false
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (914) is inconsistent.
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (915) gives:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (916) implies:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (538), (546), (917) are inconsistent by sub-proof
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #795.
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (188), (190), (213), (262), (264), (307),
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387), (398), (407), (422), (595), (632), (918),
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #696.
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | (919) all_58_5 = e3 & op(e2, e1) = e3
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (919) implies:
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | (920) op(e2, e1) = e3
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (551), (920), (function-axioms) are
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #951.
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | (921) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (921) gives:
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | (922) all_58_8 = e3 & op(e1, e1) = e3
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (409), (922), (function-axioms) are
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | (923) all_58_14 = e3 & op(e0, e1) = e3
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (553), (923), (function-axioms) are
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #960.
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | Case 2:
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | (924) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 164.15/24.04 | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | REF_CLOSE: (157), (161), (421), (422), (924),
% 164.15/24.04 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.15/24.04 | | | | | | | | | | | | | #694.
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | Case 2:
% 164.15/24.04 | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | (925) all_54_5 = e1 | all_54_5 = e0
% 164.15/24.04 | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | REF_CLOSE: (283), (400), (411), (925) are inconsistent by
% 164.15/24.04 | | | | | | | | | | | | sub-proof #735.
% 164.15/24.04 | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | End of split
% 164.15/24.04 | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | Case 2:
% 164.15/24.04 | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | (926) all_30_2 = e0
% 164.15/24.04 | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | COMBINE_EQS: (355), (926) imply:
% 164.15/24.04 | | | | | | | | | | (927) all_8_2 = e0
% 164.15/24.04 | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | SIMP: (927) implies:
% 164.15/24.04 | | | | | | | | | | (928) all_8_2 = e0
% 164.15/24.04 | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | COMBINE_EQS: (361), (928) imply:
% 164.15/24.04 | | | | | | | | | | (929) all_56_12 = e0
% 164.15/24.04 | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | REDUCE: (374), (928) imply:
% 164.15/24.04 | | | | | | | | | | (930) ~ (all_52_1 = e0)
% 164.15/24.04 | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | REDUCE: (383), (928) imply:
% 164.15/24.04 | | | | | | | | | | (931) ~ (all_52_9 = e0)
% 164.15/24.04 | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | REDUCE: (385), (928) imply:
% 164.15/24.04 | | | | | | | | | | (932) ~ (all_52_13 = e0)
% 164.15/24.04 | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | BETA: splitting (217) gives:
% 164.15/24.04 | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | Case 1:
% 164.15/24.04 | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | (933) ~ (all_56_12 = e0)
% 164.15/24.04 | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | REDUCE: (929), (933) imply:
% 164.15/24.04 | | | | | | | | | | | (934) $false
% 164.15/24.04 | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | CLOSE: (934) is inconsistent.
% 164.15/24.04 | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | Case 2:
% 164.15/24.04 | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | (935) all_56_11 = e2 & op(e2, e0) = e2
% 164.15/24.04 | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | ALPHA: (935) implies:
% 164.15/24.04 | | | | | | | | | | | (936) all_56_11 = e2
% 164.15/24.04 | | | | | | | | | | | (937) op(e2, e0) = e2
% 164.15/24.04 | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | BETA: splitting (239) gives:
% 164.15/24.04 | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | Case 1:
% 164.15/24.04 | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | (938) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 164.15/24.04 | | | | | | | | | | | | & op(e2, e2) = e0)
% 164.15/24.04 | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | BETA: splitting (938) gives:
% 164.15/24.04 | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | Case 1:
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | (939) all_58_2 = e0 & op(e2, e3) = e0
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | REF_CLOSE: (166), (930), (939), (function-axioms) are
% 164.15/24.04 | | | | | | | | | | | | | inconsistent by sub-proof #693.
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | Case 2:
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 164.15/24.04 | | | | | | | | | | | | | e2, e0, e2, simplifying with (163), (937) gives:
% 164.15/24.04 | | | | | | | | | | | | | (940) all_52_13 = e2
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | REDUCE: (144), (940) imply:
% 164.15/24.04 | | | | | | | | | | | | | (941) ~ (all_52_1 = e2)
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | REDUCE: (116), (940) imply:
% 164.15/24.04 | | | | | | | | | | | | | (942) ~ (all_52_9 = e2)
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | BETA: splitting (79) gives:
% 164.15/24.04 | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | Case 1:
% 164.15/24.04 | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | (943) ~ (all_32_2 = e1)
% 164.15/24.04 | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | REDUCE: (356), (943) imply:
% 164.15/24.04 | | | | | | | | | | | | | | (944) ~ (all_10_2 = e1)
% 164.15/24.04 | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 164.15/24.04 | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | Case 1:
% 164.15/24.04 | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | (945) all_54_0 = e3
% 164.15/24.04 | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | COMBINE_EQS: (300), (945) imply:
% 164.15/24.04 | | | | | | | | | | | | | | | (946) all_10_2 = e3
% 164.15/24.04 | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | COMBINE_EQS: (298), (946) imply:
% 164.15/24.04 | | | | | | | | | | | | | | | (947) all_56_10 = e3
% 164.15/24.04 | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | REDUCE: (363), (946) imply:
% 164.15/24.04 | | | | | | | | | | | | | | | (948) ~ (all_52_1 = e3)
% 164.15/24.04 | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | REDUCE: (365), (946) imply:
% 164.15/24.04 | | | | | | | | | | | | | | | (949) ~ (all_52_2 = e3)
% 164.15/24.04 | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 164.15/24.04 | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | Case 1:
% 164.15/24.04 | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | (950) all_54_4 = e3
% 164.15/24.04 | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (950) imply:
% 164.15/24.04 | | | | | | | | | | | | | | | | (951) all_52_1 = e3
% 164.15/24.04 | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | REDUCE: (948), (951) imply:
% 164.15/24.04 | | | | | | | | | | | | | | | | (952) $false
% 164.15/24.04 | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | | CLOSE: (952) is inconsistent.
% 164.15/24.04 | | | | | | | | | | | | | | | |
% 164.15/24.04 | | | | | | | | | | | | | | | Case 2:
% 164.15/24.04 | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | (953) ~ (all_54_4 = e3)
% 164.15/24.05 | | | | | | | | | | | | | | | | (954) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 164.15/24.05 | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 164.15/24.05 | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.05 | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | (955) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 164.15/24.05 | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 164.15/24.05 | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (166), (403), (948), (955),
% 164.15/24.05 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.15/24.05 | | | | | | | | | | | | | | | | | #692.
% 164.15/24.05 | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.05 | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | (956) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 164.15/24.05 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 164.15/24.05 | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | BETA: splitting (956) gives:
% 164.15/24.05 | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.05 | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | (957) all_58_5 = e3 & op(e2, e1) = e3
% 164.15/24.05 | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | ALPHA: (957) implies:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | (958) op(e2, e1) = e3
% 164.15/24.05 | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | BETA: splitting (954) gives:
% 164.15/24.05 | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | (959) all_54_4 = e2
% 164.15/24.05 | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (287), (941), (959) are inconsistent by sub-proof
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | #691.
% 164.15/24.05 | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | (960) all_54_4 = e1 | all_54_4 = e0
% 164.15/24.05 | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | BETA: splitting (960) gives:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | (961) all_54_4 = e1
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (961) imply:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | (962) all_52_1 = e1
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | SIMP: (962) implies:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | (963) all_52_1 = e1
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (963) imply:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | (964) ~ (all_52_2 = e1)
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | SIMP: (964) implies:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | (965) ~ (all_52_2 = e1)
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | REDUCE: (948), (963) imply:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | (966) ~ (e3 = e1)
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (967) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (967) gives:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | (968) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (947), (948), (968), (function-axioms) are
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #988.
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | |
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.15/24.05 | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | (969) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (969) gives:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (970) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (970) implies:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (971) op(e1, e3) = e3
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (949), (971), (function-axioms) are
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #987.
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (972) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (972) gives:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (973) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (973) implies:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (974) ~ (all_56_14 = e1)
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (975) op(e1, e2) = e2
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (974) imply:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (976) ~ (all_6_2 = e1)
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | (977) ~ (all_56_14 = e0)
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (977) imply:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | (978) ~ (all_6_2 = e0)
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (305), (399), (409), (976), (978) are
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #978.
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | (979) all_56_14 = e0
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (979) imply:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | (980) all_6_2 = e0
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (980) implies:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | (981) all_6_2 = e0
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (981) imply:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | (982) ~ (all_52_2 = e0)
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (983) all_54_8 = e3
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (949), (983) are inconsistent by sub-proof
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | | #690.
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (984) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (161), (276), (965), (975), (982), (984),
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | | #687.
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (985) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (985) implies:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (986) ~ (all_56_10 = e3)
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (947), (986) imply:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | (987) $false
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (987) is inconsistent.
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | |
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.44/24.06 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (988) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (988) gives:
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (989) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (947), (958), (989), (function-axioms) are
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #685.
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (990) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (990) gives:
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | (991) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (991) implies:
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | (992) op(e2, e0) = e0
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (937), (992), (function-axioms) are
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #684.
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.07 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | (993) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (993) gives:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (994) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (994) implies:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (995) all_56_13 = e0
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (996) ~ (all_56_14 = e1)
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (996) imply:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (997) ~ (all_6_2 = e1)
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (193), (214), (274), (305), (399), (409),
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (995), (997) are inconsistent by sub-proof #976.
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (998) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (929), (936), (998) are inconsistent by sub-proof
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | | #683.
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | (999) all_54_4 = e0
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (999) imply:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | (1000) all_52_1 = e0
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | SIMP: (1000) implies:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | (1001) all_52_1 = e0
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | REDUCE: (930), (1001) imply:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | (1002) $false
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | | CLOSE: (1002) is inconsistent.
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.08 | | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | (1003) all_58_10 = e3 & op(e2, e0) = e3
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | ALPHA: (1003) implies:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | (1004) op(e2, e0) = e3
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (937), (1004), (function-axioms) are
% 164.47/24.08 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #682.
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | End of split
% 164.47/24.08 | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | End of split
% 164.47/24.08 | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | End of split
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | Case 2:
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | (1005) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | REF_CLOSE: (300), (401), (405), (944), (1005) are
% 164.47/24.08 | | | | | | | | | | | | | | | inconsistent by sub-proof #958.
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | End of split
% 164.47/24.08 | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | Case 2:
% 164.47/24.08 | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | (1006) all_32_2 = e1
% 164.47/24.08 | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | COMBINE_EQS: (356), (1006) imply:
% 164.47/24.08 | | | | | | | | | | | | | | (1007) all_10_2 = e1
% 164.47/24.08 | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | SIMP: (1007) implies:
% 164.47/24.08 | | | | | | | | | | | | | | (1008) all_10_2 = e1
% 164.47/24.08 | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | COMBINE_EQS: (298), (1008) imply:
% 164.47/24.08 | | | | | | | | | | | | | | (1009) all_56_10 = e1
% 164.47/24.08 | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | REDUCE: (363), (1008) imply:
% 164.47/24.08 | | | | | | | | | | | | | | (1010) ~ (all_52_1 = e1)
% 164.47/24.08 | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | REDUCE: (365), (1008) imply:
% 164.47/24.08 | | | | | | | | | | | | | | (1011) ~ (all_52_2 = e1)
% 164.47/24.08 | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | REDUCE: (367), (1008) imply:
% 164.47/24.08 | | | | | | | | | | | | | | (1012) ~ (all_52_3 = e1)
% 164.47/24.08 | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 164.47/24.08 | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | Case 1:
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | (1013) all_54_4 = e3
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1013) imply:
% 164.47/24.08 | | | | | | | | | | | | | | | (1014) all_52_1 = e3
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | SIMP: (1014) implies:
% 164.47/24.08 | | | | | | | | | | | | | | | (1015) all_52_1 = e3
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | REDUCE: (148), (1015) imply:
% 164.47/24.08 | | | | | | | | | | | | | | | (1016) ~ (all_52_2 = e3)
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | SIMP: (1016) implies:
% 164.47/24.08 | | | | | | | | | | | | | | | (1017) ~ (all_52_2 = e3)
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | REDUCE: (147), (1015) imply:
% 164.47/24.08 | | | | | | | | | | | | | | | (1018) ~ (all_52_3 = e3)
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | SIMP: (1018) implies:
% 164.47/24.08 | | | | | | | | | | | | | | | (1019) ~ (all_52_3 = e3)
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | REDUCE: (145), (1015) imply:
% 164.47/24.08 | | | | | | | | | | | | | | | (1020) ~ (all_52_9 = e3)
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | SIMP: (1020) implies:
% 164.47/24.08 | | | | | | | | | | | | | | | (1021) ~ (all_52_9 = e3)
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 164.47/24.08 | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | Case 1:
% 164.47/24.08 | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | (1022) all_54_6 = e3
% 164.47/24.08 | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | REF_CLOSE: (278), (1021), (1022) are inconsistent by
% 164.47/24.08 | | | | | | | | | | | | | | | | sub-proof #681.
% 164.47/24.08 | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | Case 2:
% 164.47/24.08 | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | (1023) ~ (all_54_6 = e3)
% 164.47/24.08 | | | | | | | | | | | | | | | | (1024) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 164.47/24.08 | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | BETA: splitting (1024) gives:
% 164.47/24.08 | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.08 | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | (1025) all_54_6 = e2
% 164.47/24.08 | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (942), (1025) are inconsistent by sub-proof
% 164.47/24.08 | | | | | | | | | | | | | | | | | #680.
% 164.47/24.08 | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.08 | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | (1026) all_54_6 = e1 | all_54_6 = e0
% 164.47/24.08 | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | BETA: splitting (1026) gives:
% 164.47/24.08 | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | (1027) all_54_6 = e1
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (1027) imply:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | (1028) all_52_9 = e1
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | SIMP: (1028) implies:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | (1029) all_52_9 = e1
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | REDUCE: (389), (1029) imply:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | (1030) ~ (all_6_2 = e1)
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | SIMP: (1030) implies:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | (1031) ~ (all_6_2 = e1)
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | REDUCE: (1021), (1029) imply:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | (1032) ~ (e3 = e1)
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 164.47/24.08 | | | | | | | | | | | | | | | | | |
% 164.47/24.08 | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.08 | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | (1033) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 164.47/24.09 | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (1033) gives:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | (1034) all_58_2 = e3 & op(e2, e3) = e3
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | ALPHA: (1034) implies:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | (1035) all_58_2 = e3
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | (1036) all_54_10 = e3
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (409), (1036) are inconsistent by sub-proof
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | #982.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | (1037) ~ (all_54_10 = e3)
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | (1038) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | (1039) all_56_10 = e3
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1009), (1039) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | (1040) e3 = e1
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1035), (1040) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | (1041) all_58_2 = e1
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (42), (164), (242), (403), (937),
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | (1021), (1041), (function-axioms) are inconsistent
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #677.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | (1042) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1042) gives:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | (1043) all_56_12 = e2
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (929), (1043) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | (1044) e2 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (1044) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | (1045) $false
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1045) is inconsistent.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | (1046) all_56_14 = e1 | all_56_15 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1038) gives:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | (1047) all_54_10 = e2
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (399), (1047) are inconsistent by sub-proof
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | #981.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | (1048) ~ (all_54_10 = e2)
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | (1049) all_54_10 = e1 | all_54_10 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1049) gives:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | (1050) all_54_10 = e1
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (1031), (1050) are inconsistent by
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #980.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | (1051) all_54_10 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (1051) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | (1052) all_6_2 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1052) implies:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | (1053) all_6_2 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (1053) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | (1054) all_56_14 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (1053) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | (1055) ~ (all_52_2 = e0)
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1031), (1053) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | (1056) ~ (e1 = e0)
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) ~ (all_56_14 = e0)
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1054), (1057) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) $false
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1058) is inconsistent.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) all_56_13 = e1 & op(e1, e0) = e1
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1059) implies:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) all_56_13 = e1
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1046) gives:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) all_56_14 = e1
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1054), (1061) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) e1 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1062) implies:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) e1 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1060), (1063) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) all_56_13 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (193), (214), (274), (305), (399), (409),
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1031), (1064) are inconsistent by sub-proof #976.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) all_56_15 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (1065) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_4_2 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (376), (1066) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) ~ (all_52_3 = e0)
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) all_54_8 = e3
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (1017), (1068) are inconsistent by
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #690.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1069) gives:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) all_54_8 = e2
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (1070) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) all_52_2 = e2
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1071) implies:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) all_52_2 = e2
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (1072) imply:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) ~ (all_52_3 = e2)
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1073) implies:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) ~ (all_52_3 = e2)
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (191), (265), (1012), (1019), (1067), (1074) are
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #674.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) all_54_8 = e1 | all_54_8 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (1011), (1055), (1075) are inconsistent by
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #688.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | (1076) all_58_3 = e3 & op(e2, e2) = e3
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (403), (1076), (function-axioms) are
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | (1077) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 164.47/24.09 | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (937), (1021), (1077),
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.47/24.09 | | | | | | | | | | | | | | | | | | | #678.
% 164.47/24.09 | | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | (1078) all_54_6 = e0
% 164.47/24.09 | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (931), (1078) are inconsistent by sub-proof
% 164.47/24.09 | | | | | | | | | | | | | | | | | | #673.
% 164.47/24.09 | | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | End of split
% 164.47/24.09 | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | Case 2:
% 164.47/24.09 | | | | | | | | | | | | | | |
% 164.47/24.09 | | | | | | | | | | | | | | | (1079) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 164.47/24.09 | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | REF_CLOSE: (287), (930), (941), (1010), (1079) are
% 164.47/24.10 | | | | | | | | | | | | | | | inconsistent by sub-proof #671.
% 164.47/24.10 | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | Case 2:
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | (1080) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 164.47/24.10 | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | REF_CLOSE: (5), (163), (164), (931), (937), (1080),
% 164.47/24.10 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.47/24.10 | | | | | | | | | | | | #669.
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | |
% 164.47/24.10 | | | | | | | | Case 2:
% 164.47/24.10 | | | | | | | | |
% 164.47/24.10 | | | | | | | | | (1081) all_28_2 = e3
% 164.47/24.10 | | | | | | | | |
% 164.47/24.10 | | | | | | | | | COMBINE_EQS: (340), (1081) imply:
% 164.47/24.10 | | | | | | | | | (1082) all_6_2 = e3
% 164.47/24.10 | | | | | | | | |
% 164.47/24.10 | | | | | | | | | COMBINE_EQS: (274), (1082) imply:
% 164.47/24.10 | | | | | | | | | (1083) all_56_14 = e3
% 164.47/24.10 | | | | | | | | |
% 164.47/24.10 | | | | | | | | | REDUCE: (386), (1082) imply:
% 164.47/24.10 | | | | | | | | | (1084) ~ (all_52_6 = e3)
% 164.47/24.10 | | | | | | | | |
% 164.47/24.10 | | | | | | | | | REDUCE: (388), (1082) imply:
% 164.47/24.10 | | | | | | | | | (1085) ~ (all_52_8 = e3)
% 164.47/24.10 | | | | | | | | |
% 164.47/24.10 | | | | | | | | | REDUCE: (389), (1082) imply:
% 164.47/24.10 | | | | | | | | | (1086) ~ (all_52_9 = e3)
% 164.47/24.10 | | | | | | | | |
% 164.47/24.10 | | | | | | | | | BETA: splitting (216) gives:
% 164.47/24.10 | | | | | | | | |
% 164.47/24.10 | | | | | | | | | Case 1:
% 164.47/24.10 | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | (1087) ~ (all_56_14 = e3)
% 164.47/24.10 | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | REDUCE: (1083), (1087) imply:
% 164.47/24.10 | | | | | | | | | | (1088) $false
% 164.47/24.10 | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | CLOSE: (1088) is inconsistent.
% 164.47/24.10 | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | Case 2:
% 164.47/24.10 | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | (1089) all_56_2 = e1 & op(e1, e3) = e1
% 164.47/24.10 | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | ALPHA: (1089) implies:
% 164.47/24.10 | | | | | | | | | | (1090) op(e1, e3) = e1
% 164.47/24.10 | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | BETA: splitting (221) gives:
% 164.47/24.10 | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | Case 1:
% 164.47/24.10 | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | (1091) ~ (all_56_10 = e1)
% 164.47/24.10 | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | REDUCE: (298), (1091) imply:
% 164.47/24.10 | | | | | | | | | | | (1092) ~ (all_10_2 = e1)
% 164.47/24.10 | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | BETA: splitting (203) gives:
% 164.47/24.10 | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | Case 1:
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | (1093) all_54_0 = e3
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | COMBINE_EQS: (300), (1093) imply:
% 164.47/24.10 | | | | | | | | | | | | (1094) all_10_2 = e3
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | SIMP: (1094) implies:
% 164.47/24.10 | | | | | | | | | | | | (1095) all_10_2 = e3
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | REDUCE: (363), (1095) imply:
% 164.47/24.10 | | | | | | | | | | | | (1096) ~ (all_52_1 = e3)
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | REDUCE: (369), (1095) imply:
% 164.47/24.10 | | | | | | | | | | | | (1097) ~ (all_52_4 = e3)
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | BETA: splitting (246) gives:
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | Case 1:
% 164.47/24.10 | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | (1098) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 164.47/24.10 | | | | | | | | | | | | | & op(e2, e2) = e3)
% 164.47/24.10 | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | REF_CLOSE: (42), (169), (403), (1097), (1098),
% 164.47/24.10 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.47/24.10 | | | | | | | | | | | | | #972.
% 164.47/24.10 | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | Case 2:
% 164.47/24.10 | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | (1099) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 164.47/24.10 | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 164.47/24.10 | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | BETA: splitting (1099) gives:
% 164.47/24.10 | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | Case 1:
% 164.47/24.10 | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | (1100) all_58_7 = e3 & op(e1, e2) = e3
% 164.47/24.10 | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | ALPHA: (1100) implies:
% 164.47/24.10 | | | | | | | | | | | | | | (1101) op(e1, e2) = e3
% 164.47/24.10 | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | REF_CLOSE: (161), (1084), (1101), (function-axioms) are
% 164.47/24.10 | | | | | | | | | | | | | | inconsistent by sub-proof #668.
% 164.47/24.10 | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | Case 2:
% 164.47/24.10 | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | (1102) all_58_13 = e3 & op(e0, e2) = e3
% 164.47/24.10 | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | ALPHA: (1102) implies:
% 164.47/24.10 | | | | | | | | | | | | | | (1103) op(e0, e2) = e3
% 164.47/24.10 | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 164.47/24.10 | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | Case 1:
% 164.47/24.10 | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | (1104) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 164.47/24.10 | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 164.47/24.10 | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | REF_CLOSE: (42), (166), (403), (1096), (1104),
% 164.47/24.10 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.47/24.10 | | | | | | | | | | | | | | | #692.
% 164.47/24.10 | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | Case 2:
% 164.47/24.10 | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | (1105) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 164.47/24.10 | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 164.47/24.10 | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | BETA: splitting (1105) gives:
% 164.47/24.10 | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | Case 1:
% 164.47/24.10 | | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | | (1106) all_58_5 = e3 & op(e2, e1) = e3
% 164.47/24.10 | | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | | ALPHA: (1106) implies:
% 164.47/24.10 | | | | | | | | | | | | | | | | (1107) op(e2, e1) = e3
% 164.47/24.10 | | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1086), (1107), (function-axioms) are
% 164.47/24.10 | | | | | | | | | | | | | | | | inconsistent by sub-proof #951.
% 164.47/24.10 | | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | Case 2:
% 164.47/24.10 | | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | | (1108) all_58_10 = e3 & op(e2, e0) = e3
% 164.47/24.10 | | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | | ALPHA: (1108) implies:
% 164.47/24.10 | | | | | | | | | | | | | | | | (1109) op(e2, e0) = e3
% 164.47/24.10 | | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | | REF_CLOSE: (109), (116), (117), (124), (125), (127), (138),
% 164.47/24.10 | | | | | | | | | | | | | | | | (139), (140), (142), (143), (144), (145), (148),
% 164.47/24.10 | | | | | | | | | | | | | | | | (157), (162), (163), (188), (189), (191), (192),
% 164.47/24.10 | | | | | | | | | | | | | | | | (194), (197), (198), (199), (263), (265), (266),
% 164.47/24.10 | | | | | | | | | | | | | | | | (275), (278), (283), (287), (307), (374), (376),
% 164.47/24.10 | | | | | | | | | | | | | | | | (379), (383), (385), (394), (396), (397), (398),
% 164.47/24.10 | | | | | | | | | | | | | | | | (400), (407), (1090), (1103), (1109),
% 164.47/24.10 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.47/24.10 | | | | | | | | | | | | | | | | #731.
% 164.47/24.10 | | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | Case 2:
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | (1110) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | | REF_CLOSE: (300), (401), (405), (1092), (1110) are
% 164.47/24.10 | | | | | | | | | | | | inconsistent by sub-proof #958.
% 164.47/24.10 | | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | Case 2:
% 164.47/24.10 | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | (1111) all_56_4 = e3 & op(e3, e1) = e3
% 164.47/24.10 | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | ALPHA: (1111) implies:
% 164.47/24.10 | | | | | | | | | | | (1112) op(e3, e1) = e3
% 164.47/24.10 | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | | REF_CLOSE: (168), (1085), (1112), (function-axioms) are
% 164.47/24.10 | | | | | | | | | | | inconsistent by sub-proof #975.
% 164.47/24.10 | | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | | |
% 164.47/24.10 | | | | | | | | | End of split
% 164.47/24.10 | | | | | | | | |
% 164.47/24.10 | | | | | | | | End of split
% 164.47/24.10 | | | | | | | |
% 164.47/24.10 | | | | | | | Case 2:
% 164.47/24.10 | | | | | | | |
% 164.47/24.11 | | | | | | | | (1113) all_20_2 = e2
% 164.47/24.11 | | | | | | | |
% 164.47/24.11 | | | | | | | | COMBINE_EQS: (349), (1113) imply:
% 164.47/24.11 | | | | | | | | (1114) all_4_2 = e2
% 164.47/24.11 | | | | | | | |
% 164.47/24.11 | | | | | | | | SIMP: (1114) implies:
% 164.47/24.11 | | | | | | | | (1115) all_4_2 = e2
% 164.47/24.11 | | | | | | | |
% 164.47/24.11 | | | | | | | | COMBINE_EQS: (262), (1115) imply:
% 164.47/24.11 | | | | | | | | (1116) all_56_15 = e2
% 164.47/24.11 | | | | | | | |
% 164.47/24.11 | | | | | | | | REDUCE: (395), (1115) imply:
% 164.47/24.11 | | | | | | | | (1117) ~ (all_52_12 = e2)
% 164.47/24.11 | | | | | | | |
% 164.64/24.11 | | | | | | | | REDUCE: (396), (1115) imply:
% 164.64/24.11 | | | | | | | | (1118) ~ (all_52_13 = e2)
% 164.64/24.11 | | | | | | | |
% 164.64/24.11 | | | | | | | | REDUCE: (397), (1115) imply:
% 164.64/24.11 | | | | | | | | (1119) ~ (all_52_14 = e2)
% 164.64/24.11 | | | | | | | |
% 164.64/24.11 | | | | | | | | BETA: splitting (217) gives:
% 164.64/24.11 | | | | | | | |
% 164.64/24.11 | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | |
% 164.64/24.11 | | | | | | | | | (1120) ~ (all_56_12 = e0)
% 164.64/24.11 | | | | | | | | |
% 164.64/24.11 | | | | | | | | | REDUCE: (361), (1120) imply:
% 164.64/24.11 | | | | | | | | | (1121) ~ (all_8_2 = e0)
% 164.64/24.11 | | | | | | | | |
% 164.64/24.11 | | | | | | | | | BETA: splitting (212) gives:
% 164.64/24.11 | | | | | | | | |
% 164.64/24.11 | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | (1122) ~ (all_56_15 = e2)
% 164.64/24.11 | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | REDUCE: (1116), (1122) imply:
% 164.64/24.11 | | | | | | | | | | (1123) $false
% 164.64/24.11 | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | CLOSE: (1123) is inconsistent.
% 164.64/24.11 | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | Case 2:
% 164.64/24.11 | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | (1124) all_56_7 = e0 & op(e0, e2) = e0
% 164.64/24.11 | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | ALPHA: (1124) implies:
% 164.64/24.11 | | | | | | | | | | (1125) op(e0, e2) = e0
% 164.64/24.11 | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | BETA: splitting (198) gives:
% 164.64/24.11 | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | (1126) all_54_5 = e3
% 164.64/24.11 | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | REF_CLOSE: (283), (403), (1126) are inconsistent by sub-proof
% 164.64/24.11 | | | | | | | | | | | #667.
% 164.64/24.11 | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | Case 2:
% 164.64/24.11 | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | (1127) ~ (all_54_5 = e3)
% 164.64/24.11 | | | | | | | | | | | (1128) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 164.64/24.11 | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | BETA: splitting (1128) gives:
% 164.64/24.11 | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | (1129) all_54_5 = e2
% 164.64/24.11 | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | COMBINE_EQS: (283), (1129) imply:
% 164.64/24.11 | | | | | | | | | | | | (1130) all_8_2 = e2
% 164.64/24.11 | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | SIMP: (1130) implies:
% 164.64/24.11 | | | | | | | | | | | | (1131) all_8_2 = e2
% 164.64/24.11 | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | COMBINE_EQS: (361), (1131) imply:
% 164.64/24.11 | | | | | | | | | | | | (1132) all_56_12 = e2
% 164.64/24.11 | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | REDUCE: (377), (1131) imply:
% 164.64/24.11 | | | | | | | | | | | | (1133) ~ (all_52_4 = e2)
% 164.64/24.11 | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | REDUCE: (379), (1131) imply:
% 164.64/24.11 | | | | | | | | | | | | (1134) ~ (all_52_6 = e2)
% 164.64/24.11 | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | REDUCE: (381), (1131) imply:
% 164.64/24.11 | | | | | | | | | | | | (1135) ~ (all_52_7 = e2)
% 164.64/24.11 | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | REDUCE: (403), (1131) imply:
% 164.64/24.11 | | | | | | | | | | | | (1136) ~ (e3 = e2)
% 164.64/24.11 | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | BETA: splitting (251) gives:
% 164.64/24.11 | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | (1137) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 164.64/24.11 | | | | | | | | | | | | | & op(e2, e3) = e2)
% 164.64/24.11 | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | BETA: splitting (1137) gives:
% 164.64/24.11 | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | (1138) all_58_0 = e2 & op(e3, e3) = e2
% 164.64/24.11 | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | REF_CLOSE: (45), (405), (1138), (function-axioms) are
% 164.64/24.11 | | | | | | | | | | | | | | inconsistent by sub-proof #666.
% 164.64/24.11 | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | Case 2:
% 164.64/24.11 | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | (1139) all_58_2 = e2 & op(e2, e3) = e2
% 164.64/24.11 | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (161), (166),
% 164.64/24.11 | | | | | | | | | | | | | | (169), (239), (240), (242), (245), (1133), (1134),
% 164.64/24.11 | | | | | | | | | | | | | | (1135), (1139), (function-axioms) are inconsistent
% 164.64/24.11 | | | | | | | | | | | | | | by sub-proof #664.
% 164.64/24.11 | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | End of split
% 164.64/24.11 | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | Case 2:
% 164.64/24.11 | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | (1140) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 164.64/24.11 | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 164.64/24.11 | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | BETA: splitting (1140) gives:
% 164.64/24.11 | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | (1141) all_58_6 = e2 & op(e1, e3) = e2
% 164.64/24.11 | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | ALPHA: (1141) implies:
% 164.64/24.11 | | | | | | | | | | | | | | (1142) all_58_6 = e2
% 164.64/24.11 | | | | | | | | | | | | | | (1143) op(e1, e3) = e2
% 164.64/24.11 | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 164.64/24.11 | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | (1144) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 164.64/24.11 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 164.64/24.11 | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (1117), (1118), (1144),
% 164.64/24.11 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.11 | | | | | | | | | | | | | | | #661.
% 164.64/24.11 | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | Case 2:
% 164.64/24.11 | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | (1145) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 164.64/24.11 | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.64/24.11 | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | BETA: splitting (1145) gives:
% 164.64/24.11 | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | (1146) all_58_11 = e2 & op(e1, e0) = e2
% 164.64/24.11 | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1119), (1146), (function-axioms) are
% 164.64/24.11 | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 164.64/24.11 | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | Case 2:
% 164.64/24.11 | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | (1147) all_58_15 = e2 & op(e0, e0) = e2
% 164.64/24.11 | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | ALPHA: (1147) implies:
% 164.64/24.11 | | | | | | | | | | | | | | | | (1148) all_58_15 = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | (1149) op(e0, e0) = e2
% 164.64/24.11 | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 164.64/24.11 | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | (1150) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 164.64/24.11 | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (169), (405), (1133), (1150),
% 164.64/24.11 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.11 | | | | | | | | | | | | | | | | | #659.
% 164.64/24.11 | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.11 | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | (1151) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 164.64/24.11 | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | BETA: splitting (1151) gives:
% 164.64/24.11 | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | (1152) all_58_4 = e2 & op(e3, e1) = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | ALPHA: (1152) implies:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | (1153) all_58_4 = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | | (1154) op(e3, e1) = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 164.64/24.11 | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | (1155) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 164.64/24.11 | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (1155) gives:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1156) all_58_1 = e2 & op(e3, e2) = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | ALPHA: (1156) implies:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1157) all_58_1 = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (248), (250), (254),
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1153), (1157) are inconsistent by sub-proof #895.
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1158) all_58_3 = e2 & op(e2, e2) = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | ALPHA: (1158) implies:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1159) all_58_3 = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (157), (1125) gives:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1160) all_52_7 = e0
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (162), (1143) gives:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1161) all_52_2 = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (168), (1154) gives:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1162) all_52_8 = e2
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (1161) imply:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1163) ~ (all_52_1 = e2)
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (1161) imply:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1164) ~ (all_52_3 = e2)
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | SIMP: (1164) implies:
% 164.64/24.11 | | | | | | | | | | | | | | | | | | | | (1165) ~ (all_52_3 = e2)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (1161) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1166) ~ (all_52_6 = e2)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (1161) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1167) ~ (all_52_14 = e2)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1160) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1168) ~ (all_52_3 = e0)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (1160) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1169) ~ (all_52_4 = e0)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (1160) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1170) ~ (all_52_11 = e0)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | SIMP: (1170) implies:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1171) ~ (all_52_11 = e0)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (1135), (1160) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1172) ~ (e2 = e0)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (1162) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1173) ~ (all_52_11 = e2)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | SIMP: (1173) implies:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1174) ~ (all_52_11 = e2)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1162) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1175) ~ (all_52_12 = e2)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (1162) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1176) ~ (all_10_2 = e2)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | REDUCE: (388), (1162) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | (1177) ~ (all_6_2 = e2)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | (1178) ~ (all_56_14 = e3)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (1178) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | (1179) ~ (all_6_2 = e3)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | (1180) ~ (all_56_10 = e1)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (298), (1180) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | (1181) ~ (all_10_2 = e1)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | (1182) all_54_0 = e3
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (1182) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | (1183) all_10_2 = e3
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (1183) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | (1184) all_56_10 = e3
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (1183) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | (1185) ~ (all_52_1 = e3)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (1183) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | (1186) ~ (all_52_3 = e3)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (1183) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | (1187) ~ (all_52_4 = e3)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (373), (1183) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | (1188) ~ (all_52_12 = e3)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (1183) imply:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | (1189) op(e3, e3) = e3
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | (1190) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1190) gives:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | (1191) all_58_1 = e0 & op(e3, e2) = e0
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1191) implies:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | (1192) all_58_1 = e0
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1193) all_58_15 = e0 & op(e0, e0) = e0
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1148), (1193) are inconsistent by sub-proof
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | #874.
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1194) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1194) implies:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1195) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (42), (117),
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (157), (164), (166), (168), (169), (189),
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (221), (224), (225), (226), (231), (232),
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (234), (238), (244), (246), (248), (249),
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (253), (254), (263), (265), (399), (403),
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1125), (1142), (1149), (1153), (1154), (1159),
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1165), (1168), (1171), (1174), (1179), (1184),
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1185), (1186), (1187), (1192), (1195),
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | #636.
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | (1196) all_58_3 = e0 & op(e2, e2) = e0
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1159), (1196) are inconsistent by sub-proof
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | #934.
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | (1197) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1197) gives:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | (1198) all_58_7 = e0 & op(e1, e2) = e0
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1198) implies:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | (1199) all_58_7 = e0
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1200) all_58_15 = e0 & op(e0, e0) = e0
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1148), (1200) are inconsistent by sub-proof
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | #874.
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1201) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1201) implies:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (1202) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1203) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (169), (403), (1187), (1203),
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | #972.
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1204) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1204) gives:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1205) all_58_7 = e3 & op(e1, e2) = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1205) implies:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1206) all_58_7 = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1199), (1206) are inconsistent by sub-proof
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #748.
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1207) all_58_13 = e3 & op(e0, e2) = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1207) implies:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1208) all_58_13 = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1209) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1209) gives:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1210) all_58_0 = e0 & op(e3, e3) = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1210) implies:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1211) op(e3, e3) = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1189), (1211), (function-axioms) are
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #949.
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1212) all_58_2 = e0 & op(e2, e3) = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1212) implies:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1213) all_58_2 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1214) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1214) gives:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1215) all_58_0 = e0 & op(e3, e3) = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1215) implies:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1216) op(e3, e3) = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1189), (1216), (function-axioms) are
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #949.
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1217) all_58_1 = e0 & op(e3, e2) = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1217) implies:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1218) all_58_1 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (42), (117),
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (157), (164), (166), (168), (169), (189),
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (221), (224), (225), (226), (231), (232),
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (234), (238), (244), (246), (248), (249),
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (253), (254), (263), (265), (399), (403),
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125), (1142), (1149), (1153), (1154), (1159),
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165), (1168), (1171), (1174), (1179), (1184),
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1185), (1186), (1187), (1202), (1218),
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #636.
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1219) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1219) gives:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1220) all_58_4 = e0 & op(e3, e1) = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1153), (1220) are inconsistent by sub-proof
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #946.
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1221) all_58_9 = e0 & op(e3, e0) = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1221) implies:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1222) all_58_9 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1223) all_54_12 = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1186), (1223) are inconsistent by
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #738.
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1224) ~ (all_54_12 = e3)
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1225) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1225) gives:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1226) all_54_12 = e2
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1165), (1226) are inconsistent by
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #676.
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1227) ~ (all_54_12 = e2)
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1228) all_54_12 = e1 | all_54_12 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1229) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1229) gives:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1230) all_58_6 = e3 & op(e1, e3) = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1230) implies:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1231) all_58_6 = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1142), (1231) are inconsistent by sub-proof
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #822.
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1232) all_58_7 = e3 & op(e1, e2) = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1232) implies:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1233) all_58_7 = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1234) op(e1, e2) = e3
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1199), (1233) imply:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1235) e3 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1235) implies:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1236) e3 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1208), (1236) imply:
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1237) all_58_13 = e0
% 164.64/24.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (39), (42), (109), (111), (112),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (117), (125), (132), (138), (144), (147),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (161), (164), (166), (169), (189), (191),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (193), (194), (196), (199), (200), (202),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (214), (225), (226), (227), (238), (239),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (241), (242), (244), (247), (248), (250),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (263), (265), (266), (274), (275), (277),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287), (288), (290), (305), (386), (391), (393),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399), (403), (1117), (1118), (1119), (1125),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132), (1133), (1134), (1142), (1143), (1148),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149), (1153), (1159), (1163), (1165), (1168),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1169), (1171), (1174), (1184), (1185), (1186),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1187), (1188), (1189), (1213), (1233), (1234),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1237), (function-axioms) are inconsistent by
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #613.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1238) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1238) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1239) all_58_8 = e3 & op(e1, e1) = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1179), (1239), (function-axioms) are
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1240) all_58_11 = e3 & op(e1, e0) = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1240) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1241) all_58_11 = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1242) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1242) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1243) all_58_1 = e1 & op(e3, e2) = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1243) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1244) all_58_1 = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1245) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1245) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1246) all_58_0 = e3 & op(e3, e3) = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1246) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1247) all_58_0 = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1228) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1248) all_54_12 = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (1248) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1249) all_52_3 = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1249) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1250) all_52_3 = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (1250) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1251) ~ (all_52_1 = e1)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (1250) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1252) ~ (all_52_11 = e1)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1252) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1253) ~ (all_52_11 = e1)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1186), (1250) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1254) ~ (e3 = e1)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1165), (1250) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1255) ~ (e2 = e1)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1256) all_54_4 = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1256) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257) all_52_1 = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1185), (1257) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1258) $false
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1258) is inconsistent.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1259) ~ (all_54_4 = e3)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1260) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1260) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1261) all_54_4 = e2
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1261) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1262) all_52_1 = e2
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1163), (1262) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1263) $false
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1263) is inconsistent.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1264) ~ (all_54_4 = e2)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265) all_54_4 = e1 | all_54_4 = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1266) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1266) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267) all_58_6 = e1 & op(e1, e3) = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1142), (1267) are inconsistent by sub-proof
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #774.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1268) all_58_7 = e1 & op(e1, e2) = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1268) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1269) all_58_7 = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1199), (1269) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270) e1 = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1244), (1270) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1271) all_58_1 = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (250), (1153), (1222), (1247),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1271) are inconsistent by sub-proof #639.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1272) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1272) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1273) all_58_8 = e1 & op(e1, e1) = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1273) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1274) all_58_8 = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1265) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1275) all_54_4 = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1275) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1276) all_52_1 = e1
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1251), (1276) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277) $false
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1277) is inconsistent.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1278) all_54_4 = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (1278) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1279) all_52_1 = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (1279) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1280) ~ (all_52_9 = e0)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1280) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1281) ~ (all_52_9 = e0)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1185), (1279) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1282) ~ (e3 = e0)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1251), (1279) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1283) ~ (e1 = e0)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1284) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1284) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1285) all_58_4 = e3 & op(e3, e1) = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1153), (1285) are inconsistent by sub-proof
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #952.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286) all_58_5 = e3 & op(e2, e1) = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1286) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1287) op(e2, e1) = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (164), (189), (263), (1171), (1174),
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1253), (1287), (function-axioms) are inconsistent
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #654.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1288) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1288) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289) all_58_8 = e3 & op(e1, e1) = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1179), (1289), (function-axioms) are
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1290) all_58_14 = e3 & op(e0, e1) = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1290) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1291) all_58_14 = e3
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1292) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1292) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1293) all_58_4 = e0 & op(e3, e1) = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1153), (1293) are inconsistent by sub-proof
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #902.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1294) all_58_5 = e0 & op(e2, e1) = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1281), (1294), (function-axioms) are
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #670.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1295) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1295) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1296) all_58_8 = e0 & op(e1, e1) = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1296) implies:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1297) all_58_8 = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1274), (1297) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1298) e1 = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1244), (1298) imply:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1299) all_58_1 = e0
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1225) gives:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1300) all_54_12 = e2
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1165), (1300) are inconsistent by
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #676.
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (42), (117),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (157), (164), (166), (168), (189), (221),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (231), (232), (233), (234),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (244), (246), (248), (249), (250), (253),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (263), (265), (399), (403), (1125), (1142),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149), (1153), (1154), (1159), (1168), (1171),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174), (1179), (1184), (1185), (1202), (1208),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1228), (1291), (1299), (function-axioms) are
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #637.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1301) all_58_14 = e0 & op(e0, e1) = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1301) implies:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1302) all_58_14 = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1291), (1302) imply:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1303) e3 = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1208), (1303) imply:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1304) all_58_13 = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (39), (42), (109), (111), (112),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (117), (125), (132), (138), (144), (147),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (161), (164), (166), (169), (189), (191),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (193), (194), (196), (199), (200), (202),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (214), (225), (226), (227), (238), (239),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (241), (242), (244), (246), (247), (248),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (253), (263), (265), (266), (274), (275),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277), (287), (288), (290), (305), (386), (391),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (393), (399), (403), (1117), (1118), (1119),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125), (1132), (1133), (1134), (1142), (1143),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148), (1149), (1153), (1159), (1163), (1165),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168), (1169), (1171), (1174), (1184), (1185),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1186), (1187), (1188), (1189), (1213), (1304),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #612.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1305) all_58_11 = e1 & op(e1, e0) = e1
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1241), (1305) are inconsistent by sub-proof
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #721.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1306) all_54_12 = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1168), (1306) are inconsistent by
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #653.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1307) all_58_2 = e3 & op(e2, e3) = e3
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1307) implies:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1308) op(e2, e3) = e3
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1185), (1308), (function-axioms) are
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #989.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1309) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (226),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142), (1208), (1309) are inconsistent by
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #611.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1310) all_58_3 = e1 & op(e2, e2) = e1
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1159), (1310) are inconsistent by sub-proof
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #914.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1311) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (1125), (1199), (1311),
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #610.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1312) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1312) gives:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1313) all_58_6 = e0 & op(e1, e3) = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1142), (1313) are inconsistent by sub-proof
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #712.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1314) all_58_12 = e0 & op(e0, e3) = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1314) implies:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1315) all_58_12 = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1316) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1316) gives:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1317) all_58_0 = e0 & op(e3, e3) = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1317) implies:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1318) op(e3, e3) = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1189), (1318), (function-axioms) are
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #949.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1319) all_58_1 = e0 & op(e3, e2) = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1319) implies:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1320) all_58_1 = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1321) all_54_12 = e3
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1186), (1321) are inconsistent by
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #738.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1322) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1322) gives:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1323) all_54_12 = e2
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1165), (1323) are inconsistent by
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #676.
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1324) all_54_12 = e1 | all_54_12 = e0
% 164.64/24.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (42), (117),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (157), (164), (166), (168), (189), (221),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (231), (232), (233), (234),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (244), (246), (248), (249), (250), (253),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (263), (265), (399), (403), (1125), (1142),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149), (1153), (1154), (1159), (1168), (1171),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174), (1179), (1184), (1185), (1208), (1315),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1320), (1324), (function-axioms) are inconsistent
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #638.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1325) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1325) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1326) all_58_4 = e0 & op(e3, e1) = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1153), (1326) are inconsistent by sub-proof
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #902.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1327) all_58_9 = e0 & op(e3, e0) = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1327) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1328) all_58_9 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1329) all_54_12 = e3
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1186), (1329) are inconsistent by
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #738.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1330) ~ (all_54_12 = e3)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1331) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1331) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1332) all_54_12 = e2
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1165), (1332) are inconsistent by
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #676.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1333) ~ (all_54_12 = e2)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1334) all_54_12 = e1 | all_54_12 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1335) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1335) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1336) all_58_1 = e1 & op(e3, e2) = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1336) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1337) all_58_1 = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1338) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1338) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1339) all_58_0 = e3 & op(e3, e3) = e3
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1339) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1340) all_58_0 = e3
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1334) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1341) all_54_12 = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (1341) imply:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1342) all_52_3 = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1342) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1343) all_52_3 = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (1343) imply:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1344) ~ (all_52_11 = e1)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1344) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1345) ~ (all_52_11 = e1)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1186), (1343) imply:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1346) ~ (e3 = e1)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1165), (1343) imply:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1347) ~ (e2 = e1)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1348) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1348) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1349) all_58_12 = e1 & op(e0, e3) = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1349) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1350) all_58_12 = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1315), (1350) imply:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1351) e1 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1351) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1352) e1 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1337), (1352) imply:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1353) all_58_1 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (250), (1153), (1328), (1340),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1353) are inconsistent by sub-proof #639.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1354) all_58_13 = e1 & op(e0, e2) = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1354) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1355) op(e0, e2) = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (1125), (1355), (function-axioms) are
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #889.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1356) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (39), (42), (117), (164), (166),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (189), (238), (239), (240), (241), (242), (263),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (403), (1149), (1153), (1159), (1171),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174), (1185), (1345), (1356), (function-axioms)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #624.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1357) all_54_12 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1168), (1357) are inconsistent by
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #653.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1358) all_58_2 = e3 & op(e2, e3) = e3
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1358) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1359) op(e2, e3) = e3
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1185), (1359), (function-axioms) are
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #989.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1360) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (226),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142), (1208), (1360) are inconsistent by
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #611.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1361) all_58_3 = e1 & op(e2, e2) = e1
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1159), (1361) are inconsistent by sub-proof
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #914.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1362) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (1125), (1199), (1362),
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #610.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | (1363) all_58_13 = e0 & op(e0, e2) = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1363) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | (1364) all_58_13 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | (1365) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1365) gives:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1366) all_58_0 = e0 & op(e3, e3) = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1366) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1367) op(e3, e3) = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1189), (1367), (function-axioms) are
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #949.
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1368) all_58_2 = e0 & op(e2, e3) = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1368) implies:
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1369) all_58_2 = e0
% 164.64/24.16 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (39), (42), (109), (111), (112),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (117), (125), (132), (138), (144), (147),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (161), (164), (166), (169), (189), (191),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (193), (194), (196), (199), (200), (202),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (214), (225), (226), (227), (238), (239),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (241), (242), (244), (246), (247), (248),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (253), (263), (265), (266), (274), (275),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (277), (287), (288), (290), (305), (386), (391),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (393), (399), (403), (1117), (1118), (1119),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125), (1132), (1133), (1134), (1142), (1143),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148), (1149), (1153), (1159), (1163), (1165),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168), (1169), (1171), (1174), (1184), (1185),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1186), (1187), (1188), (1189), (1364), (1369),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | #612.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (1370) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1370) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1371) all_58_6 = e0 & op(e1, e3) = e0
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (225), (226),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (1125), (1142), (1148), (1149), (1364),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1371), (function-axioms) are inconsistent by
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #609.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1372) all_58_12 = e0 & op(e0, e3) = e0
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1372) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1373) all_58_12 = e0
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1374) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (169), (403), (1187), (1374),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #972.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1375) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1375) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1376) all_58_7 = e3 & op(e1, e2) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (157), (225), (227),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (1125), (1148), (1149), (1159), (1364),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1373), (1376), (function-axioms) are inconsistent
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #607.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1377) all_58_13 = e3 & op(e0, e2) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1377) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1378) all_58_13 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1364), (1378) are inconsistent by sub-proof
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #708.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | (1379) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (300), (401), (405), (1181), (1379) are
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #958.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | (1380) all_56_10 = e1
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | (1381) all_56_4 = e3 & op(e3, e1) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1381) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | (1382) op(e3, e1) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (1380) imply:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | (1383) all_10_2 = e1
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1383) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | (1384) all_10_2 = e1
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (1384) imply:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | (1385) ~ (all_52_3 = e1)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (1384) imply:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | (1386) ~ (all_52_4 = e1)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (1384) imply:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | (1387) ~ (e2 = e1)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (1384) imply:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | (1388) op(e3, e3) = e1
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | (1389) all_54_1 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (1389) imply:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | (1390) all_52_4 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1390) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | (1391) all_52_4 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (1391) imply:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | (1392) ~ (all_52_6 = e3)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1392) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | (1393) ~ (all_52_6 = e3)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | (1394) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1394) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1395) all_58_1 = e3 & op(e3, e2) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1395) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | (1396) all_58_1 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (1397) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1397) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1398) all_58_6 = e3 & op(e1, e3) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (248), (250), (254),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142), (1153), (1396), (1398) are inconsistent by
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #606.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1399) all_58_7 = e3 & op(e1, e2) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1399) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1400) op(e1, e2) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1393), (1400), (function-axioms) are
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #668.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (1401) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1401) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1402) all_58_8 = e3 & op(e1, e1) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1179), (1402), (function-axioms) are
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1403) all_58_11 = e3 & op(e1, e0) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1403) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1404) all_58_11 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1405) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (147), (166), (191),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (265), (1153), (1165), (1168),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1385), (1396), (1405), (function-axioms) are
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #604.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1406) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1406) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1407) all_58_6 = e3 & op(e1, e3) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (248), (250), (254),
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142), (1153), (1396), (1407) are inconsistent by
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #606.
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1408) all_58_12 = e3 & op(e0, e3) = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1408) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1409) all_58_12 = e3
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1410) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1410) gives:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1411) all_58_9 = e1 & op(e3, e0) = e1
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1411) implies:
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1412) all_58_9 = e1
% 164.64/24.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (221), (248),
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (1153), (1154), (1380), (1388), (1412),
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #801.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1413) all_58_10 = e1 & op(e2, e0) = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1413) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1414) all_58_10 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1415) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (147), (166), (191), (265), (403), (1165),
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168), (1385), (1415), (function-axioms) are
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #603.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1416) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1416) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1417) all_58_5 = e3 & op(e2, e1) = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1417) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1418) all_58_5 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1419) all_54_9 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (1393), (1419) are inconsistent by
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1420) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1421) all_54_12 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (1421) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1422) all_52_3 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1422) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1423) all_52_3 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (1423) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1424) ~ (all_52_11 = e3)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1424) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1425) ~ (all_52_11 = e3)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1426) all_54_14 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (1425), (1426) are inconsistent by
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #969.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1427) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1427) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1428) all_54_14 = e2
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (1174), (1428) are inconsistent by
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1429) all_54_14 = e1 | all_54_14 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1429) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1430) all_54_14 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (263), (1430) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1431) all_52_11 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1431) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1432) all_52_11 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (1432) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1433) ~ (all_6_2 = e1)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1433) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1434) ~ (all_6_2 = e1)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1435) all_54_10 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (1179), (1435) are inconsistent by
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #982.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1436) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1436) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1437) all_54_10 = e2
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (399), (1437) are inconsistent by sub-proof
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #981.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1438) ~ (all_54_10 = e2)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1439) all_54_10 = e1 | all_54_10 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1439) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1440) all_54_10 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (1434), (1440) are inconsistent by
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #980.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1441) all_54_10 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (1441) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1442) all_6_2 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1442) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1443) all_6_2 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (1443) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1444) all_56_14 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (386), (1443) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1445) ~ (all_52_6 = e0)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (1443) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1446) ~ (all_52_14 = e0)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1420) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1447) all_54_9 = e2
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (1134), (1447) are inconsistent by
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #740.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1448) ~ (all_54_9 = e2)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1449) all_54_9 = e1 | all_54_9 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1449) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1450) all_54_9 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (1450) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1451) all_52_6 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1451) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1452) all_52_6 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (1452) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1453) ~ (all_52_14 = e1)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1453) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1454) ~ (all_52_14 = e1)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1455) ~ (all_56_14 = e0)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1444), (1455) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1456) $false
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1456) is inconsistent.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1457) all_56_13 = e1 & op(e1, e0) = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1457) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1458) op(e1, e0) = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1459) all_54_11 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (1459) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460) all_52_14 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1460) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1461) all_52_14 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (1461) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1462) op(e1, e0) = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e0,
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (1458), (1462) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1463) e3 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e1,
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (1154), (1382) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1464) e3 = e2
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1463), (1464) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1465) e2 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1465) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1466) e2 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1159), (1466) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1467) all_58_3 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (239), (241), (1414),
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1418), (1467) are inconsistent by sub-proof #921.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1468) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (1119), (1446), (1454), (1468) are
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #602.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1469) all_54_9 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (1445), (1469) are inconsistent by
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #601.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1470) all_54_14 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (1171), (1470) are inconsistent by
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #965.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1471) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1165), (1168), (1385), (1471) are
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1472) all_58_10 = e3 & op(e2, e0) = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1472) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1473) all_58_10 = e3
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1414), (1473) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1474) e3 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (147), (166), (191),
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (253), (254), (265), (1142), (1153),
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165), (1168), (1385), (1396), (1409), (1474),
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #599.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1475) gives:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) all_58_11 = e1 & op(e1, e0) = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1476) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) all_58_11 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1404), (1477) imply:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) e3 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1478) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) e3 = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (147), (166), (191),
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (253), (254), (265), (1142), (1153),
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165), (1168), (1385), (1396), (1409), (1479),
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #599.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) all_58_15 = e1 & op(e0, e0) = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1480) implies:
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) op(e0, e0) = e1
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1149), (1481), (function-axioms) are
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #640.
% 164.64/24.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1482) all_58_3 = e3 & op(e2, e2) = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (403), (1482), (function-axioms) are
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | (1483) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (147), (161), (166),
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | (168), (191), (224), (225), (226), (253), (265),
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | (1142), (1154), (1165), (1168), (1382), (1385),
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | (1388), (1393), (1483), (function-axioms) are
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #597.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | (1484) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (290), (1133), (1169), (1386), (1484) are
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #595.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | (1485) all_56_14 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | (1486) all_56_2 = e1 & op(e1, e3) = e1
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1486) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | (1487) op(e1, e3) = e1
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (1485) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | (1488) all_6_2 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (386), (1488) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | (1489) ~ (all_52_6 = e3)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (389), (1488) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | (1490) ~ (all_52_9 = e3)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (1488) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | (1491) ~ (all_52_11 = e3)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1492) ~ (all_56_10 = e1)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (298), (1492) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1493) ~ (all_10_2 = e1)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | (1494) all_54_0 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (1494) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | (1495) all_10_2 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1495) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | (1496) all_10_2 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (1496) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | (1497) ~ (all_52_3 = e3)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | (1498) all_54_14 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (1491), (1498) are inconsistent by
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #969.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | (1499) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1500) all_54_12 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1497), (1500) are inconsistent by
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #738.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1501) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1501) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) all_54_12 = e2
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1165), (1502) are inconsistent by
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #676.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) all_54_12 = e1 | all_54_12 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1503) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) all_54_12 = e1
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (1504) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) all_52_3 = e1
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1505) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) all_52_3 = e1
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (1506) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507) ~ (all_52_11 = e1)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1507) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1508) ~ (all_52_11 = e1)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1499) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1509) all_54_14 = e2
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (1174), (1509) are inconsistent by
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1510) all_54_14 = e1 | all_54_14 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (1171), (1508), (1510) are inconsistent by
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #964.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511) all_54_12 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1168), (1511) are inconsistent by
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #653.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | (1512) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (300), (401), (405), (1493), (1512) are
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #958.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1513) all_56_10 = e1
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1514) all_56_4 = e3 & op(e3, e1) = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1514) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1515) op(e3, e1) = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (1513) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1516) all_10_2 = e1
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1516) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1517) all_10_2 = e1
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (1517) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1518) ~ (all_52_3 = e1)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (1517) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1519) ~ (all_52_4 = e1)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (405), (1517) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1520) ~ (e2 = e1)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (1517) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | (1521) op(e3, e3) = e1
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | (1522) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1522) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | (1523) all_58_0 = e0 & op(e3, e3) = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1523) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | (1524) op(e3, e3) = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1521), (1524), (function-axioms) are
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #907.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | (1525) all_58_2 = e0 & op(e2, e3) = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1525) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | (1526) all_58_2 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1527) all_58_15 = e0 & op(e0, e0) = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1148), (1527) are inconsistent by sub-proof
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | #874.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1528) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1528) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | (1529) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1530) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1530) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1531) all_58_0 = e0 & op(e3, e3) = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1531) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1532) op(e3, e3) = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1521), (1532), (function-axioms) are
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #907.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1533) all_58_1 = e0 & op(e3, e2) = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1533) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1534) all_58_1 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (157),
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (191), (224), (225), (226), (244),
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (253), (265), (403), (1125), (1142),
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154), (1159), (1165), (1168), (1515), (1518),
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1534), (function-axioms) are inconsistent
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #594.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | (1535) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1535) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1536) all_58_4 = e0 & op(e3, e1) = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1153), (1536) are inconsistent by sub-proof
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | #902.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1537) all_58_9 = e0 & op(e3, e0) = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1537) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1538) all_58_9 = e0
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1539) all_54_12 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (1539) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1540) all_52_3 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1540) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1541) all_52_3 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (1541) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1542) ~ (all_52_1 = e3)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (1541) imply:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1543) ~ (all_52_11 = e3)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1544) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1544) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1545) all_58_0 = e3 & op(e3, e3) = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1545) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1546) op(e3, e3) = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (1154), (1515), (1521), (1546),
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #804.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1547) all_58_2 = e3 & op(e2, e3) = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1547) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1548) op(e2, e3) = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1542), (1548), (function-axioms) are
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #989.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1549) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1549) gives:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550) all_58_6 = e3 & op(e1, e3) = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1550) implies:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1551) op(e1, e3) = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (1487), (1551), (function-axioms) are
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1552) all_58_12 = e3 & op(e0, e3) = e3
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1552) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_58_12 = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1554) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1554) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1555) all_58_0 = e1 & op(e3, e3) = e1
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1555) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_58_0 = e1
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1557) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1557) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) all_58_12 = e1 & op(e0, e3) = e1
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1558) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) all_58_12 = e1
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (161),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (191), (224), (225), (226), (246),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (253), (254), (265), (403), (1142),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153), (1154), (1165), (1168), (1489), (1515),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518), (1521), (1556), (1559), (function-axioms)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #593.
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) all_58_13 = e1 & op(e0, e2) = e1
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1560) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) op(e0, e2) = e1
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (1125), (1561), (function-axioms) are
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #889.
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1562) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) all_58_14 = e1 & op(e0, e1) = e1
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1563) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) all_58_14 = e1
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1565) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1565) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1566) all_58_9 = e3 & op(e3, e0) = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (138), (147),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (156), (157), (166), (168), (169), (191), (221),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (227), (243), (244), (246),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (253), (254), (265), (403), (1125),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142), (1148), (1149), (1153), (1154), (1159),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165), (1168), (1513), (1515), (1518), (1519),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1538), (1553), (1566), (function-axioms)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #588.
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1567) all_58_10 = e3 & op(e2, e0) = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1567) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1568) all_58_10 = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1569) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1569) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1570) all_58_0 = e3 & op(e3, e3) = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1570) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1571) op(e3, e3) = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (1154), (1515), (1521), (1571),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #804.
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1572) all_58_1 = e3 & op(e3, e2) = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1572) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1573) all_58_1 = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1574) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1574) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1575) all_58_6 = e0 & op(e1, e3) = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1575) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1576) op(e1, e3) = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (1487), (1576), (function-axioms) are
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1577) all_58_7 = e0 & op(e1, e2) = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (157),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (166), (168), (169), (191), (221), (224),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (226), (228), (244), (246), (248), (250),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (254), (265), (403), (1125), (1142),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149), (1153), (1154), (1159), (1165), (1168),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489), (1513), (1515), (1518), (1519), (1521),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1529), (1553), (1556), (1564), (1568), (1573),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1577), (function-axioms) are inconsistent by
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #580.
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1578) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1578) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1579) all_58_8 = e0 & op(e1, e1) = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1579) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1580) all_58_8 = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1581) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (157),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (191), (224), (225), (226), (244),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (253), (265), (403), (1125), (1142),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154), (1159), (1165), (1168), (1515), (1518),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1581), (function-axioms) are inconsistent
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #592.
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1582) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1582) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1583) all_58_7 = e0 & op(e1, e2) = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (157),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (166), (168), (169), (191), (221), (224),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (226), (228), (244), (246), (248), (250),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (254), (265), (403), (1125), (1142),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149), (1153), (1154), (1159), (1165), (1168),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489), (1513), (1515), (1518), (1519), (1521),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1529), (1553), (1556), (1564), (1568), (1573),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1583), (function-axioms) are inconsistent by
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #580.
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1584) all_58_13 = e0 & op(e0, e2) = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (156), (157),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (238), (244), (246), (248), (254), (403),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153), (1159), (1490), (1491), (1556), (1573),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1580), (1584), (function-axioms) are inconsistent
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #578.
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1585) all_58_11 = e0 & op(e1, e0) = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1585) implies:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1586) all_58_11 = e0
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (157),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (166), (168), (191), (221), (224), (225),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (228), (246), (248), (250), (253), (254),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (403), (1125), (1142), (1149), (1153),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154), (1165), (1168), (1489), (1513), (1515),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518), (1521), (1553), (1556), (1564), (1568),
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1573), (1586), (function-axioms) are inconsistent
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583.
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1587) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1587) gives:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1588) all_58_4 = e3 & op(e3, e1) = e3
% 164.64/24.20 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (239), (240),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (403), (1153), (1159), (1568),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1588), (function-axioms) are inconsistent by
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #627.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1589) all_58_9 = e3 & op(e3, e0) = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (138), (147),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (156), (157), (166), (168), (169), (191), (221),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (227), (243), (244), (246),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (253), (254), (265), (403), (1125),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142), (1148), (1149), (1153), (1154), (1159),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165), (1168), (1513), (1515), (1518), (1519),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1538), (1553), (1589), (function-axioms)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #588.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1590) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1590) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1591) all_58_11 = e3 & op(e1, e0) = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1591) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1592) all_58_11 = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1593) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1593) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1594) all_58_0 = e3 & op(e3, e3) = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1594) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1595) op(e3, e3) = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (1154), (1515), (1521), (1595),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #804.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1596) all_58_1 = e3 & op(e3, e2) = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1596) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1597) all_58_1 = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1598) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1598) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1599) all_58_6 = e0 & op(e1, e3) = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1599) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1600) op(e1, e3) = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (1487), (1600), (function-axioms) are
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1601) all_58_7 = e0 & op(e1, e2) = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1601) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1602) all_58_7 = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1603) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1603) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1604) all_58_6 = e1 & op(e1, e3) = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1142), (1604) are inconsistent by sub-proof
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #774.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1605) all_58_7 = e1 & op(e1, e2) = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1605) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1606) all_58_7 = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1602), (1606) imply:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1607) e1 = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1607) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1608) e1 = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1564), (1608) imply:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1609) all_58_14 = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (157),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (166), (168), (191), (224), (225), (226),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (248), (250), (253), (254), (265), (403),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125), (1142), (1149), (1153), (1154), (1165),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168), (1489), (1515), (1518), (1521), (1556),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1609), (function-axioms) are inconsistent by
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #584.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1610) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1610) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1611) all_58_8 = e1 & op(e1, e1) = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1611) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1612) all_58_8 = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1613) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (164), (248), (254),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153), (1490), (1556), (1597), (1613),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #579.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1614) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1614) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1615) all_58_8 = e3 & op(e1, e1) = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1615) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1616) all_58_8 = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1612), (1616) imply:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1617) e3 = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1617) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1618) e3 = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (147), (166), (191),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (253), (254), (265), (1142), (1153),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165), (1168), (1518), (1553), (1597), (1618),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #599.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1619) all_58_14 = e3 & op(e0, e1) = e3
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (1491), (1619), (function-axioms) are
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #960.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1620) all_58_11 = e1 & op(e1, e0) = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1620) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1621) all_58_11 = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1592), (1621) imply:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1622) e3 = e1
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (147), (166), (191),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (253), (254), (265), (1142), (1153),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165), (1168), (1518), (1553), (1597), (1622),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #599.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1623) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1624) all_58_8 = e0 & op(e1, e1) = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1624) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1625) all_58_8 = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1626) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (157),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (191), (224), (225), (226), (244),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (253), (265), (403), (1125), (1142),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154), (1159), (1165), (1168), (1515), (1518),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1626), (function-axioms) are inconsistent
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #592.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1627) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1627) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1628) all_58_7 = e0 & op(e1, e2) = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1628) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1629) all_58_7 = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1529) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1630) all_58_12 = e0 & op(e0, e3) = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1630) implies:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631) all_58_12 = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (157),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (191), (224), (225), (226), (244),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (248), (250), (253), (254), (265), (403),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125), (1142), (1153), (1154), (1159), (1165),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168), (1515), (1518), (1521), (1629), (1631),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #591.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1632) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1632) gives:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1633) all_58_13 = e0 & op(e0, e2) = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (156), (157),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (238), (244), (246), (248), (254), (403),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153), (1159), (1490), (1491), (1556), (1597),
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1625), (1633), (function-axioms) are inconsistent
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #578.
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1634) all_58_14 = e0 & op(e0, e1) = e0
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1634) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1635) all_58_14 = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (157),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (166), (168), (191), (224), (225), (226),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (248), (250), (253), (254), (265), (403),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125), (1142), (1149), (1153), (1154), (1165),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168), (1489), (1515), (1518), (1521), (1556),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1635), (function-axioms) are inconsistent by
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #584.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1636) all_58_13 = e0 & op(e0, e2) = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (156), (157),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (238), (244), (246), (248), (254), (403),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153), (1159), (1490), (1491), (1556), (1597),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1625), (1636), (function-axioms) are inconsistent
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #578.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1637) all_58_11 = e0 & op(e1, e0) = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1637) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1638) all_58_11 = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1592), (1638) imply:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1639) e3 = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1597), (1639) imply:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1640) all_58_1 = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (147), (157),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (191), (224), (225), (226), (244),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (253), (265), (403), (1125), (1142),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154), (1159), (1165), (1168), (1515), (1518),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1640), (function-axioms) are inconsistent
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #594.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1641) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1641) gives:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1642) all_58_4 = e3 & op(e3, e1) = e3
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1642) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1643) all_58_4 = e3
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1153), (1643) imply:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1644) e3 = e2
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1644) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1645) e3 = e2
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1553), (1645) imply:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1646) all_58_12 = e2
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (249), (253), (1142),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1526), (1646) are inconsistent by sub-proof #575.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1647) all_58_9 = e3 & op(e3, e0) = e3
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (138), (147),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (156), (157), (166), (168), (169), (191), (221),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (227), (243), (244), (246),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (253), (254), (265), (403), (1125),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142), (1148), (1149), (1153), (1154), (1159),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165), (1168), (1513), (1515), (1518), (1519),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1538), (1553), (1647), (function-axioms)
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #588.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1648) all_58_15 = e3 & op(e0, e0) = e3
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1648) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1649) all_58_15 = e3
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1148), (1649) imply:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650) e3 = e2
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1650) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1651) e3 = e2
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1553), (1651) imply:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1652) all_58_12 = e2
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (249), (253), (1142),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1526), (1652) are inconsistent by sub-proof #575.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1653) all_58_15 = e1 & op(e0, e0) = e1
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1653) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1654) op(e0, e0) = e1
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1149), (1654), (function-axioms) are
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #640.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1655) all_58_2 = e1 & op(e2, e3) = e1
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1655) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1656) all_58_2 = e1
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1526), (1656) are inconsistent by sub-proof
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #776.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1657) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1657) gives:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1658) all_58_6 = e1 & op(e1, e3) = e1
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1142), (1658) are inconsistent by sub-proof
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #774.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1659) all_58_12 = e1 & op(e0, e3) = e1
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1553), (1659) are inconsistent by sub-proof
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #651.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1660) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (1165), (1168), (1518), (1660) are
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #675.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | (1661) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1661) gives:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | (1662) all_58_6 = e0 & op(e1, e3) = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1662) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | (1663) op(e1, e3) = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (1487), (1663), (function-axioms) are
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | (1664) all_58_12 = e0 & op(e0, e3) = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1664) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | (1665) all_58_12 = e0
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (138), (147),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | (156), (157), (166), (168), (169), (191), (221),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (227), (243), (244), (246),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (253), (254), (265), (403), (1125),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | (1142), (1148), (1149), (1153), (1154), (1159),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | (1165), (1168), (1513), (1515), (1518), (1519),
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1665), (function-axioms) are inconsistent
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #589.
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.22 | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | (1666) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 164.64/24.22 | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | BETA: splitting (1666) gives:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | (1667) all_58_7 = e2 & op(e1, e2) = e2
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | ALPHA: (1667) implies:
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | (1668) op(e1, e2) = e2
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1134), (1668), (function-axioms) are
% 164.64/24.22 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | | (1669) all_58_13 = e2 & op(e0, e2) = e2
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (1669) implies:
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | | (1670) op(e0, e2) = e2
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (1125), (1670), (function-axioms) are
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #631.
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.23 | | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | | | (1671) all_58_9 = e2 & op(e3, e0) = e2
% 164.64/24.23 | | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1117), (1671), (function-axioms) are
% 164.64/24.23 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #663.
% 164.64/24.23 | | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | Case 2:
% 164.64/24.23 | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | (1672) all_58_12 = e2 & op(e0, e3) = e2
% 164.64/24.23 | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (161),
% 164.64/24.23 | | | | | | | | | | | | | | (233), (247), (249), (253), (399), (1119), (1134),
% 164.64/24.23 | | | | | | | | | | | | | | (1672), (function-axioms) are inconsistent by
% 164.64/24.23 | | | | | | | | | | | | | | sub-proof #573.
% 164.64/24.23 | | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | Case 2:
% 164.64/24.23 | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | (1673) all_54_5 = e1 | all_54_5 = e0
% 164.64/24.23 | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | REF_CLOSE: (283), (400), (1121), (1673) are inconsistent by
% 164.64/24.23 | | | | | | | | | | | | sub-proof #735.
% 164.64/24.23 | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | End of split
% 164.64/24.23 | | | | | | | | |
% 164.64/24.23 | | | | | | | | Case 2:
% 164.64/24.23 | | | | | | | | |
% 164.64/24.23 | | | | | | | | | (1674) all_56_11 = e2 & op(e2, e0) = e2
% 164.64/24.23 | | | | | | | | |
% 164.64/24.23 | | | | | | | | | ALPHA: (1674) implies:
% 164.64/24.23 | | | | | | | | | (1675) op(e2, e0) = e2
% 164.64/24.23 | | | | | | | | |
% 164.64/24.23 | | | | | | | | | REF_CLOSE: (163), (1118), (1675), (function-axioms) are
% 164.64/24.23 | | | | | | | | | inconsistent by sub-proof #662.
% 164.64/24.23 | | | | | | | | |
% 164.64/24.23 | | | | | | | | End of split
% 164.64/24.23 | | | | | | | |
% 164.64/24.23 | | | | | | | End of split
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | Case 2:
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | (1676) all_16_2 = e2
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | COMBINE_EQS: (350), (1676) imply:
% 164.64/24.23 | | | | | | | (1677) all_10_2 = e2
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | SIMP: (1677) implies:
% 164.64/24.23 | | | | | | | (1678) all_10_2 = e2
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | COMBINE_EQS: (298), (1678) imply:
% 164.64/24.23 | | | | | | | (1679) all_56_10 = e2
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | REDUCE: (363), (1678) imply:
% 164.64/24.23 | | | | | | | (1680) ~ (all_52_1 = e2)
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | REDUCE: (365), (1678) imply:
% 164.64/24.23 | | | | | | | (1681) ~ (all_52_2 = e2)
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | REDUCE: (369), (1678) imply:
% 164.64/24.23 | | | | | | | (1682) ~ (all_52_4 = e2)
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | REDUCE: (371), (1678) imply:
% 164.64/24.23 | | | | | | | (1683) ~ (all_52_8 = e2)
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | REDUCE: (373), (1678) imply:
% 164.64/24.23 | | | | | | | (1684) ~ (all_52_12 = e2)
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | BETA: splitting (222) gives:
% 164.64/24.23 | | | | | | |
% 164.64/24.23 | | | | | | | Case 1:
% 164.64/24.23 | | | | | | | |
% 164.64/24.23 | | | | | | | | (1685) ~ (all_56_10 = e2)
% 164.64/24.23 | | | | | | | |
% 164.64/24.23 | | | | | | | | REDUCE: (1679), (1685) imply:
% 164.64/24.23 | | | | | | | | (1686) $false
% 164.64/24.23 | | | | | | | |
% 164.64/24.23 | | | | | | | | CLOSE: (1686) is inconsistent.
% 164.64/24.23 | | | | | | | |
% 164.64/24.23 | | | | | | | Case 2:
% 164.64/24.23 | | | | | | | |
% 164.64/24.23 | | | | | | | | (1687) all_56_1 = e3 & op(e3, e2) = e3
% 164.64/24.23 | | | | | | | |
% 164.64/24.23 | | | | | | | | ALPHA: (1687) implies:
% 164.64/24.23 | | | | | | | | (1688) all_56_1 = e3
% 164.64/24.23 | | | | | | | | (1689) op(e3, e2) = e3
% 164.64/24.23 | | | | | | | |
% 164.64/24.23 | | | | | | | | BETA: splitting (252) gives:
% 164.64/24.23 | | | | | | | |
% 164.64/24.23 | | | | | | | | Case 1:
% 164.64/24.23 | | | | | | | | |
% 164.64/24.23 | | | | | | | | | (1690) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 164.64/24.23 | | | | | | | | | op(e3, e2) = e2)
% 164.64/24.23 | | | | | | | | |
% 164.64/24.23 | | | | | | | | | BETA: splitting (1690) gives:
% 164.64/24.23 | | | | | | | | |
% 164.64/24.23 | | | | | | | | | Case 1:
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | (1691) all_58_0 = e2 & op(e3, e3) = e2
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | ALPHA: (1691) implies:
% 164.64/24.23 | | | | | | | | | | (1692) all_58_0 = e2
% 164.64/24.23 | | | | | | | | | | (1693) op(e3, e3) = e2
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 164.64/24.23 | | | | | | | | | | e2, e3, simplifying with (169), (1689) gives:
% 164.64/24.23 | | | | | | | | | | (1694) all_52_4 = e3
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | REDUCE: (135), (1694) imply:
% 164.64/24.23 | | | | | | | | | | (1695) ~ (all_52_6 = e3)
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | SIMP: (1695) implies:
% 164.64/24.23 | | | | | | | | | | (1696) ~ (all_52_6 = e3)
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | REDUCE: (134), (1694) imply:
% 164.64/24.23 | | | | | | | | | | (1697) ~ (all_52_7 = e3)
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | SIMP: (1697) implies:
% 164.64/24.23 | | | | | | | | | | (1698) ~ (all_52_7 = e3)
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | REDUCE: (133), (1694) imply:
% 164.64/24.23 | | | | | | | | | | (1699) ~ (all_52_8 = e3)
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | SIMP: (1699) implies:
% 164.64/24.23 | | | | | | | | | | (1700) ~ (all_52_8 = e3)
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | REDUCE: (132), (1694) imply:
% 164.64/24.23 | | | | | | | | | | (1701) ~ (all_52_12 = e3)
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | SIMP: (1701) implies:
% 164.64/24.23 | | | | | | | | | | (1702) ~ (all_52_12 = e3)
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | REDUCE: (377), (1694) imply:
% 164.64/24.23 | | | | | | | | | | (1703) ~ (all_8_2 = e3)
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | BETA: splitting (246) gives:
% 164.64/24.23 | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | Case 1:
% 164.64/24.23 | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | (1704) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 164.64/24.23 | | | | | | | | | | | & op(e2, e2) = e3)
% 164.64/24.23 | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | BETA: splitting (1704) gives:
% 164.64/24.23 | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | Case 1:
% 164.64/24.23 | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | (1705) all_58_1 = e3 & op(e3, e2) = e3
% 164.64/24.23 | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | ALPHA: (1705) implies:
% 164.64/24.23 | | | | | | | | | | | | (1706) all_58_1 = e3
% 164.64/24.23 | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | BETA: splitting (61) gives:
% 164.64/24.23 | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | Case 1:
% 164.64/24.23 | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | (1707) ~ (all_20_2 = e2)
% 164.64/24.23 | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | REDUCE: (349), (1707) imply:
% 164.64/24.23 | | | | | | | | | | | | | (1708) ~ (all_4_2 = e2)
% 164.64/24.23 | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | BETA: splitting (73) gives:
% 164.64/24.23 | | | | | | | | | | | | |
% 164.64/24.23 | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | (1709) ~ (all_28_2 = e3)
% 164.64/24.24 | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | REDUCE: (340), (1709) imply:
% 164.64/24.24 | | | | | | | | | | | | | | (1710) ~ (all_6_2 = e3)
% 164.64/24.24 | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 164.64/24.24 | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | (1711) ~ (all_30_2 = e0)
% 164.64/24.24 | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | REDUCE: (355), (1711) imply:
% 164.64/24.24 | | | | | | | | | | | | | | | (1712) ~ (all_8_2 = e0)
% 164.64/24.24 | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 164.64/24.24 | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | (1713) all_54_5 = e3
% 164.64/24.24 | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (1713) imply:
% 164.64/24.24 | | | | | | | | | | | | | | | | (1714) all_8_2 = e3
% 164.64/24.24 | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | REDUCE: (403), (1714) imply:
% 164.64/24.24 | | | | | | | | | | | | | | | | (1715) $false
% 164.64/24.24 | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | CLOSE: (1715) is inconsistent.
% 164.64/24.24 | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | Case 2:
% 164.64/24.24 | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | (1716) ~ (all_54_5 = e3)
% 164.64/24.24 | | | | | | | | | | | | | | | | (1717) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 164.64/24.24 | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | BETA: splitting (1717) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | (1718) all_54_5 = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (1718) imply:
% 164.64/24.24 | | | | | | | | | | | | | | | | | (1719) all_8_2 = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (1719) imply:
% 164.64/24.24 | | | | | | | | | | | | | | | | | (1720) all_56_12 = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | REDUCE: (379), (1719) imply:
% 164.64/24.24 | | | | | | | | | | | | | | | | | (1721) ~ (all_52_6 = e2)
% 164.64/24.24 | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | REDUCE: (381), (1719) imply:
% 164.64/24.24 | | | | | | | | | | | | | | | | | (1722) ~ (all_52_7 = e2)
% 164.64/24.24 | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | REDUCE: (383), (1719) imply:
% 164.64/24.24 | | | | | | | | | | | | | | | | | (1723) ~ (all_52_9 = e2)
% 164.64/24.24 | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | REDUCE: (385), (1719) imply:
% 164.64/24.24 | | | | | | | | | | | | | | | | | (1724) ~ (all_52_13 = e2)
% 164.64/24.24 | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | REDUCE: (403), (1719) imply:
% 164.64/24.24 | | | | | | | | | | | | | | | | | (1725) ~ (e3 = e2)
% 164.64/24.24 | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | (1726) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 164.64/24.24 | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1683), (1723), (1726),
% 164.64/24.24 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.24 | | | | | | | | | | | | | | | | | | #570.
% 164.64/24.24 | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.24 | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | (1727) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 164.64/24.24 | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 164.64/24.24 | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | BETA: splitting (1727) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | (1728) all_58_8 = e2 & op(e1, e1) = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (1728), (function-axioms) are
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 164.64/24.24 | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | (1729) all_58_14 = e2 & op(e0, e1) = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | ALPHA: (1729) implies:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | (1730) all_58_14 = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | (1731) op(e0, e1) = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | (1732) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1732) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | (1733) all_58_4 = e3 & op(e3, e1) = e3
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1733) implies:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | (1734) op(e3, e1) = e3
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1700), (1734), (function-axioms) are
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #975.
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | (1735) all_58_5 = e3 & op(e2, e1) = e3
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1735) implies:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | (1736) all_58_5 = e3
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | (1737) op(e2, e1) = e3
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | (1738) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (1684), (1724), (1738),
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | #661.
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | (1739) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1739) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | (1740) all_58_11 = e2 & op(e1, e0) = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1740) implies:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | (1741) all_58_11 = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | (1742) op(e1, e0) = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | (1743) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1743) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | (1744) all_58_6 = e3 & op(e1, e3) = e3
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1744) implies:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | (1745) all_58_6 = e3
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | (1746) op(e1, e3) = e3
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (1747) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1747) gives:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1748) all_58_2 = e2 & op(e2, e3) = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (161), (166),
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (239), (240), (242), (245), (1682), (1721),
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1722), (1748), (function-axioms) are inconsistent
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #664.
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1749) all_58_3 = e2 & op(e2, e2) = e2
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1749) implies:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1750) all_58_3 = e2
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, e0, simplifying with (156), (1731) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1751) all_52_11 = e2
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (159), (1742) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1752) all_52_14 = e2
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (162), (1746) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1753) all_52_2 = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (164), (1737) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1754) all_52_9 = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (1754) imply:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1755) ~ (all_52_1 = e3)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (1754) imply:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1756) ~ (all_52_13 = e3)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1756) implies:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1757) ~ (all_52_13 = e3)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (389), (1754) imply:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1758) ~ (all_6_2 = e3)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (1752) imply:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1759) ~ (all_6_2 = e2)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (397), (1752) imply:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1760) ~ (all_4_2 = e2)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1761) ~ (all_56_14 = e0)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (1761) imply:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1762) ~ (all_6_2 = e0)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1763) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1763) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1764) all_58_9 = e3 & op(e3, e0) = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1764) implies:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1765) all_58_9 = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1766) all_54_10 = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (1710), (1766) are inconsistent by
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #982.
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1767) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1768) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (201), (289), (305), (388), (399),
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1683), (1700), (1737), (1762), (1767), (1768),
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #566.
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1769) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (235), (250), (1693),
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1706), (1730), (1731), (1736), (1765), (1769),
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #563.
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1770) all_58_10 = e3 & op(e2, e0) = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1770) implies:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1771) op(e2, e0) = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1757), (1771), (function-axioms) are
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1772) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1772) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1773) all_58_11 = e3 & op(e1, e0) = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1773) implies:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1774) all_58_11 = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1741), (1774) imply:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1775) e3 = e2
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (166), (239),
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (242), (403), (1736), (1750), (1755),
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1775), (function-axioms) are inconsistent by
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #560.
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1776) all_58_15 = e3 & op(e0, e0) = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1776) implies:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1777) all_58_15 = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1778) all_54_10 = e3
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (1710), (1778) are inconsistent by
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #982.
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1779) ~ (all_54_10 = e3)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1780) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1781) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1781) gives:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1782) all_58_6 = e0 & op(e1, e3) = e0
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1745), (1782) are inconsistent by sub-proof
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #559.
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1783) all_58_7 = e0 & op(e1, e2) = e0
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1783) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1784) all_58_7 = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1785) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (162), (1746), (1784), (1785),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #558.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1786) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1786) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1787) all_58_8 = e1 & op(e1, e1) = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1787) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1788) all_58_8 = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (127), (157), (161),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (169), (188), (190), (194), (201),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (213), (224), (227), (235), (244), (250),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262), (264), (274), (275), (289), (305), (307),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386), (387), (388), (398), (399), (1679), (1682),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1683), (1688), (1693), (1696), (1698), (1700),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1706), (1708), (1710), (1721), (1722), (1730),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1731), (1736), (1750), (1755), (1762), (1777),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1780), (1784), (1788), (function-axioms) are
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #551.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1789) all_58_11 = e1 & op(e1, e0) = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1789) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1790) all_58_11 = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1741), (1790) are inconsistent by sub-proof
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #832.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1791) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1791) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1792) all_58_8 = e0 & op(e1, e1) = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1792) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1793) all_58_8 = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1794) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1794) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1795) all_58_6 = e1 & op(e1, e3) = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1795) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1796) op(e1, e3) = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (1746), (1796), (function-axioms) are
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1797) all_58_7 = e1 & op(e1, e2) = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1797) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1798) all_58_7 = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1799) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (201), (289), (305), (388), (399),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1683), (1700), (1737), (1762), (1780), (1799),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #566.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1800) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1800) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1801) all_58_8 = e1 & op(e1, e1) = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1801) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1802) all_58_8 = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1793), (1802) imply:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1803) e1 = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1798), (1803) imply:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1804) all_58_7 = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (127), (157), (161),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (169), (188), (190), (194), (201),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (213), (224), (227), (235), (244), (250),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262), (264), (274), (275), (289), (305), (307),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (386), (387), (388), (398), (399), (1679), (1682),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1683), (1688), (1693), (1696), (1698), (1700),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1706), (1708), (1710), (1721), (1722), (1730),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1731), (1736), (1750), (1755), (1762), (1777),
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1780), (1802), (1804), (function-axioms) are
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #551.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1805) all_58_14 = e1 & op(e0, e1) = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1805) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1806) op(e0, e1) = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1731), (1806), (function-axioms) are
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #967.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1807) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1807) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1808) all_58_8 = e1 & op(e1, e1) = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1793), (1808) are inconsistent by sub-proof
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #756.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1809) all_58_11 = e1 & op(e1, e0) = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1809) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1810) all_58_11 = e1
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1741), (1810) are inconsistent by sub-proof
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #832.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1811) all_58_11 = e0 & op(e1, e0) = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1811) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1812) all_58_11 = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1741), (1812) are inconsistent by sub-proof
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #879.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1813) all_56_14 = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (1813) imply:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1814) all_6_2 = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1814) implies:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1815) all_6_2 = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (388), (1815) imply:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1816) ~ (all_52_8 = e0)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1710), (1815) imply:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1817) ~ (e3 = e0)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (399), (1815) imply:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1818) ~ (e2 = e0)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1819) all_54_2 = e3
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (1700), (1819) are inconsistent by
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #550.
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1820) ~ (all_54_2 = e3)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1821) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1822) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1822) gives:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1823) all_58_12 = e3 & op(e0, e3) = e3
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1823) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1824) all_58_12 = e3
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1825) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1826) all_58_6 = e1 & op(e1, e3) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1826) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1827) op(e1, e3) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (1746), (1827), (function-axioms) are
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1828) all_58_7 = e1 & op(e1, e2) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1828) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1829) all_58_7 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1821) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1830) all_54_2 = e2
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1830) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1831) all_52_8 = e2
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1683), (1831) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1832) $false
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1832) is inconsistent.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1833) ~ (all_54_2 = e2)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1834) all_54_2 = e1 | all_54_2 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1834) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1835) all_54_2 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1835) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1836) all_52_8 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1836) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1837) ~ (all_52_12 = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1837) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1838) ~ (all_52_12 = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1700), (1836) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1839) ~ (e3 = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1683), (1836) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1840) ~ (e2 = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1841) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1841) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1842) all_58_9 = e3 & op(e3, e0) = e3
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1842) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1843) all_58_9 = e3
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1844) all_54_3 = e3
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (1844) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1845) all_52_12 = e3
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1702), (1845) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1846) $false
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1846) is inconsistent.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1847) ~ (all_54_3 = e3)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1848) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1848) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1849) all_54_3 = e2
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (1849) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1850) all_52_12 = e2
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1684), (1850) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1851) $false
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1851) is inconsistent.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1852) ~ (all_54_3 = e2)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1853) all_54_3 = e1 | all_54_3 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1854) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1854) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1855) all_58_0 = e0 & op(e3, e3) = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1692), (1855) are inconsistent by sub-proof
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #705.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1856) all_58_2 = e0 & op(e2, e3) = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1856) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1857) all_58_2 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1853) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1858) all_54_3 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (1858) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1859) all_52_12 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1838), (1859) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1860) $false
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1860) is inconsistent.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1861) all_54_3 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (1861) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1862) all_52_12 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1838), (1862) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1863) ~ (e1 = e0)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (1862) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1864) op(e3, e0) = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1865) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1865) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1866) all_58_12 = e1 & op(e0, e3) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1824), (1866) are inconsistent by sub-proof
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #651.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1867) all_58_13 = e1 & op(e0, e2) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1867) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1868) all_58_13 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1869) all_58_15 = e0 & op(e0, e0) = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1869) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1870) all_58_15 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1871) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1871) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1872) all_58_9 = e1 & op(e3, e0) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1872) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1873) op(e3, e0) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1864), (1873), (function-axioms) are
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #553.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1874) all_58_10 = e1 & op(e2, e0) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1874) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1875) all_58_10 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1876) op(e2, e0) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1877) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (239), (1693), (1736), (1750),
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1876), (1877), (function-axioms) are inconsistent
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #548.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1878) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1878) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1879) all_58_6 = e1 & op(e1, e3) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1879) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1880) op(e1, e3) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (1746), (1880), (function-axioms) are
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1881) all_58_12 = e1 & op(e0, e3) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1881) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1882) all_58_12 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1824), (1882) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1883) e3 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1843), (1883) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1884) all_58_9 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (230), (239),
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (1736), (1741), (1750), (1870), (1875),
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1876), (1884), (function-axioms) are inconsistent
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #811.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1885) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1885) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1886) all_58_11 = e1 & op(e1, e0) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1741), (1886) are inconsistent by sub-proof
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #547.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1887) all_58_15 = e1 & op(e0, e0) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1887) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1888) all_58_15 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (224), (1730), (1824), (1868),
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1888) are inconsistent by sub-proof #544.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1889) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1889) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1890) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (1730), (1824), (1868), (1890) are
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1891) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1891) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1892) all_58_14 = e1 & op(e0, e1) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1892) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1893) op(e0, e1) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1731), (1893), (function-axioms) are
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #967.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1894) all_58_15 = e1 & op(e0, e0) = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1894) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1895) all_58_15 = e1
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1896) all_58_15 = e0 & op(e0, e0) = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1896) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1897) all_58_15 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1895), (1897) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1898) e1 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1898) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1899) e1 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1829), (1899) imply:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1900) all_58_7 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (232), (235),
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (1693), (1706), (1730), (1736), (1741),
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1746), (1843), (1900), (function-axioms) are
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #543.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1901) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1901) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1902) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1903) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1902) gives:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1904) all_58_12 = e0 & op(e0, e3) = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1904) implies:
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1905) all_58_12 = e0
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (157), (227), (1698), (1730),
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1895), (1905), (function-axioms) are inconsistent
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #555.
% 164.64/24.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1906) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1906) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1907) all_58_13 = e0 & op(e0, e2) = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1907) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1908) all_58_13 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1909) op(e0, e2) = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1903) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1910) all_58_9 = e0 & op(e3, e0) = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1910) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1911) all_58_9 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1843), (1911) imply:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1912) e3 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (42), (157), (244), (246),
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (1706), (1750), (1908), (1909), (1912),
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #590.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1913) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1913) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1914) all_58_10 = e0 & op(e2, e0) = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1914) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1915) all_58_10 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1916) op(e2, e0) = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1917) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1917) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1918) all_58_2 = e1 & op(e2, e3) = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1857), (1918) are inconsistent by sub-proof
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #929.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1919) all_58_3 = e1 & op(e2, e2) = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1750), (1919) are inconsistent by sub-proof
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #914.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1920) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1920) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1921) all_58_5 = e1 & op(e2, e1) = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1921) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1922) all_58_5 = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1923) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (166), (403), (1755), (1923),
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #692.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1924) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1924) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1735), (1922) are inconsistent by sub-proof
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #910.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1925) all_58_10 = e3 & op(e2, e0) = e3
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1915), (1925) are inconsistent by sub-proof
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #542.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1926) all_58_10 = e1 & op(e2, e0) = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1926) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1927) op(e2, e0) = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1916), (1927), (function-axioms) are
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #849.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1928) all_58_11 = e0 & op(e1, e0) = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1928) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1929) all_58_11 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1741), (1929) imply:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1930) e2 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1720), (1930) imply:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1931) all_56_12 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (163), (217), (224),
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (1741), (1895), (1931), (function-axioms)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #538.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1932) all_58_14 = e0 & op(e0, e1) = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1932) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1933) all_58_14 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1730), (1933) imply:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1934) e2 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1934) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1935) e2 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1720), (1935) imply:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1936) all_56_12 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (163), (217), (224),
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (1741), (1895), (1936), (function-axioms)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #538.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1937) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1745), (1824), (1937) are inconsistent by
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #536.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1938) all_58_10 = e3 & op(e2, e0) = e3
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1938) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1939) op(e2, e0) = e3
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1757), (1939), (function-axioms) are
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1940) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1940) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1941) all_58_11 = e3 & op(e1, e0) = e3
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (166), (239),
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (242), (403), (1736), (1741), (1750),
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1755), (1941), (function-axioms) are inconsistent
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #535.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1942) all_58_15 = e3 & op(e0, e0) = e3
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1942) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1943) all_58_15 = e3
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1944) all_58_15 = e0 & op(e0, e0) = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1943), (1944) are inconsistent by sub-proof
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #887.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1945) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1945) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1946) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1947) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1947) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1948) all_58_12 = e1 & op(e0, e3) = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1824), (1948) are inconsistent by sub-proof
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #651.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1949) all_58_13 = e1 & op(e0, e2) = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1949) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1950) all_58_13 = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (1730), (1824), (1946), (1950) are
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1951) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (1731), (1943), (1951),
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #534.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1952) all_54_2 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1952) imply:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1953) all_52_8 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1816), (1953) imply:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1954) $false
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1954) is inconsistent.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1955) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1955) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1956) all_58_8 = e1 & op(e1, e1) = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1956) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1957) all_58_8 = e1
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1958) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1958) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1959) all_58_6 = e0 & op(e1, e3) = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1745), (1959) are inconsistent by sub-proof
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #559.
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1960) all_58_7 = e0 & op(e1, e2) = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1960) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1961) all_58_7 = e0
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1962) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1962) gives:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1963) all_58_9 = e3 & op(e3, e0) = e3
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1963) implies:
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1964) all_58_9 = e3
% 164.64/24.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (232), (235),
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (1693), (1706), (1730), (1736), (1741),
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1746), (1961), (1964), (function-axioms) are
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #543.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1965) all_58_10 = e3 & op(e2, e0) = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1965) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1966) op(e2, e0) = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1757), (1966), (function-axioms) are
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1967) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1967) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1968) all_58_11 = e3 & op(e1, e0) = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (166), (239),
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (242), (403), (1736), (1741), (1750),
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1755), (1968), (function-axioms) are inconsistent
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #535.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1969) all_58_15 = e3 & op(e0, e0) = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1969) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1970) all_58_15 = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1971) all_58_15 = e0 & op(e0, e0) = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1971) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1972) all_58_15 = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1970), (1972) are inconsistent by sub-proof
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #860.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1973) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1973) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1974) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1975) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1975) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1976) all_58_1 = e1 & op(e3, e2) = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1706), (1976) are inconsistent by sub-proof
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #711.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1977) all_58_3 = e1 & op(e2, e2) = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1750), (1977) are inconsistent by sub-proof
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #914.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1978) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1978) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1979) all_58_7 = e1 & op(e1, e2) = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1979) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1980) all_58_7 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1961), (1980) are inconsistent by sub-proof
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #710.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1981) all_58_13 = e1 & op(e0, e2) = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1981) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1982) all_58_13 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (1730), (1824), (1974), (1982) are
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1983) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1983) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1984) all_58_8 = e0 & op(e1, e1) = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1984) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1985) all_58_8 = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1957), (1985) are inconsistent by sub-proof
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #818.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1986) all_58_11 = e0 & op(e1, e0) = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1986) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1987) all_58_11 = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1741), (1987) are inconsistent by sub-proof
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #879.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1988) all_58_11 = e1 & op(e1, e0) = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1988) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1989) all_58_11 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1741), (1989) are inconsistent by sub-proof
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #832.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1990) all_58_13 = e3 & op(e0, e2) = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1990) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1991) all_58_13 = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (243), (244), (1706),
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1750), (1991) are inconsistent by sub-proof #707.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1992) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1992) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1993) all_58_14 = e3 & op(e0, e1) = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1993) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1994) all_58_14 = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1730), (1994) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1995) e3 = e2
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (166), (239),
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (242), (403), (1736), (1750), (1755),
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1995), (function-axioms) are inconsistent by
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #560.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1996) all_58_15 = e3 & op(e0, e0) = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1996) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1997) all_58_15 = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1821) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1998) all_54_2 = e2
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (1998) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999) all_52_8 = e2
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1683), (1999) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2000) $false
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2000) is inconsistent.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2001) all_54_2 = e1 | all_54_2 = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2001) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2002) all_54_2 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (2002) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2003) all_52_8 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (2003) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2004) ~ (all_52_12 = e1)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2004) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2005) ~ (all_52_12 = e1)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2006) all_54_3 = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (2006) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2007) all_52_12 = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1702), (2007) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2008) $false
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2008) is inconsistent.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2009) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2009) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2010) all_54_3 = e2
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (2010) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2011) all_52_12 = e2
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1684), (2011) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2012) $false
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2012) is inconsistent.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2013) ~ (all_54_3 = e2)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2014) all_54_3 = e1 | all_54_3 = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2014) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2015) all_54_3 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (2015) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2016) all_52_12 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2005), (2016) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2017) $false
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2017) is inconsistent.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2018) all_54_3 = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (288), (2018) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2019) all_52_12 = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (2019) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2020) ~ (all_52_13 = e0)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2020) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2021) ~ (all_52_13 = e0)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (2019) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2022) ~ (all_4_2 = e0)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2022) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2023) ~ (all_4_2 = e0)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2024) all_54_15 = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (2024) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2025) all_4_2 = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (2025) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2026) all_56_15 = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2027) all_58_15 = e0 & op(e0, e0) = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1997), (2027) are inconsistent by sub-proof
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #887.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2028) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2028) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2029) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2030) ~ (all_56_15 = e3)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2026), (2030) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2031) $false
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2031) is inconsistent.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2032) all_56_6 = e0 & op(e0, e3) = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2032) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2033) op(e0, e3) = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2034) all_54_7 = e3
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (1757), (2034) are inconsistent by
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #533.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2035) ~ (all_54_7 = e3)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2036) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2036) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2037) all_54_7 = e2
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (1724), (2037) are inconsistent by
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #532.
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2038) ~ (all_54_7 = e2)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2039) all_54_7 = e1 | all_54_7 = e0
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2039) gives:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2040) all_54_7 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (2040) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2041) all_52_13 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2041) implies:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2042) all_52_13 = e1
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1757), (2042) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2043) ~ (e3 = e1)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1724), (2042) imply:
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2044) ~ (e2 = e1)
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (2042) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2045) op(e2, e0) = e1
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2046) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2046) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2047) all_58_12 = e1 & op(e0, e3) = e1
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2047) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2048) op(e0, e3) = e1
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2033), (2048), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2049) all_58_13 = e1 & op(e0, e2) = e1
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2049) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2050) all_58_13 = e1
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2051) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (239), (1693), (1736), (1750),
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2045), (2051), (function-axioms) are inconsistent
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #548.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2052) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2052) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2053) all_58_6 = e1 & op(e1, e3) = e1
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2053) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2054) op(e1, e3) = e1
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (1746), (2054), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2055) all_58_12 = e1 & op(e0, e3) = e1
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2055) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2056) all_58_12 = e1
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1730), (2029), (2050), (2056) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #530.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2057) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (1731), (1997), (2057),
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #534.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2058) all_54_7 = e0
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (2021), (2058) are inconsistent by
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #529.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2059) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (307), (398), (1708), (2023), (2059) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #697.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2060) all_54_2 = e0
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (2060) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2061) all_52_8 = e0
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1816), (2061) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2062) $false
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2062) is inconsistent.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | (2063) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2063) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2064) all_58_5 = e2 & op(e2, e1) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2064) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2065) op(e2, e1) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1723), (2065), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #571.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2066) all_58_10 = e2 & op(e2, e0) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2066) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2067) op(e2, e0) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (224), (228),
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (1741), (2067), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #525.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2068) all_58_7 = e3 & op(e1, e2) = e3
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2068) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2069) op(e1, e2) = e3
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1696), (2069), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #668.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | (2070) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2070) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2071) all_58_8 = e3 & op(e1, e1) = e3
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (1710), (2071), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2072) all_58_11 = e3 & op(e1, e0) = e3
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2072) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | (2073) all_58_11 = e3
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1741), (2073) are inconsistent by sub-proof
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | | #892.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | (2074) all_58_15 = e2 & op(e0, e0) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (1708), (2074), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | (2075) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (1710), (1730), (2075),
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | #805.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | (2076) all_54_5 = e1 | all_54_5 = e0
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (283), (400), (1712), (2076) are inconsistent by
% 164.64/24.30 | | | | | | | | | | | | | | | | | sub-proof #735.
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | (2077) all_30_2 = e0
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | COMBINE_EQS: (355), (2077) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | (2078) all_8_2 = e0
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | SIMP: (2078) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | (2079) all_8_2 = e0
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | COMBINE_EQS: (361), (2079) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | (2080) all_56_12 = e0
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | REDUCE: (374), (2079) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | (2081) ~ (all_52_1 = e0)
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | REDUCE: (379), (2079) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | (2082) ~ (all_52_6 = e0)
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | REDUCE: (381), (2079) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | (2083) ~ (all_52_7 = e0)
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | REDUCE: (383), (2079) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | (2084) ~ (all_52_9 = e0)
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | REDUCE: (385), (2079) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | (2085) ~ (all_52_13 = e0)
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | REDUCE: (403), (2079) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | (2086) ~ (e3 = e0)
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | REDUCE: (400), (2079) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | (2087) ~ (e1 = e0)
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 164.64/24.30 | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | (2088) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 164.64/24.30 | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 164.64/24.30 | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | BETA: splitting (2088) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | (2089) all_58_2 = e0 & op(e2, e3) = e0
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2081), (2089), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693.
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | (2090) all_58_3 = e0 & op(e2, e2) = e0
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | ALPHA: (2090) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | (2091) all_58_3 = e0
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | (2092) ~ (all_56_12 = e0)
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | REDUCE: (2080), (2092) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | (2093) $false
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | CLOSE: (2093) is inconsistent.
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | (2094) all_56_11 = e2 & op(e2, e0) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | ALPHA: (2094) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | (2095) all_56_11 = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | (2096) op(e2, e0) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 164.64/24.30 | | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (163), (2096) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | (2097) all_52_13 = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | REDUCE: (116), (2097) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | (2098) ~ (all_52_9 = e2)
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | REDUCE: (396), (2097) imply:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | (2099) ~ (all_4_2 = e2)
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | (2100) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (2100) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | (2101) all_58_4 = e2 & op(e3, e1) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1683), (2101), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #572.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | (2102) all_58_5 = e2 & op(e2, e1) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (42), (240), (242), (403),
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | (2091), (2096), (2102), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #521.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.30 | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | (2103) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (2103) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | (2104) all_58_8 = e2 & op(e1, e1) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (2104), (function-axioms) are
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | (2105) all_58_14 = e2 & op(e0, e1) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (2105) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | (2106) all_58_14 = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | (2107) op(e0, e1) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | (2108) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2108) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | (2109) all_58_6 = e2 & op(e1, e3) = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2109) implies:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | (2110) all_58_6 = e2
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | (2111) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2111) gives:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | (2112) all_58_9 = e2 & op(e3, e0) = e2
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1684), (2112), (function-axioms) are
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #663.
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | (2113) all_58_10 = e2 & op(e2, e0) = e2
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2113) implies:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | (2114) all_58_10 = e2
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | (2115) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2115) gives:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2116) all_58_0 = e0 & op(e3, e3) = e0
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1692), (2116) are inconsistent by sub-proof
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | #705.
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2117) all_58_2 = e0 & op(e2, e3) = e0
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2081), (2117), (function-axioms) are
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693.
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | (2118) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2118) gives:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2119) all_58_6 = e0 & op(e1, e3) = e0
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2110), (2119) are inconsistent by sub-proof
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | #769.
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2120) all_58_12 = e0 & op(e0, e3) = e0
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2120) implies:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2121) all_58_12 = e0
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2122) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2122) gives:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2123) all_58_0 = e1 & op(e3, e3) = e1
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2123) implies:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2124) op(e3, e3) = e1
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1693), (2124), (function-axioms) are
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #957.
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2125) all_58_2 = e1 & op(e2, e3) = e1
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2125) implies:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2126) all_58_2 = e1
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2127) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2127) gives:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2128) all_58_12 = e1 & op(e0, e3) = e1
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2121), (2128) are inconsistent by sub-proof
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #773.
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2129) all_58_13 = e1 & op(e0, e2) = e1
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2129) implies:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2130) all_58_13 = e1
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2131) op(e0, e2) = e1
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2132) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2132) gives:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2133) all_58_1 = e2 & op(e3, e2) = e2
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2133) implies:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2134) op(e3, e2) = e2
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1682), (2134), (function-axioms) are
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #993.
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2135) all_58_3 = e2 & op(e2, e2) = e2
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2135) implies:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2136) all_58_3 = e2
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (239), (240),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (403), (2114), (2126), (2136),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #915.
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2137) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2137) gives:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2138) all_58_7 = e2 & op(e1, e2) = e2
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (39), (42), (99),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (120), (122), (138), (139), (142), (143), (148),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (156), (157), (161), (163), (164), (166), (168),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (191), (193), (195), (201), (209), (210),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (227), (228), (229), (230), (231), (234),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (238), (239), (240), (242), (247),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (252), (253), (262), (265), (274),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276), (289), (305), (313), (375), (376), (388),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (389), (391), (394), (403), (1679), (1682),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1688), (1692), (1693), (1696), (1698), (1700),
% 164.64/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1706), (1710), (2080), (2081), (2082), (2083),
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2084), (2095), (2096), (2098), (2106), (2107),
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2114), (2130), (2131), (2138), (function-axioms)
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #505.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2139) all_58_13 = e2 & op(e0, e2) = e2
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2139) implies:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2140) op(e0, e2) = e2
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2131), (2140), (function-axioms) are
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #968.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2141) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2141) gives:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2142) all_58_14 = e1 & op(e0, e1) = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2142) implies:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2143) op(e0, e1) = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2107), (2143), (function-axioms) are
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #967.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2144) all_58_15 = e1 & op(e0, e0) = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2144) implies:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2145) all_58_15 = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (157), (227), (1698), (2106),
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2121), (2145), (function-axioms) are inconsistent
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #555.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2146) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2146) gives:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2147) all_58_6 = e1 & op(e1, e3) = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2110), (2147) are inconsistent by sub-proof
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #774.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2148) all_58_12 = e1 & op(e0, e3) = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2121), (2148) are inconsistent by sub-proof
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #773.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | (2149) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (163), (224),
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (1708), (2096), (2149),
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | #504.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | (2150) all_58_7 = e2 & op(e1, e2) = e2
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2150) implies:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | (2151) all_58_7 = e2
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | (2152) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2152) gives:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | (2153) all_58_9 = e2 & op(e3, e0) = e2
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1684), (2153), (function-axioms) are
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #663.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | (2154) all_58_10 = e2 & op(e2, e0) = e2
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2154) implies:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | (2155) all_58_10 = e2
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | (2156) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2156) gives:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2157) all_58_1 = e1 & op(e3, e2) = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1706), (2157) are inconsistent by sub-proof
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | #711.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2158) all_58_3 = e1 & op(e2, e2) = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (163), (164), (166), (239), (2081),
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2084), (2096), (2158), (function-axioms) are
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #507.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | (2159) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2159) gives:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2160) all_58_7 = e1 & op(e1, e2) = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2151), (2160) are inconsistent by sub-proof
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | #503.
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2161) all_58_13 = e1 & op(e0, e2) = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2161) implies:
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2162) all_58_13 = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (2163) op(e0, e2) = e1
% 164.91/24.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (39), (42), (99),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (120), (122), (138), (139), (142), (143), (148),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (156), (157), (161), (163), (164), (166), (168),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (191), (193), (195), (201), (209), (210),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (224), (227), (228), (229), (230), (231), (234),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (238), (239), (240), (242), (247),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (250), (252), (253), (262), (265), (274),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (276), (289), (305), (313), (375), (376), (388),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (389), (391), (394), (403), (1679), (1682),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1688), (1692), (1693), (1696), (1698), (1700),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1706), (1710), (2080), (2081), (2082), (2083),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2084), (2095), (2096), (2098), (2106), (2107),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (2150), (2155), (2162), (2163), (function-axioms)
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #505.
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (2164) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (163), (224),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (1708), (2096), (2164),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | #504.
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (2165) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (224),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (228), (230), (399), (2096), (2165),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | #502.
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | (2166) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 164.91/24.32 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 164.91/24.32 | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (164), (217), (2080), (2084), (2166),
% 164.91/24.32 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.32 | | | | | | | | | | | | | | | | #500.
% 164.91/24.32 | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | (2167) all_28_2 = e3
% 164.91/24.32 | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | COMBINE_EQS: (340), (2167) imply:
% 164.91/24.32 | | | | | | | | | | | | | | (2168) all_6_2 = e3
% 164.91/24.32 | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | COMBINE_EQS: (274), (2168) imply:
% 164.91/24.32 | | | | | | | | | | | | | | (2169) all_56_14 = e3
% 164.91/24.32 | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | REDUCE: (375), (2168) imply:
% 164.91/24.32 | | | | | | | | | | | | | | (2170) ~ (all_52_2 = e3)
% 164.91/24.32 | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | REDUCE: (389), (2168) imply:
% 164.91/24.32 | | | | | | | | | | | | | | (2171) ~ (all_52_9 = e3)
% 164.91/24.32 | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | REDUCE: (391), (2168) imply:
% 164.91/24.32 | | | | | | | | | | | | | | (2172) ~ (all_52_11 = e3)
% 164.91/24.32 | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 164.91/24.32 | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | (2173) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 164.91/24.32 | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 164.91/24.32 | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (1700), (2171), (2173),
% 164.91/24.32 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.32 | | | | | | | | | | | | | | | #499.
% 164.91/24.32 | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | (2174) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 164.91/24.32 | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 164.91/24.32 | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | BETA: splitting (2174) gives:
% 164.91/24.32 | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | (2175) all_58_8 = e3 & op(e1, e1) = e3
% 164.91/24.32 | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | ALPHA: (2175) implies:
% 164.91/24.32 | | | | | | | | | | | | | | | | (2176) all_58_8 = e3
% 164.91/24.32 | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 164.91/24.32 | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | (2177) ~ (all_56_14 = e3)
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | REDUCE: (2169), (2177) imply:
% 164.91/24.32 | | | | | | | | | | | | | | | | | (2178) $false
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | CLOSE: (2178) is inconsistent.
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | (2179) all_56_2 = e1 & op(e1, e3) = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | ALPHA: (2179) implies:
% 164.91/24.32 | | | | | | | | | | | | | | | | | (2180) all_56_2 = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | (2181) op(e1, e3) = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 164.91/24.32 | | | | | | | | | | | | | | | | | e3, e1, simplifying with (162), (2181) gives:
% 164.91/24.32 | | | | | | | | | | | | | | | | | (2182) all_52_2 = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | REDUCE: (148), (2182) imply:
% 164.91/24.32 | | | | | | | | | | | | | | | | | (2183) ~ (all_52_1 = e1)
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | REDUCE: (2170), (2182) imply:
% 164.91/24.32 | | | | | | | | | | | | | | | | | (2184) ~ (e3 = e1)
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | REDUCE: (1681), (2182) imply:
% 164.91/24.32 | | | | | | | | | | | | | | | | | (2185) ~ (e2 = e1)
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 164.91/24.32 | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | (2186) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 164.91/24.32 | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | BETA: splitting (2186) gives:
% 164.91/24.32 | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | (2187) all_58_1 = e1 & op(e3, e2) = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1706), (2187) are inconsistent by sub-proof
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | #711.
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | (2188) all_58_3 = e1 & op(e2, e2) = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (400), (2188), (function-axioms) are
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498.
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | (2189) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 164.91/24.32 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.91/24.32 | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | BETA: splitting (2189) gives:
% 164.91/24.32 | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | (2190) all_58_7 = e1 & op(e1, e2) = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | (162), (163), (164), (167), (224), (228), (229),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | (230), (231), (233), (242), (247), (249), (253),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | (399), (403), (1684), (1692), (1693), (1708),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | (2171), (2176), (2181), (2190), (function-axioms)
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #489.
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | (2191) all_58_13 = e1 & op(e0, e2) = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | ALPHA: (2191) implies:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | (2192) all_58_13 = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | (2193) op(e0, e2) = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | (2194) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2194) gives:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (2195) all_58_12 = e2 & op(e0, e3) = e2
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2195) implies:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (2196) all_58_12 = e2
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (247), (249),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (253), (1692), (1693), (2181), (2196),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | #486.
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (2197) all_58_13 = e2 & op(e0, e2) = e2
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2197) implies:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (2198) op(e0, e2) = e2
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2193), (2198), (function-axioms) are
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #968.
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | (2199) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2199) gives:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (2200) all_58_14 = e2 & op(e0, e1) = e2
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2200) implies:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (2201) all_58_14 = e2
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | (2202) op(e0, e1) = e2
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | (2203) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2203) gives:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (2204) all_58_6 = e1 & op(e1, e3) = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2204) implies:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (2205) all_58_6 = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (76), (124), (138), (139), (147),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (156), (157), (161), (162), (163), (164), (166),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (169), (188), (191), (198), (199), (209), (210),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (213), (217), (227), (230), (231), (232), (233),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (234), (239), (245), (247), (248), (250), (262),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (265), (283), (287), (307), (355), (361), (374),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (376), (379), (381), (383), (387), (394), (399),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (403), (1679), (1680), (1682), (1688), (1692),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (1693), (1698), (1706), (2169), (2172), (2176),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (2180), (2181), (2183), (2193), (2201), (2202),
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (2205), (function-axioms) are inconsistent by
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #472.
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | | (2206) all_58_7 = e1 & op(e1, e2) = e1
% 164.91/24.32 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (42),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | (162), (163), (164), (167), (224), (228), (229),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | (230), (231), (233), (242), (247), (249), (253),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | (399), (403), (1684), (1692), (1693), (1708),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | (2171), (2176), (2181), (2206), (function-axioms)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #489.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | (2207) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2207) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | (2208) all_58_8 = e1 & op(e1, e1) = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2176), (2208) are inconsistent by sub-proof
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | #478.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | (2209) all_58_11 = e1 & op(e1, e0) = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2209) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | (2210) all_58_11 = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | (2211) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2211) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2212) all_58_6 = e0 & op(e1, e3) = e0
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2212) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2213) op(e1, e3) = e0
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (2181), (2213), (function-axioms) are
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2214) all_58_7 = e0 & op(e1, e2) = e0
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2214) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2215) all_58_7 = e0
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2216) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2216) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2217) all_58_1 = e2 & op(e3, e2) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2217) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2218) op(e3, e2) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1682), (2218), (function-axioms) are
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #993.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2219) all_58_3 = e2 & op(e2, e2) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2219) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2220) all_58_3 = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2221) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2221) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2222) all_58_0 = e1 & op(e3, e3) = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2222) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2223) op(e3, e3) = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1693), (2223), (function-axioms) are
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #957.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2224) all_58_2 = e1 & op(e2, e3) = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2224) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2225) all_58_2 = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2226) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2226) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2227) all_58_9 = e2 & op(e3, e0) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1684), (2227), (function-axioms) are
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #663.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2228) all_58_10 = e2 & op(e2, e0) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2228) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2229) all_58_10 = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (239), (240),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (403), (2220), (2225), (2229),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #915.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2230) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2230) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2231) all_58_11 = e2 & op(e1, e0) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2210), (2231) are inconsistent by sub-proof
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #471.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2232) all_58_15 = e2 & op(e0, e0) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (1708), (2232), (function-axioms) are
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2233) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2233) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2234) all_58_6 = e1 & op(e1, e3) = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2234) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2235) all_58_6 = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (39), (76), (124), (138), (139), (147),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (156), (157), (161), (162), (163), (164), (166),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (188), (191), (198), (199), (209), (210),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (217), (227), (230), (231), (232), (233),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (239), (245), (247), (248), (250), (262),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265), (283), (287), (307), (355), (361), (374),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (376), (379), (381), (383), (387), (394), (399),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (1679), (1680), (1682), (1688), (1692),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1693), (1698), (1706), (2169), (2172), (2176),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2180), (2181), (2183), (2193), (2201), (2202),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2235), (function-axioms) are inconsistent by
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #472.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2236) all_58_12 = e1 & op(e0, e3) = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2236) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2237) all_58_12 = e1
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2238) all_58_15 = e0 & op(e0, e0) = e0
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2238) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2239) all_58_15 = e0
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (156), (157), (227), (1698), (2172),
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2237), (2239), (function-axioms) are inconsistent
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #469.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2240) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2240) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2241) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (2192), (2201), (2237), (2241) are
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #530.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (2242) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2242) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2243) all_58_7 = e2 & op(e1, e2) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2215), (2243) are inconsistent by sub-proof
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | #468.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2244) all_58_13 = e2 & op(e0, e2) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2244) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2245) op(e0, e2) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2193), (2245), (function-axioms) are
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #968.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | (2246) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2246) gives:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2247) all_58_8 = e0 & op(e1, e1) = e0
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2247) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2248) all_58_8 = e0
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2176), (2248) are inconsistent by sub-proof
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | #480.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | (2249) all_58_11 = e0 & op(e1, e0) = e0
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2210), (2249) are inconsistent by sub-proof
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | | #513.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | (2250) all_58_15 = e2 & op(e0, e0) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (1708), (2250), (function-axioms) are
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | (2251) all_58_14 = e3 & op(e0, e1) = e3
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | REF_CLOSE: (156), (2172), (2251), (function-axioms) are
% 164.91/24.33 | | | | | | | | | | | | | | | | inconsistent by sub-proof #960.
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | (2252) all_20_2 = e2
% 164.91/24.33 | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | COMBINE_EQS: (349), (2252) imply:
% 164.91/24.33 | | | | | | | | | | | | | (2253) all_4_2 = e2
% 164.91/24.33 | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | SIMP: (2253) implies:
% 164.91/24.33 | | | | | | | | | | | | | (2254) all_4_2 = e2
% 164.91/24.33 | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | COMBINE_EQS: (262), (2254) imply:
% 164.91/24.33 | | | | | | | | | | | | | (2255) all_56_15 = e2
% 164.91/24.33 | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | REDUCE: (396), (2254) imply:
% 164.91/24.33 | | | | | | | | | | | | | (2256) ~ (all_52_13 = e2)
% 164.91/24.33 | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | REDUCE: (397), (2254) imply:
% 164.91/24.33 | | | | | | | | | | | | | (2257) ~ (all_52_14 = e2)
% 164.91/24.33 | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | BETA: splitting (212) gives:
% 164.91/24.33 | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | (2258) ~ (all_56_15 = e2)
% 164.91/24.33 | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | REDUCE: (2255), (2258) imply:
% 164.91/24.33 | | | | | | | | | | | | | | (2259) $false
% 164.91/24.33 | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | CLOSE: (2259) is inconsistent.
% 164.91/24.33 | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | (2260) all_56_7 = e0 & op(e0, e2) = e0
% 164.91/24.33 | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | ALPHA: (2260) implies:
% 164.91/24.33 | | | | | | | | | | | | | | (2261) op(e0, e2) = e0
% 164.91/24.33 | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 164.91/24.33 | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | (2262) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 164.91/24.33 | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 164.91/24.33 | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | BETA: splitting (2262) gives:
% 164.91/24.33 | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | Case 1:
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | (2263) all_58_4 = e2 & op(e3, e1) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1683), (2263), (function-axioms) are
% 164.91/24.33 | | | | | | | | | | | | | | | | inconsistent by sub-proof #572.
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | Case 2:
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | (2264) all_58_5 = e2 & op(e2, e1) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | ALPHA: (2264) implies:
% 164.91/24.33 | | | | | | | | | | | | | | | | (2265) op(e2, e1) = e2
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (198), (217), (283), (361), (383),
% 164.91/24.33 | | | | | | | | | | | | | | | | (400), (403), (2256), (2265), (function-axioms)
% 164.91/24.33 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #466.
% 164.91/24.33 | | | | | | | | | | | | | | | |
% 164.91/24.33 | | | | | | | | | | | | | | | End of split
% 164.91/24.33 | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | (2266) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 164.91/24.34 | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 164.91/24.34 | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | BETA: splitting (2266) gives:
% 164.91/24.34 | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | (2267) all_58_8 = e2 & op(e1, e1) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (2267), (function-axioms) are
% 164.91/24.34 | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 164.91/24.34 | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | (2268) all_58_14 = e2 & op(e0, e1) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | ALPHA: (2268) implies:
% 164.91/24.34 | | | | | | | | | | | | | | | | (2269) all_58_14 = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | (2270) op(e0, e1) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | (2271) ~ (all_56_12 = e0)
% 164.91/24.34 | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | REDUCE: (361), (2271) imply:
% 164.91/24.34 | | | | | | | | | | | | | | | | | (2272) ~ (all_8_2 = e0)
% 164.91/24.34 | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | (2273) all_54_5 = e3
% 164.91/24.34 | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | REF_CLOSE: (283), (403), (2273) are inconsistent by sub-proof
% 164.91/24.34 | | | | | | | | | | | | | | | | | | #667.
% 164.91/24.34 | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | (2274) ~ (all_54_5 = e3)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | (2275) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 164.91/24.34 | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | BETA: splitting (2275) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | (2276) all_54_5 = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (2276) imply:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | (2277) all_8_2 = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | SIMP: (2277) implies:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | (2278) all_8_2 = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | REDUCE: (379), (2278) imply:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | (2279) ~ (all_52_6 = e2)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | REDUCE: (381), (2278) imply:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | (2280) ~ (all_52_7 = e2)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | REDUCE: (383), (2278) imply:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | (2281) ~ (all_52_9 = e2)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | REDUCE: (403), (2278) imply:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | (2282) ~ (e3 = e2)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | (2283) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2283) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | (2284) all_58_2 = e2 & op(e2, e3) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (161), (166),
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | (169), (239), (240), (242), (245), (1682), (2279),
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | (2280), (2284), (function-axioms) are inconsistent
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | by sub-proof #664.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | (2285) all_58_3 = e2 & op(e2, e2) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2285) implies:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | (2286) all_58_3 = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | (2287) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (167), (239),
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | (240), (241), (242), (403), (1684), (2286),
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | (2287), (function-axioms) are inconsistent by
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | sub-proof #465.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | (2288) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2288) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | (2289) all_58_11 = e2 & op(e1, e0) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2257), (2289), (function-axioms) are
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | (2290) all_58_15 = e2 & op(e0, e0) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2290) implies:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | (2291) all_58_15 = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | (2292) op(e0, e0) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | (2293) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2293) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | (2294) all_58_12 = e3 & op(e0, e3) = e3
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2294) implies:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | (2295) all_58_12 = e3
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (2296) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (157), (2261), (2295), (2296),
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | | #630.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (2297) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2270), (2292), (2297), (function-axioms) are
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #629.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | (2298) all_58_13 = e3 & op(e0, e2) = e3
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2298) implies:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | (2299) all_58_13 = e3
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (243), (244), (1706),
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | (2286), (2299) are inconsistent by sub-proof #707.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | (2300) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2300) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | (2301) all_58_14 = e3 & op(e0, e1) = e3
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2301) implies:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | (2302) all_58_14 = e3
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2269), (2302) are inconsistent by sub-proof
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | #855.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | (2303) all_58_15 = e3 & op(e0, e0) = e3
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2291), (2303) are inconsistent by sub-proof
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | | #464.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | (2304) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2304) gives:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | (2305) all_58_5 = e2 & op(e2, e1) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2305) implies:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | (2306) op(e2, e1) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2281), (2306), (function-axioms) are
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #571.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | (2307) all_58_10 = e2 & op(e2, e0) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2307) implies:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | (2308) op(e2, e0) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2256), (2308), (function-axioms) are
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | (2309) all_54_5 = e1 | all_54_5 = e0
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (283), (400), (2272), (2309) are inconsistent by
% 164.91/24.34 | | | | | | | | | | | | | | | | | | | sub-proof #735.
% 164.91/24.34 | | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | (2310) all_56_11 = e2 & op(e2, e0) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | ALPHA: (2310) implies:
% 164.91/24.34 | | | | | | | | | | | | | | | | | (2311) op(e2, e0) = e2
% 164.91/24.34 | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2256), (2311), (function-axioms) are
% 164.91/24.34 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 164.91/24.34 | | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | (2312) all_58_3 = e3 & op(e2, e2) = e3
% 164.91/24.34 | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | | REF_CLOSE: (42), (403), (2312), (function-axioms) are
% 164.91/24.34 | | | | | | | | | | | | inconsistent by sub-proof #973.
% 164.91/24.34 | | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | (2313) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 164.91/24.34 | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 164.91/24.34 | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | | REF_CLOSE: (157), (161), (1696), (1698), (2313),
% 164.91/24.34 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.34 | | | | | | | | | | | #463.
% 164.91/24.34 | | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | (2314) all_58_1 = e2 & op(e3, e2) = e2
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | ALPHA: (2314) implies:
% 164.91/24.34 | | | | | | | | | | (2315) op(e3, e2) = e2
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | REF_CLOSE: (169), (1682), (2315), (function-axioms) are
% 164.91/24.34 | | | | | | | | | | inconsistent by sub-proof #993.
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | |
% 164.91/24.34 | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | |
% 164.91/24.34 | | | | | | | | | (2316) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 &
% 164.91/24.34 | | | | | | | | | op(e3, e0) = e2)
% 164.91/24.34 | | | | | | | | |
% 164.91/24.34 | | | | | | | | | BETA: splitting (2316) gives:
% 164.91/24.34 | | | | | | | | |
% 164.91/24.34 | | | | | | | | | Case 1:
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | (2317) all_58_4 = e2 & op(e3, e1) = e2
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | REF_CLOSE: (168), (1683), (2317), (function-axioms) are
% 164.91/24.34 | | | | | | | | | | inconsistent by sub-proof #572.
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | Case 2:
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | (2318) all_58_9 = e2 & op(e3, e0) = e2
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | | REF_CLOSE: (167), (1684), (2318), (function-axioms) are
% 164.91/24.34 | | | | | | | | | | inconsistent by sub-proof #663.
% 164.91/24.34 | | | | | | | | | |
% 164.91/24.34 | | | | | | | | | End of split
% 164.91/24.34 | | | | | | | | |
% 164.91/24.34 | | | | | | | | End of split
% 164.91/24.34 | | | | | | | |
% 164.91/24.34 | | | | | | | End of split
% 164.91/24.34 | | | | | | |
% 164.91/24.34 | | | | | | End of split
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | Case 2:
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | (2319) all_14_2 = e3
% 164.91/24.34 | | | | | | (2320) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3,
% 164.91/24.34 | | | | | | e2) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 164.91/24.34 | | | | | | (all_14_1 = e1) & op(e3, e2) = all_14_1 & $i(all_14_1))
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | COMBINE_EQS: (352), (2319) imply:
% 164.91/24.34 | | | | | | (2321) all_8_2 = e3
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | COMBINE_EQS: (334), (2321) imply:
% 164.91/24.34 | | | | | | (2322) all_22_2 = e3
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | COMBINE_EQS: (361), (2321) imply:
% 164.91/24.34 | | | | | | (2323) all_56_12 = e3
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | REDUCE: (374), (2321) imply:
% 164.91/24.34 | | | | | | (2324) ~ (all_52_1 = e3)
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | REDUCE: (377), (2321) imply:
% 164.91/24.34 | | | | | | (2325) ~ (all_52_4 = e3)
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | REDUCE: (379), (2321) imply:
% 164.91/24.34 | | | | | | (2326) ~ (all_52_6 = e3)
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | REDUCE: (381), (2321) imply:
% 164.91/24.34 | | | | | | (2327) ~ (all_52_7 = e3)
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | REDUCE: (383), (2321) imply:
% 164.91/24.34 | | | | | | (2328) ~ (all_52_9 = e3)
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | REDUCE: (385), (2321) imply:
% 164.91/24.34 | | | | | | (2329) ~ (all_52_13 = e3)
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | BETA: splitting (219) gives:
% 164.91/24.34 | | | | | |
% 164.91/24.34 | | | | | | Case 1:
% 164.91/24.34 | | | | | | |
% 164.91/24.34 | | | | | | | (2330) ~ (all_56_12 = e3)
% 164.91/24.34 | | | | | | |
% 164.91/24.34 | | | | | | | REDUCE: (2323), (2330) imply:
% 164.91/24.34 | | | | | | | (2331) $false
% 164.91/24.34 | | | | | | |
% 164.91/24.34 | | | | | | | CLOSE: (2331) is inconsistent.
% 164.91/24.34 | | | | | | |
% 164.91/24.34 | | | | | | Case 2:
% 164.91/24.34 | | | | | | |
% 164.91/24.34 | | | | | | | (2332) all_56_0 = e2 & op(e2, e3) = e2
% 164.91/24.34 | | | | | | |
% 164.91/24.34 | | | | | | | ALPHA: (2332) implies:
% 164.91/24.35 | | | | | | | (2333) all_56_0 = e2
% 164.91/24.35 | | | | | | | (2334) op(e2, e3) = e2
% 164.91/24.35 | | | | | | |
% 164.91/24.35 | | | | | | | BETA: splitting (242) gives:
% 164.91/24.35 | | | | | | |
% 164.91/24.35 | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | |
% 164.91/24.35 | | | | | | | | (2335) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 &
% 164.91/24.35 | | | | | | | | op(e2, e2) = e3)
% 164.91/24.35 | | | | | | | |
% 164.91/24.35 | | | | | | | | BETA: splitting (2335) gives:
% 164.91/24.35 | | | | | | | |
% 164.91/24.35 | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | (2336) all_58_2 = e3 & op(e2, e3) = e3
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | ALPHA: (2336) implies:
% 164.91/24.35 | | | | | | | | | (2337) op(e2, e3) = e3
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | REF_CLOSE: (9), (166), (2334), (2337), (function-axioms) are
% 164.91/24.35 | | | | | | | | | inconsistent by sub-proof #462.
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | (2338) all_58_3 = e3 & op(e2, e2) = e3
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | ALPHA: (2338) implies:
% 164.91/24.35 | | | | | | | | | (2339) all_58_3 = e3
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 164.91/24.35 | | | | | | | | | e3, e2, simplifying with (166), (2334) gives:
% 164.91/24.35 | | | | | | | | | (2340) all_52_1 = e2
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | REDUCE: (148), (2340) imply:
% 164.91/24.35 | | | | | | | | | (2341) ~ (all_52_2 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | SIMP: (2341) implies:
% 164.91/24.35 | | | | | | | | | (2342) ~ (all_52_2 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | REDUCE: (147), (2340) imply:
% 164.91/24.35 | | | | | | | | | (2343) ~ (all_52_3 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | SIMP: (2343) implies:
% 164.91/24.35 | | | | | | | | | (2344) ~ (all_52_3 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | REDUCE: (145), (2340) imply:
% 164.91/24.35 | | | | | | | | | (2345) ~ (all_52_9 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | SIMP: (2345) implies:
% 164.91/24.35 | | | | | | | | | (2346) ~ (all_52_9 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | REDUCE: (144), (2340) imply:
% 164.91/24.35 | | | | | | | | | (2347) ~ (all_52_13 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | SIMP: (2347) implies:
% 164.91/24.35 | | | | | | | | | (2348) ~ (all_52_13 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | REDUCE: (363), (2340) imply:
% 164.91/24.35 | | | | | | | | | (2349) ~ (all_10_2 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | SIMP: (2349) implies:
% 164.91/24.35 | | | | | | | | | (2350) ~ (all_10_2 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | REDUCE: (2324), (2340) imply:
% 164.91/24.35 | | | | | | | | | (2351) ~ (e3 = e2)
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | BETA: splitting (241) gives:
% 164.91/24.35 | | | | | | | | |
% 164.91/24.35 | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | (2352) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 164.91/24.35 | | | | | | | | | | & op(e2, e2) = e2)
% 164.91/24.35 | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | BETA: splitting (2352) gives:
% 164.91/24.35 | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | (2353) all_58_2 = e2 & op(e2, e3) = e2
% 164.91/24.35 | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | ALPHA: (2353) implies:
% 164.91/24.35 | | | | | | | | | | | (2354) all_58_2 = e2
% 164.91/24.35 | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | BETA: splitting (64) gives:
% 164.91/24.35 | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | (2355) ~ (all_22_2 = e3)
% 164.91/24.35 | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | REDUCE: (2322), (2355) imply:
% 164.91/24.35 | | | | | | | | | | | | (2356) $false
% 164.91/24.35 | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | CLOSE: (2356) is inconsistent.
% 164.91/24.35 | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | (2357) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0
% 164.91/24.35 | | | | | | | | | | | | & op(e3, e2) = all_22_1 & $i(all_22_0) &
% 164.91/24.35 | | | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2)
% 164.91/24.35 | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 164.91/24.35 | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | BETA: splitting (61) gives:
% 164.91/24.35 | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | (2358) ~ (all_20_2 = e2)
% 164.91/24.35 | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | REDUCE: (349), (2358) imply:
% 164.91/24.35 | | | | | | | | | | | | | (2359) ~ (all_4_2 = e2)
% 164.91/24.35 | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | BETA: splitting (73) gives:
% 164.91/24.35 | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | (2360) ~ (all_28_2 = e3)
% 164.91/24.35 | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | REDUCE: (340), (2360) imply:
% 164.91/24.35 | | | | | | | | | | | | | | (2361) ~ (all_6_2 = e3)
% 164.91/24.35 | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 164.91/24.35 | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | (2362) ~ (all_32_2 = e1)
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | REDUCE: (356), (2362) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | (2363) ~ (all_10_2 = e1)
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | (2364) all_54_0 = e3
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (2364) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | | (2365) all_10_2 = e3
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | REDUCE: (371), (2365) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | | (2366) ~ (all_52_8 = e3)
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | REDUCE: (45), (2365) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | | (2367) op(e3, e3) = e3
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | (2368) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (2328), (2366), (2368),
% 164.91/24.35 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.35 | | | | | | | | | | | | | | | | | #499.
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | (2369) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 164.91/24.35 | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | BETA: splitting (2369) gives:
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2370) all_58_8 = e3 & op(e1, e1) = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (2361), (2370), (function-axioms) are
% 164.91/24.35 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2371) all_58_14 = e3 & op(e0, e1) = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | ALPHA: (2371) implies:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2372) all_58_14 = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (161),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (166), (169), (224), (225), (226), (229), (234),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (235), (236), (237), (239), (240), (242), (243),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (244), (247), (248), (249), (250), (253), (254),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (399), (2320), (2325), (2334), (2339), (2354),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2357), (2359), (2367), (2372), (function-axioms)
% 164.91/24.35 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #410.
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | End of split
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | End of split
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | (2373) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | REF_CLOSE: (300), (401), (2350), (2363), (2373) are
% 164.91/24.35 | | | | | | | | | | | | | | | | inconsistent by sub-proof #958.
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | End of split
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | (2374) all_32_2 = e1
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | COMBINE_EQS: (356), (2374) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | (2375) all_10_2 = e1
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | SIMP: (2375) implies:
% 164.91/24.35 | | | | | | | | | | | | | | | (2376) all_10_2 = e1
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | COMBINE_EQS: (298), (2376) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | (2377) all_56_10 = e1
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | REDUCE: (369), (2376) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | (2378) ~ (all_52_4 = e1)
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | REDUCE: (371), (2376) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | (2379) ~ (all_52_8 = e1)
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | REDUCE: (2350), (2376) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | (2380) ~ (e2 = e1)
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | REDUCE: (45), (2376) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | (2381) op(e3, e3) = e1
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 164.91/24.35 | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | (2382) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 164.91/24.35 | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | BETA: splitting (2382) gives:
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | (2383) all_58_0 = e1 & op(e3, e3) = e1
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | ALPHA: (2383) implies:
% 164.91/24.35 | | | | | | | | | | | | | | | | | (2384) all_58_0 = e1
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2385) ~ (all_56_10 = e1)
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | REDUCE: (2377), (2385) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2386) $false
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | CLOSE: (2386) is inconsistent.
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2387) all_56_4 = e3 & op(e3, e1) = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | ALPHA: (2387) implies:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2388) all_56_4 = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2389) op(e3, e1) = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (122), (133),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (157), (161), (163), (164), (166), (168), (169),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (188), (197), (209), (210), (213), (224), (225),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (226), (227), (228), (229), (230), (231), (233),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (234), (235), (236), (237), (238), (239), (240),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (242), (243), (244), (247), (248), (249), (250),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (252), (253), (254), (262), (274), (278), (307),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (388), (389), (398), (399), (2320), (2323),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2327), (2329), (2333), (2334), (2339), (2346),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2354), (2357), (2359), (2377), (2379), (2381),
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2384), (2388), (2389), (function-axioms) are
% 164.91/24.35 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #345.
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | End of split
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | (2390) all_58_1 = e1 & op(e3, e2) = e1
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2378), (2390), (function-axioms) are
% 164.91/24.35 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #863.
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | End of split
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | (2391) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 164.91/24.35 | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | BETA: splitting (2391) gives:
% 164.91/24.35 | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | (2392) all_58_4 = e1 & op(e3, e1) = e1
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | ALPHA: (2392) implies:
% 164.91/24.35 | | | | | | | | | | | | | | | | | (2393) all_58_4 = e1
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (164), (166),
% 164.91/24.35 | | | | | | | | | | | | | | | | | (237), (238), (239), (240), (242), (399), (2328),
% 164.91/24.35 | | | | | | | | | | | | | | | | | (2334), (2339), (2354), (2361), (2393),
% 164.91/24.35 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.35 | | | | | | | | | | | | | | | | | #407.
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | (2394) all_58_9 = e1 & op(e3, e0) = e1
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | ALPHA: (2394) implies:
% 164.91/24.35 | | | | | | | | | | | | | | | | | (2395) all_58_9 = e1
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 164.91/24.35 | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2396) ~ (all_56_10 = e1)
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | REDUCE: (2377), (2396) imply:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2397) $false
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | CLOSE: (2397) is inconsistent.
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2398) all_56_4 = e3 & op(e3, e1) = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | ALPHA: (2398) implies:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2399) all_56_4 = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | | (2400) op(e3, e1) = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 164.91/24.35 | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | (2401) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 164.91/24.35 | | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (2401) gives:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | | (2402) all_58_6 = e3 & op(e1, e3) = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | | ALPHA: (2402) implies:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | | (2403) all_58_6 = e3
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.35 | | | | | | | | | | | | | | | | | | | | | (2404) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2404) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2405) all_58_0 = e1 & op(e3, e3) = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2405) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2406) all_58_0 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (39), (122), (133),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (157), (161), (163), (164), (166), (168), (169),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (188), (197), (209), (210), (213), (224), (225),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (226), (227), (228), (229), (230), (231), (233),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (234), (235), (236), (237), (238), (239), (240),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (242), (243), (244), (247), (248), (249), (250),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (252), (253), (254), (262), (274), (278), (307),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (388), (389), (398), (399), (2320), (2323),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2327), (2329), (2333), (2334), (2339), (2346),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2354), (2357), (2359), (2377), (2379), (2381),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2399), (2400), (2406), (function-axioms) are
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #345.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2407) all_58_2 = e1 & op(e2, e3) = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2407) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2408) op(e2, e3) = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (2334), (2408), (function-axioms) are
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #784.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | (2409) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2409) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2410) all_58_6 = e1 & op(e1, e3) = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2410) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2411) all_58_6 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2403), (2411) are inconsistent by sub-proof
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | #476.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2412) all_58_12 = e1 & op(e0, e3) = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2412) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2413) all_58_12 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | (2414) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (166), (2334), (2381), (2414),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | #371.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | (2415) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2415) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | (2416) all_58_6 = e0 & op(e1, e3) = e0
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2403), (2416) are inconsistent by sub-proof
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | #559.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | (2417) all_58_12 = e0 & op(e0, e3) = e0
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2413), (2417) are inconsistent by sub-proof
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | #859.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | (2418) all_58_7 = e3 & op(e1, e2) = e3
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | ALPHA: (2418) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | (2419) all_58_7 = e3
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | (2420) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2420) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2421) all_58_1 = e1 & op(e3, e2) = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2421) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2422) all_58_1 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | (2423) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (166), (169),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (243), (244), (247), (249),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | (253), (2320), (2334), (2339), (2354), (2357),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | (2419), (2423), (function-axioms) are inconsistent
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #424.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | (2424) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2424) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | (2425) all_58_14 = e2 & op(e0, e1) = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2425) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | (2426) all_58_14 = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | (2427) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2427) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2428) all_58_1 = e2 & op(e3, e2) = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2428) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2429) all_58_1 = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2422), (2429) imply:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2430) e2 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2430) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2431) e2 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2426), (2431) imply:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2432) all_58_14 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2433) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2433) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2434) all_58_4 = e2 & op(e3, e1) = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2434) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2435) all_58_4 = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (161),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (166), (169), (226), (238), (239), (240),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (243), (244), (247), (249), (253), (2320),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2328), (2334), (2339), (2354), (2357), (2359),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2361), (2419), (2435), (function-axioms) are
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #346.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2436) all_58_5 = e2 & op(e2, e1) = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2334), (2339), (2436), (function-axioms) are
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #412.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2437) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2437) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2438) all_58_8 = e2 & op(e1, e1) = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (2438), (function-axioms) are
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (2431) imply:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2439) $false
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2439) is inconsistent.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2440) all_58_3 = e2 & op(e2, e2) = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2440) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2441) all_58_3 = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (2334), (2354), (2441), (function-axioms)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #779.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | (2442) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2442) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2443) all_58_7 = e2 & op(e1, e2) = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2443) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2444) all_58_7 = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2419), (2444),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | #399.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2445) all_58_13 = e2 & op(e0, e2) = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (161), (169), (243), (244),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (2320), (2339), (2357), (2419), (2445),
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | | #425.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | (2446) all_58_15 = e2 & op(e0, e0) = e2
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (2359), (2446), (function-axioms) are
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2447) all_58_3 = e1 & op(e2, e2) = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2339), (2447) are inconsistent by sub-proof
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | #868.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | (2448) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2448) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2449) all_58_7 = e1 & op(e1, e2) = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2449) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2450) all_58_7 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2419), (2450) are inconsistent by sub-proof
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | #821.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2451) all_58_13 = e1 & op(e0, e2) = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2451) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2452) all_58_13 = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | (2453) op(e0, e2) = e1
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | (2454) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2454) gives:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | (2455) all_58_1 = e0 & op(e3, e2) = e0
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2455) implies:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | (2456) op(e3, e2) = e0
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2357), (2453), (2456), (function-axioms) are
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #443.
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | | (2457) all_58_3 = e0 & op(e2, e2) = e0
% 164.91/24.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2339), (2457) are inconsistent by sub-proof
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | #427.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | (2458) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2458) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | (2459) all_58_7 = e0 & op(e1, e2) = e0
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2459) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | (2460) all_58_7 = e0
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2419), (2460) are inconsistent by sub-proof
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | #748.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | (2461) all_58_13 = e0 & op(e0, e2) = e0
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2452), (2461) are inconsistent by sub-proof
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | #582.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2462) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (2462) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | (2463) all_58_8 = e3 & op(e1, e1) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (2361), (2463), (function-axioms) are
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | (2464) all_58_11 = e3 & op(e1, e0) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | ALPHA: (2464) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | (2465) all_58_11 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (166), (229),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (2334), (2339), (2354),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | (2359), (2395), (2465), (function-axioms) are
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #381.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | (2466) all_28_2 = e3
% 164.91/24.37 | | | | | | | | | | | | | | (2467) ( ~ (all_28_0 = e0) & op(all_28_1, e1) = all_28_0
% 164.91/24.37 | | | | | | | | | | | | | | & op(e3, e1) = all_28_1 & $i(all_28_0) &
% 164.91/24.37 | | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e3, e1)
% 164.91/24.37 | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | COMBINE_EQS: (340), (2466) imply:
% 164.91/24.37 | | | | | | | | | | | | | | (2468) all_6_2 = e3
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | COMBINE_EQS: (336), (2468) imply:
% 164.91/24.37 | | | | | | | | | | | | | | (2469) all_36_2 = e3
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | COMBINE_EQS: (274), (2468) imply:
% 164.91/24.37 | | | | | | | | | | | | | | (2470) all_56_14 = e3
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | REDUCE: (375), (2468) imply:
% 164.91/24.37 | | | | | | | | | | | | | | (2471) ~ (all_52_2 = e3)
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | REDUCE: (388), (2468) imply:
% 164.91/24.37 | | | | | | | | | | | | | | (2472) ~ (all_52_8 = e3)
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | REDUCE: (393), (2468) imply:
% 164.91/24.37 | | | | | | | | | | | | | | (2473) ~ (all_52_14 = e3)
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | REDUCE: (39), (2468) imply:
% 164.91/24.37 | | | | | | | | | | | | | | (2474) op(e1, e1) = e3
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 164.91/24.37 | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | (2475) ~ (all_56_14 = e3)
% 164.91/24.37 | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | REDUCE: (2470), (2475) imply:
% 164.91/24.37 | | | | | | | | | | | | | | | (2476) $false
% 164.91/24.37 | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | CLOSE: (2476) is inconsistent.
% 164.91/24.37 | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | (2477) all_56_2 = e1 & op(e1, e3) = e1
% 164.91/24.37 | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | ALPHA: (2477) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | (2478) all_56_2 = e1
% 164.91/24.37 | | | | | | | | | | | | | | | (2479) op(e1, e3) = e1
% 164.91/24.37 | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 164.91/24.37 | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | (2480) ~ (all_56_10 = e1)
% 164.91/24.37 | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | REDUCE: (298), (2480) imply:
% 164.91/24.37 | | | | | | | | | | | | | | | | (2481) ~ (all_10_2 = e1)
% 164.91/24.37 | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | (2482) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 164.91/24.37 | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | BETA: splitting (2482) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (2483) all_58_4 = e3 & op(e3, e1) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | ALPHA: (2483) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (2484) all_58_4 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (157), (162),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (163), (166), (203), (224), (225), (227), (228),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (229), (230), (231), (232), (233), (234), (235),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (236), (237), (238), (239), (240), (242), (243),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (244), (245), (247), (248), (249), (250), (252),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (253), (300), (401), (2327), (2329), (2334),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (2339), (2350), (2354), (2474), (2479), (2481),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (2484), (function-axioms) are inconsistent by
% 164.91/24.37 | | | | | | | | | | | | | | | | | | sub-proof #302.
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (2485) all_58_5 = e3 & op(e2, e1) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | ALPHA: (2485) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (2486) op(e2, e1) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2328), (2486), (function-axioms) are
% 164.91/24.37 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #951.
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | (2487) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 164.91/24.37 | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 164.91/24.37 | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | BETA: splitting (2487) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (2488) all_58_8 = e3 & op(e1, e1) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | ALPHA: (2488) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (2489) all_58_8 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2490) all_54_0 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (2490) imply:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2491) all_10_2 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | SIMP: (2491) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2492) all_10_2 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | REDUCE: (45), (2492) imply:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2493) op(e3, e3) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (85),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (109), (111), (112), (116), (117), (124), (138),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (139), (143), (156), (157), (159), (161), (162),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (163), (164), (166), (167), (168), (169), (191),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (203), (209), (213), (224), (225), (226), (227),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (235), (236), (237), (238), (239), (240), (242),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (243), (244), (245), (247), (248), (249), (250),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (252), (253), (254), (262), (265), (300), (376),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (387), (394), (395), (396), (397), (398), (401),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2320), (2325), (2327), (2328), (2329), (2334),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2339), (2342), (2344), (2348), (2350), (2354),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2357), (2359), (2467), (2469), (2470), (2474),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2478), (2479), (2481), (2489), (2493),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | #282.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2494) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (300), (401), (2350), (2481), (2494) are
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #958.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (2495) all_58_14 = e3 & op(e0, e1) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | ALPHA: (2495) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | (2496) all_58_14 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | (2497) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (2497) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | (2498) all_58_4 = e2 & op(e3, e1) = e2
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | ALPHA: (2498) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | (2499) all_58_4 = e2
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | (2500) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2500) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | (2501) all_58_12 = e2 & op(e0, e3) = e2
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2501) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | (2502) all_58_12 = e2
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | (2503) all_54_0 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (2503) imply:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | (2504) all_10_2 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2504) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | (2505) all_10_2 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (2505) imply:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | (2506) op(e3, e3) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | (2507) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2507) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | (2508) all_58_0 = e1 & op(e3, e3) = e1
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2508) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | (2509) all_58_0 = e1
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (247), (253), (2354),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | (2502), (2509) are inconsistent by sub-proof #435.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | (2510) all_58_2 = e1 & op(e2, e3) = e1
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2510) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | (2511) op(e2, e3) = e1
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (2334), (2511), (function-axioms) are
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #784.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | (2512) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2512) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | (2513) all_58_6 = e1 & op(e1, e3) = e1
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2513) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | (2514) all_58_6 = e1
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (2515) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2515) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2516) all_58_0 = e3 & op(e3, e3) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2516) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2517) all_58_0 = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (247), (2354), (2502), (2514),
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2517) are inconsistent by sub-proof #434.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2518) all_58_2 = e3 & op(e2, e3) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2518) implies:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2519) op(e2, e3) = e3
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (2334), (2519), (function-axioms) are
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #462.
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (2520) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2520) gives:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2521) all_58_6 = e3 & op(e1, e3) = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2521) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2522) all_58_6 = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (247), (249),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2334), (2502), (2522), (function-axioms) are
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #461.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2523) all_58_12 = e3 & op(e0, e3) = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (162), (166), (247), (2334),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479), (2506), (2523), (function-axioms) are
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #301.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | (2524) all_58_12 = e1 & op(e0, e3) = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2524) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | (2525) all_58_12 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (162), (166), (247), (2334),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | (2479), (2506), (2525), (function-axioms) are
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #296.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | (2526) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (300), (401), (2350), (2481), (2526) are
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #958.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | (2527) all_58_13 = e2 & op(e0, e2) = e2
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2527) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | (2528) all_58_13 = e2
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | (2529) all_54_0 = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (2529) imply:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | (2530) all_10_2 = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2530) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | (2531) all_10_2 = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (2531) imply:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | (2532) op(e3, e3) = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | (2533) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2533) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | (2534) all_58_9 = e3 & op(e3, e0) = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2534) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | (2535) all_58_9 = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (2536) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2536) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2537) all_58_6 = e3 & op(e1, e3) = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2537) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2538) all_58_6 = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2539) op(e1, e3) = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2540) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2540) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2541) all_58_0 = e1 & op(e3, e3) = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2541) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2542) all_58_0 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2543) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2543) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2544) all_58_9 = e2 & op(e3, e0) = e2
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2535), (2544),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #349.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2545) all_58_10 = e2 & op(e2, e0) = e2
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2334), (2339), (2545), (function-axioms) are
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2546) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2546) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2547) all_58_11 = e2 & op(e1, e0) = e2
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2547) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2548) all_58_11 = e2
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2549) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2549) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2550) all_58_0 = e0 & op(e3, e3) = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2550) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2551) op(e3, e3) = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2532), (2551), (function-axioms) are
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #949.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2552) all_58_1 = e0 & op(e3, e2) = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2552) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2553) op(e3, e2) = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2554) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2554) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2555) all_58_1 = e1 & op(e3, e2) = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2555) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2556) all_58_1 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2557) op(e3, e2) = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (161), (169), (243), (2320),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339), (2357), (2528), (2556), (2557),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #429.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2558) all_58_3 = e1 & op(e2, e2) = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2558) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2559) all_58_3 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2339), (2559) imply:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2560) e3 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2538), (2560) imply:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2561) all_58_6 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (166), (247), (253),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2334), (2354), (2542), (2561), (function-axioms)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #455.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2562) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2562) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2563) all_58_7 = e1 & op(e1, e2) = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2563) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2564) all_58_7 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2565) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2565) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2566) all_58_9 = e1 & op(e3, e0) = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2566) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2567) all_58_9 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2535), (2567) imply:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2568) e3 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2538), (2568) imply:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2569) all_58_6 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (166), (247), (253),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2334), (2354), (2542), (2569), (function-axioms)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #455.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2570) all_58_10 = e1 & op(e2, e0) = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2570) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2571) all_58_10 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2572) all_58_15 = e0 & op(e0, e0) = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2572) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2573) all_58_15 = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (166), (225), (247),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (2334), (2354), (2357), (2496), (2538),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2542), (2553), (2573), (function-axioms) are
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #281.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2574) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2574) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2575) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (2535), (2548), (2571), (2575) are
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #833.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2576) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2576) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2577) all_58_11 = e1 & op(e1, e0) = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2548), (2577) are inconsistent by sub-proof
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #547.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2578) all_58_15 = e1 & op(e0, e0) = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2578) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579) all_58_15 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2580) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2580) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2581) all_58_6 = e0 & op(e1, e3) = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2581) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2582) op(e1, e3) = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (2479), (2582), (function-axioms) are
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2583) all_58_7 = e0 & op(e1, e2) = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2583) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2584) all_58_7 = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2564), (2584) imply:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2585) e1 = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2579), (2585) imply:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2586) all_58_15 = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (166), (225), (247),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (2334), (2354), (2357), (2496), (2538),
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2542), (2553), (2586), (function-axioms) are
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #281.
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2587) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2587) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2588) all_58_8 = e0 & op(e1, e1) = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2588) implies:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2589) op(e1, e1) = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e1,
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (2474), (2589) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2590) e3 = e0
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (162), (2479) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2591) all_52_2 = e1
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (162), (2539) gives:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2592) all_52_2 = e3
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2591), (2592) imply:
% 164.91/24.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2593) e3 = e1
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2590), (2593) imply:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2594) e1 = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2579), (2594) imply:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2595) all_58_15 = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (166), (225), (247),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (2334), (2354), (2357), (2496), (2538),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2542), (2553), (2595), (function-axioms) are
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #281.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2596) all_58_11 = e0 & op(e1, e0) = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2596) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2597) all_58_11 = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2548), (2597) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #879.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2598) all_58_13 = e1 & op(e0, e2) = e1
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2598) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2599) op(e0, e2) = e1
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2357), (2553), (2599), (function-axioms) are
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #443.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2600) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2600) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2601) all_58_4 = e0 & op(e3, e1) = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2499), (2601) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #902.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2602) all_58_9 = e0 & op(e3, e0) = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2535), (2602) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #901.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2603) all_58_15 = e2 & op(e0, e0) = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2603) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2604) all_58_15 = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2605) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (225), (247),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (2334), (2354), (2357), (2496), (2532),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2538), (2542), (2604), (2605), (function-axioms)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #440.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2606) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2606) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2607) all_58_4 = e0 & op(e3, e1) = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2607) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2608) all_58_4 = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2499), (2608) imply:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2609) e2 = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2604), (2609) imply:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2610) all_58_15 = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2528), (2609) imply:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2611) all_58_13 = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2500) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2612) all_58_12 = e2 & op(e0, e3) = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2612) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2613) all_58_12 = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (247), (2354), (2538), (2542),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2613) are inconsistent by sub-proof #436.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2528), (2611) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #865.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2614) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2614) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2615) all_58_14 = e2 & op(e0, e1) = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2615) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2616) all_58_14 = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (166), (227),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (247), (2327), (2334),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339), (2354), (2538), (2542), (2610), (2616),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #403.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2603), (2610) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #648.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2617) all_58_9 = e0 & op(e3, e0) = e0
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2535), (2617) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #901.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2618) all_58_2 = e1 & op(e2, e3) = e1
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2618) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2619) op(e2, e3) = e1
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (2334), (2619), (function-axioms) are
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #784.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2620) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (162), (166), (247), (2334),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479), (2532), (2538), (2620), (function-axioms)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #280.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2621) all_58_7 = e3 & op(e1, e2) = e3
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2621) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2622) all_58_7 = e3
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2623) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2623) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2624) all_58_6 = e2 & op(e1, e3) = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (166), (239),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (242), (247), (249), (253), (2334), (2339),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2354), (2479), (2532), (2624), (function-axioms)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #278.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2625) all_58_7 = e2 & op(e1, e2) = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2622), (2625),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #303.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2626) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2626) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2627) all_58_8 = e2 & op(e1, e1) = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2627) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2628) op(e1, e1) = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (166), (239),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (242), (247), (249), (253), (2334), (2339),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2354), (2474), (2479), (2532), (2628),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #339.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2629) all_58_11 = e2 & op(e1, e0) = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2629) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2630) all_58_11 = e2
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2631) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (248), (250),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2334), (2499), (2535), (2631), (function-axioms)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #277.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2632) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2632) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2633) all_58_6 = e3 & op(e1, e3) = e3
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2633) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2634) all_58_6 = e3
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2635) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2635) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2636) all_58_6 = e1 & op(e1, e3) = e1
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2634), (2636) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #487.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2637) all_58_7 = e1 & op(e1, e2) = e1
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2637) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2638) all_58_7 = e1
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2622), (2638) are inconsistent by sub-proof
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #821.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2639) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (162), (231), (2479), (2622),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2630), (2639), (function-axioms) are inconsistent
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #311.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2640) all_58_12 = e3 & op(e0, e3) = e3
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (162), (166), (247), (2334),
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479), (2532), (2640), (function-axioms) are
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #301.
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (2641) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2641) gives:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2642) all_58_8 = e3 & op(e1, e1) = e3
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2642) implies:
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2643) all_58_8 = e3
% 164.91/24.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (85),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (111), (112), (116), (117), (124), (138),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (143), (156), (157), (159), (161), (162),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (164), (166), (167), (168), (169), (191),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (203), (209), (213), (224), (225), (226), (227),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (238), (239), (240), (242),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (244), (245), (247), (248), (249), (250),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (254), (262), (265), (300), (376),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (387), (394), (395), (396), (397), (398), (401),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2320), (2325), (2327), (2328), (2329), (2334),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339), (2342), (2344), (2348), (2350), (2354),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2357), (2359), (2467), (2469), (2470), (2474),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2478), (2479), (2481), (2532), (2643),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | #282.
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2644) all_58_11 = e3 & op(e1, e0) = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (162), (166),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (225), (229), (231), (232), (233), (235),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (238), (239), (240), (242), (243), (247),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (250), (253), (2320), (2334), (2339),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2354), (2357), (2474), (2479), (2496), (2499),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2528), (2532), (2644), (function-axioms) are
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #263.
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (2645) all_58_10 = e3 & op(e2, e0) = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2645) implies:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (2646) op(e2, e0) = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2329), (2646), (function-axioms) are
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | (2647) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2647) gives:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (2648) all_58_11 = e3 & op(e1, e0) = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (162), (166),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (169), (225), (229), (231), (232), (233), (235),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (236), (238), (239), (240), (242), (243), (247),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (249), (250), (253), (2320), (2334), (2339),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (2354), (2357), (2474), (2479), (2496), (2499),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (2528), (2532), (2648), (function-axioms) are
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #263.
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (2649) all_58_15 = e3 & op(e0, e0) = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2649) implies:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (2650) all_58_15 = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | (2651) op(e0, e0) = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (2652) all_58_15 = e0 & op(e0, e0) = e0
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2652) implies:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (2653) all_58_15 = e0
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2650), (2653) are inconsistent by sub-proof
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | #860.
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (2654) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2654) implies:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (2655) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2656) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2656) gives:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2657) all_58_6 = e3 & op(e1, e3) = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2657) implies:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2658) all_58_6 = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (157), (162),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (166), (169), (203), (224), (225), (227),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (238), (239), (240), (242),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (244), (245), (247), (248), (249), (250),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (254), (300), (401), (2325), (2327),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2329), (2334), (2339), (2350), (2354), (2474),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479), (2481), (2532), (2650), (2658),
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #284.
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2659) all_58_7 = e3 & op(e1, e2) = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2659) implies:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2660) all_58_7 = e3
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2661) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2661) gives:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2662) all_58_1 = e0 & op(e3, e2) = e0
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2662) implies:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2663) op(e3, e2) = e0
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2655) gives:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2664) all_58_12 = e0 & op(e0, e3) = e0
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2664) implies:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2665) all_58_12 = e0
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2666) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2666) gives:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2667) all_58_0 = e1 & op(e3, e3) = e1
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2667) implies:
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2668) all_58_0 = e1
% 164.91/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2669) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (166), (2334), (2668), (2669),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #402.
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2670) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2670) gives:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2671) all_58_6 = e3 & op(e1, e3) = e3
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2671) implies:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2672) all_58_6 = e3
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (157), (162),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (166), (169), (203), (224), (225), (227),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (238), (239), (240), (242),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (244), (245), (247), (248), (249), (250),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (254), (300), (401), (2325), (2327),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2329), (2334), (2339), (2350), (2354), (2474),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479), (2481), (2650), (2668), (2672),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #286.
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2673) all_58_12 = e3 & op(e0, e3) = e3
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2673) implies:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2674) all_58_12 = e3
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (162), (166), (247), (2334),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479), (2668), (2674), (function-axioms) are
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #324.
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2675) all_58_2 = e1 & op(e2, e3) = e1
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2675) implies:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2676) op(e2, e3) = e1
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (2334), (2676), (function-axioms) are
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #784.
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2677) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2677) gives:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2678) all_58_6 = e1 & op(e1, e3) = e1
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2678) implies:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2679) all_58_6 = e1
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2680) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2680) gives:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2681) all_58_0 = e3 & op(e3, e3) = e3
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2681) implies:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2682) all_58_0 = e3
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2683) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (162), (166), (247), (2334),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2357), (2479), (2532), (2663), (2683),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #267.
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2684) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2684) gives:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2685) all_58_14 = e1 & op(e0, e1) = e1
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (253), (2354), (2496), (2665),
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2679), (2682), (2685) are inconsistent by
% 165.87/24.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #266.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2686) all_58_15 = e1 & op(e0, e0) = e1
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (253), (2354), (2650), (2665),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2679), (2682), (2686) are inconsistent by
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #307.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2687) all_58_2 = e3 & op(e2, e3) = e3
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2687) implies:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2688) op(e2, e3) = e3
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (2334), (2688), (function-axioms) are
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #462.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2689) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2689) gives:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2690) all_58_6 = e3 & op(e1, e3) = e3
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2690) implies:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2691) all_58_6 = e3
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (157), (162),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (166), (169), (203), (224), (225), (227),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (238), (239), (240), (242),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (244), (245), (247), (248), (249), (250),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (254), (300), (401), (2325), (2327),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2329), (2334), (2339), (2350), (2354), (2474),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479), (2481), (2532), (2650), (2691),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #284.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2692) all_58_12 = e3 & op(e0, e3) = e3
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (162), (166), (247), (2334),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479), (2532), (2692), (function-axioms) are
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #301.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2693) all_58_12 = e1 & op(e0, e3) = e1
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2693) implies:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2694) all_58_12 = e1
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (162), (166), (247), (2334),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2479), (2532), (2694), (function-axioms) are
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #296.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2695) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2695) gives:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2696) all_58_13 = e0 & op(e0, e2) = e0
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2696) implies:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2697) all_58_13 = e0
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2528), (2697) are inconsistent by sub-proof
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #865.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2698) all_58_14 = e0 & op(e0, e1) = e0
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2496), (2698) are inconsistent by sub-proof
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #871.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2699) all_58_3 = e0 & op(e2, e2) = e0
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2339), (2699) are inconsistent by sub-proof
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #869.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2700) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (2528), (2660), (2700) are inconsistent
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #426.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2701) gives:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2702) all_58_8 = e3 & op(e1, e1) = e3
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2702) implies:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2703) all_58_8 = e3
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (85),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (109), (111), (112), (116), (117), (124), (138),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (139), (143), (156), (157), (159), (161), (162),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (164), (166), (167), (168), (169), (191),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203), (209), (213), (224), (225), (226), (227),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (230), (231), (232), (233), (234),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235), (236), (237), (238), (239), (240), (242),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243), (244), (245), (247), (248), (249), (250),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252), (253), (254), (262), (265), (300), (376),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (387), (394), (395), (396), (397), (398), (401),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2320), (2325), (2327), (2328), (2329), (2334),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339), (2342), (2344), (2348), (2350), (2354),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2357), (2359), (2467), (2469), (2470), (2474),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2478), (2479), (2481), (2532), (2650), (2651),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2703), (function-axioms) are inconsistent by
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #283.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2704) all_58_11 = e3 & op(e1, e0) = e3
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2704) implies:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2705) all_58_11 = e3
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (224), (228),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (239), (240), (242), (2334), (2339),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2354), (2650), (2705), (function-axioms) are
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #319.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | (2706) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (300), (401), (2350), (2481), (2706) are
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #958.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | (2707) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2707) gives:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | (2708) all_58_14 = e2 & op(e0, e1) = e2
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2496), (2708),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | #411.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | (2709) all_58_15 = e2 & op(e0, e0) = e2
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2709) implies:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | (2710) all_58_15 = e2
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (45), (162), (163), (166), (203),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | (225), (228), (230), (231), (232), (233), (235),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | (236), (238), (239), (240), (242), (247), (248),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | (249), (250), (253), (300), (401), (2329), (2334),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | (2339), (2350), (2354), (2357), (2474), (2479),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | (2481), (2496), (2499), (2710), (function-axioms)
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #260.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | (2711) all_58_5 = e2 & op(e2, e1) = e2
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | (2334), (2339), (2711), (function-axioms) are
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #412.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | (2712) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 165.87/24.41 | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | BETA: splitting (2712) gives:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | (2713) all_58_8 = e2 & op(e1, e1) = e2
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (45), (162), (166), (203), (239),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | (240), (242), (247), (249), (253), (300), (401),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | (2334), (2339), (2350), (2354), (2474), (2479),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | (2481), (2713), (function-axioms) are inconsistent
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | by sub-proof #338.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | (2714) all_58_14 = e2 & op(e0, e1) = e2
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | ALPHA: (2714) implies:
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | (2715) all_58_14 = e2
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2496), (2715),
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | | #438.
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | End of split
% 165.87/24.41 | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | Case 2:
% 165.87/24.41 | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | (2716) all_56_10 = e1
% 165.87/24.41 | | | | | | | | | | | | | | | | (2717) all_56_4 = e3 & op(e3, e1) = e3
% 165.87/24.41 | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | ALPHA: (2717) implies:
% 165.87/24.41 | | | | | | | | | | | | | | | | (2718) op(e3, e1) = e3
% 165.87/24.41 | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (2716) imply:
% 165.87/24.41 | | | | | | | | | | | | | | | | (2719) all_10_2 = e1
% 165.87/24.41 | | | | | | | | | | | | | | | |
% 165.87/24.41 | | | | | | | | | | | | | | | | SIMP: (2719) implies:
% 165.87/24.41 | | | | | | | | | | | | | | | | (2720) all_10_2 = e1
% 165.87/24.41 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | REDUCE: (365), (2720) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | (2721) ~ (all_52_2 = e1)
% 165.87/24.42 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | REDUCE: (371), (2720) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | (2722) ~ (all_52_8 = e1)
% 165.87/24.42 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | REDUCE: (2350), (2720) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | (2723) ~ (e2 = e1)
% 165.87/24.42 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | (2724) all_56_10 = e3
% 165.87/24.42 | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (2716), (2724) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | (2725) e3 = e1
% 165.87/24.42 | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | REDUCE: (8), (2725) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | (2726) $false
% 165.87/24.42 | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | CLOSE: (2726) is inconsistent.
% 165.87/24.42 | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | (2727) ~ (all_56_10 = e3)
% 165.87/24.42 | | | | | | | | | | | | | | | | | (2728) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | REDUCE: (2716), (2727) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | (2729) ~ (e3 = e1)
% 165.87/24.42 | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | BETA: splitting (2728) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | (2730) all_56_12 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.42 | | | | | | | | | | | | | | | | | | (242), (2323), (2334), (2339), (2354), (2730),
% 165.87/24.42 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.42 | | | | | | | | | | | | | | | | | | #372.
% 165.87/24.42 | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | (2731) all_56_14 = e1 | all_56_15 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | (2732) all_54_8 = e3
% 165.87/24.42 | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (2471), (2732) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | sub-proof #690.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | (2733) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (2733) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | (2734) all_54_8 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (2342), (2734) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | sub-proof #259.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | (2735) all_54_8 = e1 | all_54_8 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2731) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | (2736) all_56_14 = e1
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2470), (2736) are inconsistent by sub-proof
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | #258.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | (2737) all_56_15 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (2737) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | (2738) all_4_2 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | SIMP: (2738) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | (2739) all_4_2 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | REDUCE: (387), (2739) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | (2740) ~ (all_52_7 = e0)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | REDUCE: (396), (2739) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | (2741) ~ (all_52_13 = e0)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | (2742) all_54_7 = e3
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (2329), (2742) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | sub-proof #533.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | (2743) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2743) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | (2744) all_54_7 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (2348), (2744) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #532.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | (2745) all_54_7 = e1 | all_54_7 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2735) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | (2746) all_54_8 = e1
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (2721), (2746) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #689.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | (2747) all_54_8 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (2747) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | (2748) all_52_2 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2748) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | (2749) all_52_2 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (2749) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | (2750) ~ (all_52_6 = e0)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2750) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | (2751) ~ (all_52_6 = e0)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (2749) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | (2752) ~ (all_52_14 = e0)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2752) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | (2753) ~ (all_52_14 = e0)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2745) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | (2754) all_54_7 = e1
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (2754) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | (2755) all_52_13 = e1
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2755) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | (2756) all_52_13 = e1
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (2756) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | (2757) ~ (all_52_9 = e1)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (2756) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | (2758) ~ (all_52_14 = e1)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2758) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | (2759) ~ (all_52_14 = e1)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (2760) all_54_6 = e3
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (2328), (2760) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #681.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (2761) ~ (all_54_6 = e3)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | (2762) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2763) all_54_11 = e3
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (2473), (2763) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2764) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2762) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2765) all_54_6 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (2346), (2765) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #680.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2766) all_54_6 = e1 | all_54_6 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2766) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2767) all_54_6 = e1
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (2757), (2767) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #364.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2768) all_54_6 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (2768) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2769) all_52_9 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2769) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2770) all_52_9 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (2770) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2771) ~ (all_52_8 = e0)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2328), (2770) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2772) ~ (e3 = e0)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2764) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2773) all_54_11 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (2773) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2774) all_52_14 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2774) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2775) all_52_14 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (2775) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2776) ~ (all_52_6 = e2)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2777) all_54_9 = e3
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (2326), (2777) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2778) ~ (all_54_9 = e3)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2779) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2779) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2780) all_54_9 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (2776), (2780) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #740.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2781) all_54_9 = e1 | all_54_9 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2782) all_54_2 = e3
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (2782) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2783) all_52_8 = e3
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2472), (2783) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2784) $false
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2784) is inconsistent.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2785) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2785) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2786) all_54_2 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (289), (2786) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2787) all_52_8 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (2787) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2788) op(e3, e1) = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2789) ~ (all_36_2 = e3)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2469), (2789) imply:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2790) $false
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2790) is inconsistent.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2791) ( ~ (all_36_0 = e2) & op(all_36_1, e1) = all_36_0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_36_1 & $i(all_36_0) &
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e3, e1)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2791) gives:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2792) ~ (all_36_0 = e2) & op(all_36_1, e1) = all_36_0 &
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_36_1 & $i(all_36_0) &
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2792) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2793) op(e3, e1) = all_36_1
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (127), (166), (190), (239), (240), (242),
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264), (275), (2326), (2327), (2334), (2339),
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2354), (2467), (2718), (2740), (2751), (2781),
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2788), (2793), (function-axioms) are inconsistent
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #254.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2794) ~ (all_36_1 = e0) & op(e3, e1) = all_36_1 &
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2794) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2795) op(e3, e1) = all_36_1
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (127), (166), (190), (239), (240), (242),
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264), (275), (2326), (2327), (2334), (2339),
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2354), (2467), (2718), (2740), (2751), (2781),
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2788), (2795), (function-axioms) are inconsistent
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #254.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2796) all_54_2 = e1 | all_54_2 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (289), (2722), (2771), (2796) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #253.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2797) all_54_11 = e1 | all_54_11 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (2753), (2759), (2797) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #732.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | (2798) all_54_7 = e0
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (2741), (2798) are inconsistent by
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #529.
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | End of split
% 165.87/24.42 | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | (2799) all_20_2 = e2
% 165.87/24.42 | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | COMBINE_EQS: (349), (2799) imply:
% 165.87/24.42 | | | | | | | | | | | | | (2800) all_4_2 = e2
% 165.87/24.42 | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | SIMP: (2800) implies:
% 165.87/24.42 | | | | | | | | | | | | | (2801) all_4_2 = e2
% 165.87/24.42 | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | COMBINE_EQS: (262), (2801) imply:
% 165.87/24.42 | | | | | | | | | | | | | (2802) all_56_15 = e2
% 165.87/24.42 | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | REDUCE: (387), (2801) imply:
% 165.87/24.42 | | | | | | | | | | | | | (2803) ~ (all_52_7 = e2)
% 165.87/24.42 | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | REDUCE: (36), (2801) imply:
% 165.87/24.42 | | | | | | | | | | | | | (2804) op(e0, e0) = e2
% 165.87/24.42 | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | BETA: splitting (212) gives:
% 165.87/24.42 | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | (2805) ~ (all_56_15 = e2)
% 165.87/24.42 | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | REDUCE: (2802), (2805) imply:
% 165.87/24.42 | | | | | | | | | | | | | | (2806) $false
% 165.87/24.42 | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | CLOSE: (2806) is inconsistent.
% 165.87/24.42 | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | (2807) all_56_7 = e0 & op(e0, e2) = e0
% 165.87/24.42 | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | ALPHA: (2807) implies:
% 165.87/24.42 | | | | | | | | | | | | | | (2808) all_56_7 = e0
% 165.87/24.42 | | | | | | | | | | | | | | (2809) op(e0, e2) = e0
% 165.87/24.42 | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 165.87/24.42 | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | (2810) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 165.87/24.42 | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | BETA: splitting (2810) gives:
% 165.87/24.42 | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | Case 1:
% 165.87/24.42 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | (2811) all_58_6 = e2 & op(e1, e3) = e2
% 165.87/24.42 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.42 | | | | | | | | | | | | | | | | (242), (247), (249), (253), (2334), (2339),
% 165.87/24.42 | | | | | | | | | | | | | | | | (2354), (2811), (function-axioms) are inconsistent
% 165.87/24.42 | | | | | | | | | | | | | | | | by sub-proof #252.
% 165.87/24.42 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | Case 2:
% 165.87/24.42 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | (2812) all_58_7 = e2 & op(e1, e2) = e2
% 165.87/24.42 | | | | | | | | | | | | | | | |
% 165.87/24.42 | | | | | | | | | | | | | | | | ALPHA: (2812) implies:
% 165.87/24.42 | | | | | | | | | | | | | | | | (2813) all_58_7 = e2
% 165.87/24.42 | | | | | | | | | | | | | | | | (2814) op(e1, e2) = e2
% 165.87/24.43 | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | (2815) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 165.87/24.43 | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | BETA: splitting (2815) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2816) all_58_4 = e2 & op(e3, e1) = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | ALPHA: (2816) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2817) all_58_4 = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2818) op(e3, e1) = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (116),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (122), (139), (142), (143), (157), (161), (162),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (163), (164), (166), (168), (169), (191), (193),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (195), (196), (197), (203), (209), (216), (221),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (224), (225), (226), (227), (228), (229), (230),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (231), (232), (233), (234), (235), (236), (237),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (238), (239), (240), (242), (243), (244), (245),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (247), (248), (249), (250), (252), (253), (254),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (265), (274), (276), (277), (278), (298), (300),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (305), (365), (367), (369), (371), (375), (388),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (389), (401), (2320), (2323), (2325), (2326),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2327), (2328), (2329), (2333), (2334), (2339),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2344), (2348), (2354), (2357), (2802), (2803),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2808), (2809), (2813), (2814), (2817), (2818),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.43 | | | | | | | | | | | | | | | | | | #230.
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2819) all_58_5 = e2 & op(e2, e1) = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2334), (2339), (2819), (function-axioms) are
% 165.87/24.43 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #412.
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | (2820) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 165.87/24.43 | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 165.87/24.43 | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | BETA: splitting (2820) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2821) all_58_8 = e2 & op(e1, e1) = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (2821), (function-axioms) are
% 165.87/24.43 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2822) all_58_14 = e2 & op(e0, e1) = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | ALPHA: (2822) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2823) all_58_14 = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | | (2824) op(e0, e1) = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | (2825) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | BETA: splitting (2825) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | (2826) all_58_12 = e3 & op(e0, e3) = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | ALPHA: (2826) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | (2827) all_58_12 = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | (2828) all_58_15 = e0 & op(e0, e0) = e0
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2828) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | (2829) all_58_15 = e0
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | (2830) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2830) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | (2831) all_58_9 = e2 & op(e3, e0) = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2831) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | (2832) all_58_9 = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | (2833) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2833) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (2834) all_58_12 = e1 & op(e0, e3) = e1
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2834) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (2835) all_58_12 = e1
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (166), (227),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (2327), (2334), (2339),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (2354), (2823), (2829), (2835), (function-axioms)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #380.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (2836) all_58_13 = e1 & op(e0, e2) = e1
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2836) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (2837) all_58_13 = e1
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (2838) op(e0, e2) = e1
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (2839) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (169), (247),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (249), (2325), (2334), (2827), (2839),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | #413.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (2840) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2840) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2841) all_58_4 = e3 & op(e3, e1) = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2841) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2842) all_58_4 = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2843) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2843) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2844) all_58_1 = e0 & op(e3, e2) = e0
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2844) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2845) op(e3, e2) = e0
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2357), (2838), (2845), (function-axioms) are
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #443.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2846) all_58_3 = e0 & op(e2, e2) = e0
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2846) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2847) all_58_3 = e0
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2339), (2847) imply:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2848) e3 = e0
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2842), (2848) imply:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2849) all_58_4 = e0
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (169), (239),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (242), (247), (249), (254), (2325), (2334),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339), (2354), (2827), (2832), (2849),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #229.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2850) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (2813), (2837), (2850) are inconsistent
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #376.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2851) all_58_9 = e3 & op(e3, e0) = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2851) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2852) all_58_9 = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2832), (2852),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | #451.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | (2853) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2804), (2824), (2853), (function-axioms) are
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #629.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | (2854) all_58_10 = e2 & op(e2, e0) = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | (2334), (2339), (2854), (function-axioms) are
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | (2855) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2855) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | (2856) all_58_11 = e2 & op(e1, e0) = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2856) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | (2857) all_58_11 = e2
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | (2858) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2858) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (2859) all_58_9 = e3 & op(e3, e0) = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2859) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (2860) all_58_9 = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (2861) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (166), (239),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (242), (247), (248), (249), (250), (252),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (2328), (2334), (2339), (2354), (2827),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (2860), (2861), (function-axioms) are inconsistent
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #234.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | (2862) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2862) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2863) all_58_8 = e3 & op(e1, e1) = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2863) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2864) all_58_8 = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (231), (232),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2813), (2857), (2864), (function-axioms) are
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2865) all_58_14 = e3 & op(e0, e1) = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2865) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2866) all_58_14 = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2823), (2866),
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | | #438.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (2867) all_58_10 = e3 & op(e2, e0) = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2867) implies:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | (2868) op(e2, e0) = e3
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2329), (2868), (function-axioms) are
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | (2869) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2869) gives:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.43 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (2870) all_58_11 = e3 & op(e1, e0) = e3
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2870) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (2871) all_58_11 = e3
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2857), (2871),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | #421.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (2872) all_58_15 = e3 & op(e0, e0) = e3
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2872) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (2873) all_58_15 = e3
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (166), (227),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (2327), (2334), (2339),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (2354), (2823), (2827), (2829), (2873),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | #306.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (2874) all_58_15 = e2 & op(e0, e0) = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2874) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (2875) all_58_15 = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (163), (164),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (166), (224), (228), (230), (235), (236), (238),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (244), (247), (249), (252),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (253), (2328), (2329), (2334), (2339), (2354),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (2813), (2823), (2824), (2827), (2875),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | #223.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | (2876) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2876) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | (2877) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | (2878) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2878) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (2879) all_58_9 = e2 & op(e3, e0) = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2879) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (2880) all_58_9 = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | (2881) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2881) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (2882) all_58_1 = e1 & op(e3, e2) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2882) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (2883) all_58_1 = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (2884) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2884) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2885) all_58_0 = e0 & op(e3, e3) = e0
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2885) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2886) op(e3, e3) = e0
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2887) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2887) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2888) all_58_0 = e1 & op(e3, e3) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2888) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2889) op(e3, e3) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2886), (2889), (function-axioms) are
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #907.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2890) all_58_2 = e1 & op(e2, e3) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2890) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2891) op(e2, e3) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (2334), (2891), (function-axioms) are
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #784.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2892) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2892) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2893) all_58_6 = e1 & op(e1, e3) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2893) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2894) all_58_6 = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2895) op(e1, e3) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2896) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2896) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2897) all_58_12 = e1 & op(e0, e3) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2897) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2898) all_58_12 = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2899) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2899) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2900) all_58_0 = e3 & op(e3, e3) = e3
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2900) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2901) op(e3, e3) = e3
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (162), (166), (247), (2334),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2895), (2898), (2901), (function-axioms) are
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #296.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2902) all_58_2 = e3 & op(e2, e3) = e3
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2902) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2903) op(e2, e3) = e3
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (2334), (2903), (function-axioms) are
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #462.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2904) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2904) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2905) all_58_6 = e3 & op(e1, e3) = e3
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2894), (2905) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #246.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2826), (2898) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #490.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2906) all_58_13 = e1 & op(e0, e2) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2906) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2907) all_58_13 = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (2823), (2827), (2877), (2907) are
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #545.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2908) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2804), (2824), (2908), (function-axioms) are
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #629.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2909) all_58_12 = e1 & op(e0, e3) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2827), (2909) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #651.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2910) all_58_1 = e0 & op(e3, e2) = e0
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2883), (2910) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | #948.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (2911) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2911) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2912) all_58_4 = e0 & op(e3, e1) = e0
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2912) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2913) all_58_4 = e0
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (169), (239),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (242), (247), (249), (254), (2325), (2334),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339), (2354), (2827), (2880), (2913),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | #229.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2914) all_58_9 = e0 & op(e3, e0) = e0
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2880), (2914) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | #745.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (2915) all_58_3 = e1 & op(e2, e2) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2339), (2915) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | #868.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | (2916) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (2813), (2823), (2827),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | (2877), (2916) are inconsistent by sub-proof #225.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (2917) all_58_10 = e2 & op(e2, e0) = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (2334), (2339), (2917), (function-axioms) are
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | (2918) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2918) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (2919) all_58_11 = e2 & op(e1, e0) = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2919) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | (2920) all_58_11 = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | (2921) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2921) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (2922) all_58_1 = e1 & op(e3, e2) = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2922) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | (2923) all_58_1 = e1
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (2924) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (166), (239),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (242), (247), (249), (253), (2334), (2339),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (2354), (2827), (2923), (2924), (function-axioms)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #227.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | (2925) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2925) gives:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2926) all_58_4 = e2 & op(e3, e1) = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2926) implies:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2927) all_58_4 = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (166), (235),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (238), (239), (240), (242), (2328), (2334),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339), (2354), (2823), (2824), (2927),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | #251.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2928) all_58_9 = e2 & op(e3, e0) = e2
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (166), (224),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (239), (240), (242), (2329), (2334),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339), (2354), (2804), (2920), (2928),
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | | #219.
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.44 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | | | (2929) all_58_3 = e1 & op(e2, e2) = e1
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2339), (2929) are inconsistent by sub-proof
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | | | #868.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | | (2930) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (2813), (2823), (2827),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | | (2877), (2930) are inconsistent by sub-proof #225.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2931) all_58_15 = e2 & op(e0, e0) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2931) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2932) all_58_15 = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (163), (164),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (166), (224), (228), (230), (235), (236), (238),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (244), (247), (249), (252),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (253), (2328), (2329), (2334), (2339), (2354),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2813), (2823), (2824), (2827), (2877), (2932),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | #224.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2933) all_58_13 = e3 & op(e0, e2) = e3
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2327), (2933), (function-axioms) are
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #962.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | (2934) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (2934) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2935) all_58_14 = e3 & op(e0, e1) = e3
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | ALPHA: (2935) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2936) all_58_14 = e3
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2823), (2936),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | #438.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2937) all_58_15 = e3 & op(e0, e0) = e3
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2804), (2937),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | #220.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | (2938) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 165.87/24.45 | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 165.87/24.45 | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | BETA: splitting (2938) gives:
% 165.87/24.45 | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | (2939) all_58_8 = e2 & op(e1, e1) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (2939), (function-axioms) are
% 165.87/24.45 | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 165.87/24.45 | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | (2940) all_58_11 = e2 & op(e1, e0) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | ALPHA: (2940) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | (2941) all_58_11 = e2
% 165.87/24.45 | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | (2942) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 165.87/24.45 | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | BETA: splitting (2942) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | (2943) all_58_4 = e2 & op(e3, e1) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | ALPHA: (2943) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | (2944) all_58_4 = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | (2945) op(e3, e1) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | (2946) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (2946) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2947) all_58_1 = e2 & op(e3, e2) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | ALPHA: (2947) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2948) all_58_1 = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (248), (250), (254),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2944), (2948) are inconsistent by sub-proof #895.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2949) all_58_3 = e2 & op(e2, e2) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | ALPHA: (2949) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2950) all_58_3 = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (242), (2334), (2354), (2950), (function-axioms)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #779.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | (2951) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (2951) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2952) all_58_7 = e2 & op(e1, e2) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | ALPHA: (2952) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2953) all_58_7 = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2954) op(e1, e2) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (116),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (122), (139), (142), (143), (157), (161), (162),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (163), (164), (166), (168), (169), (191), (193),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (195), (196), (197), (203), (209), (216), (221),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (224), (225), (226), (227), (228), (229), (230),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (231), (232), (233), (234), (235), (236), (237),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (238), (239), (240), (242), (243), (244), (245),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (247), (248), (249), (250), (252), (253), (254),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (265), (274), (276), (277), (278), (298), (300),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (305), (365), (367), (369), (371), (375), (388),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (389), (401), (2320), (2323), (2325), (2326),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2327), (2328), (2329), (2333), (2334), (2339),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2344), (2348), (2354), (2357), (2802), (2803),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2808), (2809), (2944), (2945), (2953), (2954),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | #230.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2955) all_58_13 = e2 & op(e0, e2) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | ALPHA: (2955) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2956) op(e0, e2) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (2809), (2956), (function-axioms) are
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #631.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | (2957) all_58_5 = e2 & op(e2, e1) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | (2334), (2339), (2957), (function-axioms) are
% 165.87/24.45 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #412.
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | (2958) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 165.87/24.45 | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 165.87/24.45 | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | BETA: splitting (2958) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | (2959) all_58_8 = e2 & op(e1, e1) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (2959), (function-axioms) are
% 165.87/24.45 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | (2960) all_58_14 = e2 & op(e0, e1) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | ALPHA: (2960) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | (2961) all_58_14 = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | | (2962) op(e0, e1) = e2
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | (2963) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | BETA: splitting (2963) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2964) all_58_9 = e3 & op(e3, e0) = e3
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | ALPHA: (2964) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | (2965) all_58_9 = e3
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | (2966) all_58_15 = e0 & op(e0, e0) = e0
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2966) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | (2967) all_58_15 = e0
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | (2968) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2968) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2969) all_58_12 = e1 & op(e0, e3) = e1
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2969) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2970) all_58_12 = e1
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (166), (227),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (2327), (2334), (2339),
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2354), (2961), (2967), (2970), (function-axioms)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #380.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2971) all_58_13 = e1 & op(e0, e2) = e1
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2971) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2972) op(e0, e2) = e1
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (2809), (2972), (function-axioms) are
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #889.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | (2973) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2804), (2962), (2973), (function-axioms) are
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #629.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | (2974) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2974) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | (2975) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | (2976) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2976) gives:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2977) all_58_9 = e1 & op(e3, e0) = e1
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2977) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2978) all_58_9 = e1
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2965), (2978) are inconsistent by sub-proof
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | #896.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2979) all_58_10 = e1 & op(e2, e0) = e1
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2979) implies:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | (2980) all_58_10 = e1
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (2941), (2965), (2975), (2980) are
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #833.
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.45 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (2981) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2981) gives:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | | (2982) all_58_11 = e1 & op(e1, e0) = e1
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2941), (2982) are inconsistent by sub-proof
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | | #547.
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | | (2983) all_58_15 = e1 & op(e0, e0) = e1
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2983) implies:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | | (2984) op(e0, e0) = e1
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2804), (2984), (function-axioms) are
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #640.
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | (2985) all_58_10 = e3 & op(e2, e0) = e3
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | ALPHA: (2985) implies:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | (2986) op(e2, e0) = e3
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2329), (2986), (function-axioms) are
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | (2987) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 165.87/24.46 | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | BETA: splitting (2987) gives:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | (2988) all_58_11 = e3 & op(e1, e0) = e3
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2941), (2988),
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | #221.
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | (2989) all_58_15 = e3 & op(e0, e0) = e3
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | ALPHA: (2989) implies:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | (2990) all_58_15 = e3
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | (2991) op(e0, e0) = e3
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | (2992) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2992) gives:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (2993) all_58_9 = e2 & op(e3, e0) = e2
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (166), (224),
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (228), (230), (239), (240), (242), (2329), (2334),
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (2339), (2354), (2804), (2941), (2993),
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | #219.
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (2994) all_58_10 = e2 & op(e2, e0) = e2
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (2334), (2339), (2994), (function-axioms) are
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447.
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | (2995) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2995) gives:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e0,
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (2804), (2991) gives:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (2996) e3 = e2
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2339), (2996) imply:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (2997) all_58_3 = e2
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (242), (2334), (2354), (2997), (function-axioms)
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #779.
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (2998) all_58_15 = e2 & op(e0, e0) = e2
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2998) implies:
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (2999) all_58_15 = e2
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (242), (2334), (2339), (2354), (2990), (2999),
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | | #320.
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | (3000) all_58_3 = e2 & op(e2, e2) = e2
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | ALPHA: (3000) implies:
% 165.87/24.46 | | | | | | | | | | | (3001) all_58_3 = e2
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 165.87/24.46 | | | | | | | | | | | (242), (2334), (3001), (function-axioms) are
% 165.87/24.46 | | | | | | | | | | | inconsistent by sub-proof #665.
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | (3002) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 165.87/24.46 | | | | | | | | | | e2 & op(e2, e0) = e2)
% 165.87/24.46 | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | BETA: splitting (3002) gives:
% 165.87/24.46 | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | Case 1:
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | (3003) all_58_5 = e2 & op(e2, e1) = e2
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 165.87/24.46 | | | | | | | | | | | (2334), (2339), (3003), (function-axioms) are
% 165.87/24.46 | | | | | | | | | | | inconsistent by sub-proof #412.
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | (3004) all_58_10 = e2 & op(e2, e0) = e2
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 165.87/24.46 | | | | | | | | | | | (2334), (2339), (3004), (function-axioms) are
% 165.87/24.46 | | | | | | | | | | | inconsistent by sub-proof #447.
% 165.87/24.46 | | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | | |
% 165.87/24.46 | | | | | | | | | End of split
% 165.87/24.46 | | | | | | | | |
% 165.87/24.46 | | | | | | | | End of split
% 165.87/24.46 | | | | | | | |
% 165.87/24.46 | | | | | | | Case 2:
% 165.87/24.46 | | | | | | | |
% 165.87/24.46 | | | | | | | | (3005) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 &
% 165.87/24.46 | | | | | | | | op(e2, e0) = e3)
% 165.87/24.46 | | | | | | | |
% 165.87/24.46 | | | | | | | | REF_CLOSE: (163), (164), (2328), (2329), (3005),
% 165.87/24.46 | | | | | | | | (function-axioms) are inconsistent by sub-proof #218.
% 165.87/24.46 | | | | | | | |
% 165.87/24.46 | | | | | | | End of split
% 165.87/24.46 | | | | | | |
% 165.87/24.46 | | | | | | End of split
% 165.87/24.46 | | | | | |
% 165.87/24.46 | | | | | End of split
% 165.87/24.46 | | | | |
% 165.87/24.46 | | | | Case 2:
% 165.87/24.46 | | | | |
% 165.87/24.46 | | | | | (3006) all_10_2 = e0
% 166.10/24.46 | | | | | (3007) ( ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 & op(e0,
% 166.10/24.46 | | | | | e3) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 166.10/24.46 | | | | | (all_10_1 = e2) & op(e0, e3) = all_10_1 & $i(all_10_1))
% 166.10/24.46 | | | | |
% 166.10/24.46 | | | | | COMBINE_EQS: (309), (3006) imply:
% 166.10/24.46 | | | | | (3008) all_24_2 = e0
% 166.10/24.46 | | | | |
% 166.10/24.46 | | | | | COMBINE_EQS: (298), (3006) imply:
% 166.10/24.46 | | | | | (3009) all_56_10 = e0
% 166.10/24.46 | | | | |
% 166.10/24.46 | | | | | REDUCE: (363), (3006) imply:
% 166.10/24.46 | | | | | (3010) ~ (all_52_1 = e0)
% 166.10/24.46 | | | | |
% 166.10/24.46 | | | | | REDUCE: (369), (3006) imply:
% 166.10/24.46 | | | | | (3011) ~ (all_52_4 = e0)
% 166.10/24.46 | | | | |
% 166.10/24.46 | | | | | REDUCE: (371), (3006) imply:
% 166.10/24.46 | | | | | (3012) ~ (all_52_8 = e0)
% 166.10/24.46 | | | | |
% 166.10/24.46 | | | | | REDUCE: (373), (3006) imply:
% 166.10/24.46 | | | | | (3013) ~ (all_52_12 = e0)
% 166.10/24.46 | | | | |
% 166.10/24.46 | | | | | BETA: splitting (248) gives:
% 166.10/24.46 | | | | |
% 166.10/24.46 | | | | | Case 1:
% 166.10/24.46 | | | | | |
% 166.10/24.46 | | | | | | (3014) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 166.10/24.46 | | | | | | op(e3, e2) = e0)
% 166.10/24.46 | | | | | |
% 166.10/24.46 | | | | | | BETA: splitting (3014) gives:
% 166.10/24.46 | | | | | |
% 166.10/24.46 | | | | | | Case 1:
% 166.10/24.46 | | | | | | |
% 166.10/24.46 | | | | | | | (3015) all_58_0 = e0 & op(e3, e3) = e0
% 166.10/24.46 | | | | | | |
% 166.10/24.46 | | | | | | | ALPHA: (3015) implies:
% 166.10/24.46 | | | | | | | (3016) all_58_0 = e0
% 166.10/24.46 | | | | | | | (3017) op(e3, e3) = e0
% 166.10/24.46 | | | | | | |
% 166.10/24.46 | | | | | | | BETA: splitting (220) gives:
% 166.10/24.46 | | | | | | |
% 166.10/24.46 | | | | | | | Case 1:
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | (3018) ~ (all_56_10 = e0)
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | REDUCE: (3009), (3018) imply:
% 166.10/24.46 | | | | | | | | (3019) $false
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | CLOSE: (3019) is inconsistent.
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | Case 2:
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | (3020) all_56_9 = e3 & op(e3, e0) = e3
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | ALPHA: (3020) implies:
% 166.10/24.46 | | | | | | | | (3021) all_56_9 = e3
% 166.10/24.46 | | | | | | | | (3022) op(e3, e0) = e3
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12, e3,
% 166.10/24.46 | | | | | | | | e0, e3, simplifying with (167), (3022) gives:
% 166.10/24.46 | | | | | | | | (3023) all_52_12 = e3
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | REDUCE: (132), (3023) imply:
% 166.10/24.46 | | | | | | | | (3024) ~ (all_52_4 = e3)
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | REDUCE: (119), (3023) imply:
% 166.10/24.46 | | | | | | | | (3025) ~ (all_52_8 = e3)
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | REDUCE: (112), (3023) imply:
% 166.10/24.46 | | | | | | | | (3026) ~ (all_52_13 = e3)
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | SIMP: (3026) implies:
% 166.10/24.46 | | | | | | | | (3027) ~ (all_52_13 = e3)
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | REDUCE: (111), (3023) imply:
% 166.10/24.46 | | | | | | | | (3028) ~ (all_52_14 = e3)
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | SIMP: (3028) implies:
% 166.10/24.46 | | | | | | | | (3029) ~ (all_52_14 = e3)
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | REDUCE: (395), (3023) imply:
% 166.10/24.46 | | | | | | | | (3030) ~ (all_4_2 = e3)
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | SIMP: (3030) implies:
% 166.10/24.46 | | | | | | | | (3031) ~ (all_4_2 = e3)
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | BETA: splitting (254) gives:
% 166.10/24.46 | | | | | | | |
% 166.10/24.46 | | | | | | | | Case 1:
% 166.10/24.46 | | | | | | | | |
% 166.10/24.46 | | | | | | | | | (3032) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 166.10/24.46 | | | | | | | | | op(e3, e2) = e3)
% 166.10/24.46 | | | | | | | | |
% 166.10/24.46 | | | | | | | | | REF_CLOSE: (7), (169), (3017), (3024), (3032),
% 166.10/24.46 | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.46 | | | | | | | | | #217.
% 166.10/24.46 | | | | | | | | |
% 166.10/24.46 | | | | | | | | Case 2:
% 166.10/24.46 | | | | | | | | |
% 166.10/24.46 | | | | | | | | | (3033) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 166.10/24.46 | | | | | | | | | op(e3, e0) = e3)
% 166.10/24.46 | | | | | | | | |
% 166.10/24.46 | | | | | | | | | BETA: splitting (3033) gives:
% 166.10/24.46 | | | | | | | | |
% 166.10/24.46 | | | | | | | | | Case 1:
% 166.10/24.46 | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | (3034) all_58_4 = e3 & op(e3, e1) = e3
% 166.10/24.46 | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | ALPHA: (3034) implies:
% 166.10/24.46 | | | | | | | | | | (3035) op(e3, e1) = e3
% 166.10/24.46 | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | REF_CLOSE: (168), (3025), (3035), (function-axioms) are
% 166.10/24.46 | | | | | | | | | | inconsistent by sub-proof #975.
% 166.10/24.46 | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | Case 2:
% 166.10/24.46 | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | (3036) all_58_9 = e3 & op(e3, e0) = e3
% 166.10/24.46 | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | ALPHA: (3036) implies:
% 166.10/24.46 | | | | | | | | | | (3037) all_58_9 = e3
% 166.10/24.46 | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | BETA: splitting (52) gives:
% 166.10/24.46 | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | Case 1:
% 166.10/24.46 | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | (3038) ~ (all_14_2 = e3)
% 166.10/24.46 | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | REDUCE: (352), (3038) imply:
% 166.10/24.46 | | | | | | | | | | | (3039) ~ (all_8_2 = e3)
% 166.10/24.46 | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | BETA: splitting (61) gives:
% 166.10/24.46 | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | Case 1:
% 166.10/24.46 | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | (3040) ~ (all_20_2 = e2)
% 166.10/24.46 | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | REDUCE: (349), (3040) imply:
% 166.10/24.46 | | | | | | | | | | | | (3041) ~ (all_4_2 = e2)
% 166.10/24.46 | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | BETA: splitting (188) gives:
% 166.10/24.46 | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | Case 1:
% 166.10/24.46 | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | (3042) all_54_15 = e3
% 166.10/24.46 | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | REF_CLOSE: (307), (3031), (3042) are inconsistent by
% 166.10/24.46 | | | | | | | | | | | | | sub-proof #992.
% 166.10/24.46 | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | Case 2:
% 166.10/24.46 | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | (3043) ~ (all_54_15 = e3)
% 166.10/24.46 | | | | | | | | | | | | | (3044) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 166.10/24.46 | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | BETA: splitting (3044) gives:
% 166.10/24.46 | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | Case 1:
% 166.10/24.46 | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | (3045) all_54_15 = e2
% 166.10/24.46 | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | REF_CLOSE: (307), (3041), (3045) are inconsistent by
% 166.10/24.46 | | | | | | | | | | | | | | sub-proof #991.
% 166.10/24.46 | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | Case 2:
% 166.10/24.46 | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | (3046) ~ (all_54_15 = e2)
% 166.10/24.46 | | | | | | | | | | | | | | (3047) all_54_15 = e1 | all_54_15 = e0
% 166.10/24.46 | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | BETA: splitting (3047) gives:
% 166.10/24.46 | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | Case 1:
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | (3048) all_54_15 = e1
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | REF_CLOSE: (307), (398), (3048) are inconsistent by sub-proof
% 166.10/24.46 | | | | | | | | | | | | | | | #990.
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | Case 2:
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | (3049) all_54_15 = e0
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | COMBINE_EQS: (307), (3049) imply:
% 166.10/24.46 | | | | | | | | | | | | | | | (3050) all_4_2 = e0
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | SIMP: (3050) implies:
% 166.10/24.46 | | | | | | | | | | | | | | | (3051) all_4_2 = e0
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | COMBINE_EQS: (262), (3051) imply:
% 166.10/24.46 | | | | | | | | | | | | | | | (3052) all_56_15 = e0
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | REDUCE: (376), (3051) imply:
% 166.10/24.46 | | | | | | | | | | | | | | | (3053) ~ (all_52_3 = e0)
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | REDUCE: (396), (3051) imply:
% 166.10/24.46 | | | | | | | | | | | | | | | (3054) ~ (all_52_13 = e0)
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | REDUCE: (397), (3051) imply:
% 166.10/24.46 | | | | | | | | | | | | | | | (3055) ~ (all_52_14 = e0)
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | REDUCE: (3031), (3051) imply:
% 166.10/24.46 | | | | | | | | | | | | | | | (3056) ~ (e3 = e0)
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | REDUCE: (3041), (3051) imply:
% 166.10/24.46 | | | | | | | | | | | | | | | (3057) ~ (e2 = e0)
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | REDUCE: (398), (3051) imply:
% 166.10/24.46 | | | | | | | | | | | | | | | (3058) ~ (e1 = e0)
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | REDUCE: (36), (3051) imply:
% 166.10/24.46 | | | | | | | | | | | | | | | (3059) op(e0, e0) = e0
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 166.10/24.46 | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | Case 1:
% 166.10/24.46 | | | | | | | | | | | | | | | |
% 166.10/24.46 | | | | | | | | | | | | | | | | (3060) all_58_15 = e0 & op(e0, e0) = e0
% 166.10/24.47 | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | ALPHA: (3060) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | (3061) all_58_15 = e0
% 166.10/24.47 | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | (3062) ~ (all_24_2 = e0)
% 166.10/24.47 | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | REDUCE: (3008), (3062) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | (3063) $false
% 166.10/24.47 | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | CLOSE: (3063) is inconsistent.
% 166.10/24.47 | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | (3064) ( ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0
% 166.10/24.47 | | | | | | | | | | | | | | | | | & op(e0, e3) = all_24_1 & $i(all_24_0) &
% 166.10/24.47 | | | | | | | | | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0, e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 166.10/24.47 | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | (3065) ~ (all_28_2 = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | REDUCE: (340), (3065) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | (3066) ~ (all_6_2 = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | (3067) ~ (all_30_2 = e0)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | REDUCE: (355), (3067) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | (3068) ~ (all_8_2 = e0)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | (3069) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3069) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | (3070) all_58_2 = e0 & op(e2, e3) = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (3010), (3070), (function-axioms) are
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | (3071) all_58_3 = e0 & op(e2, e2) = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (161), (163), (164), (166), (169),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | (196), (198), (239), (240), (241), (242), (245),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | (277), (283), (377), (379), (381), (383), (385),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | (400), (3027), (3039), (3054), (3068), (3071),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | #214.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | (3072) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3072) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | (3073) all_58_5 = e0 & op(e2, e1) = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3073) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | (3074) all_58_5 = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | (3075) op(e2, e1) = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | (3076) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3076) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (3077) all_58_1 = e0 & op(e3, e2) = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3077) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (3078) all_58_1 = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | (3079) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (3025), (3074), (3079),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | #213.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | (3080) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3080) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3081) all_58_8 = e3 & op(e1, e1) = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3066), (3081), (function-axioms) are
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3082) all_58_14 = e3 & op(e0, e1) = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3082) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3083) all_58_14 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (3084) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3084) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3085) all_58_4 = e2 & op(e3, e1) = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3085) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3086) op(e3, e1) = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (250), (3017), (3037), (3078),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3086), (function-axioms) are inconsistent by
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #211.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3087) all_58_5 = e2 & op(e2, e1) = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3087) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3088) op(e2, e1) = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3089) all_54_5 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (283), (3039), (3089) are inconsistent by
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #667.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3090) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (283), (383), (400), (3068), (3088),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3090), (function-axioms) are inconsistent by
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #467.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (3091) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3091) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3092) all_58_8 = e2 & op(e1, e1) = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (3092), (function-axioms) are
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3093) all_58_14 = e2 & op(e0, e1) = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3093) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3094) all_58_14 = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3083), (3094) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3095) e3 = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3095) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3096) $false
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3096) is inconsistent.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (3097) all_58_3 = e0 & op(e2, e2) = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (161), (163), (164), (166), (169),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (196), (198), (239), (240), (241), (242), (245),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (277), (283), (377), (379), (381), (383), (385),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (400), (3027), (3039), (3054), (3068), (3097),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | #214.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | (3098) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3098) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (3099) all_58_7 = e0 & op(e1, e2) = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3099) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (3100) all_58_7 = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | (3101) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3101) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3102) all_58_6 = e3 & op(e1, e3) = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3102) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3103) all_58_6 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3104) op(e1, e3) = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (157), (161), (162), (166), (169),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (198), (239), (240), (242), (245), (249), (251),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (283), (377), (379), (381), (400), (3007), (3016),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3017), (3039), (3064), (3068), (3103), (3104),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | #206.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3105) all_58_7 = e3 & op(e1, e2) = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3105) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3106) all_58_7 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3100), (3106) are inconsistent by sub-proof
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | #748.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | (3107) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3107) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3108) all_58_8 = e3 & op(e1, e1) = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3066), (3108), (function-axioms) are
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3109) all_58_11 = e3 & op(e1, e0) = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3109) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3110) all_58_11 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (228), (229), (3037),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3041), (3059), (3110), (function-axioms) are
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #202.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (3111) all_58_13 = e0 & op(e0, e2) = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3111) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (3112) all_58_13 = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | (3113) op(e0, e2) = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | (3114) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (169), (3024), (3039), (3114),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | #972.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | (3115) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3115) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3116) all_58_7 = e3 & op(e1, e2) = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3116) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | (3117) all_58_7 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (3118) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (3025), (3074), (3118),
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | #213.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (3119) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3119) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3120) all_58_8 = e3 & op(e1, e1) = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3066), (3120), (function-axioms) are
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3121) all_58_14 = e3 & op(e0, e1) = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3121) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3122) all_58_14 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3123) all_54_5 = e3
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (283), (3039), (3123) are inconsistent by
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #667.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3124) ~ (all_54_5 = e3)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3125) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3125) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3126) all_54_5 = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (3126) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3127) all_8_2 = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3127) implies:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3128) all_8_2 = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (3128) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3129) all_56_12 = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (377), (3128) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3130) ~ (all_52_4 = e2)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (379), (3128) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3131) ~ (all_52_6 = e2)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (383), (3128) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3132) ~ (all_52_9 = e2)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (385), (3128) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3133) ~ (all_52_13 = e2)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3039), (3128) imply:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3134) ~ (e3 = e2)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3135) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3135) gives:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3136) all_58_9 = e2 & op(e3, e0) = e2
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3037), (3136) are inconsistent by sub-proof
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #205.
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3137) all_58_10 = e2 & op(e2, e0) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3137) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3138) op(e2, e0) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3133), (3138), (function-axioms) are
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3139) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3139) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3140) all_58_11 = e2 & op(e1, e0) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3140) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3141) all_58_11 = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3142) op(e1, e0) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3143) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3143) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3144) all_58_6 = e0 & op(e1, e3) = e0
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3144) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3145) op(e1, e3) = e0
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3146) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3146) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3147) all_58_4 = e2 & op(e3, e1) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3147) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3148) all_58_4 = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3149) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3149) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3150) all_58_12 = e2 & op(e0, e3) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3150) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3151) all_58_12 = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3152) op(e0, e3) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3153) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3007), (3017), (3064), (3152), (3153),
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #208.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3154) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3154) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3155) all_58_6 = e1 & op(e1, e3) = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3155) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3156) op(e1, e3) = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (3145), (3156), (function-axioms) are
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3157) all_58_12 = e1 & op(e0, e3) = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3157) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3158) all_58_12 = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3151), (3158) are inconsistent by sub-proof
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #862.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3159) all_58_13 = e2 & op(e0, e2) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3159) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3160) op(e0, e2) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (3113), (3160), (function-axioms) are
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #631.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3161) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3161) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3162) all_58_14 = e2 & op(e0, e1) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3162) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3163) all_58_14 = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3122), (3163) imply:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3164) e3 = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3164) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3165) e3 = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3037), (3165) imply:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3166) all_58_9 = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (248), (250),
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (3024), (3148), (3166), (function-axioms)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #939.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3167) all_58_15 = e2 & op(e0, e0) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3167) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3168) op(e0, e0) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (225), (226),
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (3061), (3112), (3113), (3168),
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #628.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3169) all_58_5 = e2 & op(e2, e1) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3169) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3170) op(e2, e1) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3132), (3170), (function-axioms) are
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #571.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3171) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (399), (3122), (3171),
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #201.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3172) all_58_7 = e0 & op(e1, e2) = e0
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3172) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3173) all_58_7 = e0
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3117), (3173) are inconsistent by sub-proof
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #748.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3174) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3174) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3175) all_58_8 = e0 & op(e1, e1) = e0
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3175) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3176) all_58_8 = e0
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3177) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3177) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3178) all_58_9 = e1 & op(e3, e0) = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3178) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3179) all_58_9 = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3037), (3179) are inconsistent by sub-proof
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #896.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3180) all_58_10 = e1 & op(e2, e0) = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3180) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3181) op(e2, e0) = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3182) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3182) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3183) all_58_4 = e2 & op(e3, e1) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3183) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3184) op(e3, e1) = e2
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3185) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3185) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3186) all_58_1 = e1 & op(e3, e2) = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3186) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3187) all_58_1 = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3188) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3188) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3189) all_58_6 = e1 & op(e1, e3) = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3189) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3190) op(e1, e3) = e1
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3191) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3191) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3192) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3129), (3130), (3192), (function-axioms)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #200.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3193) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3193) gives:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3194) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3194) implies:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3195) op(e1, e3) = e3
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (3190), (3195), (function-axioms) are
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3196) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (3131), (3184), (3196),
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #199.
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3197) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3197) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3198) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3198) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3199) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3199) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3200) op(e2, e1) = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3075), (3200), (function-axioms) are
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3201) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3021), (3201) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #198.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3202) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (3052), (3142), (3181), (3202),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #196.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3203) all_58_7 = e1 & op(e1, e2) = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3203) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3204) all_58_7 = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3117), (3204) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #821.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3205) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3205) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3206) all_58_8 = e1 & op(e1, e1) = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3206) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3207) all_58_8 = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3176), (3207) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3208) e1 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3187), (3208) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3209) all_58_1 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (250), (3017), (3037), (3184),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3209), (function-axioms) are inconsistent by
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #211.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3210) all_58_11 = e1 & op(e1, e0) = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3141), (3210) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #547.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3211) all_58_3 = e1 & op(e2, e2) = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (400), (3211), (function-axioms) are
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3212) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (157), (3113), (3117), (3212),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #657.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3213) all_58_5 = e2 & op(e2, e1) = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3213) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3214) op(e2, e1) = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3132), (3214), (function-axioms) are
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #571.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3215) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (39), (399), (3122), (3215),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #201.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3216) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3216) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3217) all_58_11 = e1 & op(e1, e0) = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3217) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3218) all_58_11 = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3141), (3218) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #832.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3219) all_58_15 = e1 & op(e0, e0) = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3219) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3220) op(e0, e0) = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3059), (3220), (function-axioms) are
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #204.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3221) all_58_11 = e0 & op(e1, e0) = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3221) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3222) op(e1, e0) = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3142), (3222), (function-axioms) are
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #197.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3223) all_58_15 = e2 & op(e0, e0) = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3223) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3224) op(e0, e0) = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (225), (226),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (3061), (3112), (3113), (3224),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #628.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3225) all_54_5 = e1 | all_54_5 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (283), (400), (3068), (3225) are inconsistent by
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #735.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | (3226) all_58_13 = e3 & op(e0, e2) = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3226) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | (3227) all_58_13 = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3112), (3227) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | #708.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | (3228) all_58_10 = e0 & op(e2, e0) = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3228) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | (3229) op(e2, e0) = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (163), (228),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | (229), (3037), (3041), (3059), (3229),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | #195.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | (3230) all_30_2 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (355), (3230) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | (3231) all_8_2 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (328), (3231) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | (3232) all_42_2 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (3231) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | (3233) all_56_12 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | REDUCE: (383), (3231) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | (3234) ~ (all_52_9 = e0)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | (3235) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3235) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | (3236) all_58_2 = e0 & op(e2, e3) = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (3010), (3236), (function-axioms) are
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #693.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | (3237) all_58_3 = e0 & op(e2, e2) = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3237) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | (3238) all_58_3 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | (3239) ~ (all_56_12 = e0)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3233), (3239) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | (3240) $false
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3240) is inconsistent.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | (3241) all_56_11 = e2 & op(e2, e0) = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3241) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | (3242) all_56_11 = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | (3243) op(e2, e0) = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | (3244) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3244) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3245) all_58_6 = e0 & op(e1, e3) = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3245) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3246) all_58_6 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | (3247) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3247) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3248) all_58_6 = e3 & op(e1, e3) = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3248) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3249) all_58_6 = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3246), (3249) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | #537.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3250) all_58_7 = e3 & op(e1, e2) = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3250) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3251) all_58_7 = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3252) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3252) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3253) all_58_6 = e2 & op(e1, e3) = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3246), (3253) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #826.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3254) all_58_7 = e2 & op(e1, e2) = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3251), (3254) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #754.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3255) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (224),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (399), (3243), (3255),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | #502.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | (3256) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3256) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3257) all_58_8 = e3 & op(e1, e1) = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (3066), (3257), (function-axioms) are
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3258) all_58_11 = e3 & op(e1, e0) = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3258) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3259) all_58_11 = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (228), (3037), (3059), (3243),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3259), (function-axioms) are inconsistent by
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #203.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3260) all_58_7 = e0 & op(e1, e2) = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3260) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3261) all_58_7 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (163), (164),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (166), (169), (239), (244), (245), (246), (3010),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3024), (3039), (3234), (3243), (3261),
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | #190.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | (3262) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3262) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3263) all_58_8 = e0 & op(e1, e1) = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3263) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3264) op(e1, e1) = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e0,
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, simplifying with (39), (3264) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3265) all_6_2 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (163), (3243) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3266) all_52_13 = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (3265) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3267) all_56_14 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (3265) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3268) ~ (all_52_2 = e0)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (3266) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3269) ~ (all_52_9 = e2)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (391), (3265) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3270) ~ (all_52_11 = e0)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (3266) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3271) ~ (all_52_14 = e2)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3271) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3272) ~ (all_52_14 = e2)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3027), (3266) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | (3273) ~ (e3 = e2)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | (3274) all_54_11 = e3
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (3029), (3274) are inconsistent by
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | (3275) ~ (all_54_11 = e3)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | (3276) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3277) ~ (all_56_14 = e0)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3267), (3277) imply:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3278) $false
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3278) is inconsistent.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3279) all_56_13 = e1 & op(e1, e0) = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3279) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (3280) all_56_13 = e1
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3281) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3281) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3282) all_58_9 = e2 & op(e3, e0) = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3037), (3282) are inconsistent by sub-proof
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #205.
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3283) all_58_10 = e2 & op(e2, e0) = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3283) implies:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3284) all_58_10 = e2
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3276) gives:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3285) all_54_11 = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (3272), (3285) are inconsistent by
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #622.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3286) ~ (all_54_11 = e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3287) all_54_11 = e1 | all_54_11 = e0
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3287) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3288) all_54_11 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (3288) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3289) all_52_14 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3289) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3290) all_52_14 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (3290) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3291) ~ (all_52_2 = e1)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (3290) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3292) ~ (all_52_6 = e1)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3029), (3290) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3293) ~ (e3 = e1)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3272), (3290) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3294) ~ (e2 = e1)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3295) ~ (all_42_2 = e0)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3232), (3295) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3296) $false
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3296) is inconsistent.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3297) ( ~ (all_42_0 = e3) & op(all_42_1, e2) = all_42_0
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_42_1 & $i(all_42_0) &
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e0, e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1))
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3298) all_54_8 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (3298) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3299) all_52_2 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3299) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3300) all_52_2 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (3300) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3301) ~ (all_52_6 = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3301) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3302) ~ (all_52_6 = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3303) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3303) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3304) all_58_6 = e3 & op(e1, e3) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3304) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3305) all_58_6 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3306) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (169), (3024), (3039), (3306),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #972.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3307) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3307) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3308) all_58_7 = e3 & op(e1, e2) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3308) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3309) op(e1, e2) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3302), (3309), (function-axioms) are
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #668.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3310) all_58_13 = e3 & op(e0, e2) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3310) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3311) all_58_13 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3312) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3312) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3313) all_58_6 = e2 & op(e1, e3) = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3305), (3313) are inconsistent by sub-proof
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #189.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3314) all_58_7 = e2 & op(e1, e2) = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3314) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3315) all_58_7 = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3316) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3316) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3317) all_58_0 = e2 & op(e3, e3) = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3317) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3318) all_58_0 = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3016), (3318) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3319) e2 = e0
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3319) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3320) e2 = e0
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3315), (3320) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3321) all_58_7 = e0
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (163), (164), (166),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (244), (245), (3010), (3234), (3243),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3311), (3321), (function-axioms) are inconsistent
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #191.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3322) all_58_2 = e2 & op(e2, e3) = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (42), (166), (240), (242),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3039), (3238), (3243), (3322), (function-axioms)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #188.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3323) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3323) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3324) all_58_6 = e2 & op(e1, e3) = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3305), (3324) are inconsistent by sub-proof
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #189.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3325) all_58_12 = e2 & op(e0, e3) = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3325) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3326) all_58_12 = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3327) op(e0, e3) = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3328) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3007), (3017), (3064), (3327), (3328),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #208.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3329) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3329) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3330) all_58_6 = e1 & op(e1, e3) = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3330) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3331) all_58_6 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3332) op(e1, e3) = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3303) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3304) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3333) op(e1, e3) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (3332), (3333), (function-axioms) are
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3334) all_58_7 = e3 & op(e1, e2) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3334) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3335) all_58_7 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (224),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (233), (399), (3243), (3331),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3335), (function-axioms) are inconsistent by
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #187.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3336) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (228), (3037), (3059),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3066), (3243), (3336), (function-axioms) are
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #186.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3337) all_58_12 = e1 & op(e0, e3) = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3337) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3338) all_58_12 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3326), (3338) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3339) e2 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3339) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3340) e2 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3315), (3340) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3341) all_58_7 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (224),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (233), (399), (3243), (3305),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3341), (function-axioms) are inconsistent by
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #185.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3342) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (224),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (399), (3243), (3342),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #502.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3343) all_58_7 = e3 & op(e1, e2) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3343) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3344) op(e1, e2) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3302), (3344), (function-axioms) are
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #668.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3345) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (228), (3037), (3059),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3066), (3243), (3345), (function-axioms) are
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #186.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3346) ~ (all_54_8 = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3347) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (276), (3346) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3348) ~ (all_52_2 = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3349) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3349) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3350) all_58_6 = e3 & op(e1, e3) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3350) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3351) op(e1, e3) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3348), (3351), (function-axioms) are
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #987.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3352) all_58_7 = e3 & op(e1, e2) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3352) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3353) all_58_7 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3354) op(e1, e2) = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3347) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3355) all_54_8 = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (3355) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3356) all_52_2 = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3356) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3357) all_52_2 = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (3357) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3358) ~ (all_52_1 = e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (3357) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3359) ~ (all_52_3 = e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3359) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3360) ~ (all_52_3 = e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (3357) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3361) ~ (all_52_6 = e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3361) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3362) ~ (all_52_6 = e2)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (3357) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3363) op(e1, e3) = e2
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3364) all_54_9 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (3364) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3365) all_52_6 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3365) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3366) all_52_6 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (3366) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3367) ~ (all_52_7 = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3367) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3368) ~ (all_52_7 = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3369) all_54_4 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (3369) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3370) all_52_1 = e3
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (3370) imply:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3371) ~ (all_52_9 = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3371) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3372) ~ (all_52_9 = e3)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3373) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3373) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3374) all_58_0 = e1 & op(e3, e3) = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3374) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3375) op(e3, e3) = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3017), (3375), (function-axioms) are
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #907.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3376) all_58_2 = e1 & op(e2, e3) = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3376) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3377) all_58_2 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (42), (164), (242), (3039), (3243),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3372), (3377), (function-axioms) are inconsistent
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #677.
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3378) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3378) gives:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3379) all_58_6 = e1 & op(e1, e3) = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3379) implies:
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3380) all_58_6 = e1
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (224),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (233), (399), (3243), (3353),
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3380), (function-axioms) are inconsistent by
% 166.10/24.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #187.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3381) all_58_12 = e1 & op(e0, e3) = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3381) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3382) op(e0, e3) = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3007) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3383) ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 &
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_10_1 & $i(all_10_0) &
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3383) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3384) op(e0, e3) = all_10_1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3385) op(all_10_1, e3) = all_10_0
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3064) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3386) ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0 &
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_24_1 & $i(all_24_0) &
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_24_1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3386) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3387) ~ (all_24_0 = e2)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3388) op(e0, e3) = all_24_1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3389) op(all_24_1, e3) = all_24_0
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_24_1, e3, e0, simplifying with (3384), (3388)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3390) all_24_1 = all_10_1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_24_1,
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (3382), (3388) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3391) all_24_1 = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3390), (3391) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3392) all_10_1 = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3389), (3391) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3393) op(e1, e3) = all_24_0
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3385), (3392) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3394) op(e1, e3) = all_10_0
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_24_0,
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (3363), (3393) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3395) all_24_0 = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_0,
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_24_0, e3, e1, simplifying with (3393), (3394)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3396) all_24_0 = all_10_0
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3395), (3396) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3397) all_10_0 = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3387), (3395) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3398) $false
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3398) is inconsistent.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3399) ~ (all_24_1 = e1) & op(e0, e3) = all_24_1 &
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_24_1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3382), (3384), (3399), (function-axioms) are
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #184.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3400) ~ (all_10_1 = e2) & op(e0, e3) = all_10_1 &
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3400) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401) op(e0, e3) = all_10_1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3064) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3402) ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0 &
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_24_1 & $i(all_24_0) &
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_24_1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3402) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3403) ~ (all_24_0 = e2)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3404) op(e0, e3) = all_24_1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3405) op(all_24_1, e3) = all_24_0
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_24_1, e3, e0, simplifying with (3401), (3404)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3406) all_24_1 = all_10_1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_24_1,
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (3382), (3404) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3407) all_24_1 = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3406), (3407) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3408) all_10_1 = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3405), (3407) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3409) op(e1, e3) = all_24_0
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_24_0,
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (3363), (3409) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3410) all_24_0 = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3403), (3410) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3411) $false
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3411) is inconsistent.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3412) ~ (all_24_1 = e1) & op(e0, e3) = all_24_1 &
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_24_1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3382), (3401), (3412), (function-axioms) are
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #184.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3413) ~ (all_54_4 = e3)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3414) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (287), (3413) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3415) ~ (all_52_1 = e3)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3414) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3416) all_54_4 = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (3416) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3417) all_52_1 = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3358), (3417) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3418) $false
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3418) is inconsistent.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3419) ~ (all_54_4 = e2)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3420) all_54_4 = e1 | all_54_4 = e0
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3420) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3421) all_54_4 = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (3421) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3422) all_52_1 = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (3422) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3423) ~ (all_52_3 = e1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3423) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3424) ~ (all_52_3 = e1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (3422) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3425) ~ (all_52_9 = e1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3425) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3426) ~ (all_52_9 = e1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3427) all_54_6 = e3
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (3427) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3428) all_52_9 = e3
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3428) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3429) all_52_9 = e3
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (3429) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3430) ~ (all_52_11 = e3)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3430) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3431) ~ (all_52_11 = e3)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (3429) imply:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3432) op(e2, e1) = e3
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3433) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3433) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3434) all_58_2 = e1 & op(e2, e3) = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3434) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3435) all_58_2 = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3436) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (147), (166), (191), (265), (3039), (3053),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3360), (3424), (3436), (function-axioms) are
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #603.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3437) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3437) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3438) all_58_5 = e3 & op(e2, e1) = e3
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3438) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3439) all_58_5 = e3
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3440) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3440) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3441) all_58_1 = e2 & op(e3, e2) = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (164),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (224), (228), (230), (233), (234), (239),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (399), (3010), (3037), (3059), (3066),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3234), (3243), (3297), (3354), (3441),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #181.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3442) all_58_3 = e2 & op(e2, e2) = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3442) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3443) all_58_3 = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (239), (240),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (3039), (3284), (3435), (3443),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #915.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3444) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3444) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3445) all_58_7 = e2 & op(e1, e2) = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3445) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3446) op(e1, e2) = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3362), (3446), (function-axioms) are
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3447) all_58_13 = e2 & op(e0, e2) = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3447) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3448) op(e0, e2) = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3449) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3449) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3450) all_58_1 = e1 & op(e3, e2) = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3450) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3451) op(e3, e2) = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3452) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3452) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3453) all_58_0 = e2 & op(e3, e3) = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3016), (3453) are inconsistent by sub-proof
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #390.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3454) all_58_1 = e2 & op(e3, e2) = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (164),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (224), (228), (230), (233), (234), (239),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (399), (3010), (3037), (3059), (3066),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3234), (3243), (3297), (3354), (3454),
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #181.
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3455) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3455) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3456) all_58_4 = e2 & op(e3, e1) = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3456) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3457) op(e3, e1) = e2
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3458) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3458) gives:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3459) all_58_12 = e1 & op(e0, e3) = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3459) implies:
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3460) all_58_12 = e1
% 166.10/24.51 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (156), (157), (227), (3061), (3368),
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3431), (3460), (function-axioms) are inconsistent
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #469.
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3461) all_58_13 = e1 & op(e0, e2) = e1
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3461) implies:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3462) op(e0, e2) = e1
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3448), (3462), (function-axioms) are
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #968.
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3463) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3463) gives:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3464) all_58_14 = e1 & op(e0, e1) = e1
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3464) implies:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3465) op(e0, e1) = e1
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e1, e0, simplifying with (156), (3465) gives:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3466) all_52_11 = e1
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (168), (3457) gives:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3467) all_52_8 = e2
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (169), (3451) gives:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3468) all_52_4 = e1
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3469) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3469) gives:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3470) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3470) gives:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3471) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3471) implies:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3472) op(e2, e3) = e3
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (147), (166), (191), (265), (3053), (3360),
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3424), (3472), (function-axioms) are inconsistent
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #605.
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3473) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3473) implies:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3474) op(e3, e2) = e2
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3451), (3474), (function-axioms) are
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #180.
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3475) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3475) gives:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3476) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3476) implies:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3477) op(e1, e3) = e3
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3348), (3477), (function-axioms) are
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #987.
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3478) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (3362), (3457), (3478),
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #199.
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3479) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3479) gives:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3480) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3480) gives:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3481) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3481) implies:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3482) op(e2, e1) = e1
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3432), (3482), (function-axioms) are
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #686.
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3483) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3483) implies:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3484) all_56_9 = e0
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3021), (3484) imply:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3485) e3 = e0
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3353), (3485) imply:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3486) all_58_7 = e0
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (163), (164),
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (169), (239), (244), (245), (246), (3010),
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3024), (3039), (3234), (3243), (3486),
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #190.
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3487) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3487) gives:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3488) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3488) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3489) op(e2, e0) = e0
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (3243), (3489), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #684.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3490) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3490) gives:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3491) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3491) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3492) all_56_13 = e0
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3280), (3492) are inconsistent by sub-proof
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #977.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3493) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3233), (3242), (3493) are inconsistent by
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #683.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3494) all_58_15 = e1 & op(e0, e0) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3494) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3495) op(e0, e0) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3059), (3495), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #204.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3496) all_58_9 = e2 & op(e3, e0) = e2
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3496) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3497) all_58_9 = e2
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3037), (3497) imply:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3498) e3 = e2
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (42), (242), (3039), (3243), (3435),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3439), (3498), (function-axioms) are inconsistent
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #508.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3499) all_58_3 = e1 & op(e2, e2) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (163), (164), (166), (239), (3010),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3234), (3243), (3499), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #507.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3500) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3500) gives:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3501) all_58_7 = e1 & op(e1, e2) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (163), (224),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (233), (234), (399), (3037), (3059),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3066), (3243), (3501), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #182.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3502) all_58_13 = e1 & op(e0, e2) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3502) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3503) op(e0, e2) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3448), (3503), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #968.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3504) all_58_10 = e3 & op(e2, e0) = e3
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3504) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3505) op(e2, e0) = e3
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3027), (3505), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3506) all_58_3 = e1 & op(e2, e2) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (163), (164), (166), (239), (3010),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3234), (3243), (3506), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #507.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3507) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (3243), (3432), (3507),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #506.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3508) ~ (all_54_6 = e3)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (278), (3508) imply:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3509) ~ (all_52_9 = e3)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3510) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3510) gives:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3511) all_58_2 = e1 & op(e2, e3) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3511) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3512) all_58_2 = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (42), (164), (242), (3039), (3243),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3509), (3512), (function-axioms) are inconsistent
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #677.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3513) all_58_3 = e1 & op(e2, e2) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (163), (164), (166), (239), (3010),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3234), (3243), (3513), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #507.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3514) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3514) gives:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3515) all_58_5 = e1 & op(e2, e1) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3515) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3516) op(e2, e1) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3517) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (147), (166), (191), (265), (3039), (3053),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3360), (3424), (3517), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #603.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3518) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3518) gives:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3519) all_58_5 = e3 & op(e2, e1) = e3
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3519) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3520) op(e2, e1) = e3
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3516), (3520), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #686.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3521) all_58_10 = e3 & op(e2, e0) = e3
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3521) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3522) op(e2, e0) = e3
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3027), (3522), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3523) all_58_10 = e1 & op(e2, e0) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3523) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3524) op(e2, e0) = e1
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3243), (3524), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #526.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3525) all_54_4 = e0
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (3525) imply:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3526) all_52_1 = e0
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3010), (3526) imply:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3527) $false
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3527) is inconsistent.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3528) ~ (all_54_9 = e3)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (275), (3528) imply:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3529) ~ (all_52_6 = e3)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3354), (3529), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #668.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3530) all_54_8 = e1 | all_54_8 = e0
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (3268), (3291), (3530) are inconsistent by
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #688.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3531) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (39), (228), (3037), (3059),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3066), (3243), (3531), (function-axioms) are
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #186.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3532) all_54_11 = e0
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (3055), (3532) are inconsistent by
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #733.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3533) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (163), (224),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (230), (3041), (3243), (3533),
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | #504.
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | (3534) all_58_11 = e0 & op(e1, e0) = e0
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3534) implies:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | (3535) all_58_11 = e0
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.53 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | (3536) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3536) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3537) all_58_9 = e1 & op(e3, e0) = e1
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3037), (3537) are inconsistent by sub-proof
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | #836.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3538) all_58_10 = e1 & op(e2, e0) = e1
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3538) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3539) op(e2, e0) = e1
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3243), (3539), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #526.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | (3540) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3059), (3535), (3540), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #179.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | (3541) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (164), (217), (3233), (3234), (3541),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | #500.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | (3542) all_28_2 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (340), (3542) imply:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | (3543) all_6_2 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | SIMP: (3543) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | (3544) all_6_2 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (3544) imply:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | (3545) all_56_14 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | REDUCE: (375), (3544) imply:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | (3546) ~ (all_52_2 = e3)
% 166.10/24.54 | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | REDUCE: (386), (3544) imply:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | (3547) ~ (all_52_6 = e3)
% 166.10/24.54 | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | REDUCE: (389), (3544) imply:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | (3548) ~ (all_52_9 = e3)
% 166.10/24.54 | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | (3549) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (3549) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | (3550) all_58_4 = e0 & op(e3, e1) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3012), (3550), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #178.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | (3551) all_58_5 = e0 & op(e2, e1) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (3551) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | (3552) all_58_5 = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | (3553) op(e2, e1) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | (3554) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3554) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | (3555) all_58_2 = e3 & op(e2, e3) = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3555) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | (3556) all_58_2 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | (3557) op(e2, e3) = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | (3558) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (162), (3546), (3547), (3558),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | #177.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | (3559) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3559) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | (3560) all_58_8 = e3 & op(e1, e1) = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3560) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | (3561) all_58_8 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | (3562) ~ (all_56_14 = e3)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3545), (3562) imply:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | (3563) $false
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3563) is inconsistent.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | (3564) all_56_2 = e1 & op(e1, e3) = e1
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3564) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | (3565) all_56_2 = e1
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | (3566) op(e1, e3) = e1
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3567) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (169), (3024), (3039), (3567),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | #972.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (3568) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3568) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3569) all_58_7 = e3 & op(e1, e2) = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3569) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3570) op(e1, e2) = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3547), (3570), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #668.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3571) all_58_13 = e3 & op(e0, e2) = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3571) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3572) all_58_13 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3573) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3573) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3574) all_58_6 = e0 & op(e1, e3) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3574) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3575) op(e1, e3) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (3566), (3575), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3576) all_58_7 = e0 & op(e1, e2) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3576) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3577) all_58_7 = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3578) op(e1, e2) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (42), (159),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (162), (163), (164), (169), (209), (229),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (241), (242), (244), (245), (248),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (252), (254), (361), (400), (3016), (3024),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3027), (3037), (3039), (3041), (3052), (3054),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3055), (3545), (3553), (3556), (3565), (3566),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3572), (3577), (3578), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #174.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3579) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3579) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3580) all_58_8 = e0 & op(e1, e1) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3561), (3580) are inconsistent by sub-proof
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #496.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3581) all_58_11 = e0 & op(e1, e0) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3581) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3582) all_58_11 = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3583) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3583) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3584) all_58_9 = e1 & op(e3, e0) = e1
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3584) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3585) all_58_9 = e1
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3037), (3585) are inconsistent by sub-proof
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #896.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3586) all_58_10 = e1 & op(e2, e0) = e1
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3586) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3587) op(e2, e0) = e1
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3588) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3588) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3589) all_58_2 = e2 & op(e2, e3) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3589) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3590) op(e2, e3) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (3557), (3590), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #462.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3591) all_58_3 = e2 & op(e2, e2) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3591) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3592) all_58_3 = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3593) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3593) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3594) all_58_1 = e0 & op(e3, e2) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3594) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3595) all_58_1 = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3596) op(e3, e2) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3597) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3597) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3598) all_58_0 = e2 & op(e3, e3) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3016), (3598) are inconsistent by sub-proof
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #390.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3599) all_58_1 = e2 & op(e3, e2) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3599) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3600) op(e3, e2) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3596), (3600), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #953.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3601) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3601) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3602) all_58_4 = e2 & op(e3, e1) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3602) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3603) op(e3, e1) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (250), (3017), (3037), (3595),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3603), (function-axioms) are inconsistent by
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #211.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3604) all_58_9 = e2 & op(e3, e0) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3604) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3605) all_58_9 = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3037), (3605) are inconsistent by sub-proof
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #790.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3606) all_58_3 = e0 & op(e2, e2) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3606) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3607) all_58_3 = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3592), (3607) are inconsistent by sub-proof
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #843.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3608) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3608) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3609) all_58_7 = e0 & op(e1, e2) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3609) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3610) all_58_7 = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3611) op(e1, e2) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (42), (159),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (161), (162), (163), (164), (169), (209), (229),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (241), (242), (244), (245), (248),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (252), (254), (361), (400), (3016), (3024),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3027), (3037), (3039), (3041), (3052), (3054),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3055), (3545), (3553), (3556), (3565), (3566),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3572), (3610), (3611), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #174.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3612) all_58_13 = e0 & op(e0, e2) = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3572), (3612) are inconsistent by sub-proof
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #885.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3613) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3613) gives:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3614) all_58_5 = e2 & op(e2, e1) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3614) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3615) all_58_5 = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3552), (3615) imply:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3616) e2 = e0
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (3616) imply:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3617) $false
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3617) is inconsistent.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3618) all_58_10 = e2 & op(e2, e0) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3618) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3619) op(e2, e0) = e2
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3587), (3619), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #526.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3620) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3059), (3582), (3620), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #179.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | (3621) all_58_11 = e3 & op(e1, e0) = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3621) implies:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | (3622) all_58_11 = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (228), (229), (3037),
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | (3041), (3059), (3622), (function-axioms) are
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #202.
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | | (3623) all_58_3 = e3 & op(e2, e2) = e3
% 166.10/24.54 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (3039), (3623), (function-axioms) are
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3624) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (3027), (3548), (3624),
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | #218.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3625) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (3625) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | (3626) all_58_8 = e0 & op(e1, e1) = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (3626) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | (3627) all_58_8 = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3628) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (162), (3546), (3547), (3628),
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | #177.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3629) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3629) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3630) all_58_8 = e3 & op(e1, e1) = e3
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3630) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3631) all_58_8 = e3
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3627), (3631) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | #480.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3632) all_58_11 = e3 & op(e1, e0) = e3
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3632) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3633) all_58_11 = e3
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (228), (229), (3037),
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3041), (3059), (3633), (function-axioms) are
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #202.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | (3634) all_58_14 = e0 & op(e0, e1) = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (3634) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | (3635) all_58_14 = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3636) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (169), (3024), (3039), (3636),
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | #972.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3637) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3637) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3638) all_58_7 = e3 & op(e1, e2) = e3
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3638) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3639) op(e1, e2) = e3
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3547), (3639), (function-axioms) are
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #668.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3640) all_58_13 = e3 & op(e0, e2) = e3
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3640) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3641) all_58_13 = e3
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3642) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3642) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (3643) all_58_12 = e2 & op(e0, e3) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3643) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (3644) all_58_12 = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (225), (3059), (3635), (3641),
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (3644), (function-axioms) are inconsistent by
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #173.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (3645) all_58_13 = e2 & op(e0, e2) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3645) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (3646) all_58_13 = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3641), (3646) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | #192.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3647) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3647) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (3648) all_58_14 = e2 & op(e0, e1) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3648) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (3649) all_58_14 = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3635), (3649) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | #806.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (3650) all_58_15 = e2 & op(e0, e0) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (3041), (3650), (function-axioms) are
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | (3651) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.10/24.55 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 166.10/24.55 | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 166.10/24.55 | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 166.10/24.55 | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | ALPHA: (3651) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | (3652) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.10/24.55 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 166.10/24.55 | | | | | | | | | | | | | | | | e0) = e0)
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | BETA: splitting (3652) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | (3653) all_58_9 = e0 & op(e3, e0) = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3037), (3653) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | #901.
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | (3654) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | BETA: splitting (3654) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | (3655) all_58_10 = e0 & op(e2, e0) = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | ALPHA: (3655) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | (3656) op(e2, e0) = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (163), (228),
% 166.10/24.55 | | | | | | | | | | | | | | | | | | (229), (3037), (3041), (3059), (3656),
% 166.10/24.55 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | #195.
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | (3657) all_58_11 = e0 & op(e1, e0) = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | ALPHA: (3657) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | (3658) all_58_11 = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3659) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (3659) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | (3660) all_58_9 = e1 & op(e3, e0) = e1
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3037), (3660) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | #836.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | (3661) all_58_10 = e1 & op(e2, e0) = e1
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | ALPHA: (3661) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | (3662) all_58_10 = e1
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | (3663) op(e2, e0) = e1
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3664) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3664) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3665) all_58_9 = e2 & op(e3, e0) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3037), (3665) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | #205.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3666) all_58_10 = e2 & op(e2, e0) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3666) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3667) op(e2, e0) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3663), (3667), (function-axioms) are
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #526.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3668) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3668) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3669) all_58_11 = e2 & op(e1, e0) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3669) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3670) all_58_11 = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (3037), (3652), (3662), (3670) are
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #833.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3671) all_58_15 = e2 & op(e0, e0) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (3041), (3671), (function-axioms) are
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3672) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3059), (3658), (3672), (function-axioms) are
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #179.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | (3673) all_20_2 = e2
% 166.10/24.55 | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | COMBINE_EQS: (349), (3673) imply:
% 166.10/24.55 | | | | | | | | | | | | (3674) all_4_2 = e2
% 166.10/24.55 | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | COMBINE_EQS: (262), (3674) imply:
% 166.10/24.55 | | | | | | | | | | | | (3675) all_56_15 = e2
% 166.10/24.55 | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | REDUCE: (396), (3674) imply:
% 166.10/24.55 | | | | | | | | | | | | (3676) ~ (all_52_13 = e2)
% 166.10/24.55 | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | REDUCE: (397), (3674) imply:
% 166.10/24.55 | | | | | | | | | | | | (3677) ~ (all_52_14 = e2)
% 166.10/24.55 | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | BETA: splitting (217) gives:
% 166.10/24.55 | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | (3678) ~ (all_56_12 = e0)
% 166.10/24.55 | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | REDUCE: (361), (3678) imply:
% 166.10/24.55 | | | | | | | | | | | | | (3679) ~ (all_8_2 = e0)
% 166.10/24.55 | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | BETA: splitting (198) gives:
% 166.10/24.55 | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | (3680) all_54_5 = e3
% 166.10/24.55 | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | REF_CLOSE: (283), (3039), (3680) are inconsistent by
% 166.10/24.55 | | | | | | | | | | | | | | sub-proof #667.
% 166.10/24.55 | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | (3681) ~ (all_54_5 = e3)
% 166.10/24.55 | | | | | | | | | | | | | | (3682) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 166.10/24.55 | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | BETA: splitting (3682) gives:
% 166.10/24.55 | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | (3683) all_54_5 = e2
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | COMBINE_EQS: (283), (3683) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | (3684) all_8_2 = e2
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | SIMP: (3684) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | (3685) all_8_2 = e2
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | COMBINE_EQS: (361), (3685) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | (3686) all_56_12 = e2
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | REDUCE: (377), (3685) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | (3687) ~ (all_52_4 = e2)
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | REDUCE: (379), (3685) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | (3688) ~ (all_52_6 = e2)
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | REDUCE: (381), (3685) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | (3689) ~ (all_52_7 = e2)
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | REDUCE: (3039), (3685) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | (3690) ~ (e3 = e2)
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 166.10/24.55 | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | (3691) all_54_1 = e3
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | REF_CLOSE: (290), (3024), (3691) are inconsistent by
% 166.10/24.55 | | | | | | | | | | | | | | | | sub-proof #956.
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | (3692) ~ (all_54_1 = e3)
% 166.10/24.55 | | | | | | | | | | | | | | | | (3693) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | (3694) ~ (all_56_15 = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | REDUCE: (3675), (3694) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | (3695) $false
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | CLOSE: (3695) is inconsistent.
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | (3696) all_56_7 = e0 & op(e0, e2) = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | ALPHA: (3696) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | (3697) op(e0, e2) = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | BETA: splitting (3693) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | (3698) all_54_1 = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | REF_CLOSE: (290), (3687), (3698) are inconsistent by
% 166.10/24.55 | | | | | | | | | | | | | | | | | | sub-proof #955.
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | (3699) ~ (all_54_1 = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | (3700) all_54_1 = e1 | all_54_1 = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | BETA: splitting (3700) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3701) all_54_1 = e1
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (3701) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3702) all_52_4 = e1
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | SIMP: (3702) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3703) all_52_4 = e1
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | REDUCE: (135), (3703) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3704) ~ (all_52_6 = e1)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | SIMP: (3704) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3705) ~ (all_52_6 = e1)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | REDUCE: (134), (3703) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3706) ~ (all_52_7 = e1)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | SIMP: (3706) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3707) ~ (all_52_7 = e1)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | REDUCE: (3024), (3703) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3708) ~ (e3 = e1)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | REDUCE: (3687), (3703) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | (3709) ~ (e2 = e1)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | (3710) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3710) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3711) all_58_0 = e2 & op(e3, e3) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3016), (3711) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | #390.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3712) all_58_2 = e2 & op(e2, e3) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (161), (166),
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (169), (239), (240), (242), (245), (3687), (3688),
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3689), (3712), (function-axioms) are inconsistent
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | by sub-proof #664.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | (3713) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3713) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3714) all_58_6 = e2 & op(e1, e3) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3714) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | (3715) op(e1, e3) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3716) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3716) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3717) all_58_0 = e2 & op(e3, e3) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3016), (3717) are inconsistent by sub-proof
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | #390.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3718) all_58_1 = e2 & op(e3, e2) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3718) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3719) op(e3, e2) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3687), (3719), (function-axioms) are
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #993.
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | (3720) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3720) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3721) all_58_4 = e2 & op(e3, e1) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3721) implies:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3722) all_58_4 = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3723) op(e3, e1) = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (157), (3697) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3724) all_52_7 = e0
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (162), (3715) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3725) all_52_2 = e2
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (3725) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3726) ~ (all_52_6 = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (3725) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3727) ~ (all_52_14 = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (3725) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3728) ~ (all_6_2 = e2)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (3724) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3729) ~ (all_52_6 = e0)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3707), (3724) imply:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | (3730) ~ (e1 = e0)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (3731) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3731) gives:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.10/24.55 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (3732) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3686), (3687), (3732), (function-axioms)
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #200.
% 166.10/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (3733) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3733) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3734) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3734) implies:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3735) ~ (all_56_14 = e1)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3736) op(e1, e3) = e3
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (3735) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3737) ~ (all_6_2 = e1)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3738) ~ (all_56_14 = e3)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (3738) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3739) ~ (all_6_2 = e3)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3740) all_54_10 = e3
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (3739), (3740) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #982.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3741) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3741) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3742) all_54_10 = e2
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (399), (3742) are inconsistent by sub-proof
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #981.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3743) all_54_10 = e1 | all_54_10 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3743) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3744) all_54_10 = e1
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (305), (3737), (3744) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #980.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3745) all_54_10 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (3745) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3746) all_6_2 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3746) implies:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3747) all_6_2 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (3747) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3748) ~ (all_52_14 = e0)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3749) all_54_11 = e3
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (3029), (3749) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3750) ~ (all_54_11 = e3)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3751) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3751) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3752) all_54_11 = e2
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (3677), (3752) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #622.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3753) ~ (all_54_11 = e2)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3754) all_54_11 = e1 | all_54_11 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3754) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3755) all_54_11 = e1
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (3755) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3756) all_52_14 = e1
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3756) implies:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3757) all_52_14 = e1
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (3757) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3758) ~ (all_52_13 = e1)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3759) all_54_7 = e3
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (3027), (3759) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #533.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3760) ~ (all_54_7 = e3)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3761) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3761) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3762) all_54_7 = e2
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (3676), (3762) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #532.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3763) ~ (all_54_7 = e2)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3764) all_54_7 = e1 | all_54_7 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3764) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3765) all_54_7 = e1
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (3758), (3765) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #172.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3766) all_54_7 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (3766) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3767) all_52_13 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3767) implies:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3768) all_52_13 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3027), (3768) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3769) ~ (e3 = e0)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3676), (3768) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3770) ~ (e2 = e0)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e3,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (3715), (3736) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3771) e3 = e2
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3037), (3771) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3772) all_58_9 = e2
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (248), (250),
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (3024), (3722), (3772), (function-axioms)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #939.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3773) all_54_11 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (3748), (3773) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #733.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3774) all_56_2 = e1 & op(e1, e3) = e1
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3774) implies:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3775) op(e1, e3) = e1
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (3736), (3775), (function-axioms) are
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3776) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (3688), (3723), (3776),
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | #199.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (3777) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3777) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (3778) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3778) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3779) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3779) implies:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3780) ~ (all_56_12 = e2)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3686), (3780) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3781) $false
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3781) is inconsistent.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3782) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3021), (3782) are inconsistent by sub-proof
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | #198.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (3783) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3783) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3784) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3784) implies:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3785) ~ (all_56_12 = e2)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3686), (3785) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3786) $false
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3786) is inconsistent.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (3787) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3787) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3788) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3788) implies:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3789) all_56_13 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3790) ~ (all_56_14 = e1)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (3790) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3791) ~ (all_6_2 = e1)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3792) ~ (all_56_14 = e3)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (3792) imply:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3793) ~ (all_6_2 = e3)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (193), (214), (274), (305), (399), (3789),
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3791), (3793) are inconsistent by sub-proof #976.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3794) all_56_14 = e3
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (274), (275), (386), (3688), (3705),
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3729), (3794) are inconsistent by sub-proof #170.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3795) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3795) implies:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3796) ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3,
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_9 & $i(all_56_9))
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3009), (3021), (3796) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #169.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | (3797) all_58_9 = e2 & op(e3, e0) = e2
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3037), (3797) are inconsistent by sub-proof
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | | #205.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | (3798) all_58_12 = e2 & op(e0, e3) = e2
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (159), (161),
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | (233), (247), (249), (253), (399), (3677), (3688),
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | (3798), (function-axioms) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | | sub-proof #573.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | (3799) all_54_1 = e0
% 166.47/24.56 | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (290), (3011), (3799) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | | | | | sub-proof #614.
% 166.47/24.56 | | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | (3800) all_54_5 = e1 | all_54_5 = e0
% 166.47/24.56 | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | | REF_CLOSE: (283), (400), (3679), (3800) are inconsistent by
% 166.47/24.56 | | | | | | | | | | | | | | | sub-proof #735.
% 166.47/24.56 | | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | (3801) all_56_11 = e2 & op(e2, e0) = e2
% 166.47/24.56 | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | ALPHA: (3801) implies:
% 166.47/24.56 | | | | | | | | | | | | | (3802) op(e2, e0) = e2
% 166.47/24.56 | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | | REF_CLOSE: (163), (3676), (3802), (function-axioms) are
% 166.47/24.56 | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 166.47/24.56 | | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | End of split
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | Case 2:
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | (3803) all_14_2 = e3
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | COMBINE_EQS: (352), (3803) imply:
% 166.47/24.56 | | | | | | | | | | | (3804) all_8_2 = e3
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | SIMP: (3804) implies:
% 166.47/24.56 | | | | | | | | | | | (3805) all_8_2 = e3
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | COMBINE_EQS: (361), (3805) imply:
% 166.47/24.56 | | | | | | | | | | | (3806) all_56_12 = e3
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | REDUCE: (374), (3805) imply:
% 166.47/24.56 | | | | | | | | | | | (3807) ~ (all_52_1 = e3)
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | REDUCE: (379), (3805) imply:
% 166.47/24.56 | | | | | | | | | | | (3808) ~ (all_52_6 = e3)
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | REDUCE: (381), (3805) imply:
% 166.47/24.56 | | | | | | | | | | | (3809) ~ (all_52_7 = e3)
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | REDUCE: (383), (3805) imply:
% 166.47/24.56 | | | | | | | | | | | (3810) ~ (all_52_9 = e3)
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | BETA: splitting (246) gives:
% 166.47/24.56 | | | | | | | | | | |
% 166.47/24.56 | | | | | | | | | | | Case 1:
% 166.47/24.56 | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | (3811) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 166.47/24.57 | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.47/24.57 | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | BETA: splitting (3811) gives:
% 166.47/24.57 | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | (3812) all_58_1 = e3 & op(e3, e2) = e3
% 166.47/24.57 | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | ALPHA: (3812) implies:
% 166.47/24.57 | | | | | | | | | | | | | (3813) op(e3, e2) = e3
% 166.47/24.57 | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | REF_CLOSE: (169), (3024), (3813), (function-axioms) are
% 166.47/24.57 | | | | | | | | | | | | | inconsistent by sub-proof #974.
% 166.47/24.57 | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | (3814) all_58_3 = e3 & op(e2, e2) = e3
% 166.47/24.57 | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | ALPHA: (3814) implies:
% 166.47/24.57 | | | | | | | | | | | | | (3815) all_58_3 = e3
% 166.47/24.57 | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | BETA: splitting (219) gives:
% 166.47/24.57 | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | (3816) ~ (all_56_12 = e3)
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | REDUCE: (3806), (3816) imply:
% 166.47/24.57 | | | | | | | | | | | | | | (3817) $false
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | CLOSE: (3817) is inconsistent.
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | (3818) all_56_0 = e2 & op(e2, e3) = e2
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | ALPHA: (3818) implies:
% 166.47/24.57 | | | | | | | | | | | | | | (3819) all_56_0 = e2
% 166.47/24.57 | | | | | | | | | | | | | | (3820) op(e2, e3) = e2
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 166.47/24.57 | | | | | | | | | | | | | | e3, e2, simplifying with (166), (3820) gives:
% 166.47/24.57 | | | | | | | | | | | | | | (3821) all_52_1 = e2
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | REDUCE: (145), (3821) imply:
% 166.47/24.57 | | | | | | | | | | | | | | (3822) ~ (all_52_9 = e2)
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | SIMP: (3822) implies:
% 166.47/24.57 | | | | | | | | | | | | | | (3823) ~ (all_52_9 = e2)
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | REDUCE: (144), (3821) imply:
% 166.47/24.57 | | | | | | | | | | | | | | (3824) ~ (all_52_13 = e2)
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | SIMP: (3824) implies:
% 166.47/24.57 | | | | | | | | | | | | | | (3825) ~ (all_52_13 = e2)
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | REDUCE: (3807), (3821) imply:
% 166.47/24.57 | | | | | | | | | | | | | | (3826) ~ (e3 = e2)
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 166.47/24.57 | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | (3827) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 166.47/24.57 | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | BETA: splitting (3827) gives:
% 166.47/24.57 | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | (3828) all_58_0 = e2 & op(e3, e3) = e2
% 166.47/24.57 | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3016), (3828) are inconsistent by sub-proof
% 166.47/24.57 | | | | | | | | | | | | | | | | #390.
% 166.47/24.57 | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | (3829) all_58_2 = e2 & op(e2, e3) = e2
% 166.47/24.57 | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | ALPHA: (3829) implies:
% 166.47/24.57 | | | | | | | | | | | | | | | | (3830) all_58_2 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | (3831) ~ (all_20_2 = e2)
% 166.47/24.57 | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | REDUCE: (349), (3831) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | (3832) ~ (all_4_2 = e2)
% 166.47/24.57 | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | (3833) all_54_15 = e3
% 166.47/24.57 | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | REF_CLOSE: (307), (3031), (3833) are inconsistent by
% 166.47/24.57 | | | | | | | | | | | | | | | | | | sub-proof #992.
% 166.47/24.57 | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | (3834) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | BETA: splitting (3834) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | (3835) all_54_15 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (3835) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | (3836) all_4_2 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | REDUCE: (3832), (3836) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | (3837) $false
% 166.47/24.57 | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | CLOSE: (3837) is inconsistent.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | (3838) all_54_15 = e1 | all_54_15 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | BETA: splitting (3838) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | (3839) all_54_15 = e1
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (3839) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | (3840) all_4_2 = e1
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (3840) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | (3841) $false
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | CLOSE: (3841) is inconsistent.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | (3842) all_54_15 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (3842) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | (3843) all_4_2 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (396), (3843) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | (3844) ~ (all_52_13 = e0)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | REDUCE: (397), (3843) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | (3845) ~ (all_52_14 = e0)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | (3846) all_54_7 = e3
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (3846) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | (3847) all_52_13 = e3
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | REDUCE: (3027), (3847) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | (3848) $false
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | CLOSE: (3848) is inconsistent.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | (3849) ~ (all_54_7 = e3)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | (3850) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3850) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | (3851) all_54_7 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (3851) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | (3852) all_52_13 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3825), (3852) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | (3853) $false
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3853) is inconsistent.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | (3854) all_54_7 = e1 | all_54_7 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3854) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | (3855) all_54_7 = e1
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (3855) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | (3856) all_52_13 = e1
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3856) implies:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | (3857) all_52_13 = e1
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (3857) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | (3858) ~ (all_52_9 = e1)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (3857) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | (3859) ~ (all_52_14 = e1)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3859) implies:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | (3860) ~ (all_52_14 = e1)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3027), (3857) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | (3861) ~ (e3 = e1)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (3857) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | (3862) op(e2, e0) = e1
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | (3863) all_54_6 = e3
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (3863) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | (3864) all_52_9 = e3
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3810), (3864) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | (3865) $false
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3865) is inconsistent.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | (3866) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | (3867) all_54_11 = e3
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (3029), (3867) are inconsistent by
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | (3868) ~ (all_54_11 = e3)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | (3869) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3869) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (3870) all_54_11 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (3870) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (3871) all_52_14 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3871) implies:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (3872) all_52_14 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (3872) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (3873) ~ (all_52_6 = e2)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (393), (3872) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (3874) ~ (all_6_2 = e2)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (3872) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | (3875) op(e1, e0) = e2
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3866) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3876) all_54_6 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (3876) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3877) all_52_9 = e2
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3823), (3877) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3878) $false
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3878) is inconsistent.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3879) ~ (all_54_6 = e2)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3880) all_54_6 = e1 | all_54_6 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3880) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3881) all_54_6 = e1
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (3881) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3882) all_52_9 = e1
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3858), (3882) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3883) $false
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3883) is inconsistent.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3884) all_54_6 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (3884) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3885) all_52_9 = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (389), (3885) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3886) ~ (all_6_2 = e0)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3886) implies:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3887) ~ (all_6_2 = e0)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3823), (3885) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3888) ~ (e2 = e0)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3858), (3885) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3889) ~ (e1 = e0)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (3885) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3890) op(e2, e1) = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3891) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3891) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3892) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (3806), (3819), (3820), (3892),
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #367.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3893) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3893) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3894) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3894) implies:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3895) ~ (all_56_14 = e1)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3896) op(e1, e3) = e3
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (3895) imply:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3897) ~ (all_6_2 = e1)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (193), (216), (274), (305), (399),
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3887), (3896), (3897), (function-axioms) are
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #168.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3898) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3806), (3819), (3873), (3898),
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #167.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3899) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3899) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3900) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3806), (3819), (3890), (3900),
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3901) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3901) gives:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3902) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3902) implies:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3903) op(e2, e0) = e0
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3862), (3903), (function-axioms) are
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #849.
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.57 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3904) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3904) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3905) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3905) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3906) op(e1, e0) = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3875), (3906), (function-axioms) are
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #197.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3907) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3907) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3908) ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3,
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_9 & $i(all_56_9))
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3009), (3021), (3908) are inconsistent by
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #169.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (3909) all_54_11 = e1 | all_54_11 = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (3845), (3860), (3909) are inconsistent by
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #732.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | (3910) all_54_7 = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (3844), (3910) are inconsistent by
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #529.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | (3911) all_20_2 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (3911) imply:
% 166.47/24.58 | | | | | | | | | | | | | | | | | (3912) all_4_2 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (3912) imply:
% 166.47/24.58 | | | | | | | | | | | | | | | | | (3913) all_56_15 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | REDUCE: (397), (3912) imply:
% 166.47/24.58 | | | | | | | | | | | | | | | | | (3914) ~ (all_52_14 = e2)
% 166.47/24.58 | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | (3915) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.47/24.58 | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | BETA: splitting (3915) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (3916) all_58_9 = e2 & op(e3, e0) = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | ALPHA: (3916) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (3917) all_58_9 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3037), (3917) imply:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (3918) e3 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3815), (3918) imply:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (3919) all_58_3 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (242), (3820), (3919), (function-axioms) are
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #665.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (3920) all_58_10 = e2 & op(e2, e0) = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (3815), (3820), (3920), (function-axioms) are
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | (3921) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.47/24.58 | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | BETA: splitting (3921) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (3922) all_58_11 = e2 & op(e1, e0) = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3914), (3922), (function-axioms) are
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (3923) all_58_15 = e2 & op(e0, e0) = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | ALPHA: (3923) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (3924) all_58_15 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | (3925) op(e0, e0) = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | (3926) all_56_10 = e3
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3009), (3926) are inconsistent by sub-proof
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | #166.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | (3927) ~ (all_56_10 = e3)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | (3928) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | REDUCE: (3009), (3927) imply:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | (3929) ~ (e3 = e0)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | (3930) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3930) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | (3931) all_58_6 = e2 & op(e1, e3) = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | (242), (247), (249), (253), (3815), (3820),
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | (3830), (3931), (function-axioms) are inconsistent
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #252.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | (3932) all_58_7 = e2 & op(e1, e2) = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3932) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | (3933) all_58_7 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | (3934) op(e1, e2) = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | (3935) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3935) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | (3936) all_58_4 = e2 & op(e3, e1) = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3936) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | (3937) op(e3, e1) = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | (3938) ~ (all_56_15 = e2)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3913), (3938) imply:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | (3939) $false
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3939) is inconsistent.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | (3940) all_56_7 = e0 & op(e0, e2) = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3940) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | (3941) all_56_7 = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (3942) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3942) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3943) all_58_1 = e0 & op(e3, e2) = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3943) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3944) all_58_1 = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (250), (3017), (3037), (3937),
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3944), (function-axioms) are inconsistent by
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #211.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3945) all_58_3 = e0 & op(e2, e2) = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3815), (3945) are inconsistent by sub-proof
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | #869.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (3946) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3946) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3947) all_58_7 = e0 & op(e1, e2) = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3947) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3948) op(e1, e2) = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3934), (3948), (function-axioms) are
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #175.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3949) all_58_13 = e0 & op(e0, e2) = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3949) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3950) all_58_13 = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3951) op(e0, e2) = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3928) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3952) all_56_12 = e2
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (3806), (3815), (3820), (3952),
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #165.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3953) ~ (all_56_12 = e2)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3954) all_56_14 = e1 | all_56_15 = e0
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3954) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3955) all_56_14 = e1
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3956) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3956) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3957) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (3806), (3819), (3820), (3957),
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #367.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3958) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3958) gives:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3959) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3959) implies:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3960) ~ (all_56_14 = e1)
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3955), (3960) imply:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3961) $false
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3961) is inconsistent.
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3962) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3962) gives:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3963) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3963) implies:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3964) ~ (all_56_14 = e1)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3955), (3964) imply:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3965) $false
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3965) is inconsistent.
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3966) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3966) implies:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3967) ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_0 & $i(all_56_0))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3806), (3819), (3967) are inconsistent by
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #368.
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3968) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3968) gives:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3969) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3806), (3819), (3913), (3941), (3969) are
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #163.
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3970) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3970) gives:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3971) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3971) implies:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3972) ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3913), (3941), (3972) are inconsistent by
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #164.
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3973) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3973) gives:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3974) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3974) implies:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3975) ~ (all_56_14 = e1)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3955), (3975) imply:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3976) $false
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3976) is inconsistent.
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3977) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3977) implies:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3978) ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3,
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_9 & $i(all_56_9))
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3009), (3021), (3978) are inconsistent by
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #169.
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3979) all_56_15 = e0
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3913), (3979) imply:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3980) e2 = e0
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3924), (3980) imply:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3981) all_58_15 = e0
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (225), (226),
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (3925), (3950), (3951), (3981),
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #628.
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | (3982) all_58_5 = e2 & op(e2, e1) = e2
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | (3815), (3820), (3982), (function-axioms) are
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #412.
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | (3983) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3983) gives:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | (3984) all_58_8 = e2 & op(e1, e1) = e2
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (3984), (function-axioms) are
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | (3985) all_58_14 = e2 & op(e0, e1) = e2
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3985) implies:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | (3986) all_58_14 = e2
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | (3987) op(e0, e1) = e2
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | (3988) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (3025), (3810), (3988),
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | #499.
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | (3989) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3989) gives:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (3990) all_58_8 = e3 & op(e1, e1) = e3
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3990) implies:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (3991) all_58_8 = e3
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3992) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3992) gives:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3993) all_58_12 = e3 & op(e0, e3) = e3
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3993) implies:
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3994) all_58_12 = e3
% 166.47/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (163), (164),
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (224), (228), (230), (235), (236), (238),
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (244), (247), (249), (252),
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253), (3027), (3810), (3815), (3820), (3830),
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3924), (3933), (3986), (3987), (3994),
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #223.
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3995) all_58_13 = e3 & op(e0, e2) = e3
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3809), (3995), (function-axioms) are
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #962.
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3996) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3996) gives:
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3997) all_58_14 = e3 & op(e0, e1) = e3
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3997) implies:
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3998) all_58_14 = e3
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (166), (235),
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (237), (239), (240), (242), (399), (3815),
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3820), (3991), (3998), (function-axioms) are
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #162.
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3999) all_58_15 = e3 & op(e0, e0) = e3
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (3031), (3999), (function-axioms) are
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (4000) all_58_14 = e3 & op(e0, e1) = e3
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4000) implies:
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (4001) all_58_14 = e3
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3986), (4001) imply:
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (4002) e3 = e2
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3815), (4002) imply:
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (4003) all_58_3 = e2
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 166.62/24.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (3820), (4003), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #665.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | (4004) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4004) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4005) all_58_8 = e2 & op(e1, e1) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (4005), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4006) all_58_11 = e2 & op(e1, e0) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3914), (4006), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | (4007) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 166.62/24.60 | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | BETA: splitting (4007) gives:
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | (4008) all_58_6 = e2 & op(e1, e3) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | ALPHA: (4008) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | (4009) all_58_6 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | (4010) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 166.62/24.60 | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.62/24.60 | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | BETA: splitting (4010) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | (4011) all_58_12 = e3 & op(e0, e3) = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | ALPHA: (4011) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | (4012) all_58_12 = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (247), (249),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | (3820), (4009), (4012), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #329.
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | (4013) all_58_13 = e3 & op(e0, e2) = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3809), (4013), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #962.
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | (4014) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 166.62/24.60 | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 166.62/24.60 | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | BETA: splitting (4014) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | (4015) all_58_14 = e3 & op(e0, e1) = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | ALPHA: (4015) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | (4016) all_58_14 = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | (4017) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 166.62/24.60 | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (4017) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (4018) all_58_6 = e3 & op(e1, e3) = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (4018) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (4019) all_58_6 = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4009), (4019) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (4020) e3 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3815), (4020) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (4021) all_58_3 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (242), (3820), (4021), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #665.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (4022) all_58_7 = e3 & op(e1, e2) = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (4022) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (4023) op(e1, e2) = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3808), (4023), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #668.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | (4024) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 166.62/24.60 | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | BETA: splitting (4024) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (4025) all_58_8 = e3 & op(e1, e1) = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (4025) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (4026) all_58_8 = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (166), (235),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (236), (237), (239), (240), (242), (399), (3815),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (3820), (4016), (4026), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #162.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (4027) all_58_11 = e3 & op(e1, e0) = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | ALPHA: (4027) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | (4028) all_58_11 = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | (4029) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4029) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4030) all_58_4 = e2 & op(e3, e1) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4030) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4031) all_58_4 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | (4032) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4032) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4033) all_58_9 = e2 & op(e3, e0) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4033) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4034) all_58_9 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (248), (250),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (254), (3024), (4031), (4034), (function-axioms)
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #939.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4035) all_58_10 = e2 & op(e2, e0) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (3815), (3820), (4035), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | (4036) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4036) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4037) all_58_11 = e2 & op(e1, e0) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4037) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4038) all_58_11 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4028), (4038) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4039) e3 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4039) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4040) e3 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3815), (4040) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4041) all_58_3 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (242), (3820), (4041), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #665.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4042) all_58_15 = e2 & op(e0, e0) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4042) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4043) all_58_15 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4044) op(e0, e0) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (224), (228), (3037),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | (4028), (4043), (4044), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #160.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4045) all_58_5 = e2 & op(e2, e1) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (3815), (3820), (4045), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #412.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | (4046) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4046) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4047) all_58_8 = e2 & op(e1, e1) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4047) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4048) all_58_8 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (232), (234),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4009), (4028), (4048) are inconsistent by
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | sub-proof #157.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4049) all_58_14 = e2 & op(e0, e1) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4049) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4050) all_58_14 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4016), (4050) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4051) e3 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4051) implies:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4052) e3 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3815), (4052) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (4053) all_58_3 = e2
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | (242), (3820), (4053), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #665.
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | (4054) all_58_15 = e3 & op(e0, e0) = e3
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (3031), (4054), (function-axioms) are
% 166.62/24.60 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 166.62/24.60 | | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | (4055) all_58_12 = e2 & op(e0, e3) = e2
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 166.62/24.60 | | | | | | | | | | | | | | | | (241), (242), (247), (249), (253), (3815), (3820),
% 166.62/24.60 | | | | | | | | | | | | | | | | (4055), (function-axioms) are inconsistent by
% 166.62/24.60 | | | | | | | | | | | | | | | | sub-proof #156.
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | (4056) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 166.62/24.60 | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.62/24.60 | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | REF_CLOSE: (157), (161), (3808), (3809), (4056),
% 166.62/24.60 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.62/24.60 | | | | | | | | | | | | #463.
% 166.62/24.60 | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | End of split
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | End of split
% 166.62/24.60 | | | | | | | |
% 166.62/24.60 | | | | | | | End of split
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | Case 2:
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | (4057) all_58_1 = e0 & op(e3, e2) = e0
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | REF_CLOSE: (169), (3011), (4057), (function-axioms) are
% 166.62/24.60 | | | | | | | inconsistent by sub-proof #155.
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | End of split
% 166.62/24.60 | | | | | |
% 166.62/24.60 | | | | | Case 2:
% 166.62/24.60 | | | | | |
% 166.62/24.60 | | | | | | (4058) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 166.62/24.60 | | | | | | op(e3, e0) = e0)
% 166.62/24.60 | | | | | |
% 166.62/24.60 | | | | | | REF_CLOSE: (7), (167), (168), (220), (3009), (3012), (4058),
% 166.62/24.60 | | | | | | (function-axioms) are inconsistent by sub-proof #152.
% 166.62/24.60 | | | | | |
% 166.62/24.60 | | | | | End of split
% 166.62/24.60 | | | | |
% 166.62/24.60 | | | | End of split
% 166.62/24.60 | | | |
% 166.62/24.60 | | | Case 2:
% 166.62/24.60 | | | |
% 166.62/24.60 | | | | (4059) all_8_2 = e1
% 166.62/24.60 | | | |
% 166.62/24.60 | | | | COMBINE_EQS: (361), (4059) imply:
% 166.62/24.60 | | | | (4060) all_56_12 = e1
% 166.62/24.60 | | | |
% 166.62/24.60 | | | | REDUCE: (374), (4059) imply:
% 166.62/24.60 | | | | (4061) ~ (all_52_1 = e1)
% 166.62/24.60 | | | |
% 166.62/24.60 | | | | REDUCE: (377), (4059) imply:
% 166.62/24.60 | | | | (4062) ~ (all_52_4 = e1)
% 166.62/24.60 | | | |
% 166.62/24.60 | | | | REDUCE: (379), (4059) imply:
% 166.62/24.60 | | | | (4063) ~ (all_52_6 = e1)
% 166.62/24.60 | | | |
% 166.62/24.60 | | | | REDUCE: (381), (4059) imply:
% 166.62/24.60 | | | | (4064) ~ (all_52_7 = e1)
% 166.62/24.60 | | | |
% 166.62/24.60 | | | | REDUCE: (383), (4059) imply:
% 166.62/24.60 | | | | (4065) ~ (all_52_9 = e1)
% 166.62/24.60 | | | |
% 166.62/24.60 | | | | REDUCE: (385), (4059) imply:
% 166.62/24.60 | | | | (4066) ~ (all_52_13 = e1)
% 166.62/24.60 | | | |
% 166.62/24.60 | | | | BETA: splitting (218) gives:
% 166.62/24.60 | | | |
% 166.62/24.60 | | | | Case 1:
% 166.62/24.60 | | | | |
% 166.62/24.60 | | | | | (4067) ~ (all_56_12 = e1)
% 166.62/24.60 | | | | |
% 166.62/24.60 | | | | | REDUCE: (4060), (4067) imply:
% 166.62/24.60 | | | | | (4068) $false
% 166.62/24.60 | | | | |
% 166.62/24.60 | | | | | CLOSE: (4068) is inconsistent.
% 166.62/24.60 | | | | |
% 166.62/24.60 | | | | Case 2:
% 166.62/24.60 | | | | |
% 166.62/24.60 | | | | | (4069) all_56_5 = e2 & op(e2, e1) = e2
% 166.62/24.60 | | | | |
% 166.62/24.60 | | | | | ALPHA: (4069) implies:
% 166.62/24.60 | | | | | (4070) all_56_5 = e2
% 166.62/24.60 | | | | | (4071) op(e2, e1) = e2
% 166.62/24.60 | | | | |
% 166.62/24.60 | | | | | BETA: splitting (244) gives:
% 166.62/24.60 | | | | |
% 166.62/24.60 | | | | | Case 1:
% 166.62/24.60 | | | | | |
% 166.62/24.60 | | | | | | (4072) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 166.62/24.60 | | | | | | op(e2, e2) = e1)
% 166.62/24.60 | | | | | |
% 166.62/24.60 | | | | | | BETA: splitting (4072) gives:
% 166.62/24.60 | | | | | |
% 166.62/24.60 | | | | | | Case 1:
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | (4073) all_58_1 = e1 & op(e3, e2) = e1
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | REF_CLOSE: (169), (4062), (4073), (function-axioms) are
% 166.62/24.60 | | | | | | | inconsistent by sub-proof #863.
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | Case 2:
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | (4074) all_58_3 = e1 & op(e2, e2) = e1
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | ALPHA: (4074) implies:
% 166.62/24.60 | | | | | | | (4075) all_58_3 = e1
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 166.62/24.60 | | | | | | | e1, e2, simplifying with (164), (4071) gives:
% 166.62/24.60 | | | | | | | (4076) all_52_9 = e2
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | REDUCE: (145), (4076) imply:
% 166.62/24.60 | | | | | | | (4077) ~ (all_52_1 = e2)
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | REDUCE: (122), (4076) imply:
% 166.62/24.60 | | | | | | | (4078) ~ (all_52_8 = e2)
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | REDUCE: (116), (4076) imply:
% 166.62/24.60 | | | | | | | (4079) ~ (all_52_13 = e2)
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | SIMP: (4079) implies:
% 166.62/24.60 | | | | | | | (4080) ~ (all_52_13 = e2)
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | REDUCE: (389), (4076) imply:
% 166.62/24.60 | | | | | | | (4081) ~ (all_6_2 = e2)
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | BETA: splitting (241) gives:
% 166.62/24.60 | | | | | | |
% 166.62/24.60 | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | |
% 166.62/24.60 | | | | | | | | (4082) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 166.62/24.60 | | | | | | | | op(e2, e2) = e2)
% 166.62/24.60 | | | | | | | |
% 166.62/24.60 | | | | | | | | BETA: splitting (4082) gives:
% 166.62/24.60 | | | | | | | |
% 166.62/24.60 | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | | (4083) all_58_2 = e2 & op(e2, e3) = e2
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | | ALPHA: (4083) implies:
% 166.62/24.60 | | | | | | | | | (4084) op(e2, e3) = e2
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (166), (239), (242),
% 166.62/24.60 | | | | | | | | | (4071), (4075), (4084), (function-axioms) are
% 166.62/24.60 | | | | | | | | | inconsistent by sub-proof #149.
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | | (4085) all_58_3 = e2 & op(e2, e2) = e2
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | | ALPHA: (4085) implies:
% 166.62/24.60 | | | | | | | | | (4086) all_58_3 = e2
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | | REF_CLOSE: (6), (4075), (4086) are inconsistent by sub-proof
% 166.62/24.60 | | | | | | | | | #924.
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | End of split
% 166.62/24.60 | | | | | | | |
% 166.62/24.60 | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | |
% 166.62/24.60 | | | | | | | | (4087) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 166.62/24.60 | | | | | | | | op(e2, e0) = e2)
% 166.62/24.60 | | | | | | | |
% 166.62/24.60 | | | | | | | | BETA: splitting (4087) gives:
% 166.62/24.60 | | | | | | | |
% 166.62/24.60 | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | | (4088) all_58_5 = e2 & op(e2, e1) = e2
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | | ALPHA: (4088) implies:
% 166.62/24.60 | | | | | | | | | (4089) all_58_5 = e2
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | | BETA: splitting (46) gives:
% 166.62/24.60 | | | | | | | | |
% 166.62/24.60 | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | (4090) ~ (all_10_2 = e0)
% 166.62/24.60 | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | BETA: splitting (55) gives:
% 166.62/24.60 | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | (4091) ~ (all_16_2 = e2)
% 166.62/24.60 | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | REDUCE: (350), (4091) imply:
% 166.62/24.60 | | | | | | | | | | | (4092) ~ (all_10_2 = e2)
% 166.62/24.60 | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | BETA: splitting (61) gives:
% 166.62/24.60 | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | (4093) ~ (all_20_2 = e2)
% 166.62/24.60 | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | REDUCE: (349), (4093) imply:
% 166.62/24.60 | | | | | | | | | | | | (4094) ~ (all_4_2 = e2)
% 166.62/24.60 | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | BETA: splitting (73) gives:
% 166.62/24.60 | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | (4095) ~ (all_28_2 = e3)
% 166.62/24.60 | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | REDUCE: (340), (4095) imply:
% 166.62/24.60 | | | | | | | | | | | | | (4096) ~ (all_6_2 = e3)
% 166.62/24.60 | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | BETA: splitting (79) gives:
% 166.62/24.60 | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | (4097) ~ (all_32_2 = e1)
% 166.62/24.60 | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | REDUCE: (356), (4097) imply:
% 166.62/24.60 | | | | | | | | | | | | | | (4098) ~ (all_10_2 = e1)
% 166.62/24.60 | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 166.62/24.60 | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | (4099) all_54_0 = e3
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | COMBINE_EQS: (300), (4099) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | (4100) all_10_2 = e3
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | COMBINE_EQS: (298), (4100) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | (4101) all_56_10 = e3
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | REDUCE: (363), (4100) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | (4102) ~ (all_52_1 = e3)
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | REDUCE: (369), (4100) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | (4103) ~ (all_52_4 = e3)
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 166.62/24.60 | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | (4104) all_54_4 = e3
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (4104) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | | (4105) all_52_1 = e3
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | REDUCE: (4102), (4105) imply:
% 166.62/24.60 | | | | | | | | | | | | | | | | (4106) $false
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | CLOSE: (4106) is inconsistent.
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | Case 2:
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | (4107) ~ (all_54_4 = e3)
% 166.62/24.60 | | | | | | | | | | | | | | | | (4108) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | BETA: splitting (4108) gives:
% 166.62/24.60 | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.60 | | | | | | | | | | | | | | | | |
% 166.62/24.60 | | | | | | | | | | | | | | | | | (4109) all_54_4 = e2
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (4109) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4110) all_52_1 = e2
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | REDUCE: (4077), (4110) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4111) $false
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | CLOSE: (4111) is inconsistent.
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4112) all_54_4 = e1 | all_54_4 = e0
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | BETA: splitting (4112) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | (4113) all_54_4 = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (4113) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | (4114) all_52_1 = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | REDUCE: (4061), (4114) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | (4115) $false
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | CLOSE: (4115) is inconsistent.
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | (4116) all_54_4 = e0
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (287), (4116) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | (4117) all_52_1 = e0
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | REDUCE: (144), (4117) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | (4118) ~ (all_52_13 = e0)
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | SIMP: (4118) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | (4119) ~ (all_52_13 = e0)
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4120) all_54_7 = e3
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (277), (4120) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4121) all_52_13 = e3
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | SIMP: (4121) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4122) all_52_13 = e3
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | REDUCE: (112), (4122) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4123) ~ (all_52_12 = e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | REDUCE: (396), (4122) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4124) ~ (all_4_2 = e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | SIMP: (4124) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4125) ~ (all_4_2 = e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | REDUCE: (163), (4122) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4126) op(e2, e0) = e3
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (4127) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4127) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (4128) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (4101), (4102), (4128), (function-axioms)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #988.
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (4129) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4060), (4070), (4101), (4129) are inconsistent by
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | sub-proof #147.
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (4130) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4130) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (4131) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4131) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (4132) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4070), (4132) are inconsistent by sub-proof
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | #146.
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (4133) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4133) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (4134) ~ (all_56_10 = e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4101), (4134) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (4135) $false
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4135) is inconsistent.
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (4136) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4136) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (4137) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (202), (220), (290), (4101), (4103),
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (4123), (4126), (4137), (function-axioms) are
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #144.
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (4138) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4138) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | (4139) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4139) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | (4140) ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4060), (4070), (4140) are inconsistent by
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #148.
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | (4141) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (262), (307), (398), (4094), (4125), (4141)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #143.
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4142) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (277), (4066), (4080), (4119), (4142) are
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #615.
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | (4143) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | REF_CLOSE: (300), (4090), (4092), (4098), (4143) are
% 166.62/24.61 | | | | | | | | | | | | | | | inconsistent by sub-proof #958.
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | (4144) all_32_2 = e1
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | COMBINE_EQS: (356), (4144) imply:
% 166.62/24.61 | | | | | | | | | | | | | | (4145) all_10_2 = e1
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | SIMP: (4145) implies:
% 166.62/24.61 | | | | | | | | | | | | | | (4146) all_10_2 = e1
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | COMBINE_EQS: (298), (4146) imply:
% 166.62/24.61 | | | | | | | | | | | | | | (4147) all_56_10 = e1
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | REDUCE: (371), (4146) imply:
% 166.62/24.61 | | | | | | | | | | | | | | (4148) ~ (all_52_8 = e1)
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | REDUCE: (373), (4146) imply:
% 166.62/24.61 | | | | | | | | | | | | | | (4149) ~ (all_52_12 = e1)
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | REDUCE: (4092), (4146) imply:
% 166.62/24.61 | | | | | | | | | | | | | | (4150) ~ (e2 = e1)
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | REDUCE: (45), (4146) imply:
% 166.62/24.61 | | | | | | | | | | | | | | (4151) op(e3, e3) = e1
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 166.62/24.61 | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | (4152) ~ (all_56_10 = e1)
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | REDUCE: (4147), (4152) imply:
% 166.62/24.61 | | | | | | | | | | | | | | | (4153) $false
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | CLOSE: (4153) is inconsistent.
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | (4154) all_56_4 = e3 & op(e3, e1) = e3
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | ALPHA: (4154) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | (4155) all_56_4 = e3
% 166.62/24.61 | | | | | | | | | | | | | | | (4156) op(e3, e1) = e3
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 166.62/24.61 | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | (4157) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 166.62/24.61 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.62/24.61 | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | BETA: splitting (4157) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4158) all_58_9 = e1 & op(e3, e0) = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | ALPHA: (4158) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4159) all_58_9 = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4160) op(e3, e0) = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (157),
% 166.62/24.61 | | | | | | | | | | | | | | | | | (162), (163), (166), (168), (217), (221), (224),
% 166.62/24.61 | | | | | | | | | | | | | | | | | (225), (226), (229), (230), (231), (232), (233),
% 166.62/24.61 | | | | | | | | | | | | | | | | | (234), (235), (238), (239), (242), (243), (244),
% 166.62/24.61 | | | | | | | | | | | | | | | | | (246), (247), (248), (249), (251), (252), (253),
% 166.62/24.61 | | | | | | | | | | | | | | | | | (254), (398), (399), (4060), (4071), (4075),
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4080), (4094), (4096), (4147), (4151), (4156),
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4159), (4160), (function-axioms) are inconsistent
% 166.62/24.61 | | | | | | | | | | | | | | | | | by sub-proof #129.
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4161) all_58_10 = e1 & op(e2, e0) = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | ALPHA: (4161) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4162) all_58_10 = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4163) op(e2, e0) = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (242),
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4071), (4075), (4162), (4163), (function-axioms)
% 166.62/24.61 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #127.
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | End of split
% 166.62/24.61 | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | Case 2:
% 166.62/24.61 | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | (4164) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 166.62/24.61 | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.62/24.61 | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | BETA: splitting (4164) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4165) all_58_11 = e1 & op(e1, e0) = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | ALPHA: (4165) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4166) all_58_11 = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | | (4167) op(e1, e0) = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | (4168) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | BETA: splitting (4168) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4169) all_58_12 = e1 & op(e0, e3) = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | ALPHA: (4169) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4170) all_58_12 = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | (4171) op(e0, e3) = e1
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | (4172) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4172) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (4173) all_58_9 = e2 & op(e3, e0) = e2
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4173) implies:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (4174) all_58_9 = e2
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | (4175) op(e3, e0) = e2
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | (4176) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4176) gives:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | | (4177) all_58_12 = e2 & op(e0, e3) = e2
% 166.62/24.61 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (163),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (221), (226), (229), (231), (232),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | (233), (234), (235), (238), (239), (242), (243),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | (244), (246), (248), (251), (252), (254), (399),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | (4071), (4075), (4080), (4094), (4096), (4147),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | (4151), (4170), (4174), (4177), (function-axioms)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #126.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | (4178) all_58_13 = e2 & op(e0, e2) = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4178) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | (4179) all_58_13 = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | (4180) op(e0, e2) = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | (4181) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4181) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | (4182) all_58_0 = e1 & op(e3, e3) = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4182) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | (4183) all_58_0 = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (4184) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (242),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (4071), (4075), (4151), (4184), (function-axioms)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #141.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (4185) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4185) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4186) all_58_6 = e2 & op(e1, e3) = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4186) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4187) all_58_6 = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (247), (253), (4151),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4171), (4183), (4187), (function-axioms) are
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #124.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4188) all_58_12 = e2 & op(e0, e3) = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (163),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (221), (226), (229), (231), (232),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (233), (234), (235), (238), (239), (242), (243),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (244), (246), (248), (251), (252), (254), (399),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4071), (4075), (4080), (4094), (4096), (4147),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4151), (4170), (4174), (4188), (function-axioms)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #126.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | (4189) all_58_1 = e1 & op(e3, e2) = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4062), (4189), (function-axioms) are
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #863.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | (4190) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4190) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | (4191) all_58_4 = e1 & op(e3, e1) = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4191) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | (4192) all_58_4 = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | (4193) op(e3, e1) = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (4194) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4194) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4195) all_58_4 = e3 & op(e3, e1) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4195) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4196) all_58_4 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4192), (4196) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | #767.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4197) all_58_5 = e3 & op(e2, e1) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4071), (4197), (function-axioms) are
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #150.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (4198) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4198) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4199) all_58_8 = e3 & op(e1, e1) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4096), (4199), (function-axioms) are
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4200) all_58_14 = e3 & op(e0, e1) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4200) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4201) all_58_14 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4202) all_58_15 = e0 & op(e0, e0) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4202) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4203) all_58_15 = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4204) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4204) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4205) all_58_9 = e3 & op(e3, e0) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (109), (112),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (144), (159), (163), (166), (167), (168), (169),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196), (209), (210), (214), (235), (238), (248),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (252), (254), (262), (274), (277), (393),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (396), (397), (399), (4060), (4062),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4070), (4071), (4078), (4096), (4147), (4148),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4149), (4151), (4155), (4167), (4174), (4175),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4201), (4205), (function-axioms) are inconsistent
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #117.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4206) all_58_10 = e3 & op(e2, e0) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4206) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4207) all_58_10 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4208) op(e2, e0) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4209) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4209) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4210) all_58_2 = e0 & op(e2, e3) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4210) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4211) all_58_2 = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4212) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4212) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4213) all_58_0 = e0 & op(e3, e3) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4213) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4214) op(e3, e3) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4151), (4214), (function-axioms) are
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #907.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4215) all_58_1 = e0 & op(e3, e2) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4215) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4216) all_58_1 = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4217) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4217) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4218) all_58_0 = e3 & op(e3, e3) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4218) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4219) all_58_0 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4220) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4220) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4221) all_58_12 = e3 & op(e0, e3) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4221) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4222) all_58_12 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4168) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4169), (4222) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #651.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4223) all_58_13 = e1 & op(e0, e2) = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4223) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4224) op(e0, e2) = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4180), (4224), (function-axioms) are
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #968.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4225) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4225) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4226) all_58_14 = e1 & op(e0, e1) = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4226) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4227) all_58_14 = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4201), (4227) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #626.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4228) all_58_15 = e1 & op(e0, e0) = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4228) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4229) all_58_15 = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4203), (4229) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #881.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4230) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4230) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4231) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4231) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4232) all_58_12 = e0 & op(e0, e3) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4222), (4232) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #646.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4233) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4233) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4234) all_58_13 = e0 & op(e0, e2) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4179), (4234) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #872.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4235) all_58_14 = e0 & op(e0, e1) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4235) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4236) all_58_14 = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4201), (4236) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #423.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4237) all_58_13 = e3 & op(e0, e2) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4237) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4238) all_58_13 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4179), (4238) imply:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4239) e3 = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4201), (4239) imply:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4240) all_58_14 = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (109), (112),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (144), (159), (163), (166), (167), (168), (169),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196), (209), (210), (214), (235), (238), (248),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (252), (254), (262), (274), (277), (393),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (396), (397), (399), (4060), (4062),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4070), (4071), (4078), (4096), (4147), (4148),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4149), (4151), (4155), (4167), (4174), (4175),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4240), (function-axioms) are inconsistent by
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #118.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4241) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4241) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (168), (4193) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4242) all_52_8 = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (168), (248), (254),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4151), (4156), (4174), (4192), (4219), (4242),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #759.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4243) all_58_15 = e3 & op(e0, e0) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4243) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4244) all_58_15 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4203), (4244) imply:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4245) e3 = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (254), (4174), (4192), (4216),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4219), (4245) are inconsistent by sub-proof #761.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4246) all_58_1 = e3 & op(e3, e2) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (248), (4151), (4174), (4192),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4246), (function-axioms) are inconsistent by
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #791.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4247) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4247) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4248) all_58_4 = e3 & op(e3, e1) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4248) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4249) all_58_4 = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4192), (4249) imply:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4250) e3 = e1
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (242),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4075), (4207), (4211), (4250) are inconsistent by
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #116.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4251) all_58_9 = e3 & op(e3, e0) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (109), (112),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (144), (159), (163), (166), (167), (168), (169),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196), (209), (210), (214), (235), (238), (248),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250), (252), (254), (262), (274), (277), (393),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (396), (397), (399), (4060), (4062),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4070), (4071), (4078), (4096), (4147), (4148),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4149), (4151), (4155), (4167), (4174), (4175),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4201), (4251), (function-axioms) are inconsistent
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #117.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4252) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4252) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4253) all_58_4 = e0 & op(e3, e1) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4253) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4254) op(e3, e1) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4193), (4254), (function-axioms) are
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #569.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4255) all_58_9 = e0 & op(e3, e0) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4255) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4256) all_58_9 = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4172) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4173), (4256) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #515.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4257) all_58_10 = e2 & op(e2, e0) = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4257) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4258) all_58_10 = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4207), (4258) imply:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4259) e3 = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4259) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4260) e3 = e2
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (4260) imply:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4261) $false
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4261) is inconsistent.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4262) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (4094), (4166), (4262),
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #514.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4263) all_58_3 = e0 & op(e2, e2) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4075), (4263) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #927.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4264) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4264) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4265) all_58_5 = e0 & op(e2, e1) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4071), (4265), (function-axioms) are
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #151.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4266) all_58_10 = e0 & op(e2, e0) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4266) implies:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4267) op(e2, e0) = e0
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4208), (4267), (function-axioms) are
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #123.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4268) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4268) gives:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4269) all_58_11 = e3 & op(e1, e0) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4166), (4269) are inconsistent by sub-proof
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #115.
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4270) all_58_15 = e3 & op(e0, e0) = e3
% 166.62/24.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4203), (4270) are inconsistent by sub-proof
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #812.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4271) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (4170), (4179), (4201), (4271) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #870.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (4272) all_58_9 = e1 & op(e3, e0) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4272) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (4273) all_58_9 = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (163),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (166), (168), (221), (226), (229), (231), (232),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (233), (234), (235), (238), (239), (242), (243),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (244), (246), (248), (251), (252), (254), (399),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (4071), (4075), (4080), (4094), (4096), (4147),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (4151), (4170), (4273), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | (4274) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4274) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (4275) all_58_14 = e2 & op(e0, e1) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4275) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (4276) all_58_14 = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (109), (112),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (144), (159), (163), (166), (167), (168), (169),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (196), (209), (210), (214), (235), (238), (248),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (250), (252), (254), (262), (274), (277), (393),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (395), (396), (397), (399), (4060), (4062),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (4070), (4071), (4078), (4096), (4147), (4148),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (4149), (4151), (4155), (4167), (4174), (4175),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (4276), (function-axioms) are inconsistent by
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #118.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (4277) all_58_15 = e2 & op(e0, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (4094), (4277), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4278) all_58_10 = e2 & op(e2, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4278) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4279) op(e2, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4080), (4279), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (4280) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4280) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4281) all_58_11 = e2 & op(e1, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4166), (4281) are inconsistent by sub-proof
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | #471.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4282) all_58_15 = e2 & op(e0, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (4094), (4282), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | (4283) all_58_13 = e1 & op(e0, e2) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4064), (4283), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #114.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | (4284) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | BETA: splitting (4284) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | (4285) all_58_14 = e1 & op(e0, e1) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | ALPHA: (4285) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | (4286) all_58_14 = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | (4287) op(e0, e1) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (4288) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4288) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4289) all_58_9 = e2 & op(e3, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4289) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4290) all_58_9 = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4291) op(e3, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | (4292) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4292) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (4293) all_58_4 = e3 & op(e3, e1) = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4293) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (4294) all_58_4 = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | (4295) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4295) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (4296) all_58_4 = e0 & op(e3, e1) = e0
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4294), (4296) are inconsistent by sub-proof
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | #704.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (4297) all_58_5 = e0 & op(e2, e1) = e0
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4071), (4297), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #151.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | (4298) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4298) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (4299) all_58_8 = e0 & op(e1, e1) = e0
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4299) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (4300) op(e1, e1) = e0
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (4301) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4301) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4302) all_58_0 = e1 & op(e3, e3) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4302) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4303) all_58_0 = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (109), (112),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (144), (159), (163), (166), (167), (168), (169),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (196), (209), (210), (214), (248), (250), (252),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (262), (274), (277), (393), (395), (396),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (397), (399), (4060), (4070), (4078), (4096),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4147), (4148), (4149), (4151), (4155), (4167),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4290), (4291), (4294), (4300), (4303),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | #119.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4304) all_58_1 = e1 & op(e3, e2) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4062), (4304), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #863.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (4305) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4305) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4306) all_58_4 = e1 & op(e3, e1) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4294), (4306) are inconsistent by sub-proof
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4307) all_58_9 = e1 & op(e3, e0) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4307) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4308) all_58_9 = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4309) op(e3, e0) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (157),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (162), (163), (166), (168), (217), (221), (224),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (226), (229), (230), (231), (232), (233),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (235), (238), (239), (242), (243), (244),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (246), (247), (248), (249), (251), (252), (253),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (398), (399), (4060), (4071), (4075),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4080), (4094), (4096), (4147), (4151), (4156),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4308), (4309), (function-axioms) are inconsistent
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #129.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (4310) all_58_14 = e0 & op(e0, e1) = e0
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4310) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | (4311) all_58_14 = e0
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4286), (4311) are inconsistent by sub-proof
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | | #586.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | (4312) all_58_5 = e3 & op(e2, e1) = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4071), (4312), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #150.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | (4313) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (39), (4096), (4287), (4313),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | | #132.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4314) all_58_10 = e2 & op(e2, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4314) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4315) op(e2, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4080), (4315), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (4316) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4316) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4317) all_58_11 = e2 & op(e1, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4166), (4317) are inconsistent by sub-proof
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | #471.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4318) all_58_15 = e2 & op(e0, e0) = e2
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (4094), (4318), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | (4319) all_58_15 = e1 & op(e0, e0) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (398), (4319), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | (4320) all_58_15 = e1 & op(e0, e0) = e1
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (398), (4320), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130.
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | (4321) all_28_2 = e3
% 166.62/24.63 | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | COMBINE_EQS: (340), (4321) imply:
% 166.62/24.63 | | | | | | | | | | | | | (4322) all_6_2 = e3
% 166.62/24.63 | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | COMBINE_EQS: (274), (4322) imply:
% 166.62/24.63 | | | | | | | | | | | | | (4323) all_56_14 = e3
% 166.62/24.63 | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | REDUCE: (388), (4322) imply:
% 166.62/24.63 | | | | | | | | | | | | | (4324) ~ (all_52_8 = e3)
% 166.62/24.63 | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | BETA: splitting (216) gives:
% 166.62/24.63 | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | (4325) ~ (all_56_14 = e3)
% 166.62/24.63 | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | REDUCE: (4323), (4325) imply:
% 166.62/24.63 | | | | | | | | | | | | | | (4326) $false
% 166.62/24.63 | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | CLOSE: (4326) is inconsistent.
% 166.62/24.63 | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | (4327) all_56_2 = e1 & op(e1, e3) = e1
% 166.62/24.63 | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | ALPHA: (4327) implies:
% 166.62/24.63 | | | | | | | | | | | | | | (4328) all_56_2 = e1
% 166.62/24.63 | | | | | | | | | | | | | | (4329) op(e1, e3) = e1
% 166.62/24.63 | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 166.62/24.63 | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | (4330) ~ (all_56_10 = e1)
% 166.62/24.63 | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | REDUCE: (298), (4330) imply:
% 166.62/24.63 | | | | | | | | | | | | | | | (4331) ~ (all_10_2 = e1)
% 166.62/24.63 | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 166.62/24.63 | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | (4332) all_54_0 = e3
% 166.62/24.63 | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | COMBINE_EQS: (300), (4332) imply:
% 166.62/24.63 | | | | | | | | | | | | | | | | (4333) all_10_2 = e3
% 166.62/24.63 | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | SIMP: (4333) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | (4334) all_10_2 = e3
% 166.62/24.63 | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (4334) imply:
% 166.62/24.63 | | | | | | | | | | | | | | | | (4335) all_56_10 = e3
% 166.62/24.63 | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | REDUCE: (363), (4334) imply:
% 166.62/24.63 | | | | | | | | | | | | | | | | (4336) ~ (all_52_1 = e3)
% 166.62/24.63 | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | REDUCE: (369), (4334) imply:
% 166.62/24.63 | | | | | | | | | | | | | | | | (4337) ~ (all_52_4 = e3)
% 166.62/24.63 | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | REDUCE: (373), (4334) imply:
% 166.62/24.63 | | | | | | | | | | | | | | | | (4338) ~ (all_52_12 = e3)
% 166.62/24.63 | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | (4339) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | BETA: splitting (4339) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | (4340) all_58_2 = e3 & op(e2, e3) = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | ALPHA: (4340) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | (4341) op(e2, e3) = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (4336), (4341), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #989.
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | (4342) all_58_3 = e3 & op(e2, e2) = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | ALPHA: (4342) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | (4343) all_58_3 = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4075), (4343) are inconsistent by sub-proof
% 166.62/24.63 | | | | | | | | | | | | | | | | | | #328.
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | End of split
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | (4344) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | BETA: splitting (4344) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | (4345) all_58_5 = e3 & op(e2, e1) = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4071), (4345), (function-axioms) are
% 166.62/24.63 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #150.
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | (4346) all_58_10 = e3 & op(e2, e0) = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | ALPHA: (4346) implies:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | (4347) op(e2, e0) = e3
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | (4348) ~ (all_56_15 = e3)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | REDUCE: (262), (4348) imply:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | (4349) ~ (all_4_2 = e3)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (4350) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4350) gives:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (4351) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (4323), (4328), (4336), (4351),
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | | #113.
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.62/24.63 | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (4352) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4352) gives:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (4353) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4353) implies:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (4354) op(e1, e3) = e3
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (4329), (4354), (function-axioms) are
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (4355) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4060), (4070), (4323), (4328), (4355) are
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #112.
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | End of split
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (4356) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4356) gives:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (4357) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4357) gives:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (4358) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4070), (4358) are inconsistent by sub-proof
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | #146.
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (4359) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4359) implies:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | (4360) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4323), (4328), (4360) are inconsistent by
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | | sub-proof #485.
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.73/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | (4361) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4361) gives:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | (4362) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (202), (220), (290), (4335), (4337),
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | (4338), (4347), (4362), (function-axioms) are
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #144.
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | (4363) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4363) gives:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | (4364) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4364) implies:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | (4365) ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4060), (4070), (4365) are inconsistent by
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #148.
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | (4366) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (262), (307), (398), (4094), (4349), (4366)
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #143.
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | (4367) all_56_15 = e3
% 166.76/24.64 | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (4367) imply:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | (4368) all_4_2 = e3
% 166.76/24.64 | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | SIMP: (4368) implies:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | (4369) all_4_2 = e3
% 166.76/24.64 | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | REDUCE: (396), (4369) imply:
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | (4370) ~ (all_52_13 = e3)
% 166.76/24.64 | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4347), (4370), (function-axioms) are
% 166.76/24.64 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 166.76/24.64 | | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | Case 2:
% 166.76/24.64 | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | (4371) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 166.76/24.64 | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | | REF_CLOSE: (300), (4090), (4092), (4331), (4371) are
% 166.76/24.64 | | | | | | | | | | | | | | | | inconsistent by sub-proof #958.
% 166.76/24.64 | | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | Case 2:
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | (4372) all_56_4 = e3 & op(e3, e1) = e3
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | ALPHA: (4372) implies:
% 166.76/24.64 | | | | | | | | | | | | | | | (4373) op(e3, e1) = e3
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | REF_CLOSE: (168), (4324), (4373), (function-axioms) are
% 166.76/24.64 | | | | | | | | | | | | | | | inconsistent by sub-proof #975.
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | End of split
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | Case 2:
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | (4374) all_20_2 = e2
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | COMBINE_EQS: (349), (4374) imply:
% 166.76/24.64 | | | | | | | | | | | | (4375) all_4_2 = e2
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | SIMP: (4375) implies:
% 166.76/24.64 | | | | | | | | | | | | (4376) all_4_2 = e2
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | COMBINE_EQS: (262), (4376) imply:
% 166.76/24.64 | | | | | | | | | | | | (4377) all_56_15 = e2
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | REDUCE: (387), (4376) imply:
% 166.76/24.64 | | | | | | | | | | | | (4378) ~ (all_52_7 = e2)
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | REDUCE: (394), (4376) imply:
% 166.76/24.64 | | | | | | | | | | | | (4379) ~ (all_52_11 = e2)
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | REDUCE: (395), (4376) imply:
% 166.76/24.64 | | | | | | | | | | | | (4380) ~ (all_52_12 = e2)
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | REDUCE: (397), (4376) imply:
% 166.76/24.64 | | | | | | | | | | | | (4381) ~ (all_52_14 = e2)
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | BETA: splitting (212) gives:
% 166.76/24.64 | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | Case 1:
% 166.76/24.64 | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | (4382) ~ (all_56_15 = e2)
% 166.76/24.64 | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | REDUCE: (4377), (4382) imply:
% 166.76/24.64 | | | | | | | | | | | | | (4383) $false
% 166.76/24.64 | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | CLOSE: (4383) is inconsistent.
% 166.76/24.64 | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | Case 2:
% 166.76/24.64 | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | (4384) all_56_7 = e0 & op(e0, e2) = e0
% 166.76/24.64 | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | ALPHA: (4384) implies:
% 166.76/24.64 | | | | | | | | | | | | | (4385) all_56_7 = e0
% 166.76/24.64 | | | | | | | | | | | | | (4386) op(e0, e2) = e0
% 166.76/24.64 | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.76/24.64 | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | Case 1:
% 166.76/24.64 | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | (4387) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.76/24.64 | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.76/24.64 | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (4080), (4380), (4387),
% 166.76/24.64 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.64 | | | | | | | | | | | | | | #661.
% 166.76/24.64 | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | Case 2:
% 166.76/24.64 | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | (4388) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.76/24.64 | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.76/24.64 | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | BETA: splitting (4388) gives:
% 166.76/24.64 | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | Case 1:
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | (4389) all_58_11 = e2 & op(e1, e0) = e2
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | REF_CLOSE: (159), (4381), (4389), (function-axioms) are
% 166.76/24.64 | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | Case 2:
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | (4390) all_58_15 = e2 & op(e0, e0) = e2
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | ALPHA: (4390) implies:
% 166.76/24.64 | | | | | | | | | | | | | | | (4391) all_58_15 = e2
% 166.76/24.64 | | | | | | | | | | | | | | | (4392) op(e0, e0) = e2
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 166.76/24.64 | | | | | | | | | | | | | | |
% 166.76/24.64 | | | | | | | | | | | | | | | Case 1:
% 166.76/24.64 | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | (4393) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 166.76/24.65 | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | BETA: splitting (4393) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | (4394) all_58_0 = e2 & op(e3, e3) = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (4092), (4394), (function-axioms) are
% 166.76/24.65 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #666.
% 166.76/24.65 | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | (4395) all_58_1 = e2 & op(e3, e2) = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | ALPHA: (4395) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | (4396) all_58_1 = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | (4397) op(e3, e2) = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | (4398) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 166.76/24.65 | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | BETA: splitting (4398) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4399) all_58_0 = e2 & op(e3, e3) = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (4092), (4399), (function-axioms) are
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #666.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4400) all_58_2 = e2 & op(e2, e3) = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | ALPHA: (4400) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4401) op(e2, e3) = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (166), (239), (242),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4071), (4075), (4401), (function-axioms) are
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #149.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.65 | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | (4402) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 166.76/24.65 | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 166.76/24.65 | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | BETA: splitting (4402) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4403) all_58_6 = e2 & op(e1, e3) = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | ALPHA: (4403) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4404) all_58_6 = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4405) op(e1, e3) = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (157), (4386) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4406) all_52_7 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (162), (4405) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4407) all_52_2 = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (169), (4397) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4408) all_52_4 = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | REDUCE: (143), (4407) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4409) ~ (all_52_3 = e2)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | SIMP: (4409) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4410) ~ (all_52_3 = e2)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | REDUCE: (139), (4406) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4411) ~ (all_52_3 = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | REDUCE: (135), (4408) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4412) ~ (all_52_6 = e2)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | SIMP: (4412) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4413) ~ (all_52_6 = e2)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | REDUCE: (369), (4408) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4414) ~ (all_10_2 = e2)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | REDUCE: (127), (4406) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4415) ~ (all_52_6 = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | REDUCE: (124), (4406) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4416) ~ (all_52_11 = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | SIMP: (4416) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4417) ~ (all_52_11 = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | REDUCE: (4378), (4406) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4418) ~ (e2 = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | REDUCE: (4064), (4406) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | (4419) ~ (e1 = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | (4420) ~ (all_56_14 = e3)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (4420) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | (4421) ~ (all_6_2 = e3)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | (4422) all_58_15 = e0 & op(e0, e0) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4391), (4422) are inconsistent by sub-proof
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | #874.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | (4423) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4423) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | (4424) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4424) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | (4425) all_58_12 = e0 & op(e0, e3) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (157), (168),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | (225), (227), (228), (234), (238), (239), (241),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | (242), (243), (247), (248), (249), (252), (253),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | (254), (4071), (4075), (4386), (4391), (4392),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | (4397), (4404), (4421), (4425), (function-axioms)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #104.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | (4426) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4426) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | (4427) all_58_13 = e0 & op(e0, e2) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4427) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | (4428) all_58_13 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | (4429) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4429) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4430) all_58_0 = e0 & op(e3, e3) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (4090), (4430), (function-axioms) are
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #103.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4431) all_58_2 = e0 & op(e2, e3) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4431) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4432) all_58_2 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (105), (138),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (157), (167), (168), (189), (191), (203), (209),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (210), (220), (225), (226), (227), (238), (239),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (247), (249), (253), (263), (265),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (274), (298), (300), (358), (367), (371), (373),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (391), (4060), (4070), (4071), (4075), (4090),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4092), (4377), (4379), (4385), (4386), (4391),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4392), (4404), (4410), (4411), (4417), (4421),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4428), (4432), (function-axioms) are inconsistent
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #97.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | (4433) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4433) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4434) all_58_6 = e0 & op(e1, e3) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4434) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4435) all_58_6 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4404), (4435) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4436) e2 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4391), (4436) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4437) all_58_15 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (225), (226),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (227), (4386), (4392), (4428), (4437),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | #628.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4438) all_58_12 = e0 & op(e0, e3) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4438) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4439) all_58_12 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4440) op(e0, e3) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (157), (225), (227),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4386), (4391), (4392), (4428), (4439), (4440),
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | #96.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | (4441) all_58_14 = e0 & op(e0, e1) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4441) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | (4442) all_58_14 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | (4443) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4443) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4444) all_58_4 = e3 & op(e3, e1) = e3
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4444) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | (4445) all_58_4 = e3
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (4446) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4446) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4447) all_58_0 = e0 & op(e3, e3) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (4090), (4447), (function-axioms) are
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #103.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4448) all_58_1 = e0 & op(e3, e2) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4448) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4449) op(e3, e2) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4397), (4449), (function-axioms) are
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #953.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | (4450) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4450) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4451) all_58_4 = e0 & op(e3, e1) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4451) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4452) all_58_4 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4445), (4452) are inconsistent by sub-proof
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | #894.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4453) all_58_9 = e0 & op(e3, e0) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4453) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4454) op(e3, e0) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4455) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4455) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4456) all_58_0 = e0 & op(e3, e3) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (4090), (4456), (function-axioms) are
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #103.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4457) all_58_2 = e0 & op(e2, e3) = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4457) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4458) all_58_2 = e0
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4459) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4459) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4460) all_58_4 = e1 & op(e3, e1) = e1
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4445), (4460) are inconsistent by sub-proof
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #702.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4461) all_58_5 = e1 & op(e2, e1) = e1
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4089), (4461) are inconsistent by sub-proof
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #852.
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4462) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4462) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4463) all_58_8 = e1 & op(e1, e1) = e1
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4463) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4464) all_58_8 = e1
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4465) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4465) gives:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4466) all_58_1 = e3 & op(e3, e2) = e3
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4466) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4467) all_58_1 = e3
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4396), (4467) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4468) e3 = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4468) implies:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4469) e3 = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4445), (4469) imply:
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4470) all_58_4 = e2
% 166.76/24.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (248), (250), (254),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4396), (4470) are inconsistent by sub-proof #895.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4471) all_58_3 = e3 & op(e2, e2) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4075), (4471) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #102.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4472) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4472) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4473) all_58_7 = e3 & op(e1, e2) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4473) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4474) all_58_7 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4475) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4075), (4397), (4475),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #109.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4476) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4476) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4477) all_58_7 = e0 & op(e1, e2) = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4477) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4478) all_58_7 = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4474), (4478) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #748.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4479) all_58_13 = e0 & op(e0, e2) = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4479) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4480) all_58_13 = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (105), (138),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (167), (168), (189), (191), (203), (209),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210), (220), (225), (226), (227), (238), (239),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (247), (249), (253), (263), (265),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274), (298), (300), (358), (367), (371), (373),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (4060), (4070), (4071), (4075), (4090),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4092), (4377), (4379), (4385), (4386), (4391),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4392), (4404), (4410), (4411), (4417), (4421),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4458), (4480), (function-axioms) are inconsistent
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #97.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4481) all_58_13 = e3 & op(e0, e2) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4481) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4482) all_58_13 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4483) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4483) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4484) all_58_9 = e1 & op(e3, e0) = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4484) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4485) op(e3, e0) = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4454), (4485), (function-axioms) are
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #553.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4486) all_58_10 = e1 & op(e2, e0) = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4486) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4487) all_58_10 = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (242),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4075), (4458), (4487) are inconsistent by
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #128.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4488) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4488) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4489) all_58_11 = e1 & op(e1, e0) = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4489) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4490) all_58_11 = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4491) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4491) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4492) all_58_2 = e3 & op(e2, e3) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4492) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4493) all_58_2 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4458), (4493) imply:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4494) e3 = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4494) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4495) e3 = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4482), (4495) imply:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4496) all_58_13 = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (105), (138),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (167), (168), (189), (191), (203), (209),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210), (220), (225), (226), (227), (238), (239),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (247), (249), (253), (263), (265),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274), (298), (300), (358), (367), (371), (373),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (391), (4060), (4070), (4071), (4075), (4090),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4092), (4377), (4379), (4385), (4386), (4391),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4392), (4404), (4410), (4411), (4417), (4421),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4458), (4496), (function-axioms) are inconsistent
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #97.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4497) all_58_3 = e3 & op(e2, e2) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4497) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4498) all_58_3 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4075), (4498) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #328.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4499) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4499) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4500) all_58_5 = e3 & op(e2, e1) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4071), (4500), (function-axioms) are
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #150.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4501) all_58_10 = e3 & op(e2, e0) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4501) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4502) all_58_10 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4503) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4503) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4504) all_58_6 = e3 & op(e1, e3) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4504) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4505) all_58_6 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4404), (4505) imply:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4506) e3 = e2
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4506) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4507) e3 = e2
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4445), (4507) imply:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4508) all_58_4 = e2
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (248), (250), (254),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4396), (4508) are inconsistent by sub-proof #895.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4509) all_58_7 = e3 & op(e1, e2) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4509) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4510) all_58_7 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4511) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4511) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4512) all_58_6 = e0 & op(e1, e3) = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4404), (4512) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #712.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4513) all_58_7 = e0 & op(e1, e2) = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4513) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4514) all_58_7 = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4510), (4514) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #748.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4515) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4515) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4516) all_58_8 = e0 & op(e1, e1) = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4464), (4516) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #718.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4517) all_58_11 = e0 & op(e1, e0) = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4490), (4517) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #513.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4518) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4518) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4519) all_58_8 = e3 & op(e1, e1) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (4421), (4519), (function-axioms) are
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #961.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4520) all_58_11 = e3 & op(e1, e0) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4520) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4521) all_58_11 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4490), (4521) imply:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4522) e3 = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (242),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4075), (4458), (4502), (4522) are inconsistent by
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #116.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4523) all_58_15 = e1 & op(e0, e0) = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4523) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4524) op(e0, e0) = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4392), (4524), (function-axioms) are
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #640.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4525) all_58_14 = e1 & op(e0, e1) = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4525) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4526) all_58_14 = e1
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4442), (4526) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #586.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4527) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4527) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4528) all_58_6 = e0 & op(e1, e3) = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4404), (4528) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #769.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4529) all_58_12 = e0 & op(e0, e3) = e0
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (157), (168),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (227), (228), (234), (238), (239), (241),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (243), (247), (248), (249), (252), (253),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254), (4071), (4075), (4386), (4391), (4392),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4397), (4404), (4421), (4529), (function-axioms)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #104.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | (4530) all_58_5 = e3 & op(e2, e1) = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4071), (4530), (function-axioms) are
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #150.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | (4531) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (39), (4421), (4442), (4531),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | | #237.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | (4532) all_56_14 = e3
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (194), (274), (275), (386), (4063), (4413),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | (4415), (4532) are inconsistent by sub-proof #170.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.66 | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | (4533) all_58_12 = e2 & op(e0, e3) = e2
% 166.76/24.66 | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | ALPHA: (4533) implies:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | (4534) all_58_12 = e2
% 166.76/24.66 | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | (4535) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (157), (4386), (4534), (4535),
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | #633.
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | (4536) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4536) gives:
% 166.76/24.66 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | (4537) all_58_14 = e1 & op(e0, e1) = e1
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4537) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | (4538) all_58_14 = e1
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | (4539) all_58_15 = e0 & op(e0, e0) = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4539) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | (4540) all_58_15 = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4391), (4540) are inconsistent by sub-proof
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | #725.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | (4541) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4541) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | (4542) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | (4543) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4543) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | (4544) all_58_12 = e3 & op(e0, e3) = e3
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4544) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | (4545) all_58_12 = e3
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4534), (4545) are inconsistent by sub-proof
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | #635.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | (4546) all_58_13 = e3 & op(e0, e2) = e3
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4546) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | (4547) all_58_13 = e3
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (4534), (4538), (4542), (4547) are
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | (4548) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4548) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | (4549) all_58_14 = e3 & op(e0, e1) = e3
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4549) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | (4550) all_58_14 = e3
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | (4551) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (157), (4386), (4534), (4551),
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | #633.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4392), (4536), (4550),
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | #632.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | (4552) all_58_15 = e3 & op(e0, e0) = e3
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4391), (4552) are inconsistent by sub-proof
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | #464.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | (4553) all_58_15 = e1 & op(e0, e0) = e1
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4553) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | (4554) op(e0, e0) = e1
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4392), (4554), (function-axioms) are
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #640.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | (4555) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 166.76/24.67 | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | BETA: splitting (4555) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | (4556) all_58_4 = e2 & op(e3, e1) = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4078), (4556), (function-axioms) are
% 166.76/24.67 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #572.
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | (4557) all_58_9 = e2 & op(e3, e0) = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4380), (4557), (function-axioms) are
% 166.76/24.67 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #663.
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | (4558) all_16_2 = e2
% 166.76/24.67 | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | COMBINE_EQS: (350), (4558) imply:
% 166.76/24.67 | | | | | | | | | | | (4559) all_10_2 = e2
% 166.76/24.67 | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | SIMP: (4559) implies:
% 166.76/24.67 | | | | | | | | | | | (4560) all_10_2 = e2
% 166.76/24.67 | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | COMBINE_EQS: (298), (4560) imply:
% 166.76/24.67 | | | | | | | | | | | (4561) all_56_10 = e2
% 166.76/24.67 | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | REDUCE: (369), (4560) imply:
% 166.76/24.67 | | | | | | | | | | | (4562) ~ (all_52_4 = e2)
% 166.76/24.67 | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | REDUCE: (373), (4560) imply:
% 166.76/24.67 | | | | | | | | | | | (4563) ~ (all_52_12 = e2)
% 166.76/24.67 | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | BETA: splitting (222) gives:
% 166.76/24.67 | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | (4564) ~ (all_56_10 = e2)
% 166.76/24.67 | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | REDUCE: (4561), (4564) imply:
% 166.76/24.67 | | | | | | | | | | | | (4565) $false
% 166.76/24.67 | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | CLOSE: (4565) is inconsistent.
% 166.76/24.67 | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | (4566) all_56_1 = e3 & op(e3, e2) = e3
% 166.76/24.67 | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | ALPHA: (4566) implies:
% 166.76/24.67 | | | | | | | | | | | | (4567) all_56_1 = e3
% 166.76/24.67 | | | | | | | | | | | | (4568) op(e3, e2) = e3
% 166.76/24.67 | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | BETA: splitting (252) gives:
% 166.76/24.67 | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | (4569) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 166.76/24.67 | | | | | | | | | | | | | & op(e3, e2) = e2)
% 166.76/24.67 | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | BETA: splitting (4569) gives:
% 166.76/24.67 | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | (4570) all_58_0 = e2 & op(e3, e3) = e2
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | ALPHA: (4570) implies:
% 166.76/24.67 | | | | | | | | | | | | | | (4571) all_58_0 = e2
% 166.76/24.67 | | | | | | | | | | | | | | (4572) op(e3, e3) = e2
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 166.76/24.67 | | | | | | | | | | | | | | e2, e3, simplifying with (169), (4568) gives:
% 166.76/24.67 | | | | | | | | | | | | | | (4573) all_52_4 = e3
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | REDUCE: (135), (4573) imply:
% 166.76/24.67 | | | | | | | | | | | | | | (4574) ~ (all_52_6 = e3)
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | SIMP: (4574) implies:
% 166.76/24.67 | | | | | | | | | | | | | | (4575) ~ (all_52_6 = e3)
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | REDUCE: (134), (4573) imply:
% 166.76/24.67 | | | | | | | | | | | | | | (4576) ~ (all_52_7 = e3)
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | SIMP: (4576) implies:
% 166.76/24.67 | | | | | | | | | | | | | | (4577) ~ (all_52_7 = e3)
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | REDUCE: (133), (4573) imply:
% 166.76/24.67 | | | | | | | | | | | | | | (4578) ~ (all_52_8 = e3)
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | SIMP: (4578) implies:
% 166.76/24.67 | | | | | | | | | | | | | | (4579) ~ (all_52_8 = e3)
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | REDUCE: (132), (4573) imply:
% 166.76/24.67 | | | | | | | | | | | | | | (4580) ~ (all_52_12 = e3)
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | SIMP: (4580) implies:
% 166.76/24.67 | | | | | | | | | | | | | | (4581) ~ (all_52_12 = e3)
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 166.76/24.67 | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | (4582) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 166.76/24.67 | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.76/24.67 | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | BETA: splitting (4582) gives:
% 166.76/24.67 | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | (4583) all_58_1 = e3 & op(e3, e2) = e3
% 166.76/24.67 | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | ALPHA: (4583) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | (4584) all_58_1 = e3
% 166.76/24.67 | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | (4585) ~ (all_20_2 = e2)
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | REDUCE: (349), (4585) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | (4586) ~ (all_4_2 = e2)
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | (4587) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.76/24.67 | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (4080), (4563), (4587),
% 166.76/24.67 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.67 | | | | | | | | | | | | | | | | | | #661.
% 166.76/24.67 | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | (4588) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.76/24.67 | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | BETA: splitting (4588) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | (4589) all_58_11 = e2 & op(e1, e0) = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | ALPHA: (4589) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | (4590) all_58_11 = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | (4591) op(e1, e0) = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | (4592) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4592) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | (4593) all_58_12 = e2 & op(e0, e3) = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4593) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | (4594) all_58_12 = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (247), (249),
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | (253), (4571), (4572), (4594), (function-axioms)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | (4595) all_58_13 = e2 & op(e0, e2) = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4595) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | (4596) op(e0, e2) = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | (4597) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (4075), (4584), (4597) are inconsistent
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #95.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | (4598) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4598) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | (4599) all_58_7 = e0 & op(e1, e2) = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4599) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | (4600) op(e1, e2) = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | (4601) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4601) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | (4602) all_58_9 = e1 & op(e3, e0) = e1
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4602) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | (4603) op(e3, e0) = e1
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (4604) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4604) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4605) all_58_0 = e0 & op(e3, e3) = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4605) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4606) all_58_0 = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4571), (4606) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4607) e2 = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4561), (4607) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4608) all_56_10 = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (220), (4581), (4608), (function-axioms)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #145.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4609) all_58_1 = e0 & op(e3, e2) = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4584), (4609) are inconsistent by sub-proof
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | #794.
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (4610) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4610) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4611) all_58_4 = e0 & op(e3, e1) = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4611) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4612) op(e3, e1) = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (157), (4596) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4613) all_52_7 = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (159), (4591) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4614) all_52_14 = e2
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (161), (4600) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4615) all_52_6 = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e3, simplifying with (167), (4603) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4616) all_52_12 = e1
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (168), (4612) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4617) all_52_8 = e0
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (4613) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4618) ~ (all_52_11 = e2)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4618) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4619) ~ (all_52_11 = e2)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (4617) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4620) ~ (all_52_11 = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4620) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4621) ~ (all_52_11 = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (4616), (4617) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4622) ~ (e1 = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (388), (4617) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4623) ~ (all_6_2 = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4623) implies:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4624) ~ (all_6_2 = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4579), (4617) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4625) ~ (e3 = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4078), (4617) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4626) ~ (e2 = e0)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (4616) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4627) ~ (all_4_2 = e1)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4581), (4616) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4628) ~ (e3 = e1)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4563), (4616) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4629) ~ (e2 = e1)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (397), (4614) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4630) ~ (all_4_2 = e2)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4631) ~ (all_44_2 = e3)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (324), (4631) imply:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4632) ~ (all_4_2 = e3)
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4633) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4633) gives:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4634) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4561), (4562), (4567), (4634),
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #520.
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4635) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4635) gives:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4636) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4636) implies:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4637) ~ (all_56_14 = e1)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4638) op(e1, e3) = e3
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (274), (4637) imply:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4639) ~ (all_6_2 = e1)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (193), (216), (274), (305), (399),
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4624), (4638), (4639), (function-axioms) are
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #168.
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4640) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4640) gives:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4641) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4641) implies:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4642) op(e1, e2) = e2
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4600), (4642), (function-axioms) are
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #175.
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4643) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4643) implies:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4644) op(e3, e1) = e1
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4612), (4644), (function-axioms) are
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #569.
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4645) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4645) gives:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4646) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4646) gives:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4647) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4647) implies:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4648) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_1 & $i(all_56_1))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4561), (4567), (4648) are inconsistent by
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #554.
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4649) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4649) implies:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4650) op(e3, e0) = e0
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (169), (250), (4062), (4572), (4612),
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4650), (function-axioms) are inconsistent by
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #93.
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4651) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4651) gives:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4652) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4652) implies:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4653) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_1 & $i(all_56_1))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4561), (4567), (4653) are inconsistent by
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #554.
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4654) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4654) gives:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4655) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4655) implies:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4656) op(e1, e0) = e0
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4591), (4656), (function-axioms) are
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #197.
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4657) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (188), (262), (307), (398), (4586), (4632), (4657)
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #143.
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4658) all_44_2 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (324), (4658) imply:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4659) all_4_2 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (4659) imply:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4660) all_56_15 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (4659) imply:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4661) ~ (all_52_11 = e3)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4662) all_54_14 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (4661), (4662) are inconsistent by
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #969.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4663) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4663) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4664) all_54_14 = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (4619), (4664) are inconsistent by
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4665) all_54_14 = e1 | all_54_14 = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4666) all_56_10 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4561), (4666) imply:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4667) e3 = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (4667) imply:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4668) $false
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4668) is inconsistent.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4669) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4669) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4670) all_56_12 = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4060), (4670) imply:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4671) e2 = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (4671) imply:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4672) $false
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4672) is inconsistent.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4673) all_56_14 = e1 | all_56_15 = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (263), (274), (391), (4621), (4660), (4665),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4673) are inconsistent by sub-proof #92.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4674) all_58_9 = e0 & op(e3, e0) = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4674) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4675) op(e3, e0) = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4603), (4675), (function-axioms) are
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #553.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4676) all_58_10 = e1 & op(e2, e0) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4676) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4677) all_58_10 = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4678) op(e2, e0) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (239), (241), (242),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4071), (4075), (4677), (4678), (function-axioms)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #127.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | (4679) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4679) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4680) all_58_11 = e1 & op(e1, e0) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4680) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4681) all_58_11 = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4590), (4681) are inconsistent by sub-proof
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | #832.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4682) all_58_15 = e1 & op(e0, e0) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (398), (4682), (function-axioms) are
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4683) all_58_13 = e0 & op(e0, e2) = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4683) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4684) op(e0, e2) = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (4596), (4684), (function-axioms) are
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #631.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | (4685) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4685) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | (4686) all_58_14 = e2 & op(e0, e1) = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4686) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | (4687) all_58_14 = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | (4688) op(e0, e1) = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | (4689) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4689) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4690) all_58_12 = e1 & op(e0, e3) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4690) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4691) op(e0, e3) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | (4692) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (4071), (4579), (4692),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | #91.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | (4693) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4693) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4694) all_58_8 = e3 & op(e1, e1) = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4694) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4695) all_58_8 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (4696) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4696) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4697) all_58_12 = e3 & op(e0, e3) = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4697) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4698) op(e0, e3) = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4691), (4698), (function-axioms) are
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #125.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4699) all_58_13 = e3 & op(e0, e2) = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (4577), (4699), (function-axioms) are
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #962.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (4700) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4700) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4701) all_58_14 = e3 & op(e0, e1) = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4687), (4701) are inconsistent by sub-proof
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | #809.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4702) all_58_15 = e3 & op(e0, e0) = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4702) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4703) all_58_15 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4704) all_58_15 = e0 & op(e0, e0) = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4704) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4705) all_58_15 = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4703), (4705) are inconsistent by sub-proof
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #860.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4706) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4706) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4707) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4707) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4708) all_58_12 = e0 & op(e0, e3) = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4708) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4709) op(e0, e3) = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4691), (4709), (function-axioms) are
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4710) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (157), (162), (167),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (220), (231), (232), (245), (4075), (4561),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4562), (4581), (4590), (4687), (4695), (4710),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #89.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4711) all_58_14 = e3 & op(e0, e1) = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4711) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4712) all_58_14 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4687), (4712) are inconsistent by sub-proof
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | #855.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4713) all_58_13 = e1 & op(e0, e2) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4713) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4714) op(e0, e2) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | (4715) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (4071), (4579), (4715),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | #91.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | (4716) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4716) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4717) all_58_8 = e3 & op(e1, e1) = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4717) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4718) all_58_8 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (4719) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (4075), (4562), (4719),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | #90.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (4720) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4720) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4721) all_58_7 = e2 & op(e1, e2) = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4721) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4722) all_58_7 = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (231), (232),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4590), (4718), (4722), (function-axioms) are
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #228.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4723) all_58_13 = e2 & op(e0, e2) = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4723) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4724) op(e0, e2) = e2
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4714), (4724), (function-axioms) are
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #968.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4725) all_58_14 = e3 & op(e0, e1) = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4725) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4726) all_58_14 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4687), (4726) are inconsistent by sub-proof
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | #855.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | (4727) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4727) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4728) all_58_14 = e1 & op(e0, e1) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4728) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4729) op(e0, e1) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4688), (4729), (function-axioms) are
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #967.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4730) all_58_15 = e1 & op(e0, e0) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4730) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4731) all_58_15 = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | (4732) op(e0, e0) = e1
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | (4733) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (4071), (4579), (4733),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | #91.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | (4734) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4734) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4735) all_58_8 = e3 & op(e1, e1) = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4735) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | (4736) all_58_8 = e3
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (4737) all_58_15 = e0 & op(e0, e0) = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4737) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (4738) op(e0, e0) = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4732), (4738), (function-axioms) are
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #204.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (4739) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4739) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | (4740) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4740) gives:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4741) all_58_12 = e0 & op(e0, e3) = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4741) implies:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4742) all_58_12 = e0
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (157), (227), (4577), (4687),
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4731), (4742), (function-axioms) are inconsistent
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #555.
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4743) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 166.76/24.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (157), (162), (167),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (169), (220), (231), (232), (245), (4075), (4561),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4562), (4581), (4590), (4687), (4736), (4743),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | #89.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | (4744) all_58_14 = e3 & op(e0, e1) = e3
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4687), (4744) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | #809.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | (4745) all_58_15 = e2 & op(e0, e0) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (4586), (4745), (function-axioms) are
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | (4746) all_58_15 = e2 & op(e0, e0) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (4586), (4746), (function-axioms) are
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | (4747) all_20_2 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (4747) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | (4748) all_4_2 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | SIMP: (4748) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | (4749) all_4_2 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (4749) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | (4750) all_56_15 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | REDUCE: (387), (4749) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | (4751) ~ (all_52_7 = e2)
% 166.76/24.70 | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | REDUCE: (397), (4749) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | (4752) ~ (all_52_14 = e2)
% 166.76/24.70 | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | (4753) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.76/24.70 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.76/24.70 | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (4080), (4563), (4753),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | #661.
% 166.76/24.70 | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | (4754) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 166.76/24.70 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.76/24.70 | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | BETA: splitting (4754) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | (4755) all_58_11 = e2 & op(e1, e0) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4752), (4755), (function-axioms) are
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | (4756) all_58_15 = e2 & op(e0, e0) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | ALPHA: (4756) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | (4757) all_58_15 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | (4758) op(e0, e0) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | (4759) ~ (all_56_15 = e2)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | REDUCE: (4750), (4759) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | (4760) $false
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | CLOSE: (4760) is inconsistent.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | (4761) all_56_7 = e0 & op(e0, e2) = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (4761) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | (4762) op(e0, e2) = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | (4763) all_56_10 = e3
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4561), (4763) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | #88.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | (4764) ~ (all_56_10 = e3)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | (4765) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4561), (4764) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | (4766) ~ (e3 = e2)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4765) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | (4767) all_56_12 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4060), (4767) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | (4768) e2 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (4768) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | (4769) $false
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4769) is inconsistent.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | (4770) all_56_14 = e1 | all_56_15 = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4770) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | (4771) all_56_14 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (274), (4771) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | (4772) all_6_2 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4772) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | (4773) all_6_2 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (388), (4773) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | (4774) ~ (all_52_8 = e1)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (399), (4773) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | (4775) ~ (e2 = e1)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (4773) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | (4776) op(e1, e1) = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | (4777) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (168), (4071), (4579), (4777),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | #91.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | (4778) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4778) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | (4779) all_58_8 = e3 & op(e1, e1) = e3
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4779) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | (4780) all_58_8 = e3
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | (4781) op(e1, e1) = e3
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (4782) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (201), (289), (4078), (4089), (4579),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (4774), (4782), (function-axioms) are inconsistent
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #87.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (4783) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4783) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4784) all_58_8 = e1 & op(e1, e1) = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4780), (4784) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | #478.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4785) all_58_14 = e1 & op(e0, e1) = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4785) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4786) all_58_14 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4787) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4787) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4788) all_58_6 = e2 & op(e1, e3) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4788) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4789) all_58_6 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (245) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4790) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (4075), (4562), (4790),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #90.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4791) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4791) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4792) all_58_7 = e2 & op(e1, e2) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4792) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4793) all_58_7 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4794) op(e1, e2) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4795) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (4075), (4584), (4795) are inconsistent
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #95.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4796) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4796) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4797) all_58_7 = e0 & op(e1, e2) = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4797) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4798) op(e1, e2) = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4794), (4798), (function-axioms) are
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #175.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4799) all_58_13 = e0 & op(e0, e2) = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4799) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4800) all_58_13 = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4801) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4801) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4802) all_58_6 = e0 & op(e1, e3) = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (225), (226),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (4757), (4758), (4762), (4789), (4800),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4802), (function-axioms) are inconsistent by
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #609.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4803) all_58_7 = e0 & op(e1, e2) = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4803) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4804) op(e1, e2) = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4794), (4804), (function-axioms) are
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #175.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4805) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4805) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4806) all_58_8 = e0 & op(e1, e1) = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4780), (4806) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #496.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4807) all_58_11 = e0 & op(e1, e0) = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4807) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4808) all_58_11 = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4809) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4809) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4810) all_58_6 = e1 & op(e1, e3) = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4810) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4811) all_58_6 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4812) op(e1, e3) = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4789), (4811) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4813) e2 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4813) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4814) e2 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4793), (4814) imply:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4815) all_58_7 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (39), (162), (231), (233),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (399), (4780), (4811), (4812), (4815),
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #493.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4816) all_58_7 = e1 & op(e1, e2) = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4816) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4817) all_58_7 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4793), (4817) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #494.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4818) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4818) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4819) all_58_8 = e1 & op(e1, e1) = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4780), (4819) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #384.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4820) all_58_11 = e1 & op(e1, e0) = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4820) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4821) all_58_11 = e1
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4808), (4821) are inconsistent by sub-proof
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #491.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4822) all_58_13 = e2 & op(e0, e2) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4822) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4823) op(e0, e2) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (4762), (4823), (function-axioms) are
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #631.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4824) all_58_7 = e2 & op(e1, e2) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4824) implies:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4825) all_58_7 = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4826) op(e1, e2) = e2
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4827) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (4075), (4584), (4827) are inconsistent
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #95.
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.76/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4828) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4828) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4829) all_58_7 = e0 & op(e1, e2) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4829) implies:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4830) op(e1, e2) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4826), (4830), (function-axioms) are
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #175.
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4831) all_58_13 = e0 & op(e0, e2) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4831) implies:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4832) all_58_13 = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4833) all_54_13 = e3
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (4577), (4833) are inconsistent by
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #971.
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4834) ~ (all_54_13 = e3)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4835) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4836) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4836) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4837) all_58_4 = e0 & op(e3, e1) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4837) implies:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4838) op(e3, e1) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4839) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4839) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4840) all_58_6 = e1 & op(e1, e3) = e1
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4840) implies:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4841) all_58_6 = e1
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4842) op(e1, e3) = e1
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4843) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4843) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4844) all_58_6 = e0 & op(e1, e3) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4844) implies:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4845) op(e1, e3) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (4842), (4845), (function-axioms) are
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4846) all_58_7 = e0 & op(e1, e2) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4846) implies:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4847) op(e1, e2) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4826), (4847), (function-axioms) are
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #175.
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4848) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4848) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4849) all_58_8 = e0 & op(e1, e1) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4780), (4849) are inconsistent by sub-proof
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #496.
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4850) all_58_11 = e0 & op(e1, e0) = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4850) implies:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4851) all_58_11 = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4852) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4852) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4853) all_58_9 = e3 & op(e3, e0) = e3
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4581), (4853), (function-axioms) are
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86.
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4854) all_58_10 = e3 & op(e2, e0) = e3
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4854) implies:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4855) all_58_10 = e3
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4835) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4856) all_54_13 = e2
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (4751), (4856) are inconsistent by
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #970.
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4857) all_54_13 = e1 | all_54_13 = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4857) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4858) all_54_13 = e1
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (4064), (4858) are inconsistent by
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #257.
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4859) all_54_13 = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (4859) imply:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4860) all_52_7 = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4860) implies:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4861) all_52_7 = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (4861) imply:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4862) ~ (all_52_6 = e0)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4577), (4861) imply:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4863) ~ (e3 = e0)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4064), (4861) imply:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4864) ~ (e1 = e0)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4865) all_54_9 = e3
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (4575), (4865) are inconsistent by
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741.
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4866) ~ (all_54_9 = e3)
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4867) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4867) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4868) all_54_9 = e2
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (275), (4868) imply:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4869) all_52_6 = e2
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4869) implies:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4870) all_52_6 = e2
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e1,
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (4776), (4781) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4871) e3 = e1
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4855), (4871) imply:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4872) all_58_10 = e1
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4852) gives:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4873) all_58_9 = e3 & op(e3, e0) = e3
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4581), (4873), (function-axioms) are
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86.
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4855), (4872) imply:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4874) e3 = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4871) imply:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4875) $false
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4875) is inconsistent.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4876) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (231), (232),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (4757), (4780), (4825), (4841), (4851),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4876), (function-axioms) are inconsistent by
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #85.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4877) all_54_9 = e1 | all_54_9 = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (275), (4063), (4862), (4877) are inconsistent by
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #171.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4878) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (231), (232),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (4757), (4780), (4825), (4841), (4851),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4878), (function-axioms) are inconsistent by
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #85.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4879) all_58_7 = e1 & op(e1, e2) = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4879) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4880) all_58_7 = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4825), (4880) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #494.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4881) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4881) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4882) all_58_8 = e1 & op(e1, e1) = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4780), (4882) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #478.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4883) all_58_11 = e1 & op(e1, e0) = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4883) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4884) all_58_11 = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4885) all_58_15 = e0 & op(e0, e0) = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4885) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4886) all_58_15 = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (225), (226),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (4758), (4762), (4832), (4886),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #628.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4887) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4887) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4888) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4889) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4889) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4890) all_58_9 = e3 & op(e3, e0) = e3
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4581), (4890), (function-axioms) are
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4891) all_58_10 = e3 & op(e2, e0) = e3
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4891) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4892) all_58_10 = e3
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4888) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4893) all_58_9 = e0 & op(e3, e0) = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4893) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4894) op(e3, e0) = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (169), (250), (4062), (4572), (4838),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4894), (function-axioms) are inconsistent by
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #93.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4895) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4895) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4896) all_58_10 = e0 & op(e2, e0) = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4892), (4896) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #932.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4897) all_58_11 = e0 & op(e1, e0) = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4884), (4897) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #513.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4898) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4898) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4899) all_58_11 = e3 & op(e1, e0) = e3
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (231), (232),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4780), (4825), (4899), (function-axioms) are
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #477.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4900) all_58_15 = e3 & op(e0, e0) = e3
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4757), (4900) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #464.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4901) all_58_5 = e0 & op(e2, e1) = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4071), (4901), (function-axioms) are
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #151.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4902) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4902) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4903) all_58_8 = e0 & op(e1, e1) = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4903) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4904) all_58_8 = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4780), (4904) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #480.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4905) all_58_14 = e0 & op(e0, e1) = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4786), (4905) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #884.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4906) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4906) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4907) all_58_8 = e2 & op(e1, e1) = e2
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (399), (4907), (function-axioms) are
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #845.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4908) all_58_11 = e2 & op(e1, e0) = e2
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4752), (4908), (function-axioms) are
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | (4909) all_58_14 = e3 & op(e0, e1) = e3
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4909) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | (4910) all_58_14 = e3
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | (4911) op(e0, e1) = e3
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (4912) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4912) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4913) all_58_4 = e0 & op(e3, e1) = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4913) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4914) op(e3, e1) = e0
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4915) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (4062), (4572), (4915),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #94.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4916) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4916) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4917) all_58_4 = e1 & op(e3, e1) = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4917) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4918) op(e3, e1) = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4914), (4918), (function-axioms) are
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #569.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4919) all_58_9 = e1 & op(e3, e0) = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4919) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4920) op(e3, e0) = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4921) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4921) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4922) all_58_12 = e1 & op(e0, e3) = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4922) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4923) op(e0, e3) = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4924) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4924) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4925) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4561), (4562), (4567), (4925),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #520.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4926) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4926) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4927) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4927) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4928) ~ (all_56_14 = e1)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4771), (4928) imply:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4929) $false
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4929) is inconsistent.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4930) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4930) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4931) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4931) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4932) ~ (all_56_14 = e1)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4771), (4932) imply:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4933) $false
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4933) is inconsistent.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4934) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4934) implies:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4935) op(e3, e1) = e1
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4914), (4935), (function-axioms) are
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #569.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4936) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4936) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4937) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4561), (4567), (4920), (4937),
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #552.
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4938) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4938) gives:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4939) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4939) implies:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4940) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_1 & $i(all_56_1))
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4561), (4567), (4940) are inconsistent by
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #554.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4941) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4941) gives:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4942) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4942) implies:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4943) ~ (all_56_14 = e1)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4771), (4943) imply:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4944) $false
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4944) is inconsistent.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4945) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4945) implies:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4946) ~ (all_56_15 = e0)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4947) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (157), (4762), (4911), (4923), (4947),
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #98.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4948) all_58_13 = e1 & op(e0, e2) = e1
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4948) implies:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4949) op(e0, e2) = e1
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (157), (4762), (4949), (function-axioms) are
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #889.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4950) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4758), (4910), (4950),
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #632.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4951) all_58_5 = e0 & op(e2, e1) = e0
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4071), (4951), (function-axioms) are
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #151.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (4952) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4952) gives:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4953) all_58_8 = e0 & op(e1, e1) = e0
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4953) implies:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4954) all_58_8 = e0
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4955) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (168), (201), (289), (4078), (4089), (4579),
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4774), (4955), (function-axioms) are inconsistent
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #87.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4956) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4956) gives:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4957) all_58_8 = e1 & op(e1, e1) = e1
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4954), (4957) are inconsistent by sub-proof
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #756.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4958) all_58_14 = e1 & op(e0, e1) = e1
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4958) implies:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4959) op(e0, e1) = e1
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4911), (4959), (function-axioms) are
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #133.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4960) all_58_14 = e0 & op(e0, e1) = e0
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4960) implies:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4961) all_58_14 = e0
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4910), (4961) are inconsistent by sub-proof
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | #423.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | (4962) all_56_15 = e0
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4750), (4962) imply:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | (4963) e2 = e0
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4963) implies:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | (4964) e2 = e0
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4561), (4964) imply:
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | (4965) all_56_10 = e0
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (220), (4581), (4965), (function-axioms)
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #145.
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | (4966) all_58_3 = e3 & op(e2, e2) = e3
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | ALPHA: (4966) implies:
% 166.94/24.72 | | | | | | | | | | | | | | | | (4967) all_58_3 = e3
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4075), (4967) are inconsistent by sub-proof
% 166.94/24.72 | | | | | | | | | | | | | | | | #328.
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | (4968) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 166.94/24.72 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.94/24.72 | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | REF_CLOSE: (157), (161), (4575), (4577), (4968),
% 166.94/24.72 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.72 | | | | | | | | | | | | | | | #463.
% 166.94/24.72 | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | (4969) all_58_1 = e2 & op(e3, e2) = e2
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | ALPHA: (4969) implies:
% 166.94/24.72 | | | | | | | | | | | | | | (4970) op(e3, e2) = e2
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REF_CLOSE: (169), (4562), (4970), (function-axioms) are
% 166.94/24.72 | | | | | | | | | | | | | | inconsistent by sub-proof #993.
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | (4971) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 166.94/24.72 | | | | | | | | | | | | | & op(e3, e0) = e2)
% 166.94/24.72 | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | BETA: splitting (4971) gives:
% 166.94/24.72 | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | (4972) all_58_4 = e2 & op(e3, e1) = e2
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REF_CLOSE: (168), (4078), (4972), (function-axioms) are
% 166.94/24.72 | | | | | | | | | | | | | | inconsistent by sub-proof #572.
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | (4973) all_58_9 = e2 & op(e3, e0) = e2
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REF_CLOSE: (167), (4563), (4973), (function-axioms) are
% 166.94/24.72 | | | | | | | | | | | | | | inconsistent by sub-proof #663.
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | (4974) all_10_2 = e0
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | COMBINE_EQS: (298), (4974) imply:
% 166.94/24.72 | | | | | | | | | | (4975) all_56_10 = e0
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | REDUCE: (363), (4974) imply:
% 166.94/24.72 | | | | | | | | | | (4976) ~ (all_52_1 = e0)
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | REDUCE: (371), (4974) imply:
% 166.94/24.72 | | | | | | | | | | (4977) ~ (all_52_8 = e0)
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | REF_CLOSE: (6), (119), (144), (167), (196), (199), (201),
% 166.94/24.72 | | | | | | | | | | (210), (220), (262), (274), (277), (287), (289),
% 166.94/24.72 | | | | | | | | | | (388), (396), (4060), (4061), (4066), (4077),
% 166.94/24.72 | | | | | | | | | | (4078), (4080), (4975), (4976), (4977),
% 166.94/24.72 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.72 | | | | | | | | | | #81.
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | End of split
% 166.94/24.72 | | | | | | | | |
% 166.94/24.72 | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | |
% 166.94/24.72 | | | | | | | | | (4978) all_58_10 = e2 & op(e2, e0) = e2
% 166.94/24.72 | | | | | | | | |
% 166.94/24.72 | | | | | | | | | ALPHA: (4978) implies:
% 166.94/24.72 | | | | | | | | | (4979) op(e2, e0) = e2
% 166.94/24.72 | | | | | | | | |
% 166.94/24.72 | | | | | | | | | REF_CLOSE: (163), (4080), (4979), (function-axioms) are
% 166.94/24.72 | | | | | | | | | inconsistent by sub-proof #662.
% 166.94/24.72 | | | | | | | | |
% 166.94/24.72 | | | | | | | | End of split
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | End of split
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | End of split
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | Case 2:
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | (4980) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 166.94/24.72 | | | | | | op(e0, e2) = e1)
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | BETA: splitting (4980) gives:
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | Case 1:
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | | (4981) all_58_7 = e1 & op(e1, e2) = e1
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | | REF_CLOSE: (161), (4063), (4981), (function-axioms) are
% 166.94/24.72 | | | | | | | inconsistent by sub-proof #80.
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | Case 2:
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | | (4982) all_58_13 = e1 & op(e0, e2) = e1
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | | REF_CLOSE: (157), (4064), (4982), (function-axioms) are
% 166.94/24.72 | | | | | | | inconsistent by sub-proof #114.
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | End of split
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | End of split
% 166.94/24.72 | | | | |
% 166.94/24.72 | | | | End of split
% 166.94/24.72 | | | |
% 166.94/24.72 | | | End of split
% 166.94/24.72 | | |
% 166.94/24.72 | | Case 2:
% 166.94/24.72 | | |
% 166.94/24.72 | | | (4983) all_6_2 = e2
% 166.94/24.72 | | | (4984) ( ~ (all_6_0 = e3) & op(all_6_1, e1) = all_6_0 & op(e2, e1) =
% 166.94/24.72 | | | all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) &
% 166.94/24.72 | | | op(e2, e1) = all_6_1 & $i(all_6_1))
% 166.94/24.72 | | |
% 166.94/24.72 | | | COMBINE_EQS: (347), (4983) imply:
% 166.94/24.72 | | | (4985) all_18_2 = e2
% 166.94/24.72 | | |
% 166.94/24.72 | | | COMBINE_EQS: (274), (4983) imply:
% 166.94/24.72 | | | (4986) all_56_14 = e2
% 166.94/24.72 | | |
% 166.94/24.72 | | | REDUCE: (375), (4983) imply:
% 166.94/24.72 | | | (4987) ~ (all_52_2 = e2)
% 166.94/24.72 | | |
% 166.94/24.72 | | | REDUCE: (386), (4983) imply:
% 166.94/24.72 | | | (4988) ~ (all_52_6 = e2)
% 166.94/24.72 | | |
% 166.94/24.72 | | | REDUCE: (388), (4983) imply:
% 166.94/24.72 | | | (4989) ~ (all_52_8 = e2)
% 166.94/24.72 | | |
% 166.94/24.72 | | | REDUCE: (389), (4983) imply:
% 166.94/24.72 | | | (4990) ~ (all_52_9 = e2)
% 166.94/24.72 | | |
% 166.94/24.72 | | | REDUCE: (391), (4983) imply:
% 166.94/24.72 | | | (4991) ~ (all_52_11 = e2)
% 166.94/24.72 | | |
% 166.94/24.72 | | | REDUCE: (393), (4983) imply:
% 166.94/24.72 | | | (4992) ~ (all_52_14 = e2)
% 166.94/24.72 | | |
% 166.94/24.72 | | | BETA: splitting (215) gives:
% 166.94/24.72 | | |
% 166.94/24.72 | | | Case 1:
% 166.94/24.72 | | | |
% 166.94/24.72 | | | | (4993) ~ (all_56_14 = e2)
% 166.94/24.72 | | | |
% 166.94/24.72 | | | | REDUCE: (4986), (4993) imply:
% 166.94/24.72 | | | | (4994) $false
% 166.94/24.72 | | | |
% 166.94/24.72 | | | | CLOSE: (4994) is inconsistent.
% 166.94/24.72 | | | |
% 166.94/24.72 | | | Case 2:
% 166.94/24.72 | | | |
% 166.94/24.72 | | | | (4995) all_56_3 = e1 & op(e1, e2) = e1
% 166.94/24.72 | | | |
% 166.94/24.72 | | | | ALPHA: (4995) implies:
% 166.94/24.72 | | | | (4996) all_56_3 = e1
% 166.94/24.72 | | | | (4997) op(e1, e2) = e1
% 166.94/24.72 | | | |
% 166.94/24.72 | | | | BETA: splitting (237) gives:
% 166.94/24.72 | | | |
% 166.94/24.72 | | | | Case 1:
% 166.94/24.72 | | | | |
% 166.94/24.72 | | | | | (4998) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 166.94/24.72 | | | | | e1) = e2)
% 166.94/24.72 | | | | |
% 166.94/24.72 | | | | | REF_CLOSE: (164), (168), (4989), (4990), (4998), (function-axioms) are
% 166.94/24.72 | | | | | inconsistent by sub-proof #570.
% 166.94/24.72 | | | | |
% 166.94/24.72 | | | | Case 2:
% 166.94/24.72 | | | | |
% 166.94/24.72 | | | | | (4999) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 166.94/24.72 | | | | | e1) = e2)
% 166.94/24.72 | | | | |
% 166.94/24.72 | | | | | BETA: splitting (4999) gives:
% 166.94/24.72 | | | | |
% 166.94/24.72 | | | | | Case 1:
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | (5000) all_58_8 = e2 & op(e1, e1) = e2
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | ALPHA: (5000) implies:
% 166.94/24.72 | | | | | | (5001) all_58_8 = e2
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1, e2,
% 166.94/24.72 | | | | | | e1, simplifying with (161), (4997) gives:
% 166.94/24.72 | | | | | | (5002) all_52_6 = e1
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | REDUCE: (142), (5002) imply:
% 166.94/24.72 | | | | | | (5003) ~ (all_52_2 = e1)
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | REDUCE: (135), (5002) imply:
% 166.94/24.72 | | | | | | (5004) ~ (all_52_4 = e1)
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | REDUCE: (127), (5002) imply:
% 166.94/24.72 | | | | | | (5005) ~ (all_52_7 = e1)
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | SIMP: (5005) implies:
% 166.94/24.72 | | | | | | (5006) ~ (all_52_7 = e1)
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | REDUCE: (125), (5002) imply:
% 166.94/24.72 | | | | | | (5007) ~ (all_52_14 = e1)
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | SIMP: (5007) implies:
% 166.94/24.72 | | | | | | (5008) ~ (all_52_14 = e1)
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | REDUCE: (379), (5002) imply:
% 166.94/24.72 | | | | | | (5009) ~ (all_8_2 = e1)
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | SIMP: (5009) implies:
% 166.94/24.72 | | | | | | (5010) ~ (all_8_2 = e1)
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | REDUCE: (4988), (5002) imply:
% 166.94/24.72 | | | | | | (5011) ~ (e2 = e1)
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | BETA: splitting (244) gives:
% 166.94/24.72 | | | | | |
% 166.94/24.72 | | | | | | Case 1:
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | | (5012) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 166.94/24.72 | | | | | | | op(e2, e2) = e1)
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | | BETA: splitting (5012) gives:
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | | (5013) all_58_1 = e1 & op(e3, e2) = e1
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | | REF_CLOSE: (169), (5004), (5013), (function-axioms) are
% 166.94/24.72 | | | | | | | | inconsistent by sub-proof #863.
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | | (5014) all_58_3 = e1 & op(e2, e2) = e1
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | | REF_CLOSE: (42), (5010), (5014), (function-axioms) are
% 166.94/24.72 | | | | | | | | inconsistent by sub-proof #498.
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | End of split
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | Case 2:
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | | (5015) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 166.94/24.72 | | | | | | | op(e0, e2) = e1)
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | | BETA: splitting (5015) gives:
% 166.94/24.72 | | | | | | |
% 166.94/24.72 | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | | (5016) all_58_7 = e1 & op(e1, e2) = e1
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | | ALPHA: (5016) implies:
% 166.94/24.72 | | | | | | | | (5017) all_58_7 = e1
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | | BETA: splitting (46) gives:
% 166.94/24.72 | | | | | | | |
% 166.94/24.72 | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | |
% 166.94/24.72 | | | | | | | | | (5018) ~ (all_10_2 = e0)
% 166.94/24.72 | | | | | | | | |
% 166.94/24.72 | | | | | | | | | BETA: splitting (52) gives:
% 166.94/24.72 | | | | | | | | |
% 166.94/24.72 | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | (5019) ~ (all_14_2 = e3)
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | REDUCE: (352), (5019) imply:
% 166.94/24.72 | | | | | | | | | | (5020) ~ (all_8_2 = e3)
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | BETA: splitting (58) gives:
% 166.94/24.72 | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | (5021) ~ (all_18_2 = e2)
% 166.94/24.72 | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | REDUCE: (4985), (5021) imply:
% 166.94/24.72 | | | | | | | | | | | (5022) $false
% 166.94/24.72 | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | CLOSE: (5022) is inconsistent.
% 166.94/24.72 | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | (5023) ( ~ (all_18_0 = e0) & op(all_18_1, e1) = all_18_0
% 166.94/24.72 | | | | | | | | | | | & op(e2, e1) = all_18_1 & $i(all_18_0) &
% 166.94/24.72 | | | | | | | | | | | $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e2, e1)
% 166.94/24.72 | | | | | | | | | | | = all_18_1 & $i(all_18_1))
% 166.94/24.72 | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | BETA: splitting (55) gives:
% 166.94/24.72 | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | (5024) ~ (all_16_2 = e2)
% 166.94/24.72 | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | REDUCE: (350), (5024) imply:
% 166.94/24.72 | | | | | | | | | | | | (5025) ~ (all_10_2 = e2)
% 166.94/24.72 | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | BETA: splitting (61) gives:
% 166.94/24.72 | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | (5026) ~ (all_20_2 = e2)
% 166.94/24.72 | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | REDUCE: (349), (5026) imply:
% 166.94/24.72 | | | | | | | | | | | | | (5027) ~ (all_4_2 = e2)
% 166.94/24.72 | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | BETA: splitting (76) gives:
% 166.94/24.72 | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | (5028) ~ (all_30_2 = e0)
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REDUCE: (355), (5028) imply:
% 166.94/24.72 | | | | | | | | | | | | | | (5029) ~ (all_8_2 = e0)
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (42), (45), (79), (82),
% 166.94/24.72 | | | | | | | | | | | | | | (109), (111), (124), (132), (133), (134), (139),
% 166.94/24.72 | | | | | | | | | | | | | | (140), (143), (144), (147), (148), (156), (157),
% 166.94/24.72 | | | | | | | | | | | | | | (158), (161), (162), (163), (164), (166), (167),
% 166.94/24.72 | | | | | | | | | | | | | | (168), (169), (188), (190), (192), (195), (198),
% 166.94/24.72 | | | | | | | | | | | | | | (199), (202), (203), (209), (221), (224), (225),
% 166.94/24.72 | | | | | | | | | | | | | | (227), (228), (230), (231), (234), (239), (240),
% 166.94/24.72 | | | | | | | | | | | | | | (241), (242), (243), (245), (247), (249), (251),
% 166.94/24.72 | | | | | | | | | | | | | | (252), (253), (262), (264), (266), (276), (283),
% 166.94/24.72 | | | | | | | | | | | | | | (287), (290), (298), (300), (307), (332), (356),
% 166.94/24.72 | | | | | | | | | | | | | | (361), (363), (365), (369), (373), (377), (381),
% 166.94/24.72 | | | | | | | | | | | | | | (383), (385), (387), (395), (396), (397), (398),
% 166.94/24.72 | | | | | | | | | | | | | | (4984), (4988), (4989), (5001), (5003), (5004),
% 166.94/24.72 | | | | | | | | | | | | | | (5006), (5010), (5017), (5018), (5020), (5023),
% 166.94/24.72 | | | | | | | | | | | | | | (5025), (5029), (function-axioms) are inconsistent
% 166.94/24.72 | | | | | | | | | | | | | | by sub-proof #67.
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | (5030) all_30_2 = e0
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | COMBINE_EQS: (355), (5030) imply:
% 166.94/24.72 | | | | | | | | | | | | | | (5031) all_8_2 = e0
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | SIMP: (5031) implies:
% 166.94/24.72 | | | | | | | | | | | | | | (5032) all_8_2 = e0
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | COMBINE_EQS: (361), (5032) imply:
% 166.94/24.72 | | | | | | | | | | | | | | (5033) all_56_12 = e0
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REDUCE: (374), (5032) imply:
% 166.94/24.72 | | | | | | | | | | | | | | (5034) ~ (all_52_1 = e0)
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REDUCE: (377), (5032) imply:
% 166.94/24.72 | | | | | | | | | | | | | | (5035) ~ (all_52_4 = e0)
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REDUCE: (383), (5032) imply:
% 166.94/24.72 | | | | | | | | | | | | | | (5036) ~ (all_52_9 = e0)
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REDUCE: (385), (5032) imply:
% 166.94/24.72 | | | | | | | | | | | | | | (5037) ~ (all_52_13 = e0)
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REDUCE: (5020), (5032) imply:
% 166.94/24.72 | | | | | | | | | | | | | | (5038) ~ (e3 = e0)
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | REDUCE: (5010), (5032) imply:
% 166.94/24.72 | | | | | | | | | | | | | | (5039) ~ (e1 = e0)
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 166.94/24.72 | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | (5040) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 166.94/24.72 | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.94/24.72 | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | BETA: splitting (5040) gives:
% 166.94/24.72 | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | Case 1:
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | (5041) all_58_1 = e0 & op(e3, e2) = e0
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5035), (5041), (function-axioms) are
% 166.94/24.72 | | | | | | | | | | | | | | | | inconsistent by sub-proof #155.
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | Case 2:
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | (5042) all_58_3 = e0 & op(e2, e2) = e0
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.72 | | | | | | | | | | | | | | | | ALPHA: (5042) implies:
% 166.94/24.72 | | | | | | | | | | | | | | | | (5043) all_58_3 = e0
% 166.94/24.72 | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | (5044) ~ (all_56_12 = e0)
% 166.94/24.73 | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | REDUCE: (5033), (5044) imply:
% 166.94/24.73 | | | | | | | | | | | | | | | | | (5045) $false
% 166.94/24.73 | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | CLOSE: (5045) is inconsistent.
% 166.94/24.73 | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | (5046) all_56_11 = e2 & op(e2, e0) = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | ALPHA: (5046) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | (5047) all_56_11 = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | | (5048) op(e2, e0) = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 166.94/24.73 | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (163), (5048) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | (5049) all_52_13 = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | REDUCE: (396), (5049) imply:
% 166.94/24.73 | | | | | | | | | | | | | | | | | (5050) ~ (all_4_2 = e2)
% 166.94/24.73 | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | (5051) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.94/24.73 | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | BETA: splitting (5051) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | (5052) all_58_9 = e1 & op(e3, e0) = e1
% 166.94/24.73 | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | ALPHA: (5052) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | (5053) all_58_9 = e1
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | (5054) op(e3, e0) = e1
% 166.94/24.73 | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | (5055) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5055) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | (5056) all_58_0 = e2 & op(e3, e3) = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5025), (5056), (function-axioms) are
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #666.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | (5057) all_58_2 = e2 & op(e2, e3) = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (42), (166), (240), (242),
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | (5020), (5043), (5048), (5057), (function-axioms)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #188.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | (5058) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5058) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | (5059) all_58_6 = e2 & op(e1, e3) = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5059) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | (5060) all_58_6 = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (231), (234), (5001),
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | (5017), (5060) are inconsistent by sub-proof #158.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | (5061) all_58_12 = e2 & op(e0, e3) = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5061) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | (5062) all_58_12 = e2
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | (5063) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5063) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | (5064) all_58_1 = e3 & op(e3, e2) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5064) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | (5065) all_58_1 = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (162), (168),
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | (228), (231), (234), (247), (249), (252), (253),
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | (398), (4989), (5001), (5017), (5048), (5062),
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | (5065), (function-axioms) are inconsistent by
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #66.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | (5066) all_58_3 = e3 & op(e2, e2) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5020), (5066), (function-axioms) are
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | (5067) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5067) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | (5068) all_58_7 = e3 & op(e1, e2) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5017), (5068) are inconsistent by sub-proof
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | #183.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | (5069) all_58_13 = e3 & op(e0, e2) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5069) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | (5070) all_58_13 = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | (5071) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (5006), (5062), (5071),
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | #79.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | (5072) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5072) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | (5073) all_58_14 = e1 & op(e0, e1) = e1
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5073) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | (5074) all_58_14 = e1
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | (5075) op(e0, e1) = e1
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (5076) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5076) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5077) all_58_0 = e0 & op(e3, e3) = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5018), (5077), (function-axioms) are
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #103.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5078) all_58_1 = e0 & op(e3, e2) = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5035), (5078), (function-axioms) are
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #155.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (5079) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5079) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5080) all_58_4 = e0 & op(e3, e1) = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5080) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5081) all_58_4 = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5082) op(e3, e1) = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5083) all_58_15 = e0 & op(e0, e0) = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5083) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5084) op(e0, e0) = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5085) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (5048), (5053), (5085),
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #528.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5086) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5086) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5087) all_58_11 = e3 & op(e1, e0) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5087) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5088) all_58_11 = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5089) op(e1, e0) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5090) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5090) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5091) all_58_6 = e0 & op(e1, e3) = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5091) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5092) op(e1, e3) = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5093) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5093) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5094) all_58_4 = e3 & op(e3, e1) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5081), (5094) are inconsistent by sub-proof
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #844.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5095) all_58_5 = e3 & op(e2, e1) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5095) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5096) op(e2, e1) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5097) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5097) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5098) all_58_0 = e3 & op(e3, e3) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5098) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5099) op(e3, e3) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, simplifying with (36), (5084) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5100) all_4_2 = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e1, simplifying with (159), (5089) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5101) all_52_14 = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (162), (5092) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5102) all_52_2 = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e3,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (164), (5096) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5103) all_52_9 = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e3, simplifying with (167), (5054) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5104) all_52_12 = e1
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (168), (5082) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5105) all_52_8 = e0
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (45), (5099) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5106) all_10_2 = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (5106) imply:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5107) all_56_10 = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5027), (5100) imply:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5108) ~ (e2 = e0)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5109) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5109) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5110) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5110) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5111) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5111) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5112) ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4986), (4996), (5112) are inconsistent by
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #65.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5113) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5113) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5114) ~ (all_56_10 = e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5107), (5114) imply:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5115) $false
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5115) is inconsistent.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5116) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5116) gives:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5117) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5117) implies:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5118) op(e1, e3) = e3
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5092), (5118), (function-axioms) are
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #64.
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5119) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (4988), (5082), (5119),
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #63.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5120) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5120) gives:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5121) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5121) gives:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5122) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5122) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5123) op(e2, e1) = e1
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5096), (5123), (function-axioms) are
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #686.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5124) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5124) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5125) op(e3, e0) = e0
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5054), (5125), (function-axioms) are
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #553.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5126) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5126) gives:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5127) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5127) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5128) op(e2, e0) = e0
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (5048), (5128), (function-axioms) are
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #684.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5129) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5129) gives:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5130) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5130) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5131) op(e1, e0) = e0
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5089), (5131), (function-axioms) are
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #62.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5132) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5033), (5047), (5132) are inconsistent by
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #683.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5133) all_58_1 = e3 & op(e3, e2) = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5133) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5134) all_58_1 = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (162), (168),
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (231), (234), (247), (249), (252), (253),
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (4989), (5001), (5017), (5048), (5062),
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5134), (function-axioms) are inconsistent by
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #66.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5135) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5135) gives:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5136) all_58_4 = e3 & op(e3, e1) = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5081), (5136) are inconsistent by sub-proof
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #844.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5137) all_58_9 = e3 & op(e3, e0) = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5137) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5138) all_58_9 = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (228), (5048), (5084), (5088),
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5138), (function-axioms) are inconsistent by
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #203.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5139) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5139) gives:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5140) all_58_8 = e3 & op(e1, e1) = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5140) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5141) all_58_8 = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5001), (5141) imply:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5142) e3 = e2
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5088), (5142) imply:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5143) all_58_11 = e2
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (163), (217), (224),
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (5033), (5053), (5143), (function-axioms)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #134.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5144) all_58_14 = e3 & op(e0, e1) = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5144) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5145) op(e0, e1) = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5075), (5145), (function-axioms) are
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #133.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5146) all_58_7 = e0 & op(e1, e2) = e0
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5146) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5147) all_58_7 = e0
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (163), (164), (166),
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (244), (245), (5034), (5036), (5048),
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5070), (5147), (function-axioms) are inconsistent
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #191.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5148) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5148) gives:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5149) all_58_8 = e0 & op(e1, e1) = e0
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5001), (5149) are inconsistent by sub-proof
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #398.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5150) all_58_11 = e0 & op(e1, e0) = e0
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5150) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5151) all_58_11 = e0
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5088), (5151) are inconsistent by sub-proof
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #474.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5152) all_58_15 = e3 & op(e0, e0) = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5152) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5153) all_58_15 = e3
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (224), (5062), (5070), (5074),
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5153) are inconsistent by sub-proof #882.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5154) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5154) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5155) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (5062), (5070), (5074), (5155) are
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5156) all_58_9 = e0 & op(e3, e0) = e0
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5156) implies:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5157) op(e3, e0) = e0
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5054), (5157), (function-axioms) are
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #553.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | (5158) all_58_15 = e1 & op(e0, e0) = e1
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (398), (5158), (function-axioms) are
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130.
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.74 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | (5159) all_58_10 = e1 & op(e2, e0) = e1
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | ALPHA: (5159) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | (5160) op(e2, e0) = e1
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5048), (5160), (function-axioms) are
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #526.
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | (5161) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 166.94/24.75 | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (231), (234),
% 166.94/24.75 | | | | | | | | | | | | | | | | | | (398), (5001), (5017), (5161), (function-axioms)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #68.
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | (5162) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 166.94/24.75 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | BETA: splitting (5162) gives:
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | (5163) all_58_7 = e0 & op(e1, e2) = e0
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5017), (5163) are inconsistent by sub-proof
% 166.94/24.75 | | | | | | | | | | | | | | | | #727.
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | (5164) all_58_13 = e0 & op(e0, e2) = e0
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | ALPHA: (5164) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | (5165) all_58_13 = e0
% 166.94/24.75 | | | | | | | | | | | | | | | | (5166) op(e0, e2) = e0
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | (5167) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 166.94/24.75 | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | BETA: splitting (5167) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | (5168) all_58_1 = e3 & op(e3, e2) = e3
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | ALPHA: (5168) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | (5169) all_58_1 = e3
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | (5170) ~ (all_56_12 = e0)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | REDUCE: (5033), (5170) imply:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | (5171) $false
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | CLOSE: (5171) is inconsistent.
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | (5172) all_56_11 = e2 & op(e2, e0) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | ALPHA: (5172) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | (5173) op(e2, e0) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | (5174) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5174) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | (5175) all_58_12 = e2 & op(e0, e3) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5175) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | (5176) all_58_12 = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (162), (168),
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | (228), (231), (234), (247), (249), (252), (253),
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | (398), (4989), (5001), (5017), (5169), (5173),
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | (5176), (function-axioms) are inconsistent by
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | sub-proof #66.
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | (5177) all_58_13 = e2 & op(e0, e2) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5177) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | (5178) op(e0, e2) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (5166), (5178), (function-axioms) are
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #631.
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | (5179) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5179) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | (5180) all_58_14 = e2 & op(e0, e1) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4991), (5180), (function-axioms) are
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | (5181) all_58_15 = e2 & op(e0, e0) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5027), (5181), (function-axioms) are
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | (5182) all_58_3 = e3 & op(e2, e2) = e3
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5020), (5182), (function-axioms) are
% 166.94/24.75 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | (5183) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 166.94/24.75 | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (5017), (5165), (5183) are inconsistent
% 166.94/24.75 | | | | | | | | | | | | | | | | | by sub-proof #60.
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | (5184) all_20_2 = e2
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | COMBINE_EQS: (349), (5184) imply:
% 166.94/24.75 | | | | | | | | | | | | | (5185) all_4_2 = e2
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | REDUCE: (396), (5185) imply:
% 166.94/24.75 | | | | | | | | | | | | | (5186) ~ (all_52_13 = e2)
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | BETA: splitting (217) gives:
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | (5187) ~ (all_56_12 = e0)
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | REDUCE: (361), (5187) imply:
% 166.94/24.75 | | | | | | | | | | | | | | (5188) ~ (all_8_2 = e0)
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (36), (42), (45), (79), (82),
% 166.94/24.75 | | | | | | | | | | | | | | (109), (111), (124), (132), (133), (134), (139),
% 166.94/24.75 | | | | | | | | | | | | | | (140), (143), (144), (147), (148), (156), (157),
% 166.94/24.75 | | | | | | | | | | | | | | (158), (161), (162), (163), (164), (166), (167),
% 166.94/24.75 | | | | | | | | | | | | | | (168), (169), (188), (190), (192), (195), (198),
% 166.94/24.75 | | | | | | | | | | | | | | (199), (202), (203), (209), (221), (224), (225),
% 166.94/24.75 | | | | | | | | | | | | | | (227), (228), (230), (231), (234), (239), (240),
% 166.94/24.75 | | | | | | | | | | | | | | (241), (242), (243), (245), (247), (249), (251),
% 166.94/24.75 | | | | | | | | | | | | | | (252), (253), (262), (264), (266), (276), (283),
% 166.94/24.75 | | | | | | | | | | | | | | (287), (290), (298), (300), (307), (332), (356),
% 166.94/24.75 | | | | | | | | | | | | | | (361), (363), (365), (369), (373), (377), (381),
% 166.94/24.75 | | | | | | | | | | | | | | (383), (385), (387), (395), (396), (397), (398),
% 166.94/24.75 | | | | | | | | | | | | | | (4984), (4988), (4989), (5001), (5003), (5004),
% 166.94/24.75 | | | | | | | | | | | | | | (5006), (5010), (5017), (5018), (5020), (5023),
% 166.94/24.75 | | | | | | | | | | | | | | (5025), (5188), (function-axioms) are inconsistent
% 166.94/24.75 | | | | | | | | | | | | | | by sub-proof #67.
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | (5189) all_56_11 = e2 & op(e2, e0) = e2
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | ALPHA: (5189) implies:
% 166.94/24.75 | | | | | | | | | | | | | | (5190) op(e2, e0) = e2
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | REF_CLOSE: (163), (5186), (5190), (function-axioms) are
% 166.94/24.75 | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | (5191) all_16_2 = e2
% 166.94/24.75 | | | | | | | | | | | | (5192) ( ~ (all_16_0 = e0) & op(all_16_1, e3) = all_16_0
% 166.94/24.75 | | | | | | | | | | | | & op(e2, e3) = all_16_1 & $i(all_16_0) &
% 166.94/24.75 | | | | | | | | | | | | $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e2, e3)
% 166.94/24.75 | | | | | | | | | | | | = all_16_1 & $i(all_16_1))
% 166.94/24.75 | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | COMBINE_EQS: (350), (5191) imply:
% 166.94/24.75 | | | | | | | | | | | | (5193) all_10_2 = e2
% 166.94/24.75 | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | SIMP: (5193) implies:
% 166.94/24.75 | | | | | | | | | | | | (5194) all_10_2 = e2
% 166.94/24.75 | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | COMBINE_EQS: (357), (5194) imply:
% 166.94/24.75 | | | | | | | | | | | | (5195) all_38_2 = e2
% 166.94/24.75 | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | COMBINE_EQS: (298), (5194) imply:
% 166.94/24.75 | | | | | | | | | | | | (5196) all_56_10 = e2
% 166.94/24.75 | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | REDUCE: (369), (5194) imply:
% 166.94/24.75 | | | | | | | | | | | | (5197) ~ (all_52_4 = e2)
% 166.94/24.75 | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | REDUCE: (373), (5194) imply:
% 166.94/24.75 | | | | | | | | | | | | (5198) ~ (all_52_12 = e2)
% 166.94/24.75 | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | BETA: splitting (222) gives:
% 166.94/24.75 | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | (5199) ~ (all_56_10 = e2)
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | REDUCE: (5196), (5199) imply:
% 166.94/24.75 | | | | | | | | | | | | | (5200) $false
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | CLOSE: (5200) is inconsistent.
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | (5201) all_56_1 = e3 & op(e3, e2) = e3
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | ALPHA: (5201) implies:
% 166.94/24.75 | | | | | | | | | | | | | (5202) all_56_1 = e3
% 166.94/24.75 | | | | | | | | | | | | | (5203) op(e3, e2) = e3
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | BETA: splitting (252) gives:
% 166.94/24.75 | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | (5204) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 166.94/24.75 | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | BETA: splitting (5204) gives:
% 166.94/24.75 | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | (5205) all_58_0 = e2 & op(e3, e3) = e2
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | ALPHA: (5205) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | (5206) all_58_0 = e2
% 166.94/24.75 | | | | | | | | | | | | | | | (5207) op(e3, e3) = e2
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 166.94/24.75 | | | | | | | | | | | | | | | e2, e3, simplifying with (169), (5203) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | (5208) all_52_4 = e3
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | REDUCE: (134), (5208) imply:
% 166.94/24.75 | | | | | | | | | | | | | | | (5209) ~ (all_52_7 = e3)
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | SIMP: (5209) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | (5210) ~ (all_52_7 = e3)
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | REDUCE: (132), (5208) imply:
% 166.94/24.75 | | | | | | | | | | | | | | | (5211) ~ (all_52_12 = e3)
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | SIMP: (5211) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | (5212) ~ (all_52_12 = e3)
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | REDUCE: (377), (5208) imply:
% 166.94/24.75 | | | | | | | | | | | | | | | (5213) ~ (all_8_2 = e3)
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 166.94/24.75 | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | (5214) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 166.94/24.75 | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | BETA: splitting (5214) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | (5215) all_58_1 = e3 & op(e3, e2) = e3
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | ALPHA: (5215) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | (5216) all_58_1 = e3
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | (5217) ~ (all_20_2 = e2)
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | REDUCE: (349), (5217) imply:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | (5218) ~ (all_4_2 = e2)
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | (5219) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | BETA: splitting (5219) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | (5220) all_58_9 = e2 & op(e3, e0) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5198), (5220), (function-axioms) are
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #663.
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | (5221) all_58_10 = e2 & op(e2, e0) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | ALPHA: (5221) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | (5222) all_58_10 = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | (5223) op(e2, e0) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | (5224) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5224) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | (5225) all_58_9 = e1 & op(e3, e0) = e1
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5225) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | (5226) op(e3, e0) = e1
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | (5227) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5227) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | (5228) all_58_12 = e2 & op(e0, e3) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5228) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | (5229) all_58_12 = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (247), (249),
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | (253), (5206), (5207), (5229), (function-axioms)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #138.
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | (5230) all_58_13 = e2 & op(e0, e2) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5230) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | (5231) op(e0, e2) = e2
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (248) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | (5232) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5232) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (5233) all_58_0 = e0 & op(e3, e3) = e0
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5018), (5233), (function-axioms) are
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #103.
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (5234) all_58_1 = e0 & op(e3, e2) = e0
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5216), (5234) are inconsistent by sub-proof
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | #794.
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | (5235) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5235) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (5236) all_58_4 = e0 & op(e3, e1) = e0
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5236) implies:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | (5237) op(e3, e1) = e0
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5238) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5238) gives:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5239) all_58_1 = e0 & op(e3, e2) = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5216), (5239) are inconsistent by sub-proof
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #794.
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5240) all_58_3 = e0 & op(e2, e2) = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5240) implies:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5241) all_58_3 = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5242) op(e2, e2) = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5243) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5243) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5244) all_58_2 = e2 & op(e2, e3) = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (42), (166), (240), (242),
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5020), (5223), (5241), (5244), (function-axioms)
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #188.
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5245) all_58_3 = e2 & op(e2, e2) = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5245) implies:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5246) all_58_3 = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (239), (240),
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241), (242), (5020), (5222), (5246),
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #908.
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5247) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5247) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5248) all_58_5 = e2 & op(e2, e1) = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (42), (240), (242), (5020),
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5223), (5241), (5248), (function-axioms) are
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #521.
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (157), (5231) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5249) all_52_7 = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (163), (5223) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5250) all_52_13 = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_8_2, e0,
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e2, simplifying with (42), (5242) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5251) all_8_2 = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e3, simplifying with (167), (5226) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5252) all_52_12 = e1
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (168), (5237) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5253) all_52_8 = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (361), (5251) imply:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5254) all_56_12 = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5210), (5249) imply:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5255) ~ (e3 = e2)
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (5252) imply:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5256) ~ (all_4_2 = e1)
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (5250) imply:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5257) ~ (all_52_14 = e2)
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (396), (5250) imply:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5258) ~ (all_4_2 = e2)
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5259) all_56_10 = e3
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5196), (5259) imply:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5260) e3 = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (5260) imply:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5261) $false
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5261) is inconsistent.
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5262) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5262) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5263) all_56_12 = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5254), (5263) imply:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5264) e2 = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5196), (5264) imply:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5265) all_56_10 = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (220), (5212), (5265), (function-axioms)
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #145.
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5266) all_56_14 = e1 | all_56_15 = e0
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5267) ~ (all_56_12 = e0)
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5254), (5267) imply:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5268) $false
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5268) is inconsistent.
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5269) all_56_11 = e2 & op(e2, e0) = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5269) implies:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5270) all_56_11 = e2
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5266) gives:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5271) all_56_14 = e1
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 166.94/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4986), (5271) are inconsistent by sub-proof
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #59.
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5272) all_56_15 = e0
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (5272) imply:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5273) all_4_2 = e0
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (397), (5273) imply:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5274) ~ (all_52_14 = e0)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5218), (5273) imply:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5275) ~ (e2 = e0)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (5273) imply:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5276) ~ (e1 = e0)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5277) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5277) gives:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5278) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5196), (5197), (5202), (5278),
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #520.
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5279) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5279) gives:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5280) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5280) implies:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5281) op(e1, e3) = e3
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5282) all_54_11 = e3
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5282) imply:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5283) all_52_14 = e3
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5283) implies:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5284) all_52_14 = e3
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5284) imply:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5285) ~ (all_52_2 = e3)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5281), (5285), (function-axioms) are
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #987.
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5286) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (4992), (5008), (5274), (5286) are
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #602.
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5287) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (4988), (5237), (5287),
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #63.
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5288) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5288) gives:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5289) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5196), (5202), (5226), (5289),
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #552.
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5290) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5290) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5291) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5291) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5292) op(e2, e0) = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (163), (217), (5254), (5292),
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #501.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5293) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5293) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5294) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5294) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5295) op(e1, e0) = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5296) all_54_11 = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5296) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5297) all_52_14 = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5297) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5298) all_52_14 = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5298) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5299) ~ (all_52_2 = e3)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5300) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5300) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5301) all_58_6 = e3 & op(e1, e3) = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5301) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5302) op(e1, e3) = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5299), (5302), (function-axioms) are
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #987.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5303) all_58_7 = e3 & op(e1, e2) = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5017), (5303) are inconsistent by sub-proof
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #183.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5304) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5304) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5305) all_58_8 = e3 & op(e1, e1) = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5001), (5305) are inconsistent by sub-proof
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #272.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5306) all_58_11 = e3 & op(e1, e0) = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5306) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5307) all_58_11 = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5308) op(e1, e0) = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5309) all_54_8 = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (5299), (5309) are inconsistent by
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #690.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5310) ~ (all_54_8 = e3)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5311) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5311) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5312) all_54_8 = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (4987), (5312) are inconsistent by
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #259.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5313) all_54_8 = e1 | all_54_8 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (162), (234), (276), (5001), (5003),
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5017), (5295), (5299), (5307), (5308), (5313),
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #58.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5314) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (4992), (5008), (5274), (5314) are
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #602.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5315) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5254), (5270), (5315) are inconsistent by
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #683.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5316) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (157), (5017), (5231), (5316),
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | #57.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (5317) all_58_9 = e0 & op(e3, e0) = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5317) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (5318) op(e3, e0) = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5226), (5318), (function-axioms) are
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #553.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | (5319) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5319) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | (5320) all_58_14 = e2 & op(e0, e1) = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4991), (5320), (function-axioms) are
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | (5321) all_58_15 = e2 & op(e0, e0) = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5218), (5321), (function-axioms) are
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5322) all_58_10 = e1 & op(e2, e0) = e1
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5322) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5323) op(e2, e0) = e1
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5223), (5323), (function-axioms) are
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #526.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | (5324) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (231), (234),
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | (398), (5001), (5017), (5324), (function-axioms)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #68.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | (5325) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | BETA: splitting (5325) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | (5326) all_58_11 = e2 & op(e1, e0) = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4992), (5326), (function-axioms) are
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | (5327) all_58_15 = e2 & op(e0, e0) = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5218), (5327), (function-axioms) are
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | (5328) all_20_2 = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | (5329) ( ~ (all_20_0 = e1) & op(all_20_1, e0) = all_20_0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_20_1 & $i(all_20_0) &
% 167.09/24.77 | | | | | | | | | | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e2, e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 167.09/24.77 | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (5328) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | (5330) all_4_2 = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (342), (5330) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | (5331) all_26_2 = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | REDUCE: (376), (5330) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | (5332) ~ (all_52_3 = e2)
% 167.09/24.77 | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | REDUCE: (387), (5330) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | (5333) ~ (all_52_7 = e2)
% 167.09/24.77 | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | REDUCE: (396), (5330) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | (5334) ~ (all_52_13 = e2)
% 167.09/24.77 | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | BETA: splitting (241) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | (5335) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | BETA: splitting (5335) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | (5336) all_58_2 = e2 & op(e2, e3) = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (161), (166),
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | (169), (239), (240), (242), (245), (4988), (5197),
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | (5333), (5336), (function-axioms) are inconsistent
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | by sub-proof #664.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | (5337) all_58_3 = e2 & op(e2, e2) = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | ALPHA: (5337) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | (5338) all_58_3 = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | (5339) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5339) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5340) all_58_1 = e0 & op(e3, e2) = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5216), (5340) are inconsistent by sub-proof
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | #794.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5341) all_58_3 = e0 & op(e2, e2) = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5341) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5342) all_58_3 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5338), (5342) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5343) e2 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5343) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5344) e2 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5196), (5344) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5345) all_56_10 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (220), (5212), (5345), (function-axioms)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #145.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | (5346) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5346) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5347) all_58_7 = e0 & op(e1, e2) = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5017), (5347) are inconsistent by sub-proof
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | #727.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5348) all_58_13 = e0 & op(e0, e2) = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5348) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | (5349) all_58_13 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | (5350) all_54_13 = e3
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (5210), (5350) are inconsistent by
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #971.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | (5351) ~ (all_54_13 = e3)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | (5352) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5352) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | (5353) all_54_13 = e2
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (5333), (5353) are inconsistent by
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #970.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | (5354) ~ (all_54_13 = e2)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | (5355) all_54_13 = e1 | all_54_13 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5355) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | (5356) all_54_13 = e1
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (5006), (5356) are inconsistent by
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #257.
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | (5357) all_54_13 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (5357) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | (5358) all_52_7 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5358) implies:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | (5359) all_52_7 = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (5359) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | (5360) ~ (all_52_3 = e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5210), (5359) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | (5361) ~ (e3 = e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5333), (5359) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | (5362) ~ (e2 = e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5006), (5359) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | (5363) ~ (e1 = e0)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (5359) imply:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | (5364) op(e0, e2) = e0
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (5365) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.09/24.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (167), (239),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (240), (241), (242), (5020), (5198), (5338),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (5365), (function-axioms) are inconsistent by
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #465.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (5366) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5366) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5367) all_58_11 = e2 & op(e1, e0) = e2
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4992), (5367), (function-axioms) are
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5368) all_58_15 = e2 & op(e0, e0) = e2
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5368) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5369) all_58_15 = e2
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5370) op(e0, e0) = e2
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (70) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5371) ~ (all_26_2 = e2)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5331), (5371) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5372) $false
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5372) is inconsistent.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5373) ( ~ (all_26_0 = e3) & op(all_26_1, e0) = all_26_0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e0) = all_26_1 & $i(all_26_0) &
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e2, e0)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5374) ~ (all_38_2 = e2)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5195), (5374) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5375) $false
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5375) is inconsistent.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5376) ( ~ (all_38_0 = e1) & op(all_38_1, e3) = all_38_0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = all_38_1 & $i(all_38_0) &
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2, e3)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5377) all_54_11 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5377) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5378) all_52_14 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5378) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5379) ~ (all_52_2 = e3)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5380) all_54_8 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (5379), (5380) are inconsistent by
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #690.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5381) ~ (all_54_8 = e3)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5382) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5383) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (5017), (5379), (5383),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #75.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5384) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5384) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5385) all_58_8 = e3 & op(e1, e1) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5001), (5385) are inconsistent by sub-proof
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #475.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5386) all_58_11 = e3 & op(e1, e0) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5386) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5387) all_58_11 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5388) op(e1, e0) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5382) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5389) all_54_8 = e2
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (4987), (5389) are inconsistent by
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #259.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5390) ~ (all_54_8 = e2)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5391) all_54_8 = e1 | all_54_8 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5391) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5392) all_54_8 = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (5003), (5392) are inconsistent by
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #689.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5393) all_54_8 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (5393) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5394) all_52_2 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5394) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5395) all_52_2 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (5395) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5396) ~ (all_52_3 = e0)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (5395) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5397) op(e1, e3) = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5398) all_54_12 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (5398) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5399) all_52_3 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (5399) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5400) op(e0, e3) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5401) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5401) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5402) all_58_0 = e1 & op(e3, e3) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5402) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5403) op(e3, e3) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5207), (5403), (function-axioms) are
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #957.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5404) all_58_2 = e1 & op(e2, e3) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5404) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5405) op(e2, e3) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5376) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5406) ~ (all_38_0 = e1) & op(all_38_1, e3) = all_38_0 &
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_38_1 & $i(all_38_0) &
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5406) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5407) op(e2, e3) = all_38_1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5192), (5397), (5405), (5407), (function-axioms)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #56.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5408) ~ (all_38_1 = e0) & op(e2, e3) = all_38_1 &
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5408) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5409) op(e2, e3) = all_38_1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5192), (5397), (5405), (5409), (function-axioms)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #56.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5410) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5410) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5411) all_58_6 = e1 & op(e1, e3) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5411) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5412) op(e1, e3) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (276), (5003), (5391), (5412),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #232.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5413) all_58_12 = e1 & op(e0, e3) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5413) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5414) op(e0, e3) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5400), (5414), (function-axioms) are
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #125.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5415) ~ (all_54_12 = e3)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5416) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (265), (5415) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5417) ~ (all_52_3 = e3)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5418) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5418) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5419) all_58_12 = e3 & op(e0, e3) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5419) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5420) op(e0, e3) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5416) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5421) all_54_12 = e2
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (5332), (5421) are inconsistent by
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #676.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5422) all_54_12 = e1 | all_54_12 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (265), (5360), (5417), (5420), (5422),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #55.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5423) all_58_13 = e3 & op(e0, e2) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5423) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5424) all_58_13 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (243), (244), (5216),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5338), (5424) are inconsistent by sub-proof #707.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5425) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5425) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5426) all_58_14 = e3 & op(e0, e1) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5426) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5427) all_58_14 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5428) op(e0, e1) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5429) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5429) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5430) all_58_0 = e3 & op(e3, e3) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5430) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5431) op(e3, e3) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5207), (5431), (function-axioms) are
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5432) all_58_2 = e3 & op(e2, e3) = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5432) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5433) all_58_2 = e3
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5434) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (5004), (5207), (5434),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #94.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5435) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5435) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5436) all_58_4 = e1 & op(e3, e1) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5436) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5437) op(e3, e1) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5438) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5438) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5439) all_58_4 = e0 & op(e3, e1) = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5439) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5440) op(e3, e1) = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5437), (5440), (function-axioms) are
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #569.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5441) all_58_5 = e0 & op(e2, e1) = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5441) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5442) op(e2, e1) = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4984), (5023), (5428), (5442),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #70.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5443) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5443) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5444) all_58_8 = e0 & op(e1, e1) = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5444) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5445) all_58_8 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5001), (5445) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5446) e2 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5446) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5447) e2 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5369), (5447) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5448) all_58_15 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (225), (226),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (5349), (5364), (5370), (5448),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #628.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5449) all_58_14 = e0 & op(e0, e1) = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5449) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5450) all_58_14 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5427), (5450) imply:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5451) e3 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (42), (157), (244), (246),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5020), (5216), (5338), (5349), (5364), (5451),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #590.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5452) all_58_9 = e1 & op(e3, e0) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5452) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5453) all_58_9 = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5454) op(e3, e0) = e1
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5455) all_58_15 = e0 & op(e0, e0) = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5455) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5456) all_58_15 = e0
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (225), (226),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (5349), (5364), (5370), (5456),
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #628.
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5457) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5457) implies:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5458) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5459) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5459) gives:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5460) all_58_2 = e1 & op(e2, e3) = e1
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5460) implies:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5461) all_58_2 = e1
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5433), (5461) imply:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5462) e3 = e1
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5387), (5462) imply:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5463) all_58_11 = e1
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (231), (234), (5001),
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5017), (5463) are inconsistent by sub-proof #76.
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5464) all_58_3 = e1 & op(e2, e2) = e1
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5010), (5464), (function-axioms) are
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #498.
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5465) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5465) gives:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5466) all_58_5 = e1 & op(e2, e1) = e1
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5466) implies:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5467) op(e2, e1) = e1
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5468) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5468) gives:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5469) all_58_4 = e0 & op(e3, e1) = e0
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5469) implies:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5470) op(e3, e1) = e0
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5471) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5471) gives:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5472) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5196), (5197), (5202), (5472),
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #520.
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5473) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5473) gives:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5474) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5474) implies:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5475) op(e1, e3) = e3
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5379), (5475), (function-axioms) are
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #987.
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5476) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (4988), (5470), (5476),
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #63.
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5477) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5477) gives:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5478) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5196), (5202), (5454), (5478),
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #552.
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5479) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5479) gives:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5480) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5480) implies:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5481) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_1 & $i(all_56_1))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5196), (5202), (5481) are inconsistent by
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #554.
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5482) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5482) gives:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5483) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5483) implies:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5484) op(e1, e0) = e0
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (162), (234), (276), (5001), (5003),
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5017), (5379), (5387), (5388), (5391), (5484),
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #58.
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5485) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5485) implies:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5486) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1)
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (157), (225), (5364), (5370),
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5428), (5486), (function-axioms) are inconsistent
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #53.
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5487) all_58_5 = e0 & op(e2, e1) = e0
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5487) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5488) op(e2, e1) = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5467), (5488), (function-axioms) are
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5489) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5489) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5490) all_58_8 = e0 & op(e1, e1) = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (225), (226),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (5001), (5349), (5364), (5369), (5370),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5490), (function-axioms) are inconsistent by
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #52.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5491) all_58_14 = e0 & op(e0, e1) = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5491) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5492) all_58_14 = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5427), (5492) imply:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5493) e3 = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5493) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5494) e3 = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (42), (157), (244), (246),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5020), (5216), (5338), (5349), (5364), (5494),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #590.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5495) all_58_10 = e1 & op(e2, e0) = e1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5495) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5496) all_58_10 = e1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5458) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5497) all_58_9 = e0 & op(e3, e0) = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5453), (5497) are inconsistent by sub-proof
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #897.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5498) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5498) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5499) all_58_10 = e0 & op(e2, e0) = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5496), (5499) are inconsistent by sub-proof
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #925.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5500) all_58_11 = e0 & op(e1, e0) = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5387), (5500) are inconsistent by sub-proof
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #724.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5501) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5501) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5502) all_58_6 = e3 & op(e1, e3) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5502) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5503) op(e1, e3) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5379), (5503), (function-axioms) are
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #987.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5504) all_58_12 = e3 & op(e0, e3) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5504) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5505) all_58_12 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (157), (225), (5364), (5370),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5427), (5505), (function-axioms) are inconsistent
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #100.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5506) all_58_15 = e3 & op(e0, e0) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5506) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5507) all_58_15 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5369), (5507) are inconsistent by sub-proof
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #856.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5508) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5509) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5509) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5510) all_58_6 = e3 & op(e1, e3) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5510) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5511) all_58_6 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5512) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5512) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5513) all_58_9 = e3 & op(e3, e0) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5212), (5513), (function-axioms) are
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #86.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5514) all_58_10 = e3 & op(e2, e0) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5514) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5515) all_58_10 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5516) op(e2, e0) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5517) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5517) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5518) all_58_9 = e1 & op(e3, e0) = e1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5518) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5519) op(e3, e0) = e1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5329) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5520) ~ (all_20_0 = e1) & op(all_20_1, e0) = all_20_0 &
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_20_1 & $i(all_20_0) &
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5520) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5521) ~ (all_20_0 = e1)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5522) op(e2, e0) = all_20_1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5523) op(all_20_1, e0) = all_20_0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5373) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5524) ~ (all_26_0 = e3) & op(all_26_1, e0) = all_26_0 &
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_26_1 & $i(all_26_0) &
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5524) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5525) op(e2, e0) = all_26_1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5516), (5519), (5521), (5522), (5523), (5525),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #51.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5526) ~ (all_26_1 = e1) & op(e2, e0) = all_26_1 &
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5526) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5527) op(e2, e0) = all_26_1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5516), (5519), (5521), (5522), (5523), (5527),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #51.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5528) ~ (all_20_1 = e3) & op(e2, e0) = all_20_1 &
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5528) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5529) ~ (all_20_1 = e3)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5530) op(e2, e0) = all_20_1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5373) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5531) ~ (all_26_0 = e3) & op(all_26_1, e0) = all_26_0 &
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_26_1 & $i(all_26_0) &
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5531) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5532) op(e2, e0) = all_26_1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5516), (5529), (5530), (5532), (function-axioms)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #50.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5533) ~ (all_26_1 = e1) & op(e2, e0) = all_26_1 &
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5533) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5534) op(e2, e0) = all_26_1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5516), (5529), (5530), (5534), (function-axioms)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #50.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5535) all_58_10 = e1 & op(e2, e0) = e1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5515), (5535) are inconsistent by sub-proof
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #851.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5536) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5536) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5537) all_58_11 = e1 & op(e1, e0) = e1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5537) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5538) all_58_11 = e1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (231), (5001), (5017), (5511),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5538) are inconsistent by sub-proof #78.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5539) all_58_15 = e1 & op(e0, e0) = e1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5539) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5540) op(e0, e0) = e1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5370), (5540), (function-axioms) are
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #640.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5541) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5541) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5542) all_58_11 = e3 & op(e1, e0) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5542) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5543) all_58_11 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (157), (225),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (227), (231), (244), (246), (5001), (5017),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5020), (5216), (5338), (5349), (5364), (5369),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5370), (5511), (5543), (function-axioms) are
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #49.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5544) all_58_15 = e3 & op(e0, e0) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5544) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5545) all_58_15 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5369), (5545) imply:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5546) e3 = e2
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5546) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5547) e3 = e2
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5511), (5547) imply:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5548) all_58_6 = e2
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (231), (234), (5001),
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5017), (5548) are inconsistent by sub-proof #158.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5549) all_58_7 = e3 & op(e1, e2) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5549) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5550) all_58_7 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5017), (5550) are inconsistent by sub-proof
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #821.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5551) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5551) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5552) all_58_8 = e3 & op(e1, e1) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5001), (5552) are inconsistent by sub-proof
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #475.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5553) all_58_11 = e3 & op(e1, e0) = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5553) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5554) all_58_11 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5508) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5555) all_54_11 = e2
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5555) imply:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5556) all_52_14 = e2
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4992), (5556) imply:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5557) $false
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5557) is inconsistent.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5558) ~ (all_54_11 = e2)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5559) all_54_11 = e1 | all_54_11 = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5559) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5560) all_54_11 = e1
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (5008), (5560) are inconsistent by
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #734.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5561) all_54_11 = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5561) imply:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5562) all_52_14 = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5562) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5563) all_52_14 = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5563) imply:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5564) ~ (all_52_2 = e0)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5565) all_54_8 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (5565) imply:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5566) all_52_2 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5566) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5567) all_52_2 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (5567) imply:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5568) ~ (all_52_1 = e3)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (5567) imply:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5569) ~ (all_52_3 = e3)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5569) implies:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5570) ~ (all_52_3 = e3)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5571) all_54_12 = e3
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (5570), (5571) are inconsistent by
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #738.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5572) ~ (all_54_12 = e3)
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5573) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5573) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5574) all_54_12 = e2
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (5332), (5574) are inconsistent by
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #676.
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5575) all_54_12 = e1 | all_54_12 = e0
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5576) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5576) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5577) all_58_0 = e3 & op(e3, e3) = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5577) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5578) op(e3, e3) = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5207), (5578), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5579) all_58_2 = e3 & op(e2, e3) = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5579) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5580) op(e2, e3) = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (5568), (5580), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #989.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5581) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5581) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5582) all_58_6 = e3 & op(e1, e3) = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5582) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5583) all_58_6 = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (42), (157), (225),
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (227), (231), (244), (246), (5001), (5017),
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5020), (5216), (5338), (5349), (5364), (5369),
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5370), (5554), (5583), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #49.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5584) all_58_12 = e3 & op(e0, e3) = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5584) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5585) op(e0, e3) = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (265), (5360), (5570), (5575), (5585),
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #55.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5586) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (4987), (5003), (5564), (5586) are
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #48.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | (5587) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.09/24.81 | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (5587) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | (5588) all_58_5 = e2 & op(e2, e1) = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | ALPHA: (5588) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | (5589) op(e2, e1) = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (198), (217), (283), (361), (383),
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | (5010), (5020), (5334), (5589), (function-axioms)
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #466.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | (5590) all_58_10 = e2 & op(e2, e0) = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | ALPHA: (5590) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | (5591) op(e2, e0) = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5334), (5591), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #662.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | (5592) all_58_3 = e3 & op(e2, e2) = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (5020), (5592), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | (5593) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 167.09/24.81 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 167.09/24.81 | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | BETA: splitting (5593) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | (5594) all_58_7 = e3 & op(e1, e2) = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | ALPHA: (5594) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | (5595) all_58_7 = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5017), (5595) are inconsistent by sub-proof
% 167.09/24.81 | | | | | | | | | | | | | | | | | #821.
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | (5596) all_58_13 = e3 & op(e0, e2) = e3
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (5210), (5596), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #962.
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | (5597) all_58_1 = e2 & op(e3, e2) = e2
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | ALPHA: (5597) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | (5598) op(e3, e2) = e2
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | REF_CLOSE: (169), (5197), (5598), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | | | inconsistent by sub-proof #993.
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | (5599) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 167.09/24.81 | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 167.09/24.81 | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | BETA: splitting (5599) gives:
% 167.09/24.81 | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | (5600) all_58_4 = e2 & op(e3, e1) = e2
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | REF_CLOSE: (168), (4989), (5600), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | | | inconsistent by sub-proof #572.
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | (5601) all_58_9 = e2 & op(e3, e0) = e2
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | REF_CLOSE: (167), (5198), (5601), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | | | inconsistent by sub-proof #663.
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | (5602) all_14_2 = e3
% 167.09/24.81 | | | | | | | | | | (5603) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0
% 167.09/24.81 | | | | | | | | | | & op(e3, e2) = all_14_1 & $i(all_14_0) &
% 167.09/24.81 | | | | | | | | | | $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3, e2)
% 167.09/24.81 | | | | | | | | | | = all_14_1 & $i(all_14_1))
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | COMBINE_EQS: (352), (5602) imply:
% 167.09/24.81 | | | | | | | | | | (5604) all_8_2 = e3
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | SIMP: (5604) implies:
% 167.09/24.81 | | | | | | | | | | (5605) all_8_2 = e3
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | COMBINE_EQS: (334), (5605) imply:
% 167.09/24.81 | | | | | | | | | | (5606) all_22_2 = e3
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | COMBINE_EQS: (361), (5605) imply:
% 167.09/24.81 | | | | | | | | | | (5607) all_56_12 = e3
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | REDUCE: (374), (5605) imply:
% 167.09/24.81 | | | | | | | | | | (5608) ~ (all_52_1 = e3)
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | REDUCE: (377), (5605) imply:
% 167.09/24.81 | | | | | | | | | | (5609) ~ (all_52_4 = e3)
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | REDUCE: (381), (5605) imply:
% 167.09/24.81 | | | | | | | | | | (5610) ~ (all_52_7 = e3)
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | REDUCE: (383), (5605) imply:
% 167.09/24.81 | | | | | | | | | | (5611) ~ (all_52_9 = e3)
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | REDUCE: (385), (5605) imply:
% 167.09/24.81 | | | | | | | | | | (5612) ~ (all_52_13 = e3)
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | BETA: splitting (219) gives:
% 167.09/24.81 | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | (5613) ~ (all_56_12 = e3)
% 167.09/24.81 | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | REDUCE: (5607), (5613) imply:
% 167.09/24.81 | | | | | | | | | | | (5614) $false
% 167.09/24.81 | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | CLOSE: (5614) is inconsistent.
% 167.09/24.81 | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | (5615) all_56_0 = e2 & op(e2, e3) = e2
% 167.09/24.81 | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | ALPHA: (5615) implies:
% 167.09/24.81 | | | | | | | | | | | (5616) all_56_0 = e2
% 167.09/24.81 | | | | | | | | | | | (5617) op(e2, e3) = e2
% 167.09/24.81 | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | BETA: splitting (242) gives:
% 167.09/24.81 | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | (5618) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 167.09/24.81 | | | | | | | | | | | | & op(e2, e2) = e3)
% 167.09/24.81 | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | BETA: splitting (5618) gives:
% 167.09/24.81 | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | (5619) all_58_2 = e3 & op(e2, e3) = e3
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | ALPHA: (5619) implies:
% 167.09/24.81 | | | | | | | | | | | | | (5620) op(e2, e3) = e3
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | REF_CLOSE: (9), (166), (5617), (5620), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | inconsistent by sub-proof #462.
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | (5621) all_58_3 = e3 & op(e2, e2) = e3
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | ALPHA: (5621) implies:
% 167.09/24.81 | | | | | | | | | | | | | (5622) all_58_3 = e3
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 167.09/24.81 | | | | | | | | | | | | | e3, e2, simplifying with (166), (5617) gives:
% 167.09/24.81 | | | | | | | | | | | | | (5623) all_52_1 = e2
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | REDUCE: (148), (5623) imply:
% 167.09/24.81 | | | | | | | | | | | | | (5624) ~ (all_52_2 = e2)
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | REDUCE: (145), (5623) imply:
% 167.09/24.81 | | | | | | | | | | | | | (5625) ~ (all_52_9 = e2)
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | REDUCE: (144), (5623) imply:
% 167.09/24.81 | | | | | | | | | | | | | (5626) ~ (all_52_13 = e2)
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | SIMP: (5626) implies:
% 167.09/24.81 | | | | | | | | | | | | | (5627) ~ (all_52_13 = e2)
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | REDUCE: (363), (5623) imply:
% 167.09/24.81 | | | | | | | | | | | | | (5628) ~ (all_10_2 = e2)
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | SIMP: (5628) implies:
% 167.09/24.81 | | | | | | | | | | | | | (5629) ~ (all_10_2 = e2)
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | REDUCE: (5608), (5623) imply:
% 167.09/24.81 | | | | | | | | | | | | | (5630) ~ (e3 = e2)
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | BETA: splitting (241) gives:
% 167.09/24.81 | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | (5631) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 167.09/24.81 | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 167.09/24.81 | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | BETA: splitting (5631) gives:
% 167.09/24.81 | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | (5632) all_58_2 = e2 & op(e2, e3) = e2
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | ALPHA: (5632) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | (5633) all_58_2 = e2
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 167.09/24.81 | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | (5634) ~ (all_20_2 = e2)
% 167.09/24.81 | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | REDUCE: (349), (5634) imply:
% 167.09/24.81 | | | | | | | | | | | | | | | | (5635) ~ (all_4_2 = e2)
% 167.09/24.81 | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | (5636) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 167.09/24.81 | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | BETA: splitting (5636) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | (5637) all_58_9 = e2 & op(e3, e0) = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | ALPHA: (5637) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | (5638) all_58_9 = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | (5639) op(e3, e0) = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | (5640) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 167.09/24.81 | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (5640) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | (5641) all_58_9 = e1 & op(e3, e0) = e1
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5638), (5641) are inconsistent by sub-proof
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | #701.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | (5642) all_58_10 = e1 & op(e2, e0) = e1
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | ALPHA: (5642) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | (5643) op(e2, e0) = e1
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | (5644) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5644) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | (5645) all_58_12 = e2 & op(e0, e3) = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5645) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | (5646) all_58_12 = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | (242), (247), (249), (253), (5617), (5622),
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | (5633), (5646), (function-axioms) are inconsistent
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #433.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | (5647) all_58_13 = e2 & op(e0, e2) = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5647) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | (5648) all_58_13 = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | (5649) op(e0, e2) = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | (5650) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5650) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | (5651) all_58_2 = e0 & op(e2, e3) = e0
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (166), (5617), (5651), (function-axioms) are
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #782.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | (5652) all_58_3 = e0 & op(e2, e2) = e0
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5622), (5652) are inconsistent by sub-proof
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | #869.
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | (5653) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5653) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | (5654) all_58_5 = e0 & op(e2, e1) = e0
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5654) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | (5655) op(e2, e1) = e0
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | (5656) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5656) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (5657) all_58_1 = e0 & op(e3, e2) = e0
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5657) implies:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (5658) op(e3, e2) = e0
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (157), (5649) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (5659) all_52_7 = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, e2, simplifying with (163), (5643) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (5660) all_52_13 = e1
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (164), (5655) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (5661) all_52_9 = e0
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e3, simplifying with (167), (5639) gives:
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | (5662) all_52_12 = e2
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.81 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (169), (5658) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5663) all_52_4 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (5663) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5664) ~ (all_10_2 = e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (5659) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5665) ~ (all_52_11 = e2)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (5661) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5666) ~ (all_52_11 = e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5666) implies:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5667) ~ (all_52_11 = e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (5660), (5661) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5668) ~ (e1 = e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5611), (5661) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5669) ~ (e3 = e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4990), (5661) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5670) ~ (e2 = e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (5662) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5671) ~ (all_52_14 = e2)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (395), (5662) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5672) ~ (all_4_2 = e2)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (396), (5660) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5673) ~ (all_4_2 = e1)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5612), (5660) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (5674) ~ (e3 = e1)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5675) ~ (all_22_2 = e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5606), (5675) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5676) $false
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5676) is inconsistent.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5677) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_22_1 & $i(all_22_0) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5678) ~ (all_34_2 = e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (332), (5678) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5679) ~ (all_4_2 = e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5680) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5680) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5681) all_58_9 = e3 & op(e3, e0) = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5681) implies:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5682) all_58_9 = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5638), (5682) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5683) e3 = e2
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5622), (5683) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5684) all_58_3 = e2
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (5617), (5684), (function-axioms) are
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #665.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5685) all_58_10 = e3 & op(e2, e0) = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5685) implies:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5686) op(e2, e0) = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5612), (5686), (function-axioms) are
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5687) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5687) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5688) all_58_11 = e3 & op(e1, e0) = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5688) implies:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5689) all_58_11 = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5690) all_58_15 = e0 & op(e0, e0) = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5690) implies:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5691) all_58_15 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5692) all_54_15 = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (307), (5679), (5692) are inconsistent by
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #992.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5693) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5693) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5694) all_54_15 = e2
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (307), (5635), (5694) are inconsistent by
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #991.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5695) all_54_15 = e1 | all_54_15 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5695) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5696) all_54_15 = e1
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (307), (398), (5696) are inconsistent by sub-proof
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #990.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5697) all_54_15 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (307), (5697) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5698) all_4_2 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5698) implies:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5699) all_4_2 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (5699) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5700) all_56_15 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (397), (5699) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5701) ~ (all_52_14 = e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5702) all_54_11 = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5702) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5703) all_52_14 = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5703) implies:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5704) all_52_14 = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5704) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5705) ~ (all_52_2 = e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (5704) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5706) op(e1, e0) = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5707) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (161), (162), (166), (4988), (5607), (5616),
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5617), (5705), (5707), (function-axioms) are
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #47.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5708) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5708) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5709) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5607), (5616), (5655), (5709),
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5710) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5710) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5711) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5711) implies:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5712) op(e2, e0) = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5643), (5712), (function-axioms) are
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #849.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5713) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5713) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5714) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5714) implies:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5715) ~ (all_56_14 = e1)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5716) op(e1, e0) = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5717) all_54_8 = e3
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (5705), (5717) are inconsistent by
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #690.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5718) ~ (all_54_8 = e3)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5719) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5719) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5720) all_54_8 = e2
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (4987), (5720) are inconsistent by
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #259.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5721) ~ (all_54_8 = e2)
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5722) all_54_8 = e1 | all_54_8 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5722) gives:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5723) all_54_8 = e1
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (5003), (5723) are inconsistent by
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #689.
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5724) all_54_8 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (5724) imply:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5725) all_52_2 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5725) implies:
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5726) all_52_2 = e0
% 167.09/24.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e0,
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (5706), (5716) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5727) e3 = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5689), (5727) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5728) all_58_11 = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5729) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5729) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5730) all_58_9 = e3 & op(e3, e0) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5730) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5731) all_58_9 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5638), (5731) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5732) e3 = e2
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5732) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5733) e3 = e2
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5622), (5733) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5734) all_58_3 = e2
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (5617), (5734), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #665.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5735) all_58_10 = e3 & op(e2, e0) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5735) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5736) op(e2, e0) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5612), (5736), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #562.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5687) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5689), (5728) are inconsistent by sub-proof
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #474.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5737) all_58_15 = e3 & op(e0, e0) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5691), (5737) are inconsistent by sub-proof
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #812.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5738) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5738) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5739) ~ (all_56_15 = e0)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5700), (5739) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5740) $false
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5740) is inconsistent.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5741) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (4992), (5008), (5701), (5741) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #602.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5742) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (166), (229),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (5617), (5622), (5633),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5635), (5643), (5689), (5742), (function-axioms)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #46.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5743) all_58_15 = e3 & op(e0, e0) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5679), (5743), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #161.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5744) all_34_2 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (332), (5744) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5745) all_4_2 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (5745) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5746) all_56_15 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (394), (5745) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5747) ~ (all_52_11 = e3)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5748) ~ (all_56_15 = e3)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5746), (5748) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5749) $false
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5749) is inconsistent.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5750) all_56_6 = e0 & op(e0, e3) = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5750) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5751) op(e0, e3) = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5752) all_54_14 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (5747), (5752) are inconsistent by
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #969.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5753) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5754) all_56_10 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (5754) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5755) all_10_2 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5755) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5756) all_10_2 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (5756) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5757) ~ (all_52_2 = e3)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (5756) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5758) ~ (all_52_8 = e3)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5759) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5759) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5760) all_58_6 = e3 & op(e1, e3) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5760) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5761) op(e1, e3) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (5757), (5761), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #987.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5762) all_58_7 = e3 & op(e1, e2) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5762) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5763) all_58_7 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (161), (169), (243), (244),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5603), (5622), (5648), (5658), (5677), (5763),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #428.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5764) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5764) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5765) all_58_8 = e3 & op(e1, e1) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (5001), (5617), (5622), (5765),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #45.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5766) all_58_11 = e3 & op(e1, e0) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5766) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5767) all_58_11 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5768) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5768) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5769) all_58_0 = e1 & op(e3, e3) = e1
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5769) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5770) all_58_0 = e1
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5771) all_58_15 = e0 & op(e0, e0) = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5771) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5772) op(e0, e0) = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5773) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (5609), (5770), (5773),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #250.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5774) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5774) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5775) all_58_4 = e3 & op(e3, e1) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5775) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5776) op(e3, e1) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5758), (5776), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #975.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5777) all_58_9 = e3 & op(e3, e0) = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5777) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5778) all_58_9 = e3
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (9), (36), (228), (229), (5635),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5767), (5772), (5778), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #202.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5779) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (166), (229),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (240), (242), (5617), (5622), (5633),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5635), (5643), (5767), (5779), (function-axioms)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #46.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5780) all_58_2 = e1 & op(e2, e3) = e1
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5780) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5781) op(e2, e3) = e1
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (5617), (5781), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #784.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5782) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5782) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5783) all_58_6 = e1 & op(e1, e3) = e1
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5783) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5784) op(e1, e3) = e1
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (195), (276), (4987), (5003), (5757),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5784), (function-axioms) are inconsistent by
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #231.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5785) all_58_12 = e1 & op(e0, e3) = e1
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5785) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5786) op(e0, e3) = e1
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5751), (5786), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #531.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5787) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5753) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5788) all_54_14 = e2
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (4991), (5788) are inconsistent by
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #737.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5789) all_54_14 = e1 | all_54_14 = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5787) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5790) all_56_12 = e2
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5607), (5790) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5791) e3 = e2
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5622), (5791) imply:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5792) all_58_3 = e2
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (5617), (5792), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #665.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5793) all_56_14 = e1 | all_56_15 = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (263), (274), (391), (5667), (5746), (5789),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5793) are inconsistent by sub-proof #92.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | (5794) all_58_3 = e0 & op(e2, e2) = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5622), (5794) are inconsistent by sub-proof
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | | #869.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | (5795) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (157), (5017), (5649), (5795),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | | #57.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | (5796) all_58_10 = e0 & op(e2, e0) = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5796) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | (5797) op(e2, e0) = e0
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5643), (5797), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #849.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | (5798) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5798) gives:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | (5799) all_58_14 = e2 & op(e0, e1) = e2
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4991), (5799), (function-axioms) are
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | (5800) all_58_15 = e2 & op(e0, e0) = e2
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5800) implies:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | (5801) all_58_15 = e2
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (163), (166), (224),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | (228), (230), (239), (240), (242), (5612), (5617),
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | (5622), (5633), (5638), (5801), (function-axioms)
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #226.
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.83 | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.83 | | | | | | | | | | | | | | | | | | |
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | (5802) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 167.09/24.83 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | BETA: splitting (5802) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5803) all_58_11 = e1 & op(e1, e0) = e1
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | ALPHA: (5803) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5804) all_58_11 = e1
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | (5805) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (231), (5001), (5017), (5804),
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | (5805) are inconsistent by sub-proof #77.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | (5806) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5806) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | (5807) all_58_8 = e3 & op(e1, e1) = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5807) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | (5808) all_58_8 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5001), (5808) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | (5809) e3 = e2
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | SIMP: (5809) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | (5810) e3 = e2
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5622), (5810) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | (5811) all_58_3 = e2
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | (242), (5617), (5811), (function-axioms) are
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #665.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | (5812) all_58_11 = e3 & op(e1, e0) = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5804), (5812) are inconsistent by sub-proof
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | #115.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5813) all_58_15 = e1 & op(e0, e0) = e1
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (398), (5813), (function-axioms) are
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #130.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | (5814) all_58_10 = e2 & op(e2, e0) = e2
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 167.09/24.84 | | | | | | | | | | | | | | | | | | (5617), (5622), (5814), (function-axioms) are
% 167.09/24.84 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #447.
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | End of split
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | (5815) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 167.09/24.84 | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | BETA: splitting (5815) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | (5816) all_58_11 = e2 & op(e1, e0) = e2
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4992), (5816), (function-axioms) are
% 167.09/24.84 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | (5817) all_58_15 = e2 & op(e0, e0) = e2
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5635), (5817), (function-axioms) are
% 167.09/24.84 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #854.
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | End of split
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | End of split
% 167.09/24.84 | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | (5818) all_20_2 = e2
% 167.09/24.84 | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | COMBINE_EQS: (349), (5818) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | (5819) all_4_2 = e2
% 167.09/24.84 | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | COMBINE_EQS: (262), (5819) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | (5820) all_56_15 = e2
% 167.09/24.84 | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | REDUCE: (376), (5819) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | (5821) ~ (all_52_3 = e2)
% 167.09/24.84 | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | REDUCE: (387), (5819) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | (5822) ~ (all_52_7 = e2)
% 167.09/24.84 | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | REDUCE: (36), (5819) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | (5823) op(e0, e0) = e2
% 167.09/24.84 | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | (5824) all_54_13 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (5610), (5824) are inconsistent by
% 167.09/24.84 | | | | | | | | | | | | | | | | | sub-proof #971.
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | (5825) ~ (all_54_13 = e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | (5826) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | BETA: splitting (5826) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | (5827) all_54_13 = e2
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (5822), (5827) are inconsistent by
% 167.09/24.84 | | | | | | | | | | | | | | | | | | sub-proof #970.
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | (5828) ~ (all_54_13 = e2)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | (5829) all_54_13 = e1 | all_54_13 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | (5830) ~ (all_56_15 = e2)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | REDUCE: (5820), (5830) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | (5831) $false
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | CLOSE: (5831) is inconsistent.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | (5832) all_56_7 = e0 & op(e0, e2) = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | ALPHA: (5832) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | (5833) all_56_7 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | BETA: splitting (5829) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5834) all_54_13 = e1
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (264), (5006), (5834) are inconsistent by
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | sub-proof #257.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5835) all_54_13 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (5835) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5836) all_52_7 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | SIMP: (5836) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5837) all_52_7 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (5837) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5838) ~ (all_52_11 = e0)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | SIMP: (5838) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5839) ~ (all_52_11 = e0)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | REDUCE: (5610), (5837) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5840) ~ (e3 = e0)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | REDUCE: (5822), (5837) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5841) ~ (e2 = e0)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | REDUCE: (5006), (5837) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5842) ~ (e1 = e0)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | REDUCE: (157), (5837) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | (5843) op(e0, e2) = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | (5844) all_56_10 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (5844) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | (5845) all_10_2 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (5845) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | (5846) ~ (all_52_2 = e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (5845) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | (5847) ~ (all_52_3 = e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (5845) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | (5848) ~ (all_52_8 = e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | (5849) all_54_12 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (5847), (5849) are inconsistent by
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | sub-proof #738.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | (5850) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | (5851) all_54_8 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (5846), (5851) are inconsistent by
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #690.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | (5852) ~ (all_54_8 = e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | (5853) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5853) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | (5854) all_54_8 = e2
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (4987), (5854) are inconsistent by
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #259.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | (5855) all_54_8 = e1 | all_54_8 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | (5856) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (5611), (5848), (5856),
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | #499.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | (5857) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5857) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (5858) all_58_8 = e3 & op(e1, e1) = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (242), (5001), (5617), (5622), (5858),
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | #45.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (5859) all_58_14 = e3 & op(e0, e1) = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5859) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (5860) op(e0, e1) = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5855) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5861) all_54_8 = e1
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (276), (5003), (5861) are inconsistent by
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #689.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5862) all_54_8 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (5862) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5863) all_52_2 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5863) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5864) all_52_2 = e0
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (5864) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5865) ~ (all_52_3 = e0)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5865) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5866) ~ (all_52_3 = e0)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5864) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5867) ~ (all_52_14 = e0)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5867) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5868) ~ (all_52_14 = e0)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5869) all_54_11 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (266), (5869) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5870) all_52_14 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5870) implies:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5871) all_52_14 = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (5871) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5872) ~ (all_52_12 = e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (159), (5871) imply:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5873) op(e1, e0) = e3
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5874) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (161), (162), (166), (4988), (5607), (5616),
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5617), (5846), (5874), (function-axioms) are
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #47.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5875) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5875) gives:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5876) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5607), (5616), (5820), (5833), (5876) are
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #163.
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5877) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5877) gives:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5878) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5878) implies:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5879) ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7))
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5820), (5833), (5879) are inconsistent by
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #164.
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5880) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5880) gives:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5881) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5881) implies:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5882) op(e1, e0) = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5850) gives:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5883) all_54_12 = e2
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (5821), (5883) are inconsistent by
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #676.
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5884) all_54_12 = e1 | all_54_12 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5884) gives:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5885) all_54_12 = e1
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (265), (5885) imply:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5886) all_52_3 = e1
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5886) implies:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5887) all_52_3 = e1
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (5887) imply:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5888) ~ (all_52_11 = e1)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5888) implies:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5889) ~ (all_52_11 = e1)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e0,
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (5873), (5882) gives:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5890) e3 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5844), (5890) imply:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5891) all_56_10 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (220), (5872), (5891), (function-axioms)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #145.
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5892) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (4991), (5839), (5889), (5892) are
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #655.
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5893) all_54_12 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (265), (5866), (5893) are inconsistent by
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #653.
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5894) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5894) implies:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5895) ~ (all_56_15 = e0)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5896) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1)
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (157), (225), (5823), (5843),
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5860), (5896), (function-axioms) are inconsistent
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #53.
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5897) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (266), (4992), (5008), (5868), (5897) are
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #602.
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | (5898) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5898) gives:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | (5899) all_56_12 = e2
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | (242), (5607), (5617), (5622), (5899),
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | #165.
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | (5900) all_56_14 = e1 | all_56_15 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5900) gives:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | (5901) all_56_14 = e1
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4986), (5901) are inconsistent by sub-proof
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | #59.
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | (5902) all_56_15 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5820), (5902) imply:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | (5903) e2 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5903) implies:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | (5904) e2 = e0
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (5904) imply:
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | (5905) $false
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5905) is inconsistent.
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | (5906) all_58_3 = e2 & op(e2, e2) = e2
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | ALPHA: (5906) implies:
% 167.09/24.85 | | | | | | | | | | | | | | | (5907) all_58_3 = e2
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (239), (240),
% 167.09/24.85 | | | | | | | | | | | | | | | (242), (5617), (5907), (function-axioms) are
% 167.09/24.85 | | | | | | | | | | | | | | | inconsistent by sub-proof #665.
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | (5908) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 167.09/24.85 | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.09/24.85 | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | BETA: splitting (5908) gives:
% 167.09/24.85 | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | (5909) all_58_5 = e2 & op(e2, e1) = e2
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 167.09/24.85 | | | | | | | | | | | | | | | (5617), (5622), (5909), (function-axioms) are
% 167.09/24.85 | | | | | | | | | | | | | | | inconsistent by sub-proof #412.
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | (5910) all_58_10 = e2 & op(e2, e0) = e2
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (239), (240),
% 167.09/24.85 | | | | | | | | | | | | | | | (5617), (5622), (5910), (function-axioms) are
% 167.09/24.85 | | | | | | | | | | | | | | | inconsistent by sub-proof #447.
% 167.09/24.85 | | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | (5911) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 167.09/24.85 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.09/24.85 | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | REF_CLOSE: (163), (164), (5611), (5612), (5911),
% 167.09/24.85 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.09/24.85 | | | | | | | | | | | | #218.
% 167.09/24.85 | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | End of split
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | Case 2:
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | | (5912) all_10_2 = e0
% 167.09/24.85 | | | | | | | | | (5913) ( ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 &
% 167.09/24.85 | | | | | | | | | op(e0, e3) = all_10_1 & $i(all_10_0) &
% 167.09/24.85 | | | | | | | | | $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e0, e3) =
% 167.09/24.85 | | | | | | | | | all_10_1 & $i(all_10_1))
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | | COMBINE_EQS: (309), (5912) imply:
% 167.09/24.85 | | | | | | | | | (5914) all_24_2 = e0
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | | COMBINE_EQS: (298), (5912) imply:
% 167.09/24.85 | | | | | | | | | (5915) all_56_10 = e0
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | | REDUCE: (363), (5912) imply:
% 167.09/24.85 | | | | | | | | | (5916) ~ (all_52_1 = e0)
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | | REDUCE: (365), (5912) imply:
% 167.09/24.85 | | | | | | | | | (5917) ~ (all_52_2 = e0)
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | | REDUCE: (367), (5912) imply:
% 167.09/24.85 | | | | | | | | | (5918) ~ (all_52_3 = e0)
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | | REDUCE: (369), (5912) imply:
% 167.09/24.85 | | | | | | | | | (5919) ~ (all_52_4 = e0)
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | | REDUCE: (371), (5912) imply:
% 167.09/24.85 | | | | | | | | | (5920) ~ (all_52_8 = e0)
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | | BETA: splitting (213) gives:
% 167.09/24.85 | | | | | | | | |
% 167.09/24.85 | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | (5921) ~ (all_56_15 = e3)
% 167.09/24.85 | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | REDUCE: (262), (5921) imply:
% 167.09/24.85 | | | | | | | | | | (5922) ~ (all_4_2 = e3)
% 167.09/24.85 | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | BETA: splitting (248) gives:
% 167.09/24.85 | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | (5923) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 167.09/24.85 | | | | | | | | | | | & op(e3, e2) = e0)
% 167.09/24.85 | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | BETA: splitting (5923) gives:
% 167.09/24.85 | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | (5924) all_58_0 = e0 & op(e3, e3) = e0
% 167.09/24.85 | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | ALPHA: (5924) implies:
% 167.09/24.85 | | | | | | | | | | | | (5925) all_58_0 = e0
% 167.09/24.85 | | | | | | | | | | | | (5926) op(e3, e3) = e0
% 167.09/24.85 | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | BETA: splitting (195) gives:
% 167.09/24.85 | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | Case 1:
% 167.09/24.85 | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | (5927) all_54_8 = e3
% 167.09/24.85 | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | COMBINE_EQS: (276), (5927) imply:
% 167.09/24.85 | | | | | | | | | | | | | (5928) all_52_2 = e3
% 167.09/24.85 | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | REDUCE: (148), (5928) imply:
% 167.09/24.85 | | | | | | | | | | | | | (5929) ~ (all_52_1 = e3)
% 167.09/24.85 | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | REDUCE: (143), (5928) imply:
% 167.09/24.85 | | | | | | | | | | | | | (5930) ~ (all_52_3 = e3)
% 167.09/24.85 | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | SIMP: (5930) implies:
% 167.09/24.85 | | | | | | | | | | | | | (5931) ~ (all_52_3 = e3)
% 167.09/24.85 | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | REDUCE: (140), (5928) imply:
% 167.09/24.85 | | | | | | | | | | | | | (5932) ~ (all_52_14 = e3)
% 167.09/24.85 | | | | | | | | | | | | |
% 167.09/24.85 | | | | | | | | | | | | | SIMP: (5932) implies:
% 167.09/24.85 | | | | | | | | | | | | | (5933) ~ (all_52_14 = e3)
% 167.09/24.85 | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | REDUCE: (162), (5928) imply:
% 167.33/24.85 | | | | | | | | | | | | | (5934) op(e1, e3) = e3
% 167.33/24.85 | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | BETA: splitting (192) gives:
% 167.33/24.85 | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | Case 1:
% 167.33/24.85 | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | (5935) all_54_11 = e3
% 167.33/24.85 | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | COMBINE_EQS: (266), (5935) imply:
% 167.33/24.85 | | | | | | | | | | | | | | (5936) all_52_14 = e3
% 167.33/24.85 | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | REDUCE: (5933), (5936) imply:
% 167.33/24.85 | | | | | | | | | | | | | | (5937) $false
% 167.33/24.85 | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | CLOSE: (5937) is inconsistent.
% 167.33/24.85 | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | Case 2:
% 167.33/24.85 | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | (5938) ~ (all_54_11 = e3)
% 167.33/24.85 | | | | | | | | | | | | | | (5939) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 167.33/24.85 | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | BETA: splitting (253) gives:
% 167.33/24.85 | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | Case 1:
% 167.33/24.85 | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | (5940) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 167.33/24.85 | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 167.33/24.85 | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | BETA: splitting (5940) gives:
% 167.33/24.85 | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | Case 1:
% 167.33/24.85 | | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | | (5941) all_58_0 = e3 & op(e3, e3) = e3
% 167.33/24.85 | | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | | ALPHA: (5941) implies:
% 167.33/24.85 | | | | | | | | | | | | | | | | (5942) op(e3, e3) = e3
% 167.33/24.85 | | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5926), (5942), (function-axioms) are
% 167.33/24.85 | | | | | | | | | | | | | | | | inconsistent by sub-proof #949.
% 167.33/24.85 | | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | Case 2:
% 167.33/24.85 | | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | | (5943) all_58_2 = e3 & op(e2, e3) = e3
% 167.33/24.85 | | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | | ALPHA: (5943) implies:
% 167.33/24.85 | | | | | | | | | | | | | | | | (5944) op(e2, e3) = e3
% 167.33/24.85 | | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | | REF_CLOSE: (166), (5929), (5944), (function-axioms) are
% 167.33/24.85 | | | | | | | | | | | | | | | | inconsistent by sub-proof #989.
% 167.33/24.85 | | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | End of split
% 167.33/24.85 | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | Case 2:
% 167.33/24.85 | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | (5945) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 167.33/24.85 | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 167.33/24.85 | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | BETA: splitting (5945) gives:
% 167.33/24.85 | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | Case 1:
% 167.33/24.85 | | | | | | | | | | | | | | | |
% 167.33/24.85 | | | | | | | | | | | | | | | | (5946) all_58_6 = e3 & op(e1, e3) = e3
% 167.33/24.85 | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | REF_CLOSE: (67), (119), (147), (157), (161), (162), (163),
% 167.33/24.86 | | | | | | | | | | | | | | | | (164), (166), (167), (169), (188), (191), (198),
% 167.33/24.86 | | | | | | | | | | | | | | | | (199), (201), (210), (217), (220), (239), (240),
% 167.33/24.86 | | | | | | | | | | | | | | | | (242), (245), (249), (251), (262), (265), (266),
% 167.33/24.86 | | | | | | | | | | | | | | | | (274), (283), (287), (289), (307), (361), (374),
% 167.33/24.86 | | | | | | | | | | | | | | | | (376), (377), (379), (381), (383), (385), (388),
% 167.33/24.86 | | | | | | | | | | | | | | | | (396), (397), (398), (4989), (4992), (5008),
% 167.33/24.86 | | | | | | | | | | | | | | | | (5010), (5913), (5914), (5915), (5916), (5918),
% 167.33/24.86 | | | | | | | | | | | | | | | | (5920), (5922), (5925), (5926), (5929), (5931),
% 167.33/24.86 | | | | | | | | | | | | | | | | (5933), (5939), (5946), (function-axioms) are
% 167.33/24.86 | | | | | | | | | | | | | | | | inconsistent by sub-proof #44.
% 167.33/24.86 | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | (5947) all_58_12 = e3 & op(e0, e3) = e3
% 167.33/24.86 | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | ALPHA: (5947) implies:
% 167.33/24.86 | | | | | | | | | | | | | | | | (5948) all_58_12 = e3
% 167.33/24.86 | | | | | | | | | | | | | | | | (5949) op(e0, e3) = e3
% 167.33/24.86 | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 167.33/24.86 | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | (5950) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 167.33/24.86 | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 167.33/24.86 | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | BETA: splitting (5950) gives:
% 167.33/24.86 | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | (5951) all_58_0 = e1 & op(e3, e3) = e1
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | ALPHA: (5951) implies:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | (5952) op(e3, e3) = e1
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5926), (5952), (function-axioms) are
% 167.33/24.86 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #907.
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | (5953) all_58_2 = e1 & op(e2, e3) = e1
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | ALPHA: (5953) implies:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | (5954) op(e2, e3) = e1
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | (5955) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 167.33/24.86 | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | BETA: splitting (5955) gives:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (5956) all_58_6 = e3 & op(e1, e3) = e3
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (67), (119), (147), (157), (161), (162), (163),
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (164), (166), (167), (169), (188), (191), (198),
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (199), (201), (210), (217), (220), (239), (240),
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (242), (245), (249), (251), (262), (265), (266),
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (274), (283), (287), (289), (307), (361), (374),
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (376), (377), (379), (381), (383), (385), (388),
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (396), (397), (398), (4989), (4992), (5008),
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (5010), (5913), (5914), (5915), (5916), (5918),
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (5920), (5922), (5925), (5926), (5929), (5931),
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (5933), (5939), (5956), (function-axioms) are
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #44.
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (5957) all_58_7 = e3 & op(e1, e2) = e3
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5017), (5957) are inconsistent by sub-proof
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | #183.
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | (5958) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 167.33/24.86 | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | BETA: splitting (5958) gives:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (5959) all_58_8 = e3 & op(e1, e1) = e3
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5001), (5959) are inconsistent by sub-proof
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | #475.
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (5960) all_58_11 = e3 & op(e1, e0) = e3
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | ALPHA: (5960) implies:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | (5961) all_58_11 = e3
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | (5962) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5962) gives:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | (5963) all_58_0 = e2 & op(e3, e3) = e2
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5925), (5963) are inconsistent by sub-proof
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | #390.
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | (5964) all_58_2 = e2 & op(e2, e3) = e2
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5964) implies:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | (5965) op(e2, e3) = e2
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (5954), (5965), (function-axioms) are
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #784.
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | (5966) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5966) gives:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | (5967) all_58_6 = e2 & op(e1, e3) = e2
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5967) implies:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | (5968) all_58_6 = e2
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (231), (232), (234),
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | (5001), (5961), (5968) are inconsistent by
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | sub-proof #157.
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | (5969) all_58_12 = e2 & op(e0, e3) = e2
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5969) implies:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | (5970) all_58_12 = e2
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5948), (5970) are inconsistent by sub-proof
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | | #635.
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | (5971) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 167.33/24.86 | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 167.33/24.86 | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | BETA: splitting (5971) gives:
% 167.33/24.86 | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | (5972) all_58_6 = e1 & op(e1, e3) = e1
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | ALPHA: (5972) implies:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | (5973) op(e1, e3) = e1
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (5934), (5973), (function-axioms) are
% 167.33/24.86 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | (5974) all_58_12 = e1 & op(e0, e3) = e1
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | ALPHA: (5974) implies:
% 167.33/24.86 | | | | | | | | | | | | | | | | | | (5975) op(e0, e3) = e1
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5949), (5975), (function-axioms) are
% 167.33/24.86 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #125.
% 167.33/24.86 | | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | (5976) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 167.33/24.86 | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | | REF_CLOSE: (276), (4987), (5003), (5917), (5976) are
% 167.33/24.86 | | | | | | | | | | | | | inconsistent by sub-proof #48.
% 167.33/24.86 | | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | (5977) all_58_1 = e0 & op(e3, e2) = e0
% 167.33/24.86 | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | | REF_CLOSE: (169), (5919), (5977), (function-axioms) are
% 167.33/24.86 | | | | | | | | | | | | inconsistent by sub-proof #155.
% 167.33/24.86 | | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | (5978) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 167.33/24.86 | | | | | | | | | | | & op(e3, e0) = e0)
% 167.33/24.86 | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | | REF_CLOSE: (7), (167), (168), (220), (5915), (5920), (5978),
% 167.33/24.86 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 167.33/24.86 | | | | | | | | | | | #152.
% 167.33/24.86 | | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | (5979) all_56_15 = e3
% 167.33/24.86 | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | COMBINE_EQS: (262), (5979) imply:
% 167.33/24.86 | | | | | | | | | | (5980) all_4_2 = e3
% 167.33/24.86 | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | SIMP: (5980) implies:
% 167.33/24.86 | | | | | | | | | | (5981) all_4_2 = e3
% 167.33/24.86 | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | REDUCE: (395), (5981) imply:
% 167.33/24.86 | | | | | | | | | | (5982) ~ (all_52_12 = e3)
% 167.33/24.86 | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | | REF_CLOSE: (167), (220), (5915), (5982), (function-axioms)
% 167.33/24.86 | | | | | | | | | | are inconsistent by sub-proof #145.
% 167.33/24.86 | | | | | | | | | |
% 167.33/24.86 | | | | | | | | | End of split
% 167.33/24.86 | | | | | | | | |
% 167.33/24.86 | | | | | | | | End of split
% 167.33/24.86 | | | | | | | |
% 167.33/24.86 | | | | | | | Case 2:
% 167.33/24.86 | | | | | | | |
% 167.33/24.86 | | | | | | | | (5983) all_58_13 = e1 & op(e0, e2) = e1
% 167.33/24.86 | | | | | | | |
% 167.33/24.86 | | | | | | | | REF_CLOSE: (157), (5006), (5983), (function-axioms) are
% 167.33/24.86 | | | | | | | | inconsistent by sub-proof #114.
% 167.33/24.86 | | | | | | | |
% 167.33/24.86 | | | | | | | End of split
% 167.33/24.86 | | | | | | |
% 167.33/24.86 | | | | | | End of split
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | Case 2:
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | | (5984) all_58_14 = e2 & op(e0, e1) = e2
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | | REF_CLOSE: (156), (4991), (5984), (function-axioms) are inconsistent
% 167.33/24.86 | | | | | | by sub-proof #61.
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | End of split
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | End of split
% 167.33/24.86 | | | |
% 167.33/24.86 | | | End of split
% 167.33/24.86 | | |
% 167.33/24.86 | | End of split
% 167.33/24.86 | |
% 167.33/24.86 | Case 2:
% 167.33/24.86 | |
% 167.33/24.86 | | (5985) all_4_2 = e1
% 167.33/24.86 | | (5986) ( ~ (all_4_0 = e2) & op(all_4_1, e0) = all_4_0 & op(e1, e0) =
% 167.33/24.86 | | all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) &
% 167.33/24.86 | | op(e1, e0) = all_4_1 & $i(all_4_1))
% 167.33/24.86 | |
% 167.33/24.86 | | COMBINE_EQS: (354), (5985) imply:
% 167.33/24.86 | | (5987) all_12_2 = e1
% 167.33/24.86 | |
% 167.33/24.86 | | COMBINE_EQS: (262), (5985) imply:
% 167.33/24.86 | | (5988) all_56_15 = e1
% 167.33/24.86 | |
% 167.33/24.86 | | REDUCE: (376), (5985) imply:
% 167.33/24.86 | | (5989) ~ (all_52_3 = e1)
% 167.33/24.86 | |
% 167.33/24.86 | | REDUCE: (387), (5985) imply:
% 167.33/24.86 | | (5990) ~ (all_52_7 = e1)
% 167.33/24.86 | |
% 167.33/24.86 | | REDUCE: (394), (5985) imply:
% 167.33/24.86 | | (5991) ~ (all_52_11 = e1)
% 167.33/24.86 | |
% 167.33/24.86 | | REDUCE: (395), (5985) imply:
% 167.33/24.86 | | (5992) ~ (all_52_12 = e1)
% 167.33/24.86 | |
% 167.33/24.86 | | REDUCE: (396), (5985) imply:
% 167.33/24.86 | | (5993) ~ (all_52_13 = e1)
% 167.33/24.86 | |
% 167.33/24.86 | | REDUCE: (397), (5985) imply:
% 167.33/24.86 | | (5994) ~ (all_52_14 = e1)
% 167.33/24.86 | |
% 167.33/24.86 | | BETA: splitting (228) gives:
% 167.33/24.86 | |
% 167.33/24.86 | | Case 1:
% 167.33/24.86 | | |
% 167.33/24.86 | | | (5995) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 167.33/24.86 | | | = e1)
% 167.33/24.86 | | |
% 167.33/24.86 | | | BETA: splitting (5995) gives:
% 167.33/24.86 | | |
% 167.33/24.86 | | | Case 1:
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | (5996) all_58_9 = e1 & op(e3, e0) = e1
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | REF_CLOSE: (167), (5992), (5996), (function-axioms) are inconsistent by
% 167.33/24.86 | | | | sub-proof #43.
% 167.33/24.86 | | | |
% 167.33/24.86 | | | Case 2:
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | (5997) all_58_10 = e1 & op(e2, e0) = e1
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | ALPHA: (5997) implies:
% 167.33/24.86 | | | | (5998) op(e2, e0) = e1
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | GROUND_INST: instantiating (function-axioms) with all_52_13, e1, e0, e2,
% 167.33/24.86 | | | | simplifying with (163), (5998) gives:
% 167.33/24.86 | | | | (5999) all_52_13 = e1
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | REDUCE: (5993), (5999) imply:
% 167.33/24.86 | | | | (6000) $false
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | CLOSE: (6000) is inconsistent.
% 167.33/24.86 | | | |
% 167.33/24.86 | | | End of split
% 167.33/24.86 | | |
% 167.33/24.86 | | Case 2:
% 167.33/24.86 | | |
% 167.33/24.86 | | | (6001) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 167.33/24.86 | | | e0) = e1)
% 167.33/24.86 | | |
% 167.33/24.86 | | | BETA: splitting (6001) gives:
% 167.33/24.86 | | |
% 167.33/24.86 | | | Case 1:
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | (6002) all_58_11 = e1 & op(e1, e0) = e1
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | REF_CLOSE: (159), (5994), (6002), (function-axioms) are inconsistent by
% 167.33/24.86 | | | | sub-proof #42.
% 167.33/24.86 | | | |
% 167.33/24.86 | | | Case 2:
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | (6003) all_58_15 = e1 & op(e0, e0) = e1
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | ALPHA: (6003) implies:
% 167.33/24.86 | | | | (6004) all_58_15 = e1
% 167.33/24.86 | | | | (6005) op(e0, e0) = e1
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | BETA: splitting (211) gives:
% 167.33/24.86 | | | |
% 167.33/24.86 | | | | Case 1:
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | (6006) ~ (all_56_15 = e1)
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | REDUCE: (5988), (6006) imply:
% 167.33/24.86 | | | | | (6007) $false
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | CLOSE: (6007) is inconsistent.
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | Case 2:
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | (6008) all_56_8 = e0 & op(e0, e1) = e0
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | ALPHA: (6008) implies:
% 167.33/24.86 | | | | | (6009) all_56_8 = e0
% 167.33/24.86 | | | | | (6010) op(e0, e1) = e0
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11, e0, e1,
% 167.33/24.86 | | | | | e0, simplifying with (156), (6010) gives:
% 167.33/24.86 | | | | | (6011) all_52_11 = e0
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | REDUCE: (138), (6011) imply:
% 167.33/24.86 | | | | | (6012) ~ (all_52_3 = e0)
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | REDUCE: (124), (6011) imply:
% 167.33/24.86 | | | | | (6013) ~ (all_52_7 = e0)
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | REDUCE: (120), (6011) imply:
% 167.33/24.86 | | | | | (6014) ~ (all_52_8 = e0)
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | REDUCE: (117), (6011) imply:
% 167.33/24.86 | | | | | (6015) ~ (all_52_9 = e0)
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | REDUCE: (391), (6011) imply:
% 167.33/24.86 | | | | | (6016) ~ (all_6_2 = e0)
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | SIMP: (6016) implies:
% 167.33/24.86 | | | | | (6017) ~ (all_6_2 = e0)
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | REDUCE: (5991), (6011) imply:
% 167.33/24.86 | | | | | (6018) ~ (e1 = e0)
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | BETA: splitting (224) gives:
% 167.33/24.86 | | | | |
% 167.33/24.86 | | | | | Case 1:
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | | (6019) all_58_15 = e0 & op(e0, e0) = e0
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | | ALPHA: (6019) implies:
% 167.33/24.86 | | | | | | (6020) op(e0, e0) = e0
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | | REF_CLOSE: (4), (6005), (6020), (function-axioms) are inconsistent
% 167.33/24.86 | | | | | | by sub-proof #204.
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | Case 2:
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | | (6021) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 167.33/24.86 | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0))
% 167.33/24.86 | | | | | | & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 167.33/24.86 | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | | ALPHA: (6021) implies:
% 167.33/24.86 | | | | | | (6022) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 167.33/24.86 | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | | BETA: splitting (6022) gives:
% 167.33/24.86 | | | | | |
% 167.33/24.86 | | | | | | Case 1:
% 167.33/24.86 | | | | | | |
% 167.33/24.86 | | | | | | | (6023) all_58_12 = e0 & op(e0, e3) = e0
% 167.33/24.86 | | | | | | |
% 167.33/24.86 | | | | | | | ALPHA: (6023) implies:
% 167.33/24.86 | | | | | | | (6024) all_58_12 = e0
% 167.33/24.86 | | | | | | |
% 167.33/24.86 | | | | | | | BETA: splitting (227) gives:
% 167.33/24.86 | | | | | | |
% 167.33/24.86 | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | |
% 167.33/24.86 | | | | | | | | (6025) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 167.33/24.86 | | | | | | | | op(e0, e2) = e3)
% 167.33/24.86 | | | | | | | |
% 167.33/24.86 | | | | | | | | BETA: splitting (6025) gives:
% 167.33/24.86 | | | | | | | |
% 167.33/24.86 | | | | | | | | Case 1:
% 167.33/24.86 | | | | | | | | |
% 167.33/24.86 | | | | | | | | | (6026) all_58_12 = e3 & op(e0, e3) = e3
% 167.33/24.86 | | | | | | | | |
% 167.33/24.86 | | | | | | | | | ALPHA: (6026) implies:
% 167.33/24.86 | | | | | | | | | (6027) all_58_12 = e3
% 167.33/24.86 | | | | | | | | |
% 167.33/24.86 | | | | | | | | | REF_CLOSE: (7), (6024), (6027) are inconsistent by sub-proof
% 167.33/24.86 | | | | | | | | | #608.
% 167.33/24.86 | | | | | | | | |
% 167.33/24.86 | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | (6028) all_58_13 = e3 & op(e0, e2) = e3
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | ALPHA: (6028) implies:
% 167.33/24.87 | | | | | | | | | (6029) all_58_13 = e3
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | BETA: splitting (226) gives:
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | (6030) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 167.33/24.87 | | | | | | | | | | e2 & op(e0, e2) = e2)
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | BETA: splitting (6030) gives:
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | (6031) all_58_12 = e2 & op(e0, e3) = e2
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | ALPHA: (6031) implies:
% 167.33/24.87 | | | | | | | | | | | (6032) all_58_12 = e2
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | REF_CLOSE: (5), (6024), (6032) are inconsistent by sub-proof
% 167.33/24.87 | | | | | | | | | | | #729.
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | (6033) all_58_13 = e2 & op(e0, e2) = e2
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | REF_CLOSE: (9), (6029), (6033) are inconsistent by sub-proof
% 167.33/24.87 | | | | | | | | | | | #861.
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | End of split
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | (6034) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 167.33/24.87 | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | BETA: splitting (6034) gives:
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | (6035) all_58_14 = e2 & op(e0, e1) = e2
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | ALPHA: (6035) implies:
% 167.33/24.87 | | | | | | | | | | | (6036) all_58_14 = e2
% 167.33/24.87 | | | | | | | | | | | (6037) op(e0, e1) = e2
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e1,
% 167.33/24.87 | | | | | | | | | | | e0, simplifying with (6010), (6037) gives:
% 167.33/24.87 | | | | | | | | | | | (6038) e2 = e0
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | COMBINE_EQS: (6036), (6038) imply:
% 167.33/24.87 | | | | | | | | | | | (6039) all_58_14 = e0
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (226), (227), (6004),
% 167.33/24.87 | | | | | | | | | | | (6005), (6024), (6039), (function-axioms) are
% 167.33/24.87 | | | | | | | | | | | inconsistent by sub-proof #39.
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | (6040) all_58_15 = e2 & op(e0, e0) = e2
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | ALPHA: (6040) implies:
% 167.33/24.87 | | | | | | | | | | | (6041) op(e0, e0) = e2
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | REF_CLOSE: (6), (6005), (6041), (function-axioms) are
% 167.33/24.87 | | | | | | | | | | | inconsistent by sub-proof #640.
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | End of split
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | End of split
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | End of split
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | | (6042) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 167.33/24.87 | | | | | | | | op(e0, e0) = e3)
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | | BETA: splitting (6042) gives:
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | (6043) all_58_14 = e3 & op(e0, e1) = e3
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | ALPHA: (6043) implies:
% 167.33/24.87 | | | | | | | | | (6044) all_58_14 = e3
% 167.33/24.87 | | | | | | | | | (6045) op(e0, e1) = e3
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e1,
% 167.33/24.87 | | | | | | | | | e0, simplifying with (6010), (6045) gives:
% 167.33/24.87 | | | | | | | | | (6046) e3 = e0
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | COMBINE_EQS: (6044), (6046) imply:
% 167.33/24.87 | | | | | | | | | (6047) all_58_14 = e0
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (226), (227), (6004),
% 167.33/24.87 | | | | | | | | | (6005), (6024), (6047), (function-axioms) are
% 167.33/24.87 | | | | | | | | | inconsistent by sub-proof #39.
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | (6048) all_58_15 = e3 & op(e0, e0) = e3
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | REF_CLOSE: (8), (6004), (6048) are inconsistent by sub-proof
% 167.33/24.87 | | | | | | | | | #878.
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | End of split
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | End of split
% 167.33/24.87 | | | | | | |
% 167.33/24.87 | | | | | | Case 2:
% 167.33/24.87 | | | | | | |
% 167.33/24.87 | | | | | | | (6049) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 167.33/24.87 | | | | | | | op(e0, e1) = e0)
% 167.33/24.87 | | | | | | |
% 167.33/24.87 | | | | | | | BETA: splitting (6049) gives:
% 167.33/24.87 | | | | | | |
% 167.33/24.87 | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | | (6050) all_58_13 = e0 & op(e0, e2) = e0
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | | ALPHA: (6050) implies:
% 167.33/24.87 | | | | | | | | (6051) all_58_13 = e0
% 167.33/24.87 | | | | | | | | (6052) op(e0, e2) = e0
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | | BETA: splitting (227) gives:
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | (6053) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3
% 167.33/24.87 | | | | | | | | | & op(e0, e2) = e3)
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | BETA: splitting (6053) gives:
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | (6054) all_58_12 = e3 & op(e0, e3) = e3
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | ALPHA: (6054) implies:
% 167.33/24.87 | | | | | | | | | | (6055) op(e0, e3) = e3
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | BETA: splitting (226) gives:
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | (6056) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 167.33/24.87 | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | BETA: splitting (6056) gives:
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | (6057) all_58_12 = e2 & op(e0, e3) = e2
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | ALPHA: (6057) implies:
% 167.33/24.87 | | | | | | | | | | | | (6058) op(e0, e3) = e2
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | REF_CLOSE: (9), (6055), (6058), (function-axioms) are
% 167.33/24.87 | | | | | | | | | | | | inconsistent by sub-proof #38.
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | (6059) all_58_13 = e2 & op(e0, e2) = e2
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | ALPHA: (6059) implies:
% 167.33/24.87 | | | | | | | | | | | | (6060) op(e0, e2) = e2
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | REF_CLOSE: (5), (157), (6052), (6060), (function-axioms) are
% 167.33/24.87 | | | | | | | | | | | | inconsistent by sub-proof #631.
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | End of split
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | (6061) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 167.33/24.87 | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | BETA: splitting (6061) gives:
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | (6062) all_58_14 = e2 & op(e0, e1) = e2
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | ALPHA: (6062) implies:
% 167.33/24.87 | | | | | | | | | | | | (6063) all_58_14 = e2
% 167.33/24.87 | | | | | | | | | | | | (6064) op(e0, e1) = e2
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e2, e1,
% 167.33/24.87 | | | | | | | | | | | | e0, simplifying with (6010), (6064) gives:
% 167.33/24.87 | | | | | | | | | | | | (6065) e2 = e0
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | COMBINE_EQS: (6063), (6065) imply:
% 167.33/24.87 | | | | | | | | | | | | (6066) all_58_14 = e0
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (40), (42),
% 167.33/24.87 | | | | | | | | | | | | (43), (45), (46), (49), (52), (55), (64), (67),
% 167.33/24.87 | | | | | | | | | | | | (73), (76), (102), (112), (116), (119), (122),
% 167.33/24.87 | | | | | | | | | | | | (125), (127), (132), (133), (134), (135), (139),
% 167.33/24.87 | | | | | | | | | | | | (144), (145), (147), (156), (157), (158), (159),
% 167.33/24.87 | | | | | | | | | | | | (161), (162), (163), (164), (166), (167), (168),
% 167.33/24.87 | | | | | | | | | | | | (169), (190), (191), (193), (196), (197), (198),
% 167.33/24.87 | | | | | | | | | | | | (199), (201), (202), (203), (209), (210), (215),
% 167.33/24.87 | | | | | | | | | | | | (216), (217), (218), (219), (220), (221), (222),
% 167.33/24.87 | | | | | | | | | | | | (224), (225), (226), (227), (228), (229), (230),
% 167.33/24.87 | | | | | | | | | | | | (231), (232), (233), (234), (235), (236), (237),
% 167.33/24.87 | | | | | | | | | | | | (238), (239), (240), (241), (242), (243), (244),
% 167.33/24.87 | | | | | | | | | | | | (245), (246), (247), (248), (249), (250), (251),
% 167.33/24.87 | | | | | | | | | | | | (252), (253), (254), (262), (264), (265), (274),
% 167.33/24.87 | | | | | | | | | | | | (277), (278), (283), (287), (289), (290), (298),
% 167.33/24.87 | | | | | | | | | | | | (300), (305), (309), (319), (334), (340), (350),
% 167.33/24.87 | | | | | | | | | | | | (352), (355), (361), (363), (367), (369), (371),
% 167.33/24.87 | | | | | | | | | | | | (373), (374), (377), (379), (381), (383), (385),
% 167.33/24.87 | | | | | | | | | | | | (386), (388), (389), (393), (396), (5986), (5987),
% 167.33/24.87 | | | | | | | | | | | | (5988), (5989), (5990), (5992), (5993), (5994),
% 167.33/24.87 | | | | | | | | | | | | (6004), (6005), (6009), (6010), (6012), (6013),
% 167.33/24.87 | | | | | | | | | | | | (6014), (6015), (6017), (6066), (function-axioms)
% 167.33/24.87 | | | | | | | | | | | | are inconsistent by sub-proof #1.
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | (6067) all_58_15 = e2 & op(e0, e0) = e2
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | ALPHA: (6067) implies:
% 167.33/24.87 | | | | | | | | | | | | (6068) op(e0, e0) = e2
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | | REF_CLOSE: (6), (6005), (6068), (function-axioms) are
% 167.33/24.87 | | | | | | | | | | | | inconsistent by sub-proof #640.
% 167.33/24.87 | | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | | End of split
% 167.33/24.87 | | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | End of split
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | (6069) all_58_13 = e3 & op(e0, e2) = e3
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | ALPHA: (6069) implies:
% 167.33/24.87 | | | | | | | | | | (6070) all_58_13 = e3
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | REF_CLOSE: (7), (6051), (6070) are inconsistent by sub-proof
% 167.33/24.87 | | | | | | | | | | #708.
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | End of split
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | (6071) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3
% 167.33/24.87 | | | | | | | | | & op(e0, e0) = e3)
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | BETA: splitting (6071) gives:
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | | Case 1:
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | (6072) all_58_14 = e3 & op(e0, e1) = e3
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | ALPHA: (6072) implies:
% 167.33/24.87 | | | | | | | | | | (6073) all_58_14 = e3
% 167.33/24.87 | | | | | | | | | | (6074) op(e0, e1) = e3
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e1,
% 167.33/24.87 | | | | | | | | | | e0, simplifying with (6010), (6074) gives:
% 167.33/24.87 | | | | | | | | | | (6075) e3 = e0
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | COMBINE_EQS: (6073), (6075) imply:
% 167.33/24.87 | | | | | | | | | | (6076) all_58_14 = e0
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (40), (42),
% 167.33/24.87 | | | | | | | | | | (43), (45), (46), (49), (52), (55), (64), (67),
% 167.33/24.87 | | | | | | | | | | (73), (76), (102), (112), (116), (119), (122),
% 167.33/24.87 | | | | | | | | | | (125), (127), (132), (133), (134), (135), (139),
% 167.33/24.87 | | | | | | | | | | (144), (145), (147), (156), (157), (158), (159),
% 167.33/24.87 | | | | | | | | | | (161), (162), (163), (164), (166), (167), (168),
% 167.33/24.87 | | | | | | | | | | (169), (190), (191), (193), (196), (197), (198),
% 167.33/24.87 | | | | | | | | | | (199), (201), (202), (203), (209), (210), (215),
% 167.33/24.87 | | | | | | | | | | (216), (217), (218), (219), (220), (221), (222),
% 167.33/24.87 | | | | | | | | | | (224), (225), (226), (227), (228), (229), (230),
% 167.33/24.87 | | | | | | | | | | (231), (232), (233), (234), (235), (236), (237),
% 167.33/24.87 | | | | | | | | | | (238), (239), (240), (241), (242), (243), (244),
% 167.33/24.87 | | | | | | | | | | (245), (246), (247), (248), (249), (250), (251),
% 167.33/24.87 | | | | | | | | | | (252), (253), (254), (262), (264), (265), (274),
% 167.33/24.87 | | | | | | | | | | (277), (278), (283), (287), (289), (290), (298),
% 167.33/24.87 | | | | | | | | | | (300), (305), (309), (319), (334), (340), (350),
% 167.33/24.87 | | | | | | | | | | (352), (355), (361), (363), (367), (369), (371),
% 167.33/24.87 | | | | | | | | | | (373), (374), (377), (379), (381), (383), (385),
% 167.33/24.87 | | | | | | | | | | (386), (388), (389), (393), (396), (5986), (5987),
% 167.33/24.87 | | | | | | | | | | (5988), (5989), (5990), (5992), (5993), (5994),
% 167.33/24.87 | | | | | | | | | | (6004), (6005), (6009), (6010), (6012), (6013),
% 167.33/24.87 | | | | | | | | | | (6014), (6015), (6017), (6076), (function-axioms)
% 167.33/24.87 | | | | | | | | | | are inconsistent by sub-proof #1.
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | (6077) all_58_15 = e3 & op(e0, e0) = e3
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | | REF_CLOSE: (8), (6004), (6077) are inconsistent by sub-proof
% 167.33/24.87 | | | | | | | | | | #878.
% 167.33/24.87 | | | | | | | | | |
% 167.33/24.87 | | | | | | | | | End of split
% 167.33/24.87 | | | | | | | | |
% 167.33/24.87 | | | | | | | | End of split
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | Case 2:
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | | (6078) all_58_14 = e0 & op(e0, e1) = e0
% 167.33/24.87 | | | | | | | |
% 167.33/24.87 | | | | | | | | ALPHA: (6078) implies:
% 167.33/24.87 | | | | | | | | (6079) all_58_14 = e0
% 167.33/24.87 | | | | | | | |
% 167.33/24.88 | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (40), (42), (43),
% 167.33/24.88 | | | | | | | | (45), (46), (49), (52), (55), (64), (67), (73), (76),
% 167.33/24.88 | | | | | | | | (102), (112), (116), (119), (122), (125), (127),
% 167.33/24.88 | | | | | | | | (132), (133), (134), (135), (139), (144), (145),
% 167.33/24.88 | | | | | | | | (147), (156), (157), (158), (159), (161), (162),
% 167.33/24.88 | | | | | | | | (163), (164), (166), (167), (168), (169), (190),
% 167.33/24.88 | | | | | | | | (191), (193), (196), (197), (198), (199), (201),
% 167.33/24.88 | | | | | | | | (202), (203), (209), (210), (215), (216), (217),
% 167.33/24.88 | | | | | | | | (218), (219), (220), (221), (222), (224), (225),
% 167.33/24.88 | | | | | | | | (226), (227), (228), (229), (230), (231), (232),
% 167.33/24.88 | | | | | | | | (233), (234), (235), (236), (237), (238), (239),
% 167.33/24.88 | | | | | | | | (240), (241), (242), (243), (244), (245), (246),
% 167.33/24.88 | | | | | | | | (247), (248), (249), (250), (251), (252), (253),
% 167.33/24.88 | | | | | | | | (254), (262), (264), (265), (274), (277), (278),
% 167.33/24.88 | | | | | | | | (283), (287), (289), (290), (298), (300), (305),
% 167.33/24.88 | | | | | | | | (309), (319), (334), (340), (350), (352), (355),
% 167.33/24.88 | | | | | | | | (361), (363), (367), (369), (371), (373), (374),
% 167.33/24.88 | | | | | | | | (377), (379), (381), (383), (385), (386), (388),
% 167.33/24.88 | | | | | | | | (389), (393), (396), (5986), (5987), (5988), (5989),
% 167.33/24.88 | | | | | | | | (5990), (5992), (5993), (5994), (6004), (6005),
% 167.33/24.88 | | | | | | | | (6009), (6010), (6012), (6013), (6014), (6015),
% 167.33/24.88 | | | | | | | | (6017), (6079), (function-axioms) are inconsistent by
% 167.33/24.88 | | | | | | | | sub-proof #1.
% 167.33/24.88 | | | | | | | |
% 167.33/24.88 | | | | | | | End of split
% 167.33/24.88 | | | | | | |
% 167.33/24.88 | | | | | | End of split
% 167.33/24.88 | | | | | |
% 167.33/24.88 | | | | | End of split
% 167.33/24.88 | | | | |
% 167.33/24.88 | | | | End of split
% 167.33/24.88 | | | |
% 167.33/24.88 | | | End of split
% 167.33/24.88 | | |
% 167.33/24.88 | | End of split
% 167.33/24.88 | |
% 167.33/24.88 | End of split
% 167.33/24.88 |
% 167.33/24.88 End of proof
% 167.33/24.88
% 167.33/24.88 Sub-proof #1 shows that the following formulas are inconsistent:
% 167.33/24.88 ----------------------------------------------------------------
% 167.33/24.88 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 167.33/24.88 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 167.33/24.88 (2) op(e2, e1) = all_52_9
% 167.33/24.88 (3) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 167.33/24.88 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 167.33/24.88 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.33/24.88 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 167.33/24.88 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.33/24.88 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 167.33/24.88 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.33/24.88 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.33/24.88 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.33/24.88 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 167.33/24.88 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 167.33/24.88 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.33/24.88 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.33/24.88 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.33/24.88 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.33/24.88 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 167.33/24.88 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.33/24.88 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.33/24.88 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.33/24.88 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 167.33/24.88 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 167.33/24.88 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.33/24.88 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.33/24.88 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.33/24.88 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 167.33/24.88 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 167.33/24.88 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.33/24.88 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.33/24.88 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 167.33/24.88 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.33/24.88 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 167.33/24.88 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.33/24.88 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.33/24.88 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.33/24.88 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 167.33/24.88 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 167.33/24.88 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.33/24.88 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.33/24.88 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 167.33/24.88 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.33/24.88 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 167.33/24.88 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.33/24.88 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.33/24.88 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.33/24.88 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 167.33/24.88 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.33/24.88 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 167.33/24.88 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 167.33/24.88 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 167.33/24.88 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 167.33/24.88 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.33/24.88 (4) ~ (all_52_14 = e1)
% 167.33/24.88 (5) all_54_2 = all_52_8
% 167.33/24.88 (6) all_58_15 = e1
% 167.33/24.88 (7) ~ (all_52_6 = all_52_14)
% 167.33/24.88 (8) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 167.33/24.88 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 167.33/24.88 (9) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 167.33/24.88 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 167.33/24.88 (10) op(e0, e1) = all_52_11
% 167.33/24.88 (11) ~ (all_52_4 = all_52_7)
% 167.33/24.88 (12) all_16_2 = all_10_2
% 167.33/24.88 (13) ~ (all_6_2 = e2) | ( ~ (all_6_0 = e3) & op(all_6_1, e1) = all_6_0 &
% 167.33/24.88 op(e2, e1) = all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0)
% 167.33/24.88 & op(e2, e1) = all_6_1 & $i(all_6_1))
% 167.33/24.88 (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 167.33/24.88 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 167.33/24.88 (15) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 167.33/24.88 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 167.33/24.88 (16) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 167.33/24.88 (17) all_54_12 = all_52_3
% 167.33/24.88 (18) all_28_2 = all_6_2
% 167.33/24.88 (19) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 167.33/24.88 (20) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 167.33/24.88 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 167.33/24.88 (21) all_54_6 = all_52_9
% 167.33/24.88 (22) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 167.33/24.88 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 167.33/24.88 (23) ~ (all_52_1 = all_8_2)
% 167.33/24.88 (24) op(e0, e0) = e1
% 167.33/24.88 (25) all_56_10 = all_10_2
% 167.33/24.88 (26) ~ (all_56_12 = e3) | (all_56_0 = e2 & op(e2, e3) = e2)
% 167.33/24.88 (27) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 167.33/24.88 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 167.33/24.88 (28) all_56_8 = e0
% 167.33/24.88 (29) ~ (all_56_12 = e1) | (all_56_5 = e2 & op(e2, e1) = e2)
% 167.33/24.88 (30) all_54_10 = all_6_2
% 167.33/24.88 (31) ~ (all_52_12 = e1)
% 167.33/24.88 (32) ~ (all_52_13 = all_8_2)
% 167.33/24.88 (33) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 167.33/24.88 (34) ~ (all_8_2 = e1) | ( ~ (all_8_0 = e3) & op(all_8_1, e2) = all_8_0 &
% 167.33/24.88 op(e1, e2) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0)
% 167.33/24.88 & op(e1, e2) = all_8_1 & $i(all_8_1))
% 167.33/24.88 (35) op(e3, e3) = all_10_2
% 167.33/24.88 (36) ~ (all_52_1 = all_52_13)
% 167.33/24.88 (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 167.33/24.88 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 167.33/24.88 (38) ~ (all_52_3 = e1)
% 167.33/24.88 (39) ~ (all_52_6 = all_52_7)
% 167.33/24.88 (40) ~ (e3 = e1)
% 167.33/24.88 (41) all_56_14 = all_6_2
% 167.33/24.88 (42) op(e3, e0) = all_52_12
% 167.33/24.88 (43) ~ (all_48_2 = e1) | ( ~ (all_48_0 = e0) & op(all_48_1, e2) = all_48_0 &
% 167.33/24.88 op(e1, e2) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 167.33/24.88 e3) & op(e1, e2) = all_48_1 & $i(all_48_1))
% 167.33/24.88 (44) ~ (all_16_2 = e2) | ( ~ (all_16_0 = e0) & op(all_16_1, e3) = all_16_0 &
% 167.33/24.88 op(e2, e3) = all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 =
% 167.33/24.88 e1) & op(e2, e3) = all_16_1 & $i(all_16_1))
% 167.33/24.88 (45) ~ (all_52_1 = all_52_3)
% 167.33/24.88 (46) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 167.33/24.88 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 167.33/24.88 e1)
% 167.33/24.88 (47) op(e0, e3) = all_52_3
% 167.33/24.88 (48) op(e1, e3) = all_52_2
% 167.33/24.88 (49) all_56_15 = e1
% 167.33/24.88 (50) ~ (all_56_14 = e2) | (all_56_3 = e1 & op(e1, e2) = e1)
% 167.33/24.88 (51) op(e3, e1) = all_52_8
% 167.33/24.88 (52) ~ (all_14_2 = e3) | ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 &
% 167.33/24.88 op(e3, e2) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 =
% 167.33/24.88 e1) & op(e3, e2) = all_14_1 & $i(all_14_1))
% 167.33/24.88 (53) ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0 &
% 167.33/24.88 op(e0, e3) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 167.33/24.88 e1) & op(e0, e3) = all_24_1 & $i(all_24_1))
% 167.33/24.88 (54) ~ (all_56_10 = e2) | (all_56_1 = e3 & op(e3, e2) = e3)
% 167.33/24.88 (55) ~ (e1 = e0)
% 167.33/24.88 (56) all_22_2 = all_8_2
% 167.33/24.88 (57) ~ (all_52_6 = all_8_2)
% 167.33/24.88 (58) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 167.33/24.88 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 167.33/24.88 e3)
% 167.33/24.88 (59) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 167.33/24.88 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 167.33/24.88 (60) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 167.33/24.88 (61) ~ (all_56_12 = e0) | (all_56_11 = e2 & op(e2, e0) = e2)
% 167.33/24.88 (62) op(e1, e2) = all_52_6
% 167.33/24.88 (63) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 167.33/24.88 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 167.33/24.88 (64) ~ (all_52_8 = all_10_2)
% 167.33/24.88 (65) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 167.33/24.88 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 167.33/24.88 (66) op(e2, e3) = all_52_1
% 167.33/24.88 (67) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 167.33/24.88 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 167.33/24.88 (68) ~ (all_52_13 = e1)
% 167.33/24.88 (69) ~ (all_52_6 = all_6_2)
% 167.33/24.88 (70) ~ (all_52_3 = all_52_7)
% 167.33/24.88 (71) all_54_1 = all_52_4
% 167.33/24.88 (72) all_12_2 = e1
% 167.45/24.91 (73) ( ~ (all_4_0 = e2) & op(all_4_1, e0) = all_4_0 & op(e1, e0) = all_4_1 &
% 167.45/24.91 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e1, e0) = all_4_1
% 167.45/24.91 & $i(all_4_1))
% 167.45/24.91 (74) ~ (all_52_14 = all_6_2)
% 167.45/24.91 (75) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 167.45/24.91 (76) op(e2, e2) = all_8_2
% 167.45/24.91 (77) all_56_12 = all_8_2
% 167.45/24.91 (78) op(e1, e1) = all_6_2
% 167.45/24.91 (79) ~ (all_52_4 = all_10_2)
% 167.45/24.91 (80) ~ (all_10_2 = e0) | ( ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 &
% 167.45/24.91 op(e0, e3) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 =
% 167.45/24.91 e2) & op(e0, e3) = all_10_1 & $i(all_10_1))
% 167.45/24.91 (81) all_54_4 = all_52_1
% 167.45/24.91 (82) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 167.45/24.91 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 167.45/24.91 (83) all_56_15 = all_4_2
% 167.45/24.91 (84) ~ (e3 = e0)
% 167.45/24.91 (85) ~ (all_52_4 = all_52_6)
% 167.45/24.91 (86) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 &
% 167.45/24.91 op(e3, e2) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 167.45/24.91 e0) & op(e3, e2) = all_22_1 & $i(all_22_1))
% 167.45/24.91 (87) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 167.45/24.91 (88) ~ (all_52_8 = e0)
% 167.45/24.91 (89) ~ (all_52_7 = all_8_2)
% 167.45/24.91 (90) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 167.45/24.91 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 167.45/24.91 (91) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 167.45/24.91 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 167.45/24.91 (92) op(e0, e1) = e0
% 167.45/24.91 (93) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 167.45/24.91 (94) ~ (all_52_9 = all_6_2)
% 167.45/24.91 (95) ~ (all_28_2 = e3) | ( ~ (all_28_0 = e0) & op(all_28_1, e1) = all_28_0 &
% 167.45/24.91 op(e3, e1) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 167.45/24.91 e2) & op(e3, e1) = all_28_1 & $i(all_28_1))
% 167.45/24.91 (96) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 167.45/24.91 (97) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 167.45/24.91 (98) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 167.45/24.91 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 167.45/24.91 (99) all_58_14 = e0
% 167.45/24.91 (100) all_14_2 = all_8_2
% 167.45/24.91 (101) ~ (all_6_2 = e0)
% 167.45/24.91 (102) ~ (all_52_3 = all_10_2)
% 167.45/24.91 (103) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 167.45/24.91 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 167.45/24.91 (104) ~ (all_52_8 = all_52_9)
% 167.45/24.91 (105) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 167.45/24.91 (106) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 167.45/24.91 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 167.45/24.91 (107) ~ (all_52_7 = e0)
% 167.45/24.91 (108) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 167.45/24.91 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 167.45/24.91 (109) ~ (all_12_2 = e1) | ( ~ (all_12_0 = e3) & op(all_12_1, e0) = all_12_0
% 167.45/24.91 & op(e1, e0) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 167.45/24.91 (all_12_1 = e2) & op(e1, e0) = all_12_1 & $i(all_12_1))
% 167.45/24.91 (110) ~ (all_52_4 = all_52_12)
% 167.45/24.92 (111) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 167.45/24.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 167.45/24.92 (112) ~ (all_52_4 = all_8_2)
% 167.45/24.92 (113) ~ (all_52_8 = all_6_2)
% 167.45/24.92 (114) ~ (e2 = e0)
% 167.45/24.92 (115) op(e1, e0) = all_52_14
% 167.45/24.92 (116) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 167.45/24.92 (117) ~ (all_52_13 = all_4_2)
% 167.45/24.92 (118) ~ (all_52_9 = all_8_2)
% 167.45/24.92 (119) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 167.45/24.92 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 167.45/24.92 (120) ~ (all_52_12 = all_10_2)
% 167.45/24.92 (121) ~ (all_52_9 = e0)
% 167.45/24.92 (122) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 167.45/24.92 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 167.45/24.92 (123) ~ (all_52_12 = all_52_13)
% 167.45/24.92 (124) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 167.45/24.92 (125) ~ (all_52_4 = all_52_8)
% 167.45/24.92 (126) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 167.45/24.92 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 167.45/24.92 (127) all_54_5 = all_8_2
% 167.45/24.92 (128) ~ (all_52_8 = all_52_12)
% 167.45/24.92 (129) ~ (e2 = e1)
% 167.45/24.92 (130) all_24_2 = all_10_2
% 167.45/24.92 (131) ~ (all_56_14 = e3) | (all_56_2 = e1 & op(e1, e3) = e1)
% 167.45/24.92 (132) op(e3, e2) = all_52_4
% 167.45/24.92 (133) ~ (all_52_1 = all_52_9)
% 167.45/24.92 (134) all_30_2 = all_8_2
% 167.45/24.92 (135) ~ (all_52_3 = e0)
% 167.45/24.92 (136) ~ (all_52_7 = e1)
% 167.45/24.92 (137) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 167.45/24.92 (138) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 167.45/24.92 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 167.45/24.92 (139) all_54_0 = all_10_2
% 167.45/24.92 (140) all_48_2 = all_8_2
% 167.45/24.92 (141) op(e0, e2) = all_52_7
% 167.45/24.92 (142) all_54_7 = all_52_13
% 167.45/24.92 (143) ~ (all_52_1 = all_10_2)
% 167.45/24.92 (144) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 167.45/24.92 | (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 167.45/24.92 e3)
% 167.45/24.92 (145) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 167.45/24.92 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 167.45/24.92 (146) ~ (all_30_2 = e0) | ( ~ (all_30_0 = e1) & op(all_30_1, e2) = all_30_0
% 167.45/24.92 & op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~
% 167.45/24.92 (all_30_1 = e3) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 167.45/24.92 (147) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 167.45/24.92 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 167.45/24.92 (148) all_54_13 = all_52_7
% 167.45/24.92 (149) ~ (all_52_9 = all_52_13)
% 167.45/24.92 (150) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) =
% 167.45/24.92 e0) | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 167.45/24.92 op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 167.45/24.92 (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 167.45/24.92 e0)))
% 167.45/24.92 (151) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 167.45/24.92 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 167.45/24.92 (152) op(e2, e0) = all_52_13
% 167.45/24.92 (153) ~ (e3 = e2)
% 167.45/24.92
% 167.45/24.92 Begin of proof
% 167.45/24.92 |
% 167.45/24.92 | BETA: splitting (13) gives:
% 167.45/24.92 |
% 167.45/24.92 | Case 1:
% 167.45/24.92 | |
% 167.45/24.92 | | (154) ~ (all_6_2 = e2)
% 167.45/24.92 | |
% 167.45/24.92 | | BETA: splitting (34) gives:
% 167.45/24.92 | |
% 167.45/24.92 | | Case 1:
% 167.45/24.92 | | |
% 167.45/24.92 | | | (155) ~ (all_8_2 = e1)
% 167.45/24.92 | | |
% 167.45/24.92 | | | BETA: splitting (80) gives:
% 167.45/24.92 | | |
% 167.45/24.92 | | | Case 1:
% 167.45/24.92 | | | |
% 167.45/24.92 | | | | (156) ~ (all_10_2 = e0)
% 167.45/24.92 | | | |
% 167.45/24.92 | | | | BETA: splitting (52) gives:
% 167.45/24.92 | | | |
% 167.45/24.92 | | | | Case 1:
% 167.45/24.92 | | | | |
% 167.45/24.92 | | | | | (157) ~ (all_14_2 = e3)
% 167.45/24.92 | | | | |
% 167.45/24.92 | | | | | REDUCE: (100), (157) imply:
% 167.45/24.92 | | | | | (158) ~ (all_8_2 = e3)
% 167.45/24.92 | | | | |
% 167.45/24.92 | | | | | BETA: splitting (44) gives:
% 167.45/24.92 | | | | |
% 167.45/24.92 | | | | | Case 1:
% 167.45/24.92 | | | | | |
% 167.45/24.92 | | | | | | (159) ~ (all_16_2 = e2)
% 167.45/24.92 | | | | | |
% 167.45/24.92 | | | | | | REDUCE: (12), (159) imply:
% 167.45/24.92 | | | | | | (160) ~ (all_10_2 = e2)
% 167.45/24.92 | | | | | |
% 167.45/24.92 | | | | | | BETA: splitting (95) gives:
% 167.45/24.92 | | | | | |
% 167.45/24.92 | | | | | | Case 1:
% 167.45/24.92 | | | | | | |
% 167.45/24.92 | | | | | | | (161) ~ (all_28_2 = e3)
% 167.45/24.92 | | | | | | |
% 167.45/24.92 | | | | | | | REDUCE: (18), (161) imply:
% 167.45/24.92 | | | | | | | (162) ~ (all_6_2 = e3)
% 167.45/24.92 | | | | | | |
% 167.45/24.92 | | | | | | | BETA: splitting (33) gives:
% 167.45/24.92 | | | | | | |
% 167.45/24.92 | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | |
% 167.45/24.92 | | | | | | | | (163) all_54_10 = e3
% 167.45/24.92 | | | | | | | |
% 167.45/24.92 | | | | | | | | REF_CLOSE: (30), (162), (163) are inconsistent by sub-proof
% 167.45/24.92 | | | | | | | | #982.
% 167.45/24.92 | | | | | | | |
% 167.45/24.92 | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | |
% 167.45/24.92 | | | | | | | | (164) ~ (all_54_10 = e3)
% 167.45/24.92 | | | | | | | | (165) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 167.45/24.92 | | | | | | | |
% 167.45/24.92 | | | | | | | | BETA: splitting (165) gives:
% 167.45/24.92 | | | | | | | |
% 167.45/24.92 | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | |
% 167.45/24.92 | | | | | | | | | (166) all_54_10 = e2
% 167.45/24.92 | | | | | | | | |
% 167.45/24.92 | | | | | | | | | REF_CLOSE: (30), (154), (166) are inconsistent by sub-proof
% 167.45/24.92 | | | | | | | | | #981.
% 167.45/24.92 | | | | | | | | |
% 167.45/24.92 | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | |
% 167.45/24.92 | | | | | | | | | (167) ~ (all_54_10 = e2)
% 167.45/24.92 | | | | | | | | | (168) all_54_10 = e1 | all_54_10 = e0
% 167.45/24.92 | | | | | | | | |
% 167.45/24.92 | | | | | | | | | BETA: splitting (168) gives:
% 167.45/24.92 | | | | | | | | |
% 167.45/24.92 | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | (169) all_54_10 = e1
% 167.45/24.92 | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | COMBINE_EQS: (30), (169) imply:
% 167.45/24.92 | | | | | | | | | | (170) all_6_2 = e1
% 167.45/24.92 | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | SIMP: (170) implies:
% 167.45/24.92 | | | | | | | | | | (171) all_6_2 = e1
% 167.45/24.92 | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | REDUCE: (69), (171) imply:
% 167.45/24.92 | | | | | | | | | | (172) ~ (all_52_6 = e1)
% 167.45/24.92 | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | REDUCE: (113), (171) imply:
% 167.45/24.92 | | | | | | | | | | (173) ~ (all_52_8 = e1)
% 167.45/24.92 | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | REDUCE: (94), (171) imply:
% 167.45/24.92 | | | | | | | | | | (174) ~ (all_52_9 = e1)
% 167.45/24.92 | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | REDUCE: (162), (171) imply:
% 167.45/24.92 | | | | | | | | | | (175) ~ (e3 = e1)
% 167.45/24.92 | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | REDUCE: (154), (171) imply:
% 167.45/24.92 | | | | | | | | | | (176) ~ (e2 = e1)
% 167.45/24.92 | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | BETA: splitting (9) gives:
% 167.45/24.92 | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | (177) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 167.45/24.92 | | | | | | | | | | | & op(e2, e2) = e1)
% 167.45/24.92 | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | BETA: splitting (177) gives:
% 167.45/24.92 | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | (178) all_58_2 = e1 & op(e2, e3) = e1
% 167.45/24.92 | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | ALPHA: (178) implies:
% 167.45/24.92 | | | | | | | | | | | | (179) all_58_2 = e1
% 167.45/24.92 | | | | | | | | | | | | (180) op(e2, e3) = e1
% 167.45/24.92 | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | BETA: splitting (22) gives:
% 167.45/24.92 | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | (181) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 167.45/24.92 | | | | | | | | | | | | | & op(e2, e2) = e1)
% 167.45/24.92 | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | BETA: splitting (181) gives:
% 167.45/24.92 | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | (182) all_58_1 = e1 & op(e3, e2) = e1
% 167.45/24.92 | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | ALPHA: (182) implies:
% 167.45/24.92 | | | | | | | | | | | | | | (183) all_58_1 = e1
% 167.45/24.92 | | | | | | | | | | | | | | (184) op(e3, e2) = e1
% 167.45/24.92 | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 167.45/24.92 | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | (185) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 167.45/24.92 | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 167.45/24.92 | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 167.45/24.92 | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | (186) all_58_0 = e0 & op(e3, e3) = e0
% 167.45/24.92 | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (156), (186) are inconsistent by
% 167.45/24.92 | | | | | | | | | | | | | | | | sub-proof #103.
% 167.45/24.92 | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | (187) all_58_2 = e0 & op(e2, e3) = e0
% 167.45/24.92 | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | REF_CLOSE: (55), (179), (187) are inconsistent by sub-proof
% 167.45/24.92 | | | | | | | | | | | | | | | | #935.
% 167.45/24.92 | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | End of split
% 167.45/24.92 | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | (188) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 167.45/24.92 | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 167.45/24.92 | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 167.45/24.92 | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | (189) all_58_6 = e0 & op(e1, e3) = e0
% 167.45/24.92 | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 167.45/24.92 | | | | | | | | | | | | | | | | (190) all_58_6 = e0
% 167.45/24.92 | | | | | | | | | | | | | | | | (191) op(e1, e3) = e0
% 167.45/24.92 | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | (192) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 167.45/24.92 | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 167.45/24.92 | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | (193) all_58_0 = e0 & op(e3, e3) = e0
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (156), (193) are inconsistent by
% 167.45/24.92 | | | | | | | | | | | | | | | | | | sub-proof #103.
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | (194) all_58_1 = e0 & op(e3, e2) = e0
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (183), (194) are inconsistent by sub-proof
% 167.45/24.92 | | | | | | | | | | | | | | | | | | #948.
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | End of split
% 167.45/24.92 | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | (195) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 167.45/24.92 | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 167.45/24.92 | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | (196) all_58_4 = e0 & op(e3, e1) = e0
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (88), (111), (196) are inconsistent by
% 167.45/24.92 | | | | | | | | | | | | | | | | | | sub-proof #178.
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | (197) all_58_9 = e0 & op(e3, e0) = e0
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | (198) all_58_9 = e0
% 167.45/24.92 | | | | | | | | | | | | | | | | | | (199) op(e3, e0) = e0
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | (200) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 167.45/24.92 | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (129), (160), (184), (200) are
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #37.
% 167.45/24.92 | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | (201) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 167.45/24.92 | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | (202) all_58_4 = e2 & op(e3, e1) = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | (203) all_58_4 = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | (204) op(e3, e1) = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | (205) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | (206) all_58_4 = e3 & op(e3, e1) = e3
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (203), (206) are inconsistent by sub-proof
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | #36.
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | (207) all_58_5 = e3 & op(e2, e1) = e3
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | (208) op(e2, e1) = e3
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | (209) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | (210) all_58_0 = e2 & op(e3, e3) = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (160), (210) are inconsistent by
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #666.
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | (211) all_58_2 = e2 & op(e2, e3) = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | (212) op(e2, e3) = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (111), (129), (180), (212) are inconsistent
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #784.
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | (213) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | (214) all_58_6 = e2 & op(e1, e3) = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (190), (214) are inconsistent by sub-proof
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | #826.
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | (215) all_58_12 = e2 & op(e0, e3) = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (215) implies:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | (216) op(e0, e3) = e2
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | (217) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_58_12 = e3 & op(e0, e3) = e3
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (219) op(e0, e3) = e3
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (153), (216), (219) are inconsistent by
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #38.
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_58_13 = e3 & op(e0, e2) = e3
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (220) implies:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_58_13 = e3
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_58_0 = e3 & op(e3, e3) = e3
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) all_58_0 = e3
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) op(e3, e3) = e3
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_52_9, e3, e1, e2,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (2), (208) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_52_9 = e3
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_52_1, e1, e3, e2,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (66), (180) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_52_1 = e1
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_52_12, e0, e0, e3,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (42), (199) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) all_52_12 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_52_8, e2, e1, e3,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (51), (204) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_52_8 = e2
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_52_4, e1, e2, e3,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (132), (184) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_52_4 = e1
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_10_2, e3, e3, e3,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (35), (225) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_10_2 = e3
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (231) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_56_10 = e3
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (227) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) ~ (all_52_13 = e1)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (230) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_8_2 = e1)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (226) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) ~ (all_52_13 = e3)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (235) implies:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) ~ (all_52_13 = e3)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (226) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) ~ (all_8_2 = e3)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (228) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) ~ (all_52_13 = e0)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (238) implies:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) ~ (all_52_13 = e0)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (31), (228) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) ~ (e1 = e0)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) ~ (all_30_2 = e0)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (241) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) ~ (all_8_2 = e0)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) all_58_2 = e0 & op(e2, e3) = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) all_58_2 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (245) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) e1 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (183), (246) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_58_1 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (106), (129), (198), (203), (224),
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) are inconsistent by sub-proof #639.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_58_3 = e0 & op(e2, e2) = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (9), (19), (32), (57), (60), (62), (66),
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (89), (90), (98), (111), (112), (118),
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (126), (127), (132), (138), (141), (142), (152),
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (155), (158), (236), (239), (242), (248) are
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #214.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_58_5 = e0 & op(e2, e1) = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (111), (121), (250) are inconsistent by
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #670.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_58_10 = e0 & op(e2, e0) = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) op(e2, e0) = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_54_5 = e3
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (158), (253) are inconsistent by sub-proof
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #667.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_54_5 = e2
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (255) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_8_2 = e2
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (256) implies:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_8_2 = e2
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (257) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) ~ (all_52_13 = e2)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (68), (111), (142), (152), (239), (252),
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) are inconsistent by sub-proof #122.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_54_5 = e1 | all_54_5 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (155), (242), (259) are inconsistent by
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #735.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) all_30_2 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (134), (260) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_8_2 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (261) implies:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_8_2 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (262) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_56_12 = e0
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) ~ (all_56_12 = e0)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (263), (264) imply:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) $false
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (265) is inconsistent.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_56_11 = e2 & op(e2, e0) = e2
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) all_56_11 = e2
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) op(e2, e0) = e2
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (269) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (270) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) op(e2, e3) = e3
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (111), (180), (272) are inconsistent by
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) op(e3, e2) = e2
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (129), (184), (274) are inconsistent by
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #180.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (49), (111), (129), (204), (275) are
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #33.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (111), (208), (232), (277) are inconsistent
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #685.
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.45/24.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) op(e2, e0) = e0
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (152), (268), (280) are inconsistent
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #684.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8))
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (49), (283) are inconsistent by sub-proof
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #34.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (263), (267), (284) are inconsistent by sub-proof
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #683.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_58_2 = e3 & op(e2, e3) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) op(e2, e3) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (111), (180), (286) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #35.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_58_6 = e3 & op(e1, e3) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) op(e1, e3) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (111), (191), (289) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #64.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) all_58_12 = e3 & op(e0, e3) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (290) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_58_12 = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (40), (46), (55), (84), (114), (129),
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150), (153), (221), (291) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #644.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | (292) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (40), (84), (99), (292) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #40.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | (293) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (293) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | (294) all_58_8 = e3 & op(e1, e1) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (111), (162), (294) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | sub-proof #961.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | (295) all_58_14 = e3 & op(e0, e1) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (99), (295) are inconsistent by sub-proof
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | #32.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | (296) all_58_9 = e2 & op(e3, e0) = e2
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | (297) op(e3, e0) = e2
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (199), (297) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | sub-proof #699.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | (298) all_58_12 = e0 & op(e0, e3) = e0
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | (299) all_58_12 = e0
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (24), (40), (58), (84), (99), (111),
% 167.45/24.94 | | | | | | | | | | | | | | | | (114), (129), (153), (299) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | | | sub-proof #39.
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | (300) all_58_3 = e1 & op(e2, e2) = e1
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | REF_CLOSE: (76), (111), (155), (300) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | sub-proof #498.
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | (301) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 167.45/24.94 | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | BETA: splitting (301) gives:
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | (302) all_58_7 = e1 & op(e1, e2) = e1
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | REF_CLOSE: (62), (111), (172), (302) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | sub-proof #80.
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | (303) all_58_13 = e1 & op(e0, e2) = e1
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | REF_CLOSE: (111), (136), (141), (303) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | sub-proof #114.
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | (304) all_58_3 = e1 & op(e2, e2) = e1
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | REF_CLOSE: (76), (111), (155), (304) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | sub-proof #498.
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | (305) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 167.45/24.94 | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 167.45/24.94 | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | BETA: splitting (305) gives:
% 167.45/24.94 | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | (306) all_58_5 = e1 & op(e2, e1) = e1
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | ALPHA: (306) implies:
% 167.45/24.94 | | | | | | | | | | | | (307) all_58_5 = e1
% 167.45/24.94 | | | | | | | | | | | | (308) op(e2, e1) = e1
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | BETA: splitting (63) gives:
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | (309) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 167.45/24.94 | | | | | | | | | | | | | & op(e2, e1) = e3)
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | BETA: splitting (309) gives:
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | (310) all_58_4 = e3 & op(e3, e1) = e3
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | ALPHA: (310) implies:
% 167.45/24.94 | | | | | | | | | | | | | | (311) all_58_4 = e3
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | (312) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 167.45/24.94 | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | (313) all_58_4 = e2 & op(e3, e1) = e2
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | (314) all_58_4 = e2
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | COMBINE_EQS: (311), (314) imply:
% 167.45/24.94 | | | | | | | | | | | | | | | | (315) e3 = e2
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | REDUCE: (153), (315) imply:
% 167.45/24.94 | | | | | | | | | | | | | | | | (316) $false
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | CLOSE: (316) is inconsistent.
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | (317) all_58_5 = e2 & op(e2, e1) = e2
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | (318) all_58_5 = e2
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | REF_CLOSE: (129), (307), (318) are inconsistent by sub-proof
% 167.45/24.94 | | | | | | | | | | | | | | | | #522.
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | (319) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 167.45/24.94 | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | REF_CLOSE: (78), (99), (111), (114), (154), (319) are
% 167.45/24.94 | | | | | | | | | | | | | | | inconsistent by sub-proof #31.
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | (320) all_58_5 = e3 & op(e2, e1) = e3
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | ALPHA: (320) implies:
% 167.45/24.94 | | | | | | | | | | | | | | (321) op(e2, e1) = e3
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | REF_CLOSE: (40), (111), (308), (321) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | sub-proof #686.
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | (322) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 167.45/24.94 | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | REF_CLOSE: (78), (84), (99), (111), (162), (322) are
% 167.45/24.94 | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | (323) all_58_10 = e1 & op(e2, e0) = e1
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | ALPHA: (323) implies:
% 167.45/24.94 | | | | | | | | | | | | (324) all_58_10 = e1
% 167.45/24.94 | | | | | | | | | | | | (325) op(e2, e0) = e1
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | BETA: splitting (22) gives:
% 167.45/24.94 | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | (326) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 167.45/24.94 | | | | | | | | | | | | | & op(e2, e2) = e1)
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | BETA: splitting (326) gives:
% 167.45/24.94 | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | (327) all_58_1 = e1 & op(e3, e2) = e1
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | ALPHA: (327) implies:
% 167.45/24.94 | | | | | | | | | | | | | | (328) all_58_1 = e1
% 167.45/24.94 | | | | | | | | | | | | | | (329) op(e3, e2) = e1
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 167.45/24.94 | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | (330) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 167.45/24.94 | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | BETA: splitting (330) gives:
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | (331) all_58_0 = e0 & op(e3, e3) = e0
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (156), (331) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | | | sub-proof #103.
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | (332) all_58_1 = e0 & op(e3, e2) = e0
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | REF_CLOSE: (55), (328), (332) are inconsistent by sub-proof
% 167.45/24.94 | | | | | | | | | | | | | | | | #948.
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | (333) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 167.45/24.94 | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | BETA: splitting (333) gives:
% 167.45/24.94 | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | (334) all_58_4 = e0 & op(e3, e1) = e0
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | REF_CLOSE: (51), (88), (111), (334) are inconsistent by
% 167.45/24.94 | | | | | | | | | | | | | | | | sub-proof #178.
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | (335) all_58_9 = e0 & op(e3, e0) = e0
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | (336) op(e3, e0) = e0
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | (337) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 167.45/24.94 | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 167.45/24.94 | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (129), (160), (329), (337) are
% 167.45/24.94 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #37.
% 167.45/24.94 | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | (338) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 167.45/24.94 | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 167.45/24.94 | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | BETA: splitting (338) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | (339) all_58_4 = e2 & op(e3, e1) = e2
% 167.45/24.94 | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | (340) all_58_4 = e2
% 167.45/24.94 | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | (341) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | BETA: splitting (341) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | (342) all_58_0 = e3 & op(e3, e3) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | ALPHA: (342) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | (343) op(e3, e3) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | (344) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (344) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | (345) all_58_4 = e3 & op(e3, e1) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (340), (345) are inconsistent by sub-proof
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | #36.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | (346) all_58_5 = e3 & op(e2, e1) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (346) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | (347) all_58_5 = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | (348) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | (349) all_58_9 = e3 & op(e3, e0) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (349) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | (350) all_58_9 = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (55), (84), (111), (114), (328), (340),
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | (343), (350) are inconsistent by sub-proof #249.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | (351) all_58_10 = e3 & op(e2, e0) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (324), (351) are inconsistent by sub-proof
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | #813.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | (352) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (352) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | (353) all_58_11 = e3 & op(e1, e0) = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | (354) all_58_11 = e3
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | (355) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (356) all_58_9 = e2 & op(e3, e0) = e2
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (356) implies:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (357) all_58_9 = e2
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (55), (84), (111), (114), (328), (340),
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (343), (357) are inconsistent by sub-proof #944.
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (358) all_58_10 = e2 & op(e2, e0) = e2
% 167.45/24.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (358) implies:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (359) op(e2, e0) = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (129), (325), (359) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #526.
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | (360) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (360) gives:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (361) all_58_11 = e2 & op(e1, e0) = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (361) implies:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (362) all_58_11 = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (354), (362) imply:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (363) e3 = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (347), (363) imply:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (364) all_58_5 = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (63), (84), (99), (129), (147), (153),
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (340), (364) are inconsistent by sub-proof #30.
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (365) all_58_15 = e2 & op(e0, e0) = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (365) implies:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (366) op(e0, e0) = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (111), (129), (366) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #640.
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | (367) all_58_15 = e3 & op(e0, e0) = e3
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (367) implies:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | (368) all_58_15 = e3
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (40), (368) are inconsistent by sub-proof
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | | #556.
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | (369) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (369) gives:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | (370) all_58_8 = e3 & op(e1, e1) = e3
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (111), (162), (370) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | sub-proof #961.
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | (371) all_58_14 = e3 & op(e0, e1) = e3
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (99), (371) are inconsistent by sub-proof
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | | #32.
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | (372) all_58_1 = e3 & op(e3, e2) = e3
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (328), (372) are inconsistent by sub-proof
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | #121.
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | (373) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 167.45/24.95 | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | BETA: splitting (373) gives:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | (374) all_58_4 = e3 & op(e3, e1) = e3
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (340), (374) are inconsistent by sub-proof
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | #952.
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | (375) all_58_9 = e3 & op(e3, e0) = e3
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | (376) all_58_9 = e3
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (55), (65), (84), (111), (114), (129),
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | (150), (153), (324), (325), (376) are inconsistent
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | | by sub-proof #29.
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | (377) all_58_9 = e2 & op(e3, e0) = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 167.45/24.95 | | | | | | | | | | | | | | | | | | (378) op(e3, e0) = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (336), (378) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | | | | | | sub-proof #699.
% 167.45/24.95 | | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | (379) all_58_3 = e1 & op(e2, e2) = e1
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | REF_CLOSE: (76), (111), (155), (379) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | | sub-proof #498.
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | (380) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 167.45/24.95 | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | BETA: splitting (380) gives:
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | (381) all_58_7 = e1 & op(e1, e2) = e1
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | REF_CLOSE: (62), (111), (172), (381) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | | sub-proof #80.
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | (382) all_58_13 = e1 & op(e0, e2) = e1
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | REF_CLOSE: (111), (136), (141), (382) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | | sub-proof #114.
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | (383) all_54_10 = e0
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | REF_CLOSE: (30), (101), (383) are inconsistent by sub-proof
% 167.45/24.95 | | | | | | | | | | #979.
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | End of split
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | End of split
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | Case 2:
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | (384) all_28_2 = e3
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | COMBINE_EQS: (18), (384) imply:
% 167.45/24.95 | | | | | | | (385) all_6_2 = e3
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | SIMP: (385) implies:
% 167.45/24.95 | | | | | | | (386) all_6_2 = e3
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | COMBINE_EQS: (41), (386) imply:
% 167.45/24.95 | | | | | | | (387) all_56_14 = e3
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | REDUCE: (113), (386) imply:
% 167.45/24.95 | | | | | | | (388) ~ (all_52_8 = e3)
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | REDUCE: (94), (386) imply:
% 167.45/24.95 | | | | | | | (389) ~ (all_52_9 = e3)
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | BETA: splitting (131) gives:
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | (390) ~ (all_56_14 = e3)
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | REDUCE: (387), (390) imply:
% 167.45/24.95 | | | | | | | | (391) $false
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | CLOSE: (391) is inconsistent.
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | (392) all_56_2 = e1 & op(e1, e3) = e1
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | ALPHA: (392) implies:
% 167.45/24.95 | | | | | | | | (393) all_56_2 = e1
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | BETA: splitting (124) gives:
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | (394) ~ (all_56_10 = e1)
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | REDUCE: (25), (394) imply:
% 167.45/24.95 | | | | | | | | | (395) ~ (all_10_2 = e1)
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | BETA: splitting (137) gives:
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | (396) all_54_0 = e3
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | COMBINE_EQS: (139), (396) imply:
% 167.45/24.95 | | | | | | | | | | (397) all_10_2 = e3
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | REDUCE: (143), (397) imply:
% 167.45/24.95 | | | | | | | | | | (398) ~ (all_52_1 = e3)
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | REDUCE: (102), (397) imply:
% 167.45/24.95 | | | | | | | | | | (399) ~ (all_52_3 = e3)
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | BETA: splitting (97) gives:
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | (400) all_54_12 = e3
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | REF_CLOSE: (17), (399), (400) are inconsistent by sub-proof
% 167.45/24.95 | | | | | | | | | | | #738.
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | (401) ~ (all_54_12 = e3)
% 167.45/24.95 | | | | | | | | | | | (402) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | BETA: splitting (126) gives:
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | (403) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 167.45/24.95 | | | | | | | | | | | | & op(e2, e2) = e3)
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | REF_CLOSE: (66), (76), (111), (158), (398), (403) are
% 167.45/24.95 | | | | | | | | | | | | inconsistent by sub-proof #692.
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | (404) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 167.45/24.95 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | BETA: splitting (404) gives:
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | (405) all_58_5 = e3 & op(e2, e1) = e3
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | ALPHA: (405) implies:
% 167.45/24.95 | | | | | | | | | | | | | (406) op(e2, e1) = e3
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | REF_CLOSE: (2), (111), (389), (406) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | sub-proof #951.
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | (407) all_58_10 = e3 & op(e2, e0) = e3
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | ALPHA: (407) implies:
% 167.45/24.95 | | | | | | | | | | | | | (408) op(e2, e0) = e3
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | BETA: splitting (402) gives:
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | (409) all_54_12 = e2
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | COMBINE_EQS: (17), (409) imply:
% 167.45/24.95 | | | | | | | | | | | | | | (410) all_52_3 = e2
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | SIMP: (410) implies:
% 167.45/24.95 | | | | | | | | | | | | | | (411) all_52_3 = e2
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | REDUCE: (70), (411) imply:
% 167.45/24.95 | | | | | | | | | | | | | | (412) ~ (all_52_7 = e2)
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | SIMP: (412) implies:
% 167.45/24.95 | | | | | | | | | | | | | | (413) ~ (all_52_7 = e2)
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | REDUCE: (399), (411) imply:
% 167.45/24.95 | | | | | | | | | | | | | | (414) ~ (e3 = e2)
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | REDUCE: (47), (411) imply:
% 167.45/24.95 | | | | | | | | | | | | | | (415) op(e0, e3) = e2
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | (416) ~ (all_56_12 = e0)
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | REDUCE: (77), (416) imply:
% 167.45/24.95 | | | | | | | | | | | | | | | (417) ~ (all_8_2 = e0)
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | (418) all_54_5 = e3
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | REF_CLOSE: (127), (158), (418) are inconsistent by sub-proof
% 167.45/24.95 | | | | | | | | | | | | | | | | #667.
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | (419) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | BETA: splitting (419) gives:
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | (420) all_54_5 = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (420) imply:
% 167.45/24.95 | | | | | | | | | | | | | | | | | (421) all_8_2 = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | SIMP: (421) implies:
% 167.45/24.95 | | | | | | | | | | | | | | | | | (422) all_8_2 = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (422) imply:
% 167.45/24.95 | | | | | | | | | | | | | | | | | (423) all_56_12 = e2
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (10), (28), (49), (55), (92), (111), (141),
% 167.45/24.95 | | | | | | | | | | | | | | | | | (153), (387), (393), (413), (415), (423) are
% 167.45/24.95 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25.
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | (424) all_54_5 = e1 | all_54_5 = e0
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (155), (417), (424) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | | | | | sub-proof #735.
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | (425) all_56_11 = e2 & op(e2, e0) = e2
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | ALPHA: (425) implies:
% 167.45/24.95 | | | | | | | | | | | | | | | (426) op(e2, e0) = e2
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | REF_CLOSE: (111), (153), (408), (426) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | | | sub-proof #682.
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | (427) all_54_12 = e1 | all_54_12 = e0
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (135), (427) are inconsistent by
% 167.45/24.95 | | | | | | | | | | | | | | sub-proof #736.
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | (428) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | REF_CLOSE: (139), (156), (160), (395), (428) are inconsistent
% 167.45/24.95 | | | | | | | | | | by sub-proof #958.
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | End of split
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | (429) all_56_4 = e3 & op(e3, e1) = e3
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | ALPHA: (429) implies:
% 167.45/24.95 | | | | | | | | | (430) op(e3, e1) = e3
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | REF_CLOSE: (51), (111), (388), (430) are inconsistent by
% 167.45/24.95 | | | | | | | | | sub-proof #975.
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | End of split
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | End of split
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | End of split
% 167.45/24.95 | | | | | |
% 167.45/24.95 | | | | | Case 2:
% 167.45/24.95 | | | | | |
% 167.45/24.95 | | | | | | (431) all_16_2 = e2
% 167.45/24.95 | | | | | |
% 167.45/24.95 | | | | | | COMBINE_EQS: (12), (431) imply:
% 167.45/24.95 | | | | | | (432) all_10_2 = e2
% 167.45/24.95 | | | | | |
% 167.45/24.95 | | | | | | REDUCE: (102), (432) imply:
% 167.45/24.95 | | | | | | (433) ~ (all_52_3 = e2)
% 167.45/24.95 | | | | | |
% 167.45/24.95 | | | | | | REDUCE: (64), (432) imply:
% 167.45/24.95 | | | | | | (434) ~ (all_52_8 = e2)
% 167.45/24.95 | | | | | |
% 167.45/24.95 | | | | | | BETA: splitting (151) gives:
% 167.45/24.95 | | | | | |
% 167.45/24.95 | | | | | | Case 1:
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | (435) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 167.45/24.95 | | | | | | | op(e2, e1) = e2)
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | BETA: splitting (435) gives:
% 167.45/24.95 | | | | | | |
% 167.45/24.95 | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | (436) all_58_4 = e2 & op(e3, e1) = e2
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | REF_CLOSE: (51), (111), (434), (436) are inconsistent by
% 167.45/24.95 | | | | | | | | sub-proof #572.
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | (437) all_58_5 = e2 & op(e2, e1) = e2
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | ALPHA: (437) implies:
% 167.45/24.95 | | | | | | | | (438) all_58_5 = e2
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | BETA: splitting (97) gives:
% 167.45/24.95 | | | | | | | |
% 167.45/24.95 | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | (439) all_54_12 = e3
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | COMBINE_EQS: (17), (439) imply:
% 167.45/24.95 | | | | | | | | | (440) all_52_3 = e3
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | SIMP: (440) implies:
% 167.45/24.95 | | | | | | | | | (441) all_52_3 = e3
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | REDUCE: (70), (441) imply:
% 167.45/24.95 | | | | | | | | | (442) ~ (all_52_7 = e3)
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | SIMP: (442) implies:
% 167.45/24.95 | | | | | | | | | (443) ~ (all_52_7 = e3)
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | BETA: splitting (16) gives:
% 167.45/24.95 | | | | | | | | |
% 167.45/24.95 | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | (444) all_54_13 = e3
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | REF_CLOSE: (148), (443), (444) are inconsistent by sub-proof
% 167.45/24.95 | | | | | | | | | | #971.
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | (445) ~ (all_54_13 = e3)
% 167.45/24.95 | | | | | | | | | | (446) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | BETA: splitting (446) gives:
% 167.45/24.95 | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | (447) all_54_13 = e2
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | COMBINE_EQS: (148), (447) imply:
% 167.45/24.95 | | | | | | | | | | | (448) all_52_7 = e2
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | SIMP: (448) implies:
% 167.45/24.95 | | | | | | | | | | | (449) all_52_7 = e2
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | REDUCE: (89), (449) imply:
% 167.45/24.95 | | | | | | | | | | | (450) ~ (all_8_2 = e2)
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | SIMP: (450) implies:
% 167.45/24.95 | | | | | | | | | | | (451) ~ (all_8_2 = e2)
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | REDUCE: (443), (449) imply:
% 167.45/24.95 | | | | | | | | | | | (452) ~ (e3 = e2)
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | BETA: splitting (19) gives:
% 167.45/24.95 | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | (453) all_54_5 = e3
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | COMBINE_EQS: (127), (453) imply:
% 167.45/24.95 | | | | | | | | | | | | (454) all_8_2 = e3
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | REDUCE: (158), (454) imply:
% 167.45/24.95 | | | | | | | | | | | | (455) $false
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | CLOSE: (455) is inconsistent.
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | (456) ~ (all_54_5 = e3)
% 167.45/24.95 | | | | | | | | | | | | (457) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | BETA: splitting (457) gives:
% 167.45/24.95 | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | (458) all_54_5 = e2
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | COMBINE_EQS: (127), (458) imply:
% 167.45/24.95 | | | | | | | | | | | | | (459) all_8_2 = e2
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | REDUCE: (451), (459) imply:
% 167.45/24.95 | | | | | | | | | | | | | (460) $false
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | CLOSE: (460) is inconsistent.
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | (461) all_54_5 = e1 | all_54_5 = e0
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | BETA: splitting (9) gives:
% 167.45/24.95 | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | (462) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 167.45/24.95 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | BETA: splitting (462) gives:
% 167.45/24.95 | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | (463) all_58_2 = e1 & op(e2, e3) = e1
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | ALPHA: (463) implies:
% 167.45/24.95 | | | | | | | | | | | | | | | (464) all_58_2 = e1
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | BETA: splitting (461) gives:
% 167.45/24.95 | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | (465) all_54_5 = e1
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | REF_CLOSE: (127), (155), (465) are inconsistent by sub-proof
% 167.45/24.95 | | | | | | | | | | | | | | | | #24.
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | (466) all_54_5 = e0
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (466) imply:
% 167.45/24.95 | | | | | | | | | | | | | | | | (467) all_8_2 = e0
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | SIMP: (467) implies:
% 167.45/24.95 | | | | | | | | | | | | | | | | (468) all_8_2 = e0
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (468) imply:
% 167.45/24.95 | | | | | | | | | | | | | | | | (469) all_56_12 = e0
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 167.45/24.95 | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | (470) ~ (all_56_12 = e0)
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | REDUCE: (469), (470) imply:
% 167.45/24.95 | | | | | | | | | | | | | | | | | (471) $false
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | | CLOSE: (471) is inconsistent.
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.95 | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.95 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | | (472) all_56_11 = e2 & op(e2, e0) = e2
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | | ALPHA: (472) implies:
% 167.45/24.96 | | | | | | | | | | | | | | | | | (473) op(e2, e0) = e2
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (76), (111), (126), (153), (158), (438),
% 167.45/24.96 | | | | | | | | | | | | | | | | | (464), (473) are inconsistent by sub-proof #524.
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | (474) all_58_3 = e1 & op(e2, e2) = e1
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | REF_CLOSE: (76), (111), (155), (474) are inconsistent by
% 167.45/24.96 | | | | | | | | | | | | | | | sub-proof #498.
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | (475) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 167.45/24.96 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | BETA: splitting (475) gives:
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | (476) all_58_5 = e1 & op(e2, e1) = e1
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | REF_CLOSE: (129), (438), (476) are inconsistent by sub-proof
% 167.45/24.96 | | | | | | | | | | | | | | | #852.
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | (477) all_58_10 = e1 & op(e2, e0) = e1
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | ALPHA: (477) implies:
% 167.45/24.96 | | | | | | | | | | | | | | | (478) op(e2, e0) = e1
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | BETA: splitting (461) gives:
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | (479) all_54_5 = e1
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | REF_CLOSE: (127), (155), (479) are inconsistent by sub-proof
% 167.45/24.96 | | | | | | | | | | | | | | | | #24.
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | (480) all_54_5 = e0
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | COMBINE_EQS: (127), (480) imply:
% 167.45/24.96 | | | | | | | | | | | | | | | | (481) all_8_2 = e0
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | SIMP: (481) implies:
% 167.45/24.96 | | | | | | | | | | | | | | | | (482) all_8_2 = e0
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (482) imply:
% 167.45/24.96 | | | | | | | | | | | | | | | | (483) all_56_12 = e0
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | | (484) ~ (all_56_12 = e0)
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | | REDUCE: (483), (484) imply:
% 167.45/24.96 | | | | | | | | | | | | | | | | | (485) $false
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | | CLOSE: (485) is inconsistent.
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | | (486) all_56_11 = e2 & op(e2, e0) = e2
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | | ALPHA: (486) implies:
% 167.45/24.96 | | | | | | | | | | | | | | | | | (487) op(e2, e0) = e2
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (129), (478), (487) are inconsistent by
% 167.45/24.96 | | | | | | | | | | | | | | | | | sub-proof #526.
% 167.45/24.96 | | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | (488) all_54_13 = e1 | all_54_13 = e0
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | REF_CLOSE: (107), (136), (148), (488) are inconsistent by
% 167.45/24.96 | | | | | | | | | | | sub-proof #256.
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | (489) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | REF_CLOSE: (17), (38), (135), (433), (489) are inconsistent by
% 167.45/24.96 | | | | | | | | | sub-proof #675.
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | End of split
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | End of split
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | Case 2:
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | (490) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 167.45/24.96 | | | | | | | op(e0, e1) = e2)
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | REF_CLOSE: (78), (99), (111), (114), (154), (490) are inconsistent
% 167.45/24.96 | | | | | | | by sub-proof #31.
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | End of split
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | End of split
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | Case 2:
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | (491) all_14_2 = e3
% 167.45/24.96 | | | | | (492) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3,
% 167.45/24.96 | | | | | e2) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 167.45/24.96 | | | | | (all_14_1 = e1) & op(e3, e2) = all_14_1 & $i(all_14_1))
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | COMBINE_EQS: (100), (491) imply:
% 167.45/24.96 | | | | | (493) all_8_2 = e3
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | SIMP: (493) implies:
% 167.45/24.96 | | | | | (494) all_8_2 = e3
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | COMBINE_EQS: (56), (494) imply:
% 167.45/24.96 | | | | | (495) all_22_2 = e3
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | COMBINE_EQS: (77), (494) imply:
% 167.45/24.96 | | | | | (496) all_56_12 = e3
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | REDUCE: (112), (494) imply:
% 167.45/24.96 | | | | | (497) ~ (all_52_4 = e3)
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | REDUCE: (57), (494) imply:
% 167.45/24.96 | | | | | (498) ~ (all_52_6 = e3)
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | REDUCE: (89), (494) imply:
% 167.45/24.96 | | | | | (499) ~ (all_52_7 = e3)
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | BETA: splitting (26) gives:
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | Case 1:
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | | (500) ~ (all_56_12 = e3)
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | | REDUCE: (496), (500) imply:
% 167.45/24.96 | | | | | | (501) $false
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | | CLOSE: (501) is inconsistent.
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | Case 2:
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | | (502) all_56_0 = e2 & op(e2, e3) = e2
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | | ALPHA: (502) implies:
% 167.45/24.96 | | | | | | (503) op(e2, e3) = e2
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | | BETA: splitting (16) gives:
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | | Case 1:
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | (504) all_54_13 = e3
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | REF_CLOSE: (148), (499), (504) are inconsistent by sub-proof #971.
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | Case 2:
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | (505) ~ (all_54_13 = e3)
% 167.45/24.96 | | | | | | | (506) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | BETA: splitting (15) gives:
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | | (507) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 &
% 167.45/24.96 | | | | | | | | op(e2, e2) = e3)
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | | BETA: splitting (507) gives:
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | (508) all_58_1 = e3 & op(e3, e2) = e3
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | ALPHA: (508) implies:
% 167.45/24.96 | | | | | | | | | (509) op(e3, e2) = e3
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | REF_CLOSE: (111), (132), (497), (509) are inconsistent by
% 167.45/24.96 | | | | | | | | | sub-proof #974.
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | (510) all_58_3 = e3 & op(e2, e2) = e3
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | ALPHA: (510) implies:
% 167.45/24.96 | | | | | | | | | (511) all_58_3 = e3
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | BETA: splitting (506) gives:
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | (512) all_54_13 = e2
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | COMBINE_EQS: (148), (512) imply:
% 167.45/24.96 | | | | | | | | | | (513) all_52_7 = e2
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | SIMP: (513) implies:
% 167.45/24.96 | | | | | | | | | | (514) all_52_7 = e2
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | REDUCE: (70), (514) imply:
% 167.45/24.96 | | | | | | | | | | (515) ~ (all_52_3 = e2)
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | REDUCE: (141), (514) imply:
% 167.45/24.96 | | | | | | | | | | (516) op(e0, e2) = e2
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | BETA: splitting (97) gives:
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | (517) all_54_12 = e3
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | COMBINE_EQS: (17), (517) imply:
% 167.45/24.96 | | | | | | | | | | | (518) all_52_3 = e3
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | SIMP: (518) implies:
% 167.45/24.96 | | | | | | | | | | | (519) all_52_3 = e3
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | REDUCE: (102), (519) imply:
% 167.45/24.96 | | | | | | | | | | | (520) ~ (all_10_2 = e3)
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | SIMP: (520) implies:
% 167.45/24.96 | | | | | | | | | | | (521) ~ (all_10_2 = e3)
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | BETA: splitting (96) gives:
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | (522) all_56_10 = e3
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | COMBINE_EQS: (25), (522) imply:
% 167.45/24.96 | | | | | | | | | | | | (523) all_10_2 = e3
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | REDUCE: (521), (523) imply:
% 167.45/24.96 | | | | | | | | | | | | (524) $false
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | CLOSE: (524) is inconsistent.
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | (525) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | BETA: splitting (525) gives:
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | (526) all_56_12 = e2
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | COMBINE_EQS: (496), (526) imply:
% 167.45/24.96 | | | | | | | | | | | | | (527) e3 = e2
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | COMBINE_EQS: (511), (527) imply:
% 167.45/24.96 | | | | | | | | | | | | | (528) all_58_3 = e2
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | REF_CLOSE: (9), (40), (55), (66), (84), (90), (111), (114),
% 167.45/24.96 | | | | | | | | | | | | | (126), (129), (153), (503), (528) are inconsistent
% 167.45/24.96 | | | | | | | | | | | | | by sub-proof #665.
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | (529) ~ (all_56_12 = e2)
% 167.45/24.96 | | | | | | | | | | | | | (530) all_56_14 = e1 | all_56_15 = e0
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | BETA: splitting (530) gives:
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | (531) all_56_14 = e1
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | COMBINE_EQS: (41), (531) imply:
% 167.45/24.96 | | | | | | | | | | | | | | (532) all_6_2 = e1
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | SIMP: (532) implies:
% 167.45/24.96 | | | | | | | | | | | | | | (533) all_6_2 = e1
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | REDUCE: (69), (533) imply:
% 167.45/24.96 | | | | | | | | | | | | | | (534) ~ (all_52_6 = e1)
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | REDUCE: (154), (533) imply:
% 167.45/24.96 | | | | | | | | | | | | | | (535) ~ (e2 = e1)
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | REF_CLOSE: (1), (9), (14), (22), (24), (40), (55), (59),
% 167.45/24.96 | | | | | | | | | | | | | | (62), (66), (76), (82), (84), (86), (90), (99),
% 167.45/24.96 | | | | | | | | | | | | | | (103), (111), (114), (126), (129), (132), (138),
% 167.45/24.96 | | | | | | | | | | | | | | (153), (155), (492), (495), (503), (511), (516),
% 167.45/24.96 | | | | | | | | | | | | | | (534) are inconsistent by sub-proof #21.
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | (536) all_56_15 = e0
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | REF_CLOSE: (49), (55), (536) are inconsistent by sub-proof
% 167.45/24.96 | | | | | | | | | | | | | | #20.
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | (537) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | REF_CLOSE: (17), (38), (135), (515), (537) are inconsistent
% 167.45/24.96 | | | | | | | | | | | by sub-proof #675.
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | (538) all_54_13 = e1 | all_54_13 = e0
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | REF_CLOSE: (107), (136), (148), (538) are inconsistent by
% 167.45/24.96 | | | | | | | | | | sub-proof #256.
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | End of split
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | End of split
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | | (539) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 &
% 167.45/24.96 | | | | | | | | op(e0, e2) = e3)
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | | REF_CLOSE: (62), (111), (141), (498), (499), (539) are
% 167.45/24.96 | | | | | | | | inconsistent by sub-proof #463.
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | End of split
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | End of split
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | End of split
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | End of split
% 167.45/24.96 | | | |
% 167.45/24.96 | | | Case 2:
% 167.45/24.96 | | | |
% 167.45/24.96 | | | | (540) all_10_2 = e0
% 167.45/24.96 | | | | (541) ( ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 & op(e0, e3)
% 167.45/24.96 | | | | = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 =
% 167.45/24.96 | | | | e2) & op(e0, e3) = all_10_1 & $i(all_10_1))
% 167.45/24.96 | | | |
% 167.45/24.96 | | | | COMBINE_EQS: (130), (540) imply:
% 167.45/24.96 | | | | (542) all_24_2 = e0
% 167.45/24.96 | | | |
% 167.45/24.96 | | | | COMBINE_EQS: (25), (540) imply:
% 167.45/24.96 | | | | (543) all_56_10 = e0
% 167.45/24.96 | | | |
% 167.45/24.96 | | | | REDUCE: (143), (540) imply:
% 167.45/24.96 | | | | (544) ~ (all_52_1 = e0)
% 167.45/24.96 | | | |
% 167.45/24.96 | | | | REDUCE: (79), (540) imply:
% 167.45/24.96 | | | | (545) ~ (all_52_4 = e0)
% 167.45/24.96 | | | |
% 167.45/24.96 | | | | REDUCE: (120), (540) imply:
% 167.45/24.96 | | | | (546) ~ (all_52_12 = e0)
% 167.45/24.96 | | | |
% 167.45/24.96 | | | | BETA: splitting (93) gives:
% 167.45/24.96 | | | |
% 167.45/24.96 | | | | Case 1:
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | (547) ~ (all_56_10 = e0)
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | REDUCE: (543), (547) imply:
% 167.45/24.96 | | | | | (548) $false
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | CLOSE: (548) is inconsistent.
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | Case 2:
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | (549) all_56_9 = e3 & op(e3, e0) = e3
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | ALPHA: (549) implies:
% 167.45/24.96 | | | | | (550) all_56_9 = e3
% 167.45/24.96 | | | | | (551) op(e3, e0) = e3
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | BETA: splitting (37) gives:
% 167.45/24.96 | | | | |
% 167.45/24.96 | | | | | Case 1:
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | | (552) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 167.45/24.96 | | | | | | e2) = e0)
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | | BETA: splitting (552) gives:
% 167.45/24.96 | | | | | |
% 167.45/24.96 | | | | | | Case 1:
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | (553) all_58_0 = e0 & op(e3, e3) = e0
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | ALPHA: (553) implies:
% 167.45/24.96 | | | | | | | (554) all_58_0 = e0
% 167.45/24.96 | | | | | | | (555) op(e3, e3) = e0
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | GROUND_INST: instantiating (111) with all_52_12, e3, e0, e3,
% 167.45/24.96 | | | | | | | simplifying with (42), (551) gives:
% 167.45/24.96 | | | | | | | (556) all_52_12 = e3
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | REDUCE: (110), (556) imply:
% 167.45/24.96 | | | | | | | (557) ~ (all_52_4 = e3)
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | REDUCE: (128), (556) imply:
% 167.45/24.96 | | | | | | | (558) ~ (all_52_8 = e3)
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | REDUCE: (123), (556) imply:
% 167.45/24.96 | | | | | | | (559) ~ (all_52_13 = e3)
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | SIMP: (559) implies:
% 167.45/24.96 | | | | | | | (560) ~ (all_52_13 = e3)
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | BETA: splitting (108) gives:
% 167.45/24.96 | | | | | | |
% 167.45/24.96 | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | | (561) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 167.45/24.96 | | | | | | | | op(e3, e2) = e3)
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | | REF_CLOSE: (84), (111), (132), (555), (557), (561) are
% 167.45/24.96 | | | | | | | | inconsistent by sub-proof #217.
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | | (562) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 167.45/24.96 | | | | | | | | op(e3, e0) = e3)
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | | BETA: splitting (562) gives:
% 167.45/24.96 | | | | | | | |
% 167.45/24.96 | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | (563) all_58_4 = e3 & op(e3, e1) = e3
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | ALPHA: (563) implies:
% 167.45/24.96 | | | | | | | | | (564) op(e3, e1) = e3
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | REF_CLOSE: (51), (111), (558), (564) are inconsistent by
% 167.45/24.96 | | | | | | | | | sub-proof #975.
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | (565) all_58_9 = e3 & op(e3, e0) = e3
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | ALPHA: (565) implies:
% 167.45/24.96 | | | | | | | | | (566) all_58_9 = e3
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | BETA: splitting (52) gives:
% 167.45/24.96 | | | | | | | | |
% 167.45/24.96 | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | (567) ~ (all_14_2 = e3)
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | REDUCE: (100), (567) imply:
% 167.45/24.96 | | | | | | | | | | (568) ~ (all_8_2 = e3)
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | BETA: splitting (53) gives:
% 167.45/24.96 | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | (569) ~ (all_24_2 = e0)
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | REDUCE: (542), (569) imply:
% 167.45/24.96 | | | | | | | | | | | (570) $false
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | CLOSE: (570) is inconsistent.
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | (571) ( ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0
% 167.45/24.96 | | | | | | | | | | | & op(e0, e3) = all_24_1 & $i(all_24_0) &
% 167.45/24.96 | | | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0, e3)
% 167.45/24.96 | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | BETA: splitting (95) gives:
% 167.45/24.96 | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | (572) ~ (all_28_2 = e3)
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | REDUCE: (18), (572) imply:
% 167.45/24.96 | | | | | | | | | | | | (573) ~ (all_6_2 = e3)
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | BETA: splitting (63) gives:
% 167.45/24.96 | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | (574) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 167.45/24.96 | | | | | | | | | | | | | & op(e2, e1) = e3)
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | BETA: splitting (574) gives:
% 167.45/24.96 | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | Case 1:
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | (575) all_58_4 = e3 & op(e3, e1) = e3
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | ALPHA: (575) implies:
% 167.45/24.96 | | | | | | | | | | | | | | (576) op(e3, e1) = e3
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | REF_CLOSE: (51), (111), (558), (576) are inconsistent by
% 167.45/24.96 | | | | | | | | | | | | | | sub-proof #975.
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | Case 2:
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | (577) all_58_5 = e3 & op(e2, e1) = e3
% 167.45/24.96 | | | | | | | | | | | | | |
% 167.45/24.96 | | | | | | | | | | | | | | ALPHA: (577) implies:
% 167.45/24.97 | | | | | | | | | | | | | | (578) all_58_5 = e3
% 167.45/24.97 | | | | | | | | | | | | | | (579) op(e2, e1) = e3
% 167.45/24.97 | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 167.45/24.97 | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | (580) all_54_10 = e3
% 167.45/24.97 | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | COMBINE_EQS: (30), (580) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | (581) all_6_2 = e3
% 167.45/24.97 | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | REDUCE: (573), (581) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | (582) $false
% 167.45/24.97 | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | CLOSE: (582) is inconsistent.
% 167.45/24.97 | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | Case 2:
% 167.45/24.97 | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | (583) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 167.45/24.97 | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 167.45/24.97 | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | (584) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 167.45/24.97 | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 167.45/24.97 | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | BETA: splitting (584) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | (585) all_58_2 = e1 & op(e2, e3) = e1
% 167.45/24.97 | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | ALPHA: (585) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | (586) op(e2, e3) = e1
% 167.45/24.97 | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | BETA: splitting (583) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | (587) all_54_10 = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (154), (587) are inconsistent by sub-proof
% 167.45/24.97 | | | | | | | | | | | | | | | | | | #981.
% 167.45/24.97 | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.97 | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | (588) ~ (all_54_10 = e2)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | (589) all_54_10 = e1 | all_54_10 = e0
% 167.45/24.97 | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | BETA: splitting (589) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | (590) all_54_10 = e1
% 167.45/24.97 | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (590) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | (591) all_6_2 = e1
% 167.45/24.97 | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | SIMP: (591) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | (592) all_6_2 = e1
% 167.45/24.97 | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | REDUCE: (69), (592) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | (593) ~ (all_52_6 = e1)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | REDUCE: (113), (592) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | (594) ~ (all_52_8 = e1)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | REDUCE: (94), (592) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | (595) ~ (all_52_9 = e1)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | (596) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (596) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | (597) all_58_1 = e1 & op(e3, e2) = e1
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | ALPHA: (597) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | (598) op(e3, e2) = e1
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | (599) all_54_2 = e3
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (558), (599) are inconsistent by sub-proof
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | #550.
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | (600) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (600) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | (601) all_54_2 = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (601) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | (602) all_52_8 = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (602) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | (603) all_52_8 = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (104), (603) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | (604) ~ (all_52_9 = e2)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (604) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | (605) ~ (all_52_9 = e2)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | (606) all_54_6 = e3
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (606) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | (607) all_52_9 = e3
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (607) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | (608) all_52_9 = e3
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (608) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | (609) ~ (all_52_1 = e3)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (608) imply:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | (610) ~ (all_8_2 = e3)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | (611) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (611) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (612) all_58_4 = e2 & op(e3, e1) = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (612) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (613) all_58_4 = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | (614) op(e3, e1) = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (615) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (615) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (616) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (616) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (617) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (617) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (618) op(e2, e3) = e3
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (111), (609), (618) are inconsistent by
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #989.
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (619) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (619) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (620) op(e3, e2) = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (129), (598), (620) are inconsistent by
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #180.
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (621) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (49), (111), (129), (614), (621) are
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #33.
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (622) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (622) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (623) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (623) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (624) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (624) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (625) op(e2, e1) = e1
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (111), (579), (625) are inconsistent by
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #686.
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (626) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (626) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (627) op(e3, e0) = e0
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (84), (111), (551), (627) are inconsistent
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #154.
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (628) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (628) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (629) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (629) implies:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (630) op(e2, e0) = e0
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (631) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (631) gives:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (632) all_58_2 = e2 & op(e2, e3) = e2
% 167.45/24.97 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (632) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633) op(e2, e3) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (111), (129), (586), (633) are inconsistent
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #784.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (634) all_58_3 = e2 & op(e2, e2) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (634) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635) all_58_3 = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (636) ~ (all_56_12 = e0)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (636) imply:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (637) ~ (all_8_2 = e0)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (638) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (638) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (639) all_58_1 = e0 & op(e3, e2) = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (639) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (640) all_58_1 = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (106), (111), (129), (555), (566),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (614), (640) are inconsistent by sub-proof #211.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (641) all_58_3 = e0 & op(e2, e2) = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (635), (641) are inconsistent by sub-proof
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #934.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (642) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (642) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (643) all_58_7 = e0 & op(e1, e2) = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (643) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (644) all_58_7 = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (645) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (645) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (646) all_58_2 = e0 & op(e2, e3) = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (111), (544), (646) are inconsistent by
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #693.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (647) all_58_3 = e0 & op(e2, e2) = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (635), (647) are inconsistent by sub-proof
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #934.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (648) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (648) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (649) all_58_5 = e0 & op(e2, e1) = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (111), (121), (649) are inconsistent by
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #670.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_58_10 = e0 & op(e2, e0) = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (650) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (651) all_58_10 = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (652) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (652) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (653) all_58_6 = e3 & op(e1, e3) = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (653) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (654) all_58_6 = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (655) op(e1, e3) = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19), (20), (40), (48), (55), (57), (62),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (66), (82), (84), (89), (90), (98), (111), (112),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (126), (127), (132), (141), (155), (541), (554),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555), (568), (571), (637), (654), (655) are
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #206.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (656) all_58_7 = e3 & op(e1, e2) = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (656) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (657) all_58_7 = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (644), (657) imply:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (658) e3 = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (578), (658) imply:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (659) all_58_5 = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (76), (111), (568), (609), (660) are
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #692.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (661) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (578), (659) are inconsistent by sub-proof
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #919.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) all_58_10 = e3 & op(e2, e0) = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (651), (662) are inconsistent by sub-proof
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #542.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (663) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_58_8 = e3 & op(e1, e1) = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (664) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) all_58_8 = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (99), (129), (147), (578), (613),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) are inconsistent by sub-proof #19.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_58_11 = e3 & op(e1, e0) = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (666) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) all_58_11 = e3
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (668) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) all_58_9 = e2 & op(e3, e0) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (669) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) all_58_9 = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (40), (55), (84), (106), (108), (111),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (129), (153), (555), (613), (670) are
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #120.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) all_58_10 = e2 & op(e2, e0) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (671) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) all_58_10 = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (40), (55), (84), (90), (114), (129), (138),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (578), (635), (672) are inconsistent by
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #917.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (673) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) all_58_11 = e2 & op(e1, e0) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (674) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) all_58_11 = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (667), (675) imply:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) e3 = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (676) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) e3 = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (40), (55), (66), (76), (84), (90), (111),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (114), (126), (129), (153), (568), (578), (609),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (635), (677) are inconsistent by sub-proof #560.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) all_58_15 = e2 & op(e0, e0) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (678) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) all_58_15 = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) op(e0, e0) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (40), (55), (84), (111), (114), (129), (150),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (566), (667), (679), (680) are inconsistent by
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #160.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) all_58_13 = e0 & op(e0, e2) = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (681) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) op(e0, e2) = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (683) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) all_58_12 = e2 & op(e0, e3) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (684) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) op(e0, e3) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (541), (571), (586), (685) are inconsistent
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #209.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) all_58_13 = e2 & op(e0, e2) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (686) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) op(e0, e2) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (141), (682), (687) are inconsistent
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #631.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (99), (111), (114), (129), (688) are
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #22.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) all_56_12 = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (111), (114), (152), (630), (689) are
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #501.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (690) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_58_5 = e2 & op(e2, e1) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (691) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) all_58_5 = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (63), (84), (99), (129), (147), (153),
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (613), (692) are inconsistent by sub-proof #30.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_58_10 = e2 & op(e2, e0) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (693) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) op(e2, e0) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (152), (630), (694) are inconsistent
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #684.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (695) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (696) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8))
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (49), (697) are inconsistent by sub-proof
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #34.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (698) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3,
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_9 & $i(all_56_9))
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (543), (550), (699) are inconsistent by sub-proof
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #169.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (700) all_58_5 = e2 & op(e2, e1) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (700) implies:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (701) op(e2, e1) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (111), (605), (701) are inconsistent by
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #571.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | (702) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (702) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_58_8 = e2 & op(e1, e1) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (111), (154), (703) are inconsistent by
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #845.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | (704) all_58_14 = e2 & op(e0, e1) = e2
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (99), (114), (704) are inconsistent by sub-proof
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | | #23.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | (705) ~ (all_54_6 = e3)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (705) imply:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | (706) ~ (all_52_9 = e3)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (111), (579), (706) are inconsistent by
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #951.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | (707) all_54_2 = e1 | all_54_2 = e0
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (88), (594), (707) are inconsistent by
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #253.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | (708) all_58_3 = e1 & op(e2, e2) = e1
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (111), (155), (708) are inconsistent by
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | | sub-proof #498.
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | (709) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (709) gives:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.98 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | | (710) all_58_7 = e1 & op(e1, e2) = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (111), (593), (710) are inconsistent by
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | | sub-proof #80.
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | | (711) all_58_13 = e1 & op(e0, e2) = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (136), (141), (711) are inconsistent by
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | | sub-proof #114.
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | (712) all_54_10 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (101), (712) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | #979.
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | (713) all_58_3 = e1 & op(e2, e2) = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (111), (155), (713) are inconsistent by
% 167.45/24.99 | | | | | | | | | | | | | | | | | sub-proof #498.
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | (714) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 167.45/24.99 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | BETA: splitting (714) gives:
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | (715) all_58_5 = e1 & op(e2, e1) = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | ALPHA: (715) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | | | (716) op(e2, e1) = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (111), (579), (716) are inconsistent by
% 167.45/24.99 | | | | | | | | | | | | | | | | | sub-proof #686.
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | (717) all_58_10 = e1 & op(e2, e0) = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | ALPHA: (717) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | | | (718) all_58_10 = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | | (719) op(e2, e0) = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (55), (65), (84), (111), (114), (129),
% 167.45/24.99 | | | | | | | | | | | | | | | | | (150), (153), (566), (718), (719) are inconsistent
% 167.45/24.99 | | | | | | | | | | | | | | | | | by sub-proof #29.
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | (720) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 167.45/24.99 | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | REF_CLOSE: (78), (84), (99), (111), (573), (720) are
% 167.45/24.99 | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | (721) all_28_2 = e3
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | COMBINE_EQS: (18), (721) imply:
% 167.45/24.99 | | | | | | | | | | | | (722) all_6_2 = e3
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | SIMP: (722) implies:
% 167.45/24.99 | | | | | | | | | | | | (723) all_6_2 = e3
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | COMBINE_EQS: (41), (723) imply:
% 167.45/24.99 | | | | | | | | | | | | (724) all_56_14 = e3
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | BETA: splitting (131) gives:
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | (725) ~ (all_56_14 = e3)
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | REDUCE: (724), (725) imply:
% 167.45/24.99 | | | | | | | | | | | | | (726) $false
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | CLOSE: (726) is inconsistent.
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | (727) all_56_2 = e1 & op(e1, e3) = e1
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | ALPHA: (727) implies:
% 167.45/24.99 | | | | | | | | | | | | | (728) all_56_2 = e1
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | BETA: splitting (96) gives:
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | (729) all_56_10 = e3
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | COMBINE_EQS: (543), (729) imply:
% 167.45/24.99 | | | | | | | | | | | | | | (730) e3 = e0
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | REDUCE: (84), (730) imply:
% 167.45/24.99 | | | | | | | | | | | | | | (731) $false
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | CLOSE: (731) is inconsistent.
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | (732) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | BETA: splitting (732) gives:
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | (733) all_56_12 = e2
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | COMBINE_EQS: (77), (733) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | (734) all_8_2 = e2
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | SIMP: (734) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | (735) all_8_2 = e2
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | REDUCE: (89), (735) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | (736) ~ (all_52_7 = e2)
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | REDUCE: (32), (735) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | (737) ~ (all_52_13 = e2)
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | REDUCE: (568), (735) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | (738) ~ (e3 = e2)
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | (739) all_54_7 = e3
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | REF_CLOSE: (142), (560), (739) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | | | | | | | | | | #533.
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | (740) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | BETA: splitting (740) gives:
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | (741) all_54_7 = e2
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (737), (741) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | | | | | | | | | | | #532.
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | (742) ~ (all_54_7 = e2)
% 167.45/24.99 | | | | | | | | | | | | | | | | | (743) all_54_7 = e1 | all_54_7 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | BETA: splitting (743) gives:
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (744) all_54_7 = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (68), (142), (744) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | | | | | | | | | | | | #172.
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (745) all_54_7 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (745) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (746) all_52_13 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | SIMP: (746) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (747) all_52_13 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | REDUCE: (737), (747) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (748) ~ (e2 = e0)
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | REDUCE: (68), (747) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (749) ~ (e1 = e0)
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | REDUCE: (152), (747) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (750) op(e2, e0) = e0
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | (751) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (751) gives:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (752) all_58_12 = e2 & op(e0, e3) = e2
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | ALPHA: (752) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (753) op(e0, e3) = e2
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (10), (28), (49), (55), (92), (111), (141),
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (153), (724), (728), (733), (736), (753) are
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #25.
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (754) all_58_13 = e2 & op(e0, e2) = e2
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | ALPHA: (754) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (755) op(e0, e2) = e2
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (141), (736), (755) are inconsistent by
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | sub-proof #695.
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | (756) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (756) gives:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (757) all_58_14 = e2 & op(e0, e1) = e2
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | ALPHA: (757) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (758) all_58_14 = e2
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (758) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (759) e2 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (733), (759) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (760) all_56_12 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (111), (114), (152), (750), (760) are
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #501.
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (761) all_58_15 = e2 & op(e0, e0) = e2
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | ALPHA: (761) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | (762) op(e0, e0) = e2
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (111), (129), (762) are inconsistent by
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | | sub-proof #640.
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | (763) all_56_14 = e1 | all_56_15 = e0
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | BETA: splitting (763) gives:
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | (764) all_56_14 = e1
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | REF_CLOSE: (40), (724), (764) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | | | | | | | | | | #258.
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | (765) all_56_15 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | REF_CLOSE: (49), (55), (765) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | | | | | | | | | | #20.
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | (766) all_14_2 = e3
% 167.45/24.99 | | | | | | | | | | (767) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 &
% 167.45/24.99 | | | | | | | | | | op(e3, e2) = all_14_1 & $i(all_14_0) &
% 167.45/24.99 | | | | | | | | | | $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3, e2)
% 167.45/24.99 | | | | | | | | | | = all_14_1 & $i(all_14_1))
% 167.45/24.99 | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | COMBINE_EQS: (100), (766) imply:
% 167.45/24.99 | | | | | | | | | | (768) all_8_2 = e3
% 167.45/24.99 | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | COMBINE_EQS: (56), (768) imply:
% 167.45/24.99 | | | | | | | | | | (769) all_22_2 = e3
% 167.45/24.99 | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | COMBINE_EQS: (77), (768) imply:
% 167.45/24.99 | | | | | | | | | | (770) all_56_12 = e3
% 167.45/24.99 | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | REDUCE: (89), (768) imply:
% 167.45/24.99 | | | | | | | | | | (771) ~ (all_52_7 = e3)
% 167.45/24.99 | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | REDUCE: (118), (768) imply:
% 167.45/24.99 | | | | | | | | | | (772) ~ (all_52_9 = e3)
% 167.45/24.99 | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | BETA: splitting (16) gives:
% 167.45/24.99 | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | (773) all_54_13 = e3
% 167.45/24.99 | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | REF_CLOSE: (148), (771), (773) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | | | | | #971.
% 167.45/24.99 | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | (774) ~ (all_54_13 = e3)
% 167.45/24.99 | | | | | | | | | | | (775) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 167.45/24.99 | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | BETA: splitting (775) gives:
% 167.45/24.99 | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | (776) all_54_13 = e2
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | COMBINE_EQS: (148), (776) imply:
% 167.45/24.99 | | | | | | | | | | | | (777) all_52_7 = e2
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | SIMP: (777) implies:
% 167.45/24.99 | | | | | | | | | | | | (778) all_52_7 = e2
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | REDUCE: (70), (778) imply:
% 167.45/24.99 | | | | | | | | | | | | (779) ~ (all_52_3 = e2)
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | REDUCE: (11), (778) imply:
% 167.45/24.99 | | | | | | | | | | | | (780) ~ (all_52_4 = e2)
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | REDUCE: (771), (778) imply:
% 167.45/24.99 | | | | | | | | | | | | (781) ~ (e3 = e2)
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | REDUCE: (141), (778) imply:
% 167.45/24.99 | | | | | | | | | | | | (782) op(e0, e2) = e2
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | BETA: splitting (126) gives:
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | (783) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 167.45/24.99 | | | | | | | | | | | | | & op(e2, e2) = e3)
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | BETA: splitting (783) gives:
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | (784) all_58_2 = e3 & op(e2, e3) = e3
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | ALPHA: (784) implies:
% 167.45/24.99 | | | | | | | | | | | | | | (785) op(e2, e3) = e3
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (45), (66), (97), (111), (135), (779),
% 167.45/24.99 | | | | | | | | | | | | | | (785) are inconsistent by sub-proof #605.
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | (786) all_58_3 = e3 & op(e2, e2) = e3
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | ALPHA: (786) implies:
% 167.45/24.99 | | | | | | | | | | | | | | (787) all_58_3 = e3
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | (788) ~ (all_56_12 = e3)
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | REDUCE: (770), (788) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | (789) $false
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | CLOSE: (789) is inconsistent.
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | (790) all_56_0 = e2 & op(e2, e3) = e2
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | ALPHA: (790) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | (791) op(e2, e3) = e2
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | (792) all_54_1 = e3
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | REF_CLOSE: (71), (557), (792) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | | | | | | | | | | #956.
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | (793) ~ (all_54_1 = e3)
% 167.45/24.99 | | | | | | | | | | | | | | | | (794) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | BETA: splitting (794) gives:
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | (795) all_54_1 = e2
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (780), (795) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | | | | | | | | | | | #955.
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | (796) ~ (all_54_1 = e2)
% 167.45/24.99 | | | | | | | | | | | | | | | | | (797) all_54_1 = e1 | all_54_1 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | BETA: splitting (797) gives:
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | Case 1:
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (798) all_54_1 = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (798) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (799) all_52_4 = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | SIMP: (799) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (800) all_52_4 = e1
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | REDUCE: (85), (800) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (801) ~ (all_52_6 = e1)
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | SIMP: (801) implies:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (802) ~ (all_52_6 = e1)
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | REDUCE: (557), (800) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (803) ~ (e3 = e1)
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | REDUCE: (780), (800) imply:
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (804) ~ (e2 = e1)
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (9), (14), (22), (24), (40), (55), (59),
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (62), (66), (76), (82), (84), (86), (90), (99),
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (103), (111), (114), (126), (129), (132), (138),
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (153), (155), (767), (769), (782), (787), (791),
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (802) are inconsistent by sub-proof #21.
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | (805) all_54_1 = e0
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (545), (805) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | | | | | | | | | | | | #614.
% 167.45/24.99 | | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | (806) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 167.45/24.99 | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | | REF_CLOSE: (2), (111), (152), (560), (772), (806) are
% 167.45/24.99 | | | | | | | | | | | | | inconsistent by sub-proof #218.
% 167.45/24.99 | | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | Case 2:
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | (807) all_54_13 = e1 | all_54_13 = e0
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | | REF_CLOSE: (107), (136), (148), (807) are inconsistent by
% 167.45/24.99 | | | | | | | | | | | | sub-proof #256.
% 167.45/24.99 | | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | | |
% 167.45/24.99 | | | | | | | | | End of split
% 167.45/24.99 | | | | | | | | |
% 167.45/24.99 | | | | | | | | End of split
% 167.45/24.99 | | | | | | | |
% 167.45/24.99 | | | | | | | End of split
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | Case 2:
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | | (808) all_58_1 = e0 & op(e3, e2) = e0
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | | REF_CLOSE: (111), (132), (545), (808) are inconsistent by
% 167.45/24.99 | | | | | | | sub-proof #155.
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | End of split
% 167.45/24.99 | | | | | |
% 167.45/24.99 | | | | | Case 2:
% 167.45/24.99 | | | | | |
% 167.45/24.99 | | | | | | (809) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 167.45/24.99 | | | | | | e0) = e0)
% 167.45/24.99 | | | | | |
% 167.45/24.99 | | | | | | BETA: splitting (809) gives:
% 167.45/24.99 | | | | | |
% 167.45/24.99 | | | | | | Case 1:
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | | (810) all_58_4 = e0 & op(e3, e1) = e0
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | | REF_CLOSE: (51), (88), (111), (810) are inconsistent by sub-proof
% 167.45/24.99 | | | | | | | #178.
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | Case 2:
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | | (811) all_58_9 = e0 & op(e3, e0) = e0
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | | ALPHA: (811) implies:
% 167.45/24.99 | | | | | | | (812) op(e3, e0) = e0
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | | REF_CLOSE: (42), (84), (111), (551), (812) are inconsistent by
% 167.45/24.99 | | | | | | | sub-proof #154.
% 167.45/24.99 | | | | | | |
% 167.45/24.99 | | | | | | End of split
% 167.45/24.99 | | | | | |
% 167.45/24.99 | | | | | End of split
% 167.45/24.99 | | | | |
% 167.45/24.99 | | | | End of split
% 167.45/24.99 | | | |
% 167.45/24.99 | | | End of split
% 167.45/24.99 | | |
% 167.45/24.99 | | Case 2:
% 167.45/24.99 | | |
% 167.45/24.99 | | | (813) all_8_2 = e1
% 167.45/25.00 | | | (814) ( ~ (all_8_0 = e3) & op(all_8_1, e2) = all_8_0 & op(e1, e2) =
% 167.45/25.00 | | | all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) &
% 167.45/25.00 | | | op(e1, e2) = all_8_1 & $i(all_8_1))
% 167.45/25.00 | | |
% 167.45/25.00 | | | COMBINE_EQS: (140), (813) imply:
% 167.45/25.00 | | | (815) all_48_2 = e1
% 167.45/25.00 | | |
% 167.45/25.00 | | | COMBINE_EQS: (77), (813) imply:
% 167.45/25.00 | | | (816) all_56_12 = e1
% 167.45/25.00 | | |
% 167.45/25.00 | | | REDUCE: (23), (813) imply:
% 167.45/25.00 | | | (817) ~ (all_52_1 = e1)
% 167.45/25.00 | | |
% 167.45/25.00 | | | REDUCE: (112), (813) imply:
% 167.45/25.00 | | | (818) ~ (all_52_4 = e1)
% 167.45/25.00 | | |
% 167.45/25.00 | | | REDUCE: (57), (813) imply:
% 167.45/25.00 | | | (819) ~ (all_52_6 = e1)
% 167.45/25.00 | | |
% 167.45/25.00 | | | REDUCE: (118), (813) imply:
% 167.45/25.00 | | | (820) ~ (all_52_9 = e1)
% 167.45/25.00 | | |
% 167.45/25.00 | | | BETA: splitting (29) gives:
% 167.45/25.00 | | |
% 167.45/25.00 | | | Case 1:
% 167.45/25.00 | | | |
% 167.45/25.00 | | | | (821) ~ (all_56_12 = e1)
% 167.45/25.00 | | | |
% 167.45/25.00 | | | | REDUCE: (816), (821) imply:
% 167.45/25.00 | | | | (822) $false
% 167.45/25.00 | | | |
% 167.45/25.00 | | | | CLOSE: (822) is inconsistent.
% 167.45/25.00 | | | |
% 167.45/25.00 | | | Case 2:
% 167.45/25.00 | | | |
% 167.45/25.00 | | | | (823) all_56_5 = e2 & op(e2, e1) = e2
% 167.45/25.00 | | | |
% 167.45/25.00 | | | | ALPHA: (823) implies:
% 167.45/25.00 | | | | (824) all_56_5 = e2
% 167.45/25.00 | | | | (825) op(e2, e1) = e2
% 167.45/25.00 | | | |
% 167.45/25.00 | | | | BETA: splitting (9) gives:
% 167.45/25.00 | | | |
% 167.45/25.00 | | | | Case 1:
% 167.45/25.00 | | | | |
% 167.45/25.00 | | | | | (826) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2,
% 167.45/25.00 | | | | | e2) = e1)
% 167.45/25.00 | | | | |
% 167.45/25.00 | | | | | BETA: splitting (826) gives:
% 167.45/25.00 | | | | |
% 167.45/25.00 | | | | | Case 1:
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | (827) all_58_2 = e1 & op(e2, e3) = e1
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | ALPHA: (827) implies:
% 167.45/25.00 | | | | | | (828) all_58_2 = e1
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | BETA: splitting (22) gives:
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | Case 1:
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | (829) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 167.45/25.00 | | | | | | | op(e2, e2) = e1)
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | BETA: splitting (829) gives:
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | (830) all_58_1 = e1 & op(e3, e2) = e1
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | REF_CLOSE: (111), (132), (818), (830) are inconsistent by
% 167.45/25.00 | | | | | | | | sub-proof #863.
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | (831) all_58_3 = e1 & op(e2, e2) = e1
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | ALPHA: (831) implies:
% 167.45/25.00 | | | | | | | | (832) all_58_3 = e1
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | REF_CLOSE: (40), (55), (84), (90), (111), (114), (126), (153),
% 167.45/25.00 | | | | | | | | (825), (828), (832) are inconsistent by sub-proof
% 167.45/25.00 | | | | | | | | #106.
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | End of split
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | Case 2:
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | (833) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 167.45/25.00 | | | | | | | op(e0, e2) = e1)
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | BETA: splitting (833) gives:
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | (834) all_58_7 = e1 & op(e1, e2) = e1
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | ALPHA: (834) implies:
% 167.45/25.00 | | | | | | | | (835) op(e1, e2) = e1
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | GROUND_INST: instantiating (111) with all_52_6, e1, e2, e1,
% 167.45/25.00 | | | | | | | | simplifying with (62), (835) gives:
% 167.45/25.00 | | | | | | | | (836) all_52_6 = e1
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | REDUCE: (819), (836) imply:
% 167.45/25.00 | | | | | | | | (837) $false
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | CLOSE: (837) is inconsistent.
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | (838) all_58_13 = e1 & op(e0, e2) = e1
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | REF_CLOSE: (111), (136), (141), (838) are inconsistent by
% 167.45/25.00 | | | | | | | | sub-proof #114.
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | End of split
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | End of split
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | Case 2:
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | (839) all_58_3 = e1 & op(e2, e2) = e1
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | ALPHA: (839) implies:
% 167.45/25.00 | | | | | | (840) all_58_3 = e1
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | GROUND_INST: instantiating (111) with all_52_9, e2, e1, e2,
% 167.45/25.00 | | | | | | simplifying with (2), (825) gives:
% 167.45/25.00 | | | | | | (841) all_52_9 = e2
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | REDUCE: (133), (841) imply:
% 167.45/25.00 | | | | | | (842) ~ (all_52_1 = e2)
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | REDUCE: (104), (841) imply:
% 167.45/25.00 | | | | | | (843) ~ (all_52_8 = e2)
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | REDUCE: (149), (841) imply:
% 167.45/25.00 | | | | | | (844) ~ (all_52_13 = e2)
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | SIMP: (844) implies:
% 167.45/25.00 | | | | | | (845) ~ (all_52_13 = e2)
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | REDUCE: (94), (841) imply:
% 167.45/25.00 | | | | | | (846) ~ (all_6_2 = e2)
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | BETA: splitting (138) gives:
% 167.45/25.00 | | | | | |
% 167.45/25.00 | | | | | | Case 1:
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | (847) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 167.45/25.00 | | | | | | | op(e2, e2) = e2)
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | BETA: splitting (847) gives:
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | (848) all_58_2 = e2 & op(e2, e3) = e2
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | ALPHA: (848) implies:
% 167.45/25.00 | | | | | | | | (849) op(e2, e3) = e2
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | REF_CLOSE: (40), (55), (66), (84), (90), (111), (114), (126),
% 167.45/25.00 | | | | | | | | (153), (825), (840), (849) are inconsistent by
% 167.45/25.00 | | | | | | | | sub-proof #149.
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | (850) all_58_3 = e2 & op(e2, e2) = e2
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | ALPHA: (850) implies:
% 167.45/25.00 | | | | | | | | (851) all_58_3 = e2
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | REF_CLOSE: (129), (840), (851) are inconsistent by sub-proof
% 167.45/25.00 | | | | | | | | #924.
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | End of split
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | Case 2:
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | (852) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 &
% 167.45/25.00 | | | | | | | op(e2, e0) = e2)
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | BETA: splitting (852) gives:
% 167.45/25.00 | | | | | | |
% 167.45/25.00 | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | (853) all_58_5 = e2 & op(e2, e1) = e2
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | ALPHA: (853) implies:
% 167.45/25.00 | | | | | | | | (854) all_58_5 = e2
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | BETA: splitting (80) gives:
% 167.45/25.00 | | | | | | | |
% 167.45/25.00 | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | |
% 167.45/25.00 | | | | | | | | | (855) ~ (all_10_2 = e0)
% 167.45/25.00 | | | | | | | | |
% 167.45/25.00 | | | | | | | | | BETA: splitting (109) gives:
% 167.45/25.00 | | | | | | | | |
% 167.45/25.00 | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | (856) ~ (all_12_2 = e1)
% 167.45/25.00 | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | REDUCE: (72), (856) imply:
% 167.45/25.00 | | | | | | | | | | (857) $false
% 167.45/25.00 | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | CLOSE: (857) is inconsistent.
% 167.45/25.00 | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | (858) ( ~ (all_12_0 = e3) & op(all_12_1, e0) = all_12_0 &
% 167.45/25.00 | | | | | | | | | | op(e1, e0) = all_12_1 & $i(all_12_0) &
% 167.45/25.00 | | | | | | | | | | $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e1, e0)
% 167.45/25.00 | | | | | | | | | | = all_12_1 & $i(all_12_1))
% 167.45/25.00 | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | BETA: splitting (44) gives:
% 167.45/25.00 | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | (859) ~ (all_16_2 = e2)
% 167.45/25.00 | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | REDUCE: (12), (859) imply:
% 167.45/25.00 | | | | | | | | | | | (860) ~ (all_10_2 = e2)
% 167.45/25.00 | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | BETA: splitting (95) gives:
% 167.45/25.00 | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | (861) ~ (all_28_2 = e3)
% 167.45/25.00 | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | REDUCE: (18), (861) imply:
% 167.45/25.00 | | | | | | | | | | | | (862) ~ (all_6_2 = e3)
% 167.45/25.00 | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | BETA: splitting (63) gives:
% 167.45/25.00 | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | (863) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 167.45/25.00 | | | | | | | | | | | | | & op(e2, e1) = e3)
% 167.45/25.00 | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | BETA: splitting (863) gives:
% 167.45/25.00 | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | (864) all_58_4 = e3 & op(e3, e1) = e3
% 167.45/25.00 | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | ALPHA: (864) implies:
% 167.45/25.00 | | | | | | | | | | | | | | (865) all_58_4 = e3
% 167.45/25.00 | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 167.45/25.00 | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | (866) all_54_10 = e3
% 167.45/25.00 | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | REF_CLOSE: (30), (862), (866) are inconsistent by sub-proof
% 167.45/25.00 | | | | | | | | | | | | | | | #982.
% 167.45/25.00 | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | (867) ~ (all_54_10 = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | (868) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 167.45/25.00 | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | BETA: splitting (868) gives:
% 167.45/25.00 | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | (869) all_54_10 = e2
% 167.45/25.00 | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (154), (869) are inconsistent by sub-proof
% 167.45/25.00 | | | | | | | | | | | | | | | | #981.
% 167.45/25.00 | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | (870) ~ (all_54_10 = e2)
% 167.45/25.00 | | | | | | | | | | | | | | | | (871) all_54_10 = e1 | all_54_10 = e0
% 167.45/25.00 | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | (872) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 167.45/25.00 | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | BETA: splitting (872) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | (873) all_58_0 = e1 & op(e3, e3) = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | ALPHA: (873) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | (874) all_58_0 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | BETA: splitting (871) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | (875) all_54_10 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (875) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | (876) all_6_2 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | SIMP: (876) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | (877) all_6_2 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | REDUCE: (113), (877) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | (878) ~ (all_52_8 = e1)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | REDUCE: (862), (877) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | (879) ~ (e3 = e1)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | REDUCE: (154), (877) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | (880) ~ (e2 = e1)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | (881) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | BETA: splitting (881) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | (882) all_58_4 = e1 & op(e3, e1) = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (865), (882) are inconsistent by sub-proof
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | #702.
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | (883) all_58_5 = e1 & op(e2, e1) = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | ALPHA: (883) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | (884) all_58_5 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (14), (20), (24), (31), (40), (42),
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | (48), (55), (58), (59), (62), (63), (67), (78),
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | (84), (90), (99), (106), (111), (114), (115),
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | (119), (126), (129), (132), (138), (147), (151),
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | (153), (154), (818), (819), (825), (840), (884)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #17.
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | (885) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | BETA: splitting (885) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | (886) all_58_8 = e1 & op(e1, e1) = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | ALPHA: (886) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | (887) all_58_8 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | (888) all_54_2 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (888) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | (889) all_52_8 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | SIMP: (889) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | (890) all_52_8 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (890) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | (891) ~ (all_52_4 = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (890) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | (892) ~ (all_52_12 = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | SIMP: (892) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | (893) ~ (all_52_12 = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (890) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | (894) ~ (all_10_2 = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | SIMP: (894) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | (895) ~ (all_10_2 = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | (896) all_54_0 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (896) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | (897) all_10_2 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (897) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | (898) all_10_2 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (895), (898) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | (899) $false
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (899) is inconsistent.
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | (900) ~ (all_54_0 = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | (901) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (901) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | (902) all_54_0 = e2
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (860), (902) are inconsistent by sub-proof
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | #959.
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | (903) ~ (all_54_0 = e2)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | (904) all_54_0 = e1 | all_54_0 = e0
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (904) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | (905) all_54_0 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (905) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | (906) all_10_2 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (906) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | (907) all_10_2 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (907) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | (908) all_56_10 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (35), (907) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | (909) op(e3, e3) = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (910) ~ (all_56_10 = e1)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (908), (910) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (911) $false
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (911) is inconsistent.
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (912) all_56_4 = e3 & op(e3, e1) = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (912) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (913) all_56_4 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | (914) op(e3, e1) = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (915) ~ (all_48_2 = e1)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (815), (915) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (916) $false
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (916) is inconsistent.
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (917) ( ~ (all_48_0 = e0) & op(all_48_1, e2) = all_48_0
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = all_48_1 & $i(all_48_0) &
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e3) & op(e1, e2)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (918) all_54_12 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (918) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (919) all_52_3 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (919) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (920) all_52_3 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (920) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (921) ~ (all_52_7 = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (921) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (922) ~ (all_52_7 = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (920) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (923) op(e0, e3) = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (924) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (924) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (925) all_58_1 = e3 & op(e3, e2) = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (925) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (926) op(e3, e2) = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (132), (891), (926) are inconsistent by
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #974.
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (927) all_58_3 = e3 & op(e2, e2) = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (927) implies:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (928) all_58_3 = e3
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (840), (928) imply:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) e3 = e1
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (124), (139), (855), (895), (904), (913),
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (929) are inconsistent by sub-proof #15.
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (930) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (930) gives:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (931) all_58_7 = e3 & op(e1, e2) = e3
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (931) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (932) all_58_7 = e3
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (933) op(e1, e2) = e3
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (934) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (934) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (935) all_58_1 = e0 & op(e3, e2) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (935) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (936) op(e3, e2) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (917) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (937) ~ (all_48_0 = e0) & op(all_48_1, e2) = all_48_0 &
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_48_1 & $i(all_48_0) &
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (937) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (938) ~ (all_48_0 = e0)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (939) op(e1, e2) = all_48_1
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (940) op(all_48_1, e2) = all_48_0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (814) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (941) ~ (all_8_0 = e3) & op(all_8_1, e2) = all_8_0 &
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (941) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (942) op(e1, e2) = all_8_1
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943) op(all_8_1, e2) = all_8_0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_8_1, all_48_1, e2,
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (939), (942) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (944) all_48_1 = all_8_1
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with e3, all_48_1, e2, e1,
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (933), (939) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (945) all_48_1 = e3
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (944), (945) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (946) all_8_1 = e3
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (940), (945) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (947) op(e3, e2) = all_48_0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (943), (946) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (948) op(e3, e2) = all_8_0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with e0, all_48_0, e2, e3,
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (936), (947) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (949) all_48_0 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_8_0, all_48_0, e2,
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (947), (948) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (950) all_48_0 = all_8_0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (949), (950) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (951) all_8_0 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (938), (949) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (952) $false
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (952) is inconsistent.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (953) ~ (all_8_1 = e0) & op(e1, e2) = all_8_1 &
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_1)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (953) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (954) op(e1, e2) = all_8_1
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with all_8_1, all_48_1, e2,
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (939), (954) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (955) all_48_1 = all_8_1
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with e3, all_48_1, e2, e1,
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (933), (939) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (956) all_48_1 = e3
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (955), (956) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (957) all_8_1 = e3
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (940), (956) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (958) op(e3, e2) = all_48_0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (111) with e0, all_48_0, e2, e3,
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (936), (958) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (959) all_48_0 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (938), (959) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (960) $false
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (960) is inconsistent.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (961) ~ (all_48_1 = e3) & op(e1, e2) = all_48_1 &
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (961) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (962) ~ (all_48_1 = e3)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (963) op(e1, e2) = all_48_1
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (814) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) ~ (all_8_0 = e3) & op(all_8_1, e2) = all_8_0 &
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (964) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) op(e1, e2) = all_8_1
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (933), (962), (963), (965) are inconsistent
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #14.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) ~ (all_8_1 = e0) & op(e1, e2) = all_8_1 &
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_1)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (966) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) op(e1, e2) = all_8_1
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (933), (962), (963), (967) are inconsistent
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #14.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) all_58_3 = e0 & op(e2, e2) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (88), (93), (111), (116), (128), (840),
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843), (878), (908), (968) are inconsistent by
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #13.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (969) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) all_58_7 = e0 & op(e1, e2) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (932), (970) are inconsistent by sub-proof
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #890.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) all_58_13 = e0 & op(e0, e2) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (971) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) all_58_13 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (973) op(e0, e2) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (974) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (974) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (975) all_58_1 = e2 & op(e3, e2) = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (975) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (976) op(e3, e2) = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (977) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (977) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (978) all_58_0 = e0 & op(e3, e3) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (978) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (979) op(e3, e3) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (111), (909), (979) are inconsistent by
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #907.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (980) all_58_1 = e0 & op(e3, e2) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (980) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (981) op(e3, e2) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (976), (981) are inconsistent by
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #953.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (982) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (982) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (983) all_58_4 = e0 & op(e3, e1) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (88), (111), (983) are inconsistent by
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #178.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (984) all_58_9 = e0 & op(e3, e0) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (984) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (985) op(e3, e0) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (986) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (66), (84), (90), (111), (114), (126),
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (129), (153), (825), (840), (909), (986) are
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #141.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (987) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (987) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (988) all_58_6 = e2 & op(e1, e3) = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (988) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (989) all_58_6 = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (990) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (990) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (991) all_58_0 = e0 & op(e3, e3) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (991) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (992) op(e3, e3) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (111), (909), (992) are inconsistent by
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #907.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (993) all_58_2 = e0 & op(e2, e3) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (993) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994) all_58_2 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (995) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (996) all_58_6 = e0 & op(e1, e3) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (989), (996) are inconsistent by sub-proof
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #712.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (997) all_58_7 = e0 & op(e1, e2) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (932), (997) are inconsistent by sub-proof
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #890.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (998) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (998) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (999) all_58_8 = e0 & op(e1, e1) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (999) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1000) all_58_8 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (887), (1000) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1001) e1 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1001) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1002) e1 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (908), (1002) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1003) all_56_10 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (84), (93), (111), (985), (1003) are
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1004) all_58_11 = e0 & op(e1, e0) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1004) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005) all_58_11 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1006) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1006) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1007) all_58_12 = e2 & op(e0, e3) = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1007) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1008) all_58_12 = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (59), (82), (84), (129), (153), (989),
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (994), (1008) are inconsistent by sub-proof #575.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1009) all_58_13 = e2 & op(e0, e2) = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1009) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1010) op(e0, e2) = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (141), (973), (1010) are
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #631.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1011) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1011) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1012) all_58_14 = e2 & op(e0, e1) = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1012) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013) all_58_14 = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (1013) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1014) e2 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (989), (1014) imply:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1015) all_58_6 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (78), (111), (114), (153), (154), (932),
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1005), (1015) are inconsistent by sub-proof #824.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1016) all_58_15 = e2 & op(e0, e0) = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1016) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1017) op(e0, e0) = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1018) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (111), (141), (923), (973), (1018) are
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #54.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1019) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (99), (111), (129), (1017), (1019) are
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #585.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1020) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1020) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1021) all_58_6 = e0 & op(e1, e3) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (989), (1021) are inconsistent by sub-proof
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #769.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1022) all_58_12 = e0 & op(e0, e3) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1022) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023) all_58_12 = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1024) op(e0, e3) = e0
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1025) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1025) gives:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1026) all_58_12 = e2 & op(e0, e3) = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1026) implies:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1027) all_58_12 = e2
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (40), (55), (59), (82), (84), (111), (114),
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (129), (153), (989), (1027) are inconsistent by
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #574.
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1028) all_58_13 = e2 & op(e0, e2) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1028) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1029) op(e0, e2) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (141), (973), (1029) are
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #631.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1030) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1030) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1031) all_58_14 = e2 & op(e0, e1) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1031) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1032) all_58_14 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (40), (58), (84), (111), (141), (153), (922),
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1023), (1032) are inconsistent by sub-proof #555.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1033) all_58_15 = e2 & op(e0, e0) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1033) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1034) all_58_15 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1035) op(e0, e0) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (46), (55), (58), (84), (111), (129), (141),
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (972), (973), (1023), (1024), (1034),
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1035) are inconsistent by sub-proof #96.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1036) all_58_12 = e2 & op(e0, e3) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1036) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1037) op(e0, e3) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (153), (923), (1037) are inconsistent by
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #38.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1038) all_58_3 = e2 & op(e2, e2) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1038) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1039) all_58_3 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (840), (1039) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1040) e2 = e1
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (14), (20), (24), (31), (40), (42),
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (48), (55), (58), (59), (62), (63), (67), (78),
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (84), (90), (99), (106), (111), (114), (115),
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (119), (126), (129), (132), (138), (147), (151),
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (153), (154), (818), (819), (825), (840), (854),
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1040) are inconsistent by sub-proof #12.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1041) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1041) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1042) all_58_7 = e2 & op(e1, e2) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1042) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1043) all_58_7 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (932), (1043) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1044) e3 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (865), (1044) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1045) all_58_4 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (63), (84), (99), (129), (147), (153),
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854), (1045) are inconsistent by sub-proof #30.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1046) all_58_13 = e2 & op(e0, e2) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1046) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1047) op(e0, e2) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (141), (973), (1047) are
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #631.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1048) all_58_13 = e3 & op(e0, e2) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (141), (922), (1048) are inconsistent by
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #962.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1049) ~ (all_54_12 = e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1050) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (1049) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1051) ~ (all_52_3 = e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1050) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1052) all_54_12 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (1052) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1053) all_52_3 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1053) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1054) all_52_3 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (1054) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1055) ~ (all_52_7 = e2)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1055) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1056) ~ (all_52_7 = e2)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1057) all_54_13 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (1057) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1058) all_52_7 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1058) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1059) all_52_7 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (39), (1059) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1060) ~ (all_52_6 = e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1061) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1061) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1062) all_58_12 = e2 & op(e0, e3) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1062) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063) all_58_12 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064) op(e0, e3) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1065) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1065) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_58_12 = e3 & op(e0, e3) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1066) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) op(e0, e3) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1050) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1051), (1054) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) ~ (e3 = e2)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (153), (1064), (1067) are inconsistent by
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #38.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) all_54_12 = e1 | all_54_12 = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (135), (1069) are inconsistent by
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) all_58_13 = e3 & op(e0, e2) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1070) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) all_58_13 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) op(e0, e2) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) all_54_7 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (1073) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) all_52_13 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1074) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) ~ (all_52_1 = e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1076) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) all_58_2 = e3 & op(e2, e3) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1077) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) op(e2, e3) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (111), (1075), (1078) are inconsistent by
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #989.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) all_58_3 = e3 & op(e2, e2) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1079) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) all_58_3 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (840), (1080) imply:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) e3 = e1
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (124), (139), (855), (895), (904), (913),
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) are inconsistent by sub-proof #15.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1082) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) all_58_5 = e3 & op(e2, e1) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (153), (825), (1083) are inconsistent by
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) all_58_10 = e3 & op(e2, e0) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1084) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) all_58_10 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1086) all_54_4 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (1075), (1086) are inconsistent by sub-proof
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #618.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1087) ~ (all_54_4 = e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1088) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1088) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1089) all_54_4 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (842), (1089) are inconsistent by sub-proof
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #691.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1090) all_54_4 = e1 | all_54_4 = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1091) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1091) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1092) all_58_2 = e0 & op(e2, e3) = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1092) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1093) all_58_2 = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1094) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1094) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1095) all_58_6 = e3 & op(e1, e3) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1095) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1096) op(e1, e3) = e3
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1097) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1097) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1098) all_58_9 = e2 & op(e3, e0) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1098) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1099) all_58_9 = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1100) op(e3, e0) = e2
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1101) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1101) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1102) all_58_0 = e0 & op(e3, e3) = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1102) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1103) op(e3, e3) = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (111), (909), (1103) are inconsistent by
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #907.
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1104) all_58_1 = e0 & op(e3, e2) = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1104) implies:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1105) all_58_1 = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1106) op(e3, e2) = e0
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1107) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1107) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1108) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1108) gives:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1109) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1109) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) op(e2, e3) = e3
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (111), (1075), (1110) are inconsistent by
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #989.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1111) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1112) op(e3, e2) = e2
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (1106), (1112) are inconsistent by
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #953.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1113) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1113) gives:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1114) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1114) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1115) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (908), (913), (1115) are inconsistent by sub-proof
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #795.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1116) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1116) gives:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1117) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1118) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (908), (913), (1118) are inconsistent by sub-proof
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #795.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1119) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1119) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_56_4 = e1
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (124), (139), (855), (895), (904), (1120)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #16.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1121) gives:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1122) gives:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1123) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) all_56_5 = e1
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (824), (1124) imply:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) e2 = e1
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1125) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) e2 = e1
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1099), (1126) imply:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) all_58_9 = e1
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (51), (84), (108), (111), (114), (129),
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (153), (909), (914), (1105), (1106), (1127)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #137.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1128) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) op(e3, e0) = e0
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (1100), (1129) are inconsistent by
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #699.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1130) gives:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1131) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) op(e2, e0) = e0
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (60), (68), (81), (111), (142), (152),
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817), (845), (1090), (1132) are inconsistent by
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #11.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1133) gives:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1134) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (908), (913), (1135) are inconsistent by sub-proof
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #795.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1136) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (55), (92), (111), (141), (153), (1056),
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1064), (1137) are inconsistent by sub-proof #27.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (88), (111), (114), (1100), (1138) are
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #10.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) all_58_10 = e2 & op(e2, e0) = e2
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1139) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) op(e2, e0) = e2
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (152), (845), (1140) are inconsistent by
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #662.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1141) gives:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) all_58_11 = e2 & op(e1, e0) = e2
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1142) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) op(e1, e0) = e2
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1144) gives:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) all_58_6 = e0 & op(e1, e3) = e0
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1145) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) op(e1, e3) = e0
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (111), (1096), (1146) are inconsistent by
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #64.
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) all_58_7 = e0 & op(e1, e2) = e0
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1147) implies:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) op(e1, e2) = e0
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (814) gives:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) ~ (all_8_0 = e3) & op(all_8_1, e2) = all_8_0 &
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1149) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) ~ (all_8_0 = e3)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) op(e1, e2) = all_8_1
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) op(all_8_1, e2) = all_8_0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (917) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) ~ (all_48_0 = e0) & op(all_48_1, e2) = all_48_0 &
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_48_1 & $i(all_48_0) &
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1153) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) op(e1, e2) = all_48_1
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1072), (1148), (1150), (1151), (1152),
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1154) are inconsistent by sub-proof #9.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1155) ~ (all_48_1 = e3) & op(e1, e2) = all_48_1 &
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1155) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) op(e1, e2) = all_48_1
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1072), (1148), (1150), (1151), (1152),
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1156) are inconsistent by sub-proof #9.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1157) ~ (all_8_1 = e0) & op(e1, e2) = all_8_1 &
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_1)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1157) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1158) ~ (all_8_1 = e0)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1159) op(e1, e2) = all_8_1
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (917) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1160) ~ (all_48_0 = e0) & op(all_48_1, e2) = all_48_0 &
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_48_1 & $i(all_48_0) &
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1160) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1161) op(e1, e2) = all_48_1
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1148), (1158), (1159), (1161) are
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #8.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1162) ~ (all_48_1 = e3) & op(e1, e2) = all_48_1 &
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1162) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1163) op(e1, e2) = all_48_1
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1148), (1158), (1159), (1163) are
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #8.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1164) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1164) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1165) all_58_8 = e0 & op(e1, e1) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1165) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1166) all_58_8 = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (887), (1166) imply:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1167) e1 = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (908), (1167) imply:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1168) all_56_10 = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (88), (93), (111), (116), (128), (843),
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878), (1168) are inconsistent by sub-proof #83.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1169) all_58_11 = e0 & op(e1, e0) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1169) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1170) op(e1, e0) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (1143), (1170) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #197.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1171) all_58_15 = e2 & op(e0, e0) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1171) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172) op(e0, e0) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (111), (129), (1172) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #640.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1173) all_58_7 = e3 & op(e1, e2) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1173) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1174) op(e1, e2) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (111), (1060), (1174) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #668.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1175) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1175) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1176) all_58_8 = e3 & op(e1, e1) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (111), (862), (1176) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #961.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1177) all_58_11 = e3 & op(e1, e0) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1177) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1178) all_58_11 = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1179) op(e1, e0) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1180) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1180) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1181) all_58_0 = e3 & op(e3, e3) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1181) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1182) all_58_0 = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (874), (1182) imply:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1183) e3 = e1
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (84), (90), (114), (126), (129),
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (138), (153), (840), (1085), (1093), (1183) are
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #116.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1184) all_58_2 = e3 & op(e2, e3) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1184) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1185) op(e2, e3) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (111), (1075), (1185) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #989.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1186) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1186) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1187) all_58_6 = e3 & op(e1, e3) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1187) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1188) op(e1, e3) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1189) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1189) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1190) all_58_9 = e2 & op(e3, e0) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1190) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1191) op(e3, e0) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1192) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1192) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1193) all_58_0 = e0 & op(e3, e3) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1193) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1194) op(e3, e3) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (111), (909), (1194) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #907.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1195) all_58_1 = e0 & op(e3, e2) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1195) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1196) op(e3, e2) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1197) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1197) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1198) all_58_1 = e2 & op(e3, e2) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1198) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1199) op(e3, e2) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (1196), (1199) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #953.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1200) all_58_3 = e2 & op(e2, e2) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1200) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1201) all_58_3 = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (40), (55), (84), (90), (114), (129), (854),
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085), (1201) are inconsistent by sub-proof #850.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1202) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1202) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1203) all_58_7 = e2 & op(e1, e2) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1203) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1204) op(e1, e2) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1205) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1205) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1206) all_58_6 = e0 & op(e1, e3) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1206) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1207) op(e1, e3) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (111), (1188), (1207) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #64.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1208) all_58_7 = e0 & op(e1, e2) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1208) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1209) op(e1, e2) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (1204), (1209) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #175.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1210) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1210) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1211) all_58_8 = e0 & op(e1, e1) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1211) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1212) all_58_8 = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (887), (1212) imply:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1213) e1 = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1213) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1214) e1 = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (908), (1214) imply:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1215) all_56_10 = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (88), (93), (111), (116), (128), (843),
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878), (1215) are inconsistent by sub-proof #83.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1216) all_58_11 = e0 & op(e1, e0) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1216) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1217) op(e1, e0) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (111), (1179), (1217) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #62.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1218) all_58_13 = e2 & op(e0, e2) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1218) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1219) op(e0, e2) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (141), (1056), (1219) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #695.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1220) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (88), (111), (114), (1191), (1220) are
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #10.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1221) all_58_10 = e2 & op(e2, e0) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1221) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1222) op(e2, e0) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (152), (845), (1222) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #662.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1223) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1223) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1224) all_58_11 = e2 & op(e1, e0) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1224) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1225) all_58_11 = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1178), (1225) imply:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1226) e3 = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (865), (1226) imply:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1227) all_58_4 = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (63), (84), (99), (129), (147), (153),
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854), (1227) are inconsistent by sub-proof #30.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1228) all_58_15 = e2 & op(e0, e0) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1228) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1229) op(e0, e0) = e2
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (111), (129), (1229) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #640.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1230) all_58_12 = e3 & op(e0, e3) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1230) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1231) all_58_12 = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (40), (46), (55), (84), (114), (129),
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (150), (153), (1071), (1231) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #644.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1232) all_58_3 = e0 & op(e2, e2) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (88), (93), (111), (116), (128), (840),
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843), (878), (908), (1232) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #13.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1233) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1233) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1234) all_58_5 = e0 & op(e2, e1) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (825), (1234) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #151.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1235) all_58_10 = e0 & op(e2, e0) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1235) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1236) op(e2, e0) = e0
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (60), (68), (81), (111), (142), (152),
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (817), (845), (1090), (1236) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #11.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1237) ~ (all_54_7 = e3)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (1237) imply:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1238) ~ (all_52_13 = e3)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1239) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1239) gives:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1240) all_58_9 = e3 & op(e3, e0) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (111), (893), (1240) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #86.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1241) all_58_10 = e3 & op(e2, e0) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1241) implies:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1242) op(e2, e0) = e3
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (152), (1238), (1242) are inconsistent by
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #562.
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1243) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1243) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1244) all_58_11 = e3 & op(e1, e0) = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1244) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1245) all_58_11 = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1246) op(e1, e0) = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1247) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1247) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1248) all_58_2 = e3 & op(e2, e3) = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1248) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1249) all_58_2 = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1250) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1250) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1251) all_58_9 = e2 & op(e3, e0) = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1251) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1252) op(e3, e0) = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1253) ~ (all_4_0 = e2) & op(all_4_1, e0) = all_4_0 &
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1253) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1254) ~ (all_4_0 = e2)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1255) op(e1, e0) = all_4_1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1256) op(all_4_1, e0) = all_4_0
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (858) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1257) ~ (all_12_0 = e3) & op(all_12_1, e0) = all_12_0 &
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_12_1 & $i(all_12_0) &
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1257) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1258) op(e1, e0) = all_12_1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1246), (1252), (1254), (1255), (1256),
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1258) are inconsistent by sub-proof #7.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1259) ~ (all_12_1 = e2) & op(e1, e0) = all_12_1 &
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1259) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1260) op(e1, e0) = all_12_1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1246), (1252), (1254), (1255), (1256),
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1260) are inconsistent by sub-proof #7.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1261) ~ (all_4_1 = e3) & op(e1, e0) = all_4_1 &
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_4_1)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1261) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1262) ~ (all_4_1 = e3)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1263) op(e1, e0) = all_4_1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (858) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1264) ~ (all_12_0 = e3) & op(all_12_1, e0) = all_12_0 &
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_12_1 & $i(all_12_0) &
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1264) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1265) op(e1, e0) = all_12_1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1246), (1262), (1263), (1265) are
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #6.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1266) ~ (all_12_1 = e2) & op(e1, e0) = all_12_1 &
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1266) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267) op(e1, e0) = all_12_1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (1246), (1262), (1263), (1267) are
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #6.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1268) all_58_10 = e2 & op(e2, e0) = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1268) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1269) op(e2, e0) = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (152), (845), (1269) are inconsistent by
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #662.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1270) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1271) all_58_11 = e2 & op(e1, e0) = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1271) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1272) all_58_11 = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1245), (1272) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1273) e3 = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1273) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1274) e3 = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1249), (1274) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1275) all_58_2 = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (40), (55), (59), (84), (114), (153), (874),
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1063), (1275) are inconsistent by sub-proof #435.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1276) all_58_15 = e2 & op(e0, e0) = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1276) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277) op(e0, e0) = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (111), (129), (1277) are inconsistent by
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #640.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1278) all_58_3 = e3 & op(e2, e2) = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1278) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1279) all_58_3 = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (840), (1279) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1280) e3 = e1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (124), (139), (855), (895), (904), (913),
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1280) are inconsistent by sub-proof #15.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1281) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1281) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1282) all_58_5 = e3 & op(e2, e1) = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (153), (825), (1282) are inconsistent by
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #150.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1283) all_58_10 = e3 & op(e2, e0) = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1283) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1284) op(e2, e0) = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (152), (1238), (1284) are inconsistent by
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #562.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1285) all_58_15 = e3 & op(e0, e0) = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1285) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1286) all_58_15 = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (1286) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1287) e3 = e1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (124), (139), (855), (895), (904), (913),
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1287) are inconsistent by sub-proof #15.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1288) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1288) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289) all_58_14 = e3 & op(e0, e1) = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (99), (1289) are inconsistent by sub-proof
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #32.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1290) all_58_15 = e3 & op(e0, e0) = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1290) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1291) all_58_15 = e3
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6), (1291) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1292) e3 = e1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (124), (139), (855), (895), (904), (913),
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1292) are inconsistent by sub-proof #15.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1293) all_58_13 = e2 & op(e0, e2) = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1293) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1294) op(e0, e2) = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (141), (1056), (1294) are inconsistent by
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #695.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1295) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (99), (111), (114), (129), (1295) are
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #41.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1296) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (136), (148), (1056), (1296) are
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #5.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1297) all_54_12 = e1 | all_54_12 = e0
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (135), (1297) are inconsistent by
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #736.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | (1298) all_54_0 = e0
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (1298) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | (1299) all_10_2 = e0
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1299) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | (1300) all_10_2 = e0
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (1300) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | (1301) all_56_10 = e0
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (42), (88), (93), (111), (116), (128), (843),
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | | (878), (1301) are inconsistent by sub-proof #83.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | (1302) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (88), (843), (878), (1302) are inconsistent
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #84.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | (1303) all_58_14 = e1 & op(e0, e1) = e1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1303) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | (1304) op(e0, e1) = e1
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (55), (92), (111), (1304) are inconsistent
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | | by sub-proof #28.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | (1305) all_54_10 = e0
% 167.45/25.05 | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (101), (1305) are inconsistent by sub-proof
% 167.45/25.05 | | | | | | | | | | | | | | | | | | | #979.
% 167.45/25.05 | | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | (1306) all_58_1 = e1 & op(e3, e2) = e1
% 167.45/25.05 | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (132), (818), (1306) are inconsistent by
% 167.45/25.05 | | | | | | | | | | | | | | | | | | sub-proof #863.
% 167.45/25.05 | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | (1307) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 167.45/25.05 | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | BETA: splitting (1307) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | (1308) all_58_4 = e1 & op(e3, e1) = e1
% 167.45/25.05 | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (865), (1308) are inconsistent by sub-proof
% 167.45/25.05 | | | | | | | | | | | | | | | | | | #702.
% 167.45/25.05 | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | (1309) all_58_9 = e1 & op(e3, e0) = e1
% 167.45/25.05 | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (42), (111), (1309) are inconsistent by
% 167.45/25.05 | | | | | | | | | | | | | | | | | | sub-proof #43.
% 167.45/25.05 | | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | (1310) all_58_5 = e3 & op(e2, e1) = e3
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | REF_CLOSE: (111), (153), (825), (1310) are inconsistent by
% 167.45/25.05 | | | | | | | | | | | | | | sub-proof #150.
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | (1311) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 167.45/25.05 | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 167.45/25.05 | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | REF_CLOSE: (78), (84), (99), (111), (862), (1311) are
% 167.45/25.05 | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 167.45/25.05 | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | End of split
% 167.45/25.05 | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | (1312) all_28_2 = e3
% 167.45/25.05 | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | COMBINE_EQS: (18), (1312) imply:
% 167.45/25.05 | | | | | | | | | | | | (1313) all_6_2 = e3
% 167.45/25.05 | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | SIMP: (1313) implies:
% 167.45/25.05 | | | | | | | | | | | | (1314) all_6_2 = e3
% 167.45/25.05 | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | COMBINE_EQS: (41), (1314) imply:
% 167.45/25.05 | | | | | | | | | | | | (1315) all_56_14 = e3
% 167.45/25.05 | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | REDUCE: (113), (1314) imply:
% 167.45/25.05 | | | | | | | | | | | | (1316) ~ (all_52_8 = e3)
% 167.45/25.05 | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | BETA: splitting (124) gives:
% 167.45/25.05 | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | (1317) ~ (all_56_10 = e1)
% 167.45/25.05 | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | REDUCE: (25), (1317) imply:
% 167.45/25.05 | | | | | | | | | | | | | (1318) ~ (all_10_2 = e1)
% 167.45/25.05 | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | BETA: splitting (131) gives:
% 167.45/25.05 | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | (1319) ~ (all_56_14 = e3)
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | REDUCE: (1315), (1319) imply:
% 167.45/25.05 | | | | | | | | | | | | | | (1320) $false
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | CLOSE: (1320) is inconsistent.
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | (1321) all_56_2 = e1 & op(e1, e3) = e1
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | ALPHA: (1321) implies:
% 167.45/25.05 | | | | | | | | | | | | | | (1322) all_56_2 = e1
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 167.45/25.05 | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | (1323) all_56_10 = e3
% 167.45/25.05 | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | COMBINE_EQS: (25), (1323) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | (1324) all_10_2 = e3
% 167.45/25.05 | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | REDUCE: (143), (1324) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | (1325) ~ (all_52_1 = e3)
% 167.45/25.05 | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | REDUCE: (102), (1324) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | (1326) ~ (all_52_3 = e3)
% 167.45/25.05 | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 167.45/25.05 | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | (1327) all_54_12 = e3
% 167.45/25.05 | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | REF_CLOSE: (17), (1326), (1327) are inconsistent by sub-proof
% 167.45/25.05 | | | | | | | | | | | | | | | | #738.
% 167.45/25.05 | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | Case 2:
% 167.45/25.05 | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | (1328) ~ (all_54_12 = e3)
% 167.45/25.05 | | | | | | | | | | | | | | | | (1329) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 167.45/25.05 | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | BETA: splitting (1329) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | (1330) all_54_12 = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (1330) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | (1331) all_52_3 = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | REDUCE: (70), (1331) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | (1332) ~ (all_52_7 = e2)
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | SIMP: (1332) implies:
% 167.45/25.05 | | | | | | | | | | | | | | | | | (1333) ~ (all_52_7 = e2)
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | REDUCE: (1326), (1331) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | (1334) ~ (e3 = e2)
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | REDUCE: (47), (1331) imply:
% 167.45/25.05 | | | | | | | | | | | | | | | | | (1335) op(e0, e3) = e2
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.05 | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 167.45/25.05 | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.06 | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (1336) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.45/25.06 | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.45/25.06 | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.45/25.06 | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.45/25.06 | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | BETA: splitting (1336) gives:
% 167.45/25.06 | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (1337) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.45/25.06 | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (111), (1315), (1322), (1325), (1337) are
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #113.
% 167.45/25.06 | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (1338) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 167.45/25.06 | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (1338) gives:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (1339) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | ALPHA: (1339) implies:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (1340) ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (816), (824), (1340) are inconsistent by sub-proof
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | #148.
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (1341) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (816), (824), (1315), (1322), (1341) are
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #112.
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.06 | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | End of split
% 167.45/25.06 | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.06 | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (1342) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.45/25.06 | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.45/25.06 | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.45/25.06 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.45/25.06 | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.45/25.06 | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | BETA: splitting (1342) gives:
% 167.45/25.06 | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (1343) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 167.45/25.06 | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (1343) gives:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (1344) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | ALPHA: (1344) implies:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (1345) all_56_5 = e1
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (824), (1345) imply:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (1346) e2 = e1
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (14), (20), (24), (31), (40), (42),
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (48), (55), (58), (59), (62), (63), (67), (78),
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (84), (90), (99), (106), (111), (114), (115),
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (119), (126), (129), (132), (138), (147), (151),
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (153), (154), (818), (819), (825), (840), (854),
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (1346) are inconsistent by sub-proof #12.
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (1347) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | ALPHA: (1347) implies:
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | (1348) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))
% 167.45/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1315), (1322), (1348) are inconsistent by
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | sub-proof #485.
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | End of split
% 167.75/25.06 | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | Case 2:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | (1349) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 167.75/25.06 | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (1349) gives:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | Case 1:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | (1350) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | ALPHA: (1350) implies:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | (1351) op(e2, e0) = e0
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (1352) all_54_4 = e3
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (1325), (1352) are inconsistent by sub-proof
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | #618.
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (1353) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1353) gives:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | | (1354) all_54_4 = e2
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (81), (842), (1354) are inconsistent by sub-proof
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | | #691.
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | | (1355) all_54_4 = e1 | all_54_4 = e0
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (60), (68), (81), (111), (142), (152),
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | | (817), (845), (1351), (1355) are inconsistent by
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | | sub-proof #11.
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | End of split
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | (1356) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1356) gives:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | Case 1:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (1357) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1357) implies:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (1358) ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (816), (824), (1358) are inconsistent by sub-proof
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | #148.
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (1359) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1359) implies:
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | (1360) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 167.75/25.06 | | | | | | | | | | | | | | | | | | | | | = e1)
% 167.75/25.07 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (55), (92), (111), (141), (153), (1333),
% 167.75/25.07 | | | | | | | | | | | | | | | | | | | | | (1335), (1360) are inconsistent by sub-proof #27.
% 167.75/25.07 | | | | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | Case 2:
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | (1361) all_54_12 = e1 | all_54_12 = e0
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (38), (135), (1361) are inconsistent by
% 167.75/25.07 | | | | | | | | | | | | | | | | | sub-proof #736.
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | Case 2:
% 167.75/25.07 | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | (1362) ~ (all_56_10 = e3)
% 167.75/25.07 | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | REDUCE: (25), (1362) imply:
% 167.75/25.07 | | | | | | | | | | | | | | | (1363) ~ (all_10_2 = e3)
% 167.75/25.07 | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | REF_CLOSE: (137), (139), (855), (860), (1318), (1363) are
% 167.75/25.07 | | | | | | | | | | | | | | | inconsistent by sub-proof #74.
% 167.75/25.07 | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | Case 2:
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | (1364) all_56_4 = e3 & op(e3, e1) = e3
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | ALPHA: (1364) implies:
% 167.75/25.07 | | | | | | | | | | | | | (1365) op(e3, e1) = e3
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | REF_CLOSE: (51), (111), (1316), (1365) are inconsistent by
% 167.75/25.07 | | | | | | | | | | | | | sub-proof #975.
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | Case 2:
% 167.75/25.07 | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | (1366) all_16_2 = e2
% 167.75/25.07 | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | COMBINE_EQS: (12), (1366) imply:
% 167.75/25.07 | | | | | | | | | | | (1367) all_10_2 = e2
% 167.75/25.07 | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | COMBINE_EQS: (25), (1367) imply:
% 167.75/25.07 | | | | | | | | | | | (1368) all_56_10 = e2
% 167.75/25.07 | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | REDUCE: (120), (1367) imply:
% 167.75/25.07 | | | | | | | | | | | (1369) ~ (all_52_12 = e2)
% 167.75/25.07 | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | BETA: splitting (96) gives:
% 167.75/25.07 | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | Case 1:
% 167.75/25.07 | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | (1370) all_56_10 = e3
% 167.75/25.07 | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | REF_CLOSE: (153), (1368), (1370) are inconsistent by
% 167.75/25.07 | | | | | | | | | | | | sub-proof #88.
% 167.75/25.07 | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | Case 2:
% 167.75/25.07 | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | (1371) ~ (all_56_10 = e3)
% 167.75/25.07 | | | | | | | | | | | | (1372) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 167.75/25.07 | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | REDUCE: (1368), (1371) imply:
% 167.75/25.07 | | | | | | | | | | | | (1373) ~ (e3 = e2)
% 167.75/25.07 | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | BETA: splitting (1372) gives:
% 167.75/25.07 | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | Case 1:
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | (1374) all_56_12 = e2
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | COMBINE_EQS: (816), (1374) imply:
% 167.75/25.07 | | | | | | | | | | | | | (1375) e2 = e1
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | COMBINE_EQS: (854), (1375) imply:
% 167.75/25.07 | | | | | | | | | | | | | (1376) all_58_5 = e1
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (14), (20), (24), (31), (40), (42),
% 167.75/25.07 | | | | | | | | | | | | | (48), (55), (58), (59), (62), (63), (67), (78),
% 167.75/25.07 | | | | | | | | | | | | | (84), (90), (99), (106), (111), (114), (115),
% 167.75/25.07 | | | | | | | | | | | | | (119), (126), (129), (132), (138), (147), (151),
% 167.75/25.07 | | | | | | | | | | | | | (153), (154), (818), (819), (825), (840), (1376)
% 167.75/25.07 | | | | | | | | | | | | | are inconsistent by sub-proof #17.
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | Case 2:
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | (1377) ~ (all_56_12 = e2)
% 167.75/25.07 | | | | | | | | | | | | | (1378) all_56_14 = e1 | all_56_15 = e0
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | REDUCE: (816), (1377) imply:
% 167.75/25.07 | | | | | | | | | | | | | (1379) ~ (e2 = e1)
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | BETA: splitting (65) gives:
% 167.75/25.07 | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | Case 1:
% 167.75/25.07 | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | (1380) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 167.75/25.07 | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 167.75/25.07 | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | REF_CLOSE: (42), (111), (152), (845), (1369), (1380) are
% 167.75/25.07 | | | | | | | | | | | | | | inconsistent by sub-proof #661.
% 167.75/25.07 | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | Case 2:
% 167.75/25.07 | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | (1381) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 167.75/25.07 | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 167.75/25.07 | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | BETA: splitting (1381) gives:
% 167.75/25.07 | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | Case 1:
% 167.75/25.07 | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | (1382) all_58_11 = e2 & op(e1, e0) = e2
% 167.75/25.07 | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | ALPHA: (1382) implies:
% 167.75/25.07 | | | | | | | | | | | | | | | (1383) all_58_11 = e2
% 167.75/25.07 | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | BETA: splitting (1378) gives:
% 167.75/25.07 | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | Case 1:
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | (1384) all_56_14 = e1
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (1384) imply:
% 167.75/25.07 | | | | | | | | | | | | | | | | (1385) all_6_2 = e1
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | SIMP: (1385) implies:
% 167.75/25.07 | | | | | | | | | | | | | | | | (1386) all_6_2 = e1
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | REDUCE: (113), (1386) imply:
% 167.75/25.07 | | | | | | | | | | | | | | | | (1387) ~ (all_52_8 = e1)
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | Case 1:
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | (1388) ~ (all_56_10 = e2)
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | REDUCE: (1368), (1388) imply:
% 167.75/25.07 | | | | | | | | | | | | | | | | | (1389) $false
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | CLOSE: (1389) is inconsistent.
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | Case 2:
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | (1390) all_56_1 = e3 & op(e3, e2) = e3
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | ALPHA: (1390) implies:
% 167.75/25.07 | | | | | | | | | | | | | | | | | (1391) op(e3, e2) = e3
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | Case 1:
% 167.75/25.07 | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | | (1392) all_54_2 = e3
% 167.75/25.07 | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (1392) imply:
% 167.75/25.07 | | | | | | | | | | | | | | | | | | (1393) all_52_8 = e3
% 167.75/25.07 | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | | REDUCE: (125), (1393) imply:
% 167.75/25.07 | | | | | | | | | | | | | | | | | | (1394) ~ (all_52_4 = e3)
% 167.75/25.07 | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (132), (1391), (1394) are inconsistent by
% 167.75/25.07 | | | | | | | | | | | | | | | | | | sub-proof #974.
% 167.75/25.07 | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | Case 2:
% 167.75/25.07 | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | | (1395) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 167.75/25.07 | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (88), (843), (1387), (1395) are inconsistent
% 167.75/25.07 | | | | | | | | | | | | | | | | | | by sub-proof #84.
% 167.75/25.07 | | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | End of split
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | Case 2:
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | (1396) all_56_15 = e0
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (1396) imply:
% 167.75/25.07 | | | | | | | | | | | | | | | | (1397) e1 = e0
% 167.75/25.07 | | | | | | | | | | | | | | | |
% 167.75/25.07 | | | | | | | | | | | | | | | | SIMP: (1397) implies:
% 168.09/25.07 | | | | | | | | | | | | | | | | (1398) e1 = e0
% 168.09/25.07 | | | | | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | | | | | | COMBINE_EQS: (816), (1398) imply:
% 168.09/25.07 | | | | | | | | | | | | | | | | (1399) all_56_12 = e0
% 168.09/25.07 | | | | | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (40), (55), (61), (84), (111), (114), (144),
% 168.09/25.07 | | | | | | | | | | | | | | | | (150), (152), (153), (1383), (1399) are
% 168.09/25.07 | | | | | | | | | | | | | | | | inconsistent by sub-proof #538.
% 168.09/25.07 | | | | | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | | | | | End of split
% 168.09/25.07 | | | | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | | | | Case 2:
% 168.09/25.07 | | | | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | | | | | (1400) all_58_15 = e2 & op(e0, e0) = e2
% 168.09/25.07 | | | | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | | | | | ALPHA: (1400) implies:
% 168.09/25.07 | | | | | | | | | | | | | | | (1401) op(e0, e0) = e2
% 168.09/25.07 | | | | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | | | | | REF_CLOSE: (24), (111), (129), (1401) are inconsistent by
% 168.09/25.07 | | | | | | | | | | | | | | | sub-proof #640.
% 168.09/25.07 | | | | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | | | | End of split
% 168.09/25.07 | | | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | | | End of split
% 168.09/25.07 | | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | | End of split
% 168.09/25.07 | | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | | End of split
% 168.09/25.07 | | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | | End of split
% 168.09/25.07 | | | | | | | | | |
% 168.09/25.07 | | | | | | | | | End of split
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | Case 2:
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | (1402) all_10_2 = e0
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | COMBINE_EQS: (25), (1402) imply:
% 168.09/25.07 | | | | | | | | | (1403) all_56_10 = e0
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | REDUCE: (143), (1402) imply:
% 168.09/25.07 | | | | | | | | | (1404) ~ (all_52_1 = e0)
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | REF_CLOSE: (5), (36), (41), (42), (60), (68), (81), (83),
% 168.09/25.07 | | | | | | | | | (88), (93), (96), (105), (111), (113), (116),
% 168.09/25.07 | | | | | | | | | (117), (128), (129), (142), (816), (817), (842),
% 168.09/25.07 | | | | | | | | | (843), (845), (1403), (1404) are inconsistent by
% 168.09/25.07 | | | | | | | | | sub-proof #81.
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | End of split
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | Case 2:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1405) all_58_10 = e2 & op(e2, e0) = e2
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | ALPHA: (1405) implies:
% 168.09/25.07 | | | | | | | | (1406) op(e2, e0) = e2
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | REF_CLOSE: (111), (152), (845), (1406) are inconsistent by
% 168.09/25.07 | | | | | | | | sub-proof #662.
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | End of split
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | End of split
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | End of split
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | Case 2:
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | (1407) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2,
% 168.09/25.07 | | | | | e0) = e1)
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | BETA: splitting (1407) gives:
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | Case 1:
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | (1408) all_58_5 = e1 & op(e2, e1) = e1
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | ALPHA: (1408) implies:
% 168.09/25.07 | | | | | | (1409) all_58_5 = e1
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | BETA: splitting (22) gives:
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | Case 1:
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | (1410) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 168.09/25.07 | | | | | | | op(e2, e2) = e1)
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | BETA: splitting (1410) gives:
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | Case 1:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1411) all_58_1 = e1 & op(e3, e2) = e1
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | REF_CLOSE: (111), (132), (818), (1411) are inconsistent by
% 168.09/25.07 | | | | | | | | sub-proof #863.
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | Case 2:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1412) all_58_3 = e1 & op(e2, e2) = e1
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | ALPHA: (1412) implies:
% 168.09/25.07 | | | | | | | | (1413) all_58_3 = e1
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | REF_CLOSE: (1), (4), (6), (14), (20), (24), (31), (40), (42),
% 168.09/25.07 | | | | | | | | (48), (55), (58), (59), (62), (63), (67), (78), (84),
% 168.09/25.07 | | | | | | | | (90), (99), (106), (111), (114), (115), (119), (126),
% 168.09/25.07 | | | | | | | | (129), (132), (138), (147), (151), (153), (154),
% 168.09/25.07 | | | | | | | | (818), (819), (825), (1409), (1413) are inconsistent
% 168.09/25.07 | | | | | | | | by sub-proof #17.
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | End of split
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | Case 2:
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | (1414) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 168.09/25.07 | | | | | | | op(e0, e2) = e1)
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | BETA: splitting (1414) gives:
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | Case 1:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1415) all_58_7 = e1 & op(e1, e2) = e1
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | REF_CLOSE: (62), (111), (819), (1415) are inconsistent by
% 168.09/25.07 | | | | | | | | sub-proof #80.
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | Case 2:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1416) all_58_13 = e1 & op(e0, e2) = e1
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | REF_CLOSE: (111), (136), (141), (1416) are inconsistent by
% 168.09/25.07 | | | | | | | | sub-proof #114.
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | End of split
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | End of split
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | Case 2:
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | (1417) all_58_10 = e1 & op(e2, e0) = e1
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | ALPHA: (1417) implies:
% 168.09/25.07 | | | | | | (1418) all_58_10 = e1
% 168.09/25.07 | | | | | | (1419) op(e2, e0) = e1
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | BETA: splitting (22) gives:
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | Case 1:
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | (1420) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 168.09/25.07 | | | | | | | op(e2, e2) = e1)
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | BETA: splitting (1420) gives:
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | Case 1:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1421) all_58_1 = e1 & op(e3, e2) = e1
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | REF_CLOSE: (111), (132), (818), (1421) are inconsistent by
% 168.09/25.07 | | | | | | | | sub-proof #863.
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | Case 2:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1422) all_58_3 = e1 & op(e2, e2) = e1
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | ALPHA: (1422) implies:
% 168.09/25.07 | | | | | | | | (1423) all_58_3 = e1
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | REF_CLOSE: (40), (55), (84), (90), (111), (114), (126), (129),
% 168.09/25.07 | | | | | | | | (138), (153), (825), (1418), (1419), (1423) are
% 168.09/25.07 | | | | | | | | inconsistent by sub-proof #127.
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | End of split
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | Case 2:
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | (1424) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 168.09/25.07 | | | | | | | op(e0, e2) = e1)
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | BETA: splitting (1424) gives:
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | Case 1:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1425) all_58_7 = e1 & op(e1, e2) = e1
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | REF_CLOSE: (62), (111), (819), (1425) are inconsistent by
% 168.09/25.07 | | | | | | | | sub-proof #80.
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | Case 2:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1426) all_58_13 = e1 & op(e0, e2) = e1
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | REF_CLOSE: (111), (136), (141), (1426) are inconsistent by
% 168.09/25.07 | | | | | | | | sub-proof #114.
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | End of split
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | End of split
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | End of split
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | End of split
% 168.09/25.07 | | | |
% 168.09/25.07 | | | End of split
% 168.09/25.07 | | |
% 168.09/25.07 | | End of split
% 168.09/25.07 | |
% 168.09/25.07 | Case 2:
% 168.09/25.07 | |
% 168.09/25.07 | | (1427) all_6_2 = e2
% 168.09/25.07 | |
% 168.09/25.07 | | COMBINE_EQS: (41), (1427) imply:
% 168.09/25.07 | | (1428) all_56_14 = e2
% 168.09/25.07 | |
% 168.09/25.07 | | REDUCE: (69), (1427) imply:
% 168.09/25.07 | | (1429) ~ (all_52_6 = e2)
% 168.09/25.07 | |
% 168.09/25.07 | | REDUCE: (113), (1427) imply:
% 168.09/25.07 | | (1430) ~ (all_52_8 = e2)
% 168.09/25.07 | |
% 168.09/25.07 | | REDUCE: (94), (1427) imply:
% 168.09/25.07 | | (1431) ~ (all_52_9 = e2)
% 168.09/25.07 | |
% 168.09/25.07 | | BETA: splitting (50) gives:
% 168.09/25.07 | |
% 168.09/25.07 | | Case 1:
% 168.09/25.07 | | |
% 168.09/25.07 | | | (1432) ~ (all_56_14 = e2)
% 168.09/25.07 | | |
% 168.09/25.07 | | | REDUCE: (1428), (1432) imply:
% 168.09/25.07 | | | (1433) $false
% 168.09/25.07 | | |
% 168.09/25.07 | | | CLOSE: (1433) is inconsistent.
% 168.09/25.07 | | |
% 168.09/25.07 | | Case 2:
% 168.09/25.07 | | |
% 168.09/25.07 | | | (1434) all_56_3 = e1 & op(e1, e2) = e1
% 168.09/25.07 | | |
% 168.09/25.07 | | | ALPHA: (1434) implies:
% 168.09/25.07 | | | (1435) all_56_3 = e1
% 168.09/25.07 | | | (1436) op(e1, e2) = e1
% 168.09/25.07 | | |
% 168.09/25.07 | | | BETA: splitting (151) gives:
% 168.09/25.07 | | |
% 168.09/25.07 | | | Case 1:
% 168.09/25.07 | | | |
% 168.09/25.07 | | | | (1437) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2,
% 168.09/25.07 | | | | e1) = e2)
% 168.09/25.07 | | | |
% 168.09/25.07 | | | | REF_CLOSE: (2), (51), (111), (1430), (1431), (1437) are inconsistent by
% 168.09/25.07 | | | | sub-proof #570.
% 168.09/25.07 | | | |
% 168.09/25.07 | | | Case 2:
% 168.09/25.07 | | | |
% 168.09/25.07 | | | | (1438) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 168.09/25.07 | | | | e1) = e2)
% 168.09/25.07 | | | |
% 168.09/25.07 | | | | BETA: splitting (1438) gives:
% 168.09/25.07 | | | |
% 168.09/25.07 | | | | Case 1:
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | (1439) all_58_8 = e2 & op(e1, e1) = e2
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | ALPHA: (1439) implies:
% 168.09/25.07 | | | | | (1440) all_58_8 = e2
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | GROUND_INST: instantiating (111) with all_52_6, e1, e2, e1,
% 168.09/25.07 | | | | | simplifying with (62), (1436) gives:
% 168.09/25.07 | | | | | (1441) all_52_6 = e1
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | REDUCE: (85), (1441) imply:
% 168.09/25.07 | | | | | (1442) ~ (all_52_4 = e1)
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | REDUCE: (39), (1441) imply:
% 168.09/25.07 | | | | | (1443) ~ (all_52_7 = e1)
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | REDUCE: (7), (1441) imply:
% 168.09/25.07 | | | | | (1444) ~ (all_52_14 = e1)
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | REDUCE: (57), (1441) imply:
% 168.09/25.07 | | | | | (1445) ~ (all_8_2 = e1)
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | SIMP: (1445) implies:
% 168.09/25.07 | | | | | (1446) ~ (all_8_2 = e1)
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | REDUCE: (1429), (1441) imply:
% 168.09/25.07 | | | | | (1447) ~ (e2 = e1)
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | BETA: splitting (119) gives:
% 168.09/25.07 | | | | |
% 168.09/25.07 | | | | | Case 1:
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | (1448) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 168.09/25.07 | | | | | | op(e1, e2) = e1)
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | BETA: splitting (1448) gives:
% 168.09/25.07 | | | | | |
% 168.09/25.07 | | | | | | Case 1:
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | (1449) all_58_6 = e1 & op(e1, e3) = e1
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | ALPHA: (1449) implies:
% 168.09/25.07 | | | | | | | (1450) op(e1, e3) = e1
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | BETA: splitting (22) gives:
% 168.09/25.07 | | | | | | |
% 168.09/25.07 | | | | | | | Case 1:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1451) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 168.09/25.07 | | | | | | | | op(e2, e2) = e1)
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | BETA: splitting (1451) gives:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | Case 1:
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | (1452) all_58_1 = e1 & op(e3, e2) = e1
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | REF_CLOSE: (111), (132), (1442), (1452) are inconsistent by
% 168.09/25.07 | | | | | | | | | sub-proof #863.
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | Case 2:
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | (1453) all_58_3 = e1 & op(e2, e2) = e1
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | REF_CLOSE: (76), (111), (1446), (1453) are inconsistent by
% 168.09/25.07 | | | | | | | | | sub-proof #498.
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | End of split
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | Case 2:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | (1454) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 168.09/25.07 | | | | | | | | op(e0, e2) = e1)
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | BETA: splitting (1454) gives:
% 168.09/25.07 | | | | | | | |
% 168.09/25.07 | | | | | | | | Case 1:
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | (1455) all_58_7 = e1 & op(e1, e2) = e1
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | ALPHA: (1455) implies:
% 168.09/25.07 | | | | | | | | | (1456) all_58_7 = e1
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | REF_CLOSE: (40), (48), (55), (84), (91), (111), (114), (122),
% 168.09/25.07 | | | | | | | | | (153), (1440), (1450), (1456) are inconsistent by
% 168.09/25.07 | | | | | | | | | sub-proof #69.
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | Case 2:
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | (1457) all_58_13 = e1 & op(e0, e2) = e1
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | | REF_CLOSE: (111), (136), (141), (1457) are inconsistent by
% 168.09/25.07 | | | | | | | | | sub-proof #114.
% 168.09/25.07 | | | | | | | | |
% 168.09/25.07 | | | | | | | | End of split
% 168.09/25.07 | | | | | | | |
% 168.09/25.08 | | | | | | | End of split
% 168.09/25.08 | | | | | | |
% 168.09/25.08 | | | | | | Case 2:
% 168.09/25.08 | | | | | | |
% 168.09/25.08 | | | | | | | (1458) all_58_7 = e1 & op(e1, e2) = e1
% 168.09/25.08 | | | | | | |
% 168.09/25.08 | | | | | | | ALPHA: (1458) implies:
% 168.09/25.08 | | | | | | | (1459) all_58_7 = e1
% 168.09/25.08 | | | | | | |
% 168.09/25.08 | | | | | | | BETA: splitting (80) gives:
% 168.09/25.08 | | | | | | |
% 168.09/25.08 | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | |
% 168.09/25.08 | | | | | | | | (1460) ~ (all_10_2 = e0)
% 168.09/25.08 | | | | | | | |
% 168.09/25.08 | | | | | | | | BETA: splitting (52) gives:
% 168.09/25.08 | | | | | | | |
% 168.09/25.08 | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | |
% 168.09/25.08 | | | | | | | | | (1461) ~ (all_14_2 = e3)
% 168.09/25.08 | | | | | | | | |
% 168.09/25.08 | | | | | | | | | REDUCE: (100), (1461) imply:
% 168.09/25.08 | | | | | | | | | (1462) ~ (all_8_2 = e3)
% 168.09/25.08 | | | | | | | | |
% 168.09/25.08 | | | | | | | | | BETA: splitting (44) gives:
% 168.09/25.08 | | | | | | | | |
% 168.09/25.08 | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | (1463) ~ (all_16_2 = e2)
% 168.09/25.08 | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | REDUCE: (12), (1463) imply:
% 168.09/25.08 | | | | | | | | | | (1464) ~ (all_10_2 = e2)
% 168.09/25.08 | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | BETA: splitting (146) gives:
% 168.09/25.08 | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | (1465) ~ (all_30_2 = e0)
% 168.09/25.08 | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | REDUCE: (134), (1465) imply:
% 168.09/25.08 | | | | | | | | | | | (1466) ~ (all_8_2 = e0)
% 168.09/25.08 | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | BETA: splitting (19) gives:
% 168.09/25.08 | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | (1467) all_54_5 = e3
% 168.09/25.08 | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | REF_CLOSE: (127), (1462), (1467) are inconsistent by
% 168.09/25.08 | | | | | | | | | | | | sub-proof #667.
% 168.09/25.08 | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | (1468) ~ (all_54_5 = e3)
% 168.09/25.08 | | | | | | | | | | | | (1469) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 168.09/25.08 | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | BETA: splitting (103) gives:
% 168.09/25.08 | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | (1470) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 168.09/25.08 | | | | | | | | | | | | | & op(e2, e2) = e0)
% 168.09/25.08 | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | BETA: splitting (1470) gives:
% 168.09/25.08 | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | (1471) all_58_1 = e0 & op(e3, e2) = e0
% 168.09/25.08 | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | ALPHA: (1471) implies:
% 168.09/25.08 | | | | | | | | | | | | | | (1472) op(e3, e2) = e0
% 168.09/25.08 | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | BETA: splitting (1469) gives:
% 168.09/25.08 | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | (1473) all_54_5 = e2
% 168.09/25.08 | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | COMBINE_EQS: (127), (1473) imply:
% 168.09/25.08 | | | | | | | | | | | | | | | (1474) all_8_2 = e2
% 168.09/25.08 | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | SIMP: (1474) implies:
% 168.09/25.08 | | | | | | | | | | | | | | | (1475) all_8_2 = e2
% 168.09/25.08 | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | REDUCE: (112), (1475) imply:
% 168.09/25.08 | | | | | | | | | | | | | | | (1476) ~ (all_52_4 = e2)
% 168.09/25.08 | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | REDUCE: (89), (1475) imply:
% 168.09/25.08 | | | | | | | | | | | | | | | (1477) ~ (all_52_7 = e2)
% 168.09/25.08 | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | REDUCE: (1462), (1475) imply:
% 168.09/25.08 | | | | | | | | | | | | | | | (1478) ~ (e3 = e2)
% 168.09/25.08 | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 168.09/25.08 | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | (1479) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 168.09/25.08 | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | BETA: splitting (1479) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | (1480) all_58_0 = e2 & op(e3, e3) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (1464), (1480) are inconsistent by
% 168.09/25.08 | | | | | | | | | | | | | | | | | sub-proof #666.
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | (1481) all_58_1 = e2 & op(e3, e2) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | ALPHA: (1481) implies:
% 168.09/25.08 | | | | | | | | | | | | | | | | | (1482) op(e3, e2) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (1472), (1482) are inconsistent by
% 168.09/25.08 | | | | | | | | | | | | | | | | | sub-proof #953.
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | End of split
% 168.09/25.08 | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | (1483) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 168.09/25.08 | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | BETA: splitting (1483) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | (1484) all_58_4 = e2 & op(e3, e1) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (63), (67), (84), (99), (114), (129),
% 168.09/25.08 | | | | | | | | | | | | | | | | | (147), (153), (1440), (1484) are inconsistent by
% 168.09/25.08 | | | | | | | | | | | | | | | | | sub-proof #4.
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | (1485) all_58_9 = e2 & op(e3, e0) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | ALPHA: (1485) implies:
% 168.09/25.08 | | | | | | | | | | | | | | | | | (1486) op(e3, e0) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | (1487) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 168.09/25.08 | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | BETA: splitting (1487) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | (1488) all_58_0 = e2 & op(e3, e3) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (1464), (1488) are inconsistent by
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | sub-proof #666.
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | (1489) all_58_2 = e2 & op(e2, e3) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (40), (55), (62), (66), (84), (90), (98),
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | (111), (114), (126), (129), (132), (141), (153),
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | (1429), (1476), (1477), (1489) are inconsistent by
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | sub-proof #664.
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.08 | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | (1490) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 168.09/25.08 | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | BETA: splitting (1490) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | (1491) all_58_6 = e2 & op(e1, e3) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | ALPHA: (1491) implies:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | (1492) all_58_6 = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (84), (91), (114), (122), (153),
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | (1440), (1459), (1492) are inconsistent by
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | sub-proof #158.
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | (1493) all_58_12 = e2 & op(e0, e3) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | ALPHA: (1493) implies:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | (1494) op(e0, e3) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (1495) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1495) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (1496) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1496) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (1497) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1497) implies:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (1498) ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1428), (1435), (1498) are inconsistent by
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | sub-proof #65.
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (1499) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1499) implies:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (1500) op(e3, e2) = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (1472), (1500) are inconsistent by
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | sub-proof #953.
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (1501) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1501) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (1502) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1502) implies:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (1503) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (49), (1503) are inconsistent by sub-proof
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | #34.
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (1504) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1504) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | (1505) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1505) implies:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | (1506) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (49), (1506) are inconsistent by sub-proof
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | #34.
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | (1507) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1507) implies:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | (1508) all_56_4 = e1
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | (1509) ~ (all_56_10 = e3)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (25), (1509) imply:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | (1510) ~ (all_10_2 = e3)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | (1511) all_54_0 = e3
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (1511) imply:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | (1512) all_10_2 = e3
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1510), (1512) imply:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | (1513) $false
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1513) is inconsistent.
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | (1514) ~ (all_54_0 = e3)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | (1515) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1515) gives:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1516) all_54_0 = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (139), (1516) imply:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1517) all_10_2 = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (1517) imply:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1518) all_56_10 = e2
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (49), (54), (55), (77), (89), (96),
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | (107), (111), (129), (132), (136), (148), (153),
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1428), (1518) are inconsistent by sub-proof #2.
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | (1519) all_54_0 = e1 | all_54_0 = e0
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (124), (139), (1460), (1508), (1510), (1519)
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #16.
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.08 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (1520) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1520) gives:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (1521) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1521) gives:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (1522) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1522) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (1523) ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1428), (1435), (1523) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | sub-proof #65.
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (1524) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1524) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (1525) op(e3, e0) = e0
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (1486), (1525) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | sub-proof #699.
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (1526) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1526) gives:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (1527) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1527) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (1528) ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1428), (1435), (1528) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | sub-proof #65.
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (1529) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1529) gives:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (1530) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1530) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (1531) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (49), (1531) are inconsistent by sub-proof
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | #34.
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (1532) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1532) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (1533) ~ (all_56_15 = e0)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (1534) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | = e1)
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (55), (92), (111), (141), (153), (1477),
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | | (1494), (1534) are inconsistent by sub-proof #27.
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | (1535) all_54_5 = e1 | all_54_5 = e0
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | REF_CLOSE: (127), (1446), (1466), (1535) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | | sub-proof #735.
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | (1536) all_58_3 = e0 & op(e2, e2) = e0
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | ALPHA: (1536) implies:
% 168.09/25.09 | | | | | | | | | | | | | | (1537) all_58_3 = e0
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | BETA: splitting (1469) gives:
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | (1538) all_54_5 = e2
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | COMBINE_EQS: (127), (1538) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | (1539) all_8_2 = e2
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | SIMP: (1539) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | (1540) all_8_2 = e2
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | REDUCE: (112), (1540) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | (1541) ~ (all_52_4 = e2)
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | REDUCE: (89), (1540) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | (1542) ~ (all_52_7 = e2)
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | REDUCE: (32), (1540) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | (1543) ~ (all_52_13 = e2)
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | REDUCE: (1462), (1540) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | (1544) ~ (e3 = e2)
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | (1545) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2
% 168.09/25.09 | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (40), (55), (62), (66), (84), (90), (98),
% 168.09/25.09 | | | | | | | | | | | | | | | | (111), (114), (126), (129), (132), (141), (153),
% 168.09/25.09 | | | | | | | | | | | | | | | | (1429), (1537), (1541), (1542), (1545) are
% 168.09/25.09 | | | | | | | | | | | | | | | | inconsistent by sub-proof #216.
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | (1546) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 =
% 168.09/25.09 | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | BETA: splitting (1546) gives:
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | (1547) all_58_5 = e2 & op(e2, e1) = e2
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | ALPHA: (1547) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | | | (1548) op(e2, e1) = e2
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (111), (118), (127), (1446), (1466), (1469),
% 168.09/25.09 | | | | | | | | | | | | | | | | | (1548) are inconsistent by sub-proof #467.
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | (1549) all_58_10 = e2 & op(e2, e0) = e2
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | ALPHA: (1549) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | | | (1550) op(e2, e0) = e2
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (152), (1543), (1550) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | | | | sub-proof #662.
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | (1551) all_54_5 = e1 | all_54_5 = e0
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | REF_CLOSE: (127), (1446), (1466), (1551) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | | sub-proof #735.
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | (1552) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 168.09/25.09 | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | BETA: splitting (1552) gives:
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | (1553) all_58_7 = e0 & op(e1, e2) = e0
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | REF_CLOSE: (55), (1459), (1553) are inconsistent by sub-proof
% 168.09/25.09 | | | | | | | | | | | | | | #727.
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | (1554) all_58_13 = e0 & op(e0, e2) = e0
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | ALPHA: (1554) implies:
% 168.09/25.09 | | | | | | | | | | | | | | (1555) all_58_13 = e0
% 168.09/25.09 | | | | | | | | | | | | | | (1556) op(e0, e2) = e0
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | BETA: splitting (1469) gives:
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | (1557) all_54_5 = e2
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | COMBINE_EQS: (127), (1557) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | (1558) all_8_2 = e2
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | SIMP: (1558) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | (1559) all_8_2 = e2
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | REDUCE: (89), (1559) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | (1560) ~ (all_52_7 = e2)
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | (1561) all_54_13 = e3
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (1561) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | | (1562) all_52_7 = e3
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | SIMP: (1562) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | | (1563) all_52_7 = e3
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | REDUCE: (11), (1563) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | | (1564) ~ (all_52_4 = e3)
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | (1565) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 168.09/25.09 | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (111), (132), (1462), (1564), (1565) are
% 168.09/25.09 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #972.
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | (1566) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 168.09/25.09 | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (84), (1459), (1555), (1566) are
% 168.09/25.09 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #60.
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | (1567) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | BETA: splitting (1567) gives:
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | (1568) all_54_13 = e2
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | REF_CLOSE: (148), (1560), (1568) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | | | | sub-proof #970.
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | (1569) all_54_13 = e1 | all_54_13 = e0
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | BETA: splitting (1569) gives:
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | (1570) all_54_13 = e1
% 168.09/25.09 | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (148), (1570) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | (1571) all_52_7 = e1
% 168.09/25.09 | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | SIMP: (1571) implies:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | (1572) all_52_7 = e1
% 168.09/25.09 | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | REDUCE: (141), (1572) imply:
% 168.09/25.09 | | | | | | | | | | | | | | | | | | (1573) op(e0, e2) = e1
% 168.09/25.09 | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (111), (141), (1556), (1573) are
% 168.09/25.09 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #889.
% 168.09/25.09 | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | (1574) all_54_13 = e0
% 168.09/25.09 | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (107), (148), (1574) are inconsistent by sub-proof
% 168.09/25.09 | | | | | | | | | | | | | | | | | | #963.
% 168.09/25.09 | | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | (1575) all_54_5 = e1 | all_54_5 = e0
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | | REF_CLOSE: (127), (1446), (1466), (1575) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | | sub-proof #735.
% 168.09/25.09 | | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | (1576) all_30_2 = e0
% 168.09/25.09 | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | COMBINE_EQS: (134), (1576) imply:
% 168.09/25.09 | | | | | | | | | | | (1577) all_8_2 = e0
% 168.09/25.09 | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | SIMP: (1577) implies:
% 168.09/25.09 | | | | | | | | | | | (1578) all_8_2 = e0
% 168.09/25.09 | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | COMBINE_EQS: (77), (1578) imply:
% 168.09/25.09 | | | | | | | | | | | (1579) all_56_12 = e0
% 168.09/25.09 | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | REDUCE: (112), (1578) imply:
% 168.09/25.09 | | | | | | | | | | | (1580) ~ (all_52_4 = e0)
% 168.09/25.09 | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | REDUCE: (1462), (1578) imply:
% 168.09/25.09 | | | | | | | | | | | (1581) ~ (e3 = e0)
% 168.09/25.09 | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | REDUCE: (1446), (1578) imply:
% 168.09/25.09 | | | | | | | | | | | (1582) ~ (e1 = e0)
% 168.09/25.09 | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | BETA: splitting (61) gives:
% 168.09/25.09 | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | (1583) ~ (all_56_12 = e0)
% 168.09/25.09 | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | REDUCE: (1579), (1583) imply:
% 168.09/25.09 | | | | | | | | | | | | (1584) $false
% 168.09/25.09 | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | CLOSE: (1584) is inconsistent.
% 168.09/25.09 | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | (1585) all_56_11 = e2 & op(e2, e0) = e2
% 168.09/25.09 | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | ALPHA: (1585) implies:
% 168.09/25.09 | | | | | | | | | | | | (1586) op(e2, e0) = e2
% 168.09/25.09 | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | BETA: splitting (37) gives:
% 168.09/25.09 | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | (1587) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 168.09/25.09 | | | | | | | | | | | | | & op(e3, e2) = e0)
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | BETA: splitting (1587) gives:
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | (1588) all_58_0 = e0 & op(e3, e3) = e0
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (1460), (1588) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | sub-proof #103.
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | (1589) all_58_1 = e0 & op(e3, e2) = e0
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | REF_CLOSE: (111), (132), (1580), (1589) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | sub-proof #155.
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | End of split
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | (1590) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 168.09/25.09 | | | | | | | | | | | | | & op(e3, e0) = e0)
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | BETA: splitting (1590) gives:
% 168.09/25.09 | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | Case 1:
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | (1591) all_58_4 = e0 & op(e3, e1) = e0
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | REF_CLOSE: (51), (88), (111), (1591) are inconsistent by
% 168.09/25.09 | | | | | | | | | | | | | | sub-proof #178.
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | Case 2:
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | (1592) all_58_9 = e0 & op(e3, e0) = e0
% 168.09/25.09 | | | | | | | | | | | | | |
% 168.09/25.09 | | | | | | | | | | | | | | ALPHA: (1592) implies:
% 168.09/25.09 | | | | | | | | | | | | | | (1593) op(e3, e0) = e0
% 168.09/25.10 | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 168.09/25.10 | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | (1594) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 168.09/25.10 | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 168.09/25.10 | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | BETA: splitting (1594) gives:
% 168.09/25.10 | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | (1595) all_58_0 = e2 & op(e3, e3) = e2
% 168.09/25.10 | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | REF_CLOSE: (35), (111), (1464), (1595) are inconsistent by
% 168.09/25.10 | | | | | | | | | | | | | | | | sub-proof #666.
% 168.09/25.10 | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | (1596) all_58_1 = e2 & op(e3, e2) = e2
% 168.09/25.10 | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | ALPHA: (1596) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | (1597) all_58_1 = e2
% 168.09/25.10 | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | (1598) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | BETA: splitting (1598) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | (1599) all_58_1 = e3 & op(e3, e2) = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | REF_CLOSE: (153), (1597), (1599) are inconsistent by
% 168.09/25.10 | | | | | | | | | | | | | | | | | | sub-proof #904.
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | (1600) all_58_3 = e3 & op(e2, e2) = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (111), (1462), (1600) are inconsistent by
% 168.09/25.10 | | | | | | | | | | | | | | | | | | sub-proof #973.
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | End of split
% 168.09/25.10 | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | (1601) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | BETA: splitting (1601) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | (1602) all_58_7 = e3 & op(e1, e2) = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | ALPHA: (1602) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | (1603) all_58_7 = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (1459), (1603) are inconsistent by sub-proof
% 168.09/25.10 | | | | | | | | | | | | | | | | | | #821.
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | (1604) all_58_13 = e3 & op(e0, e2) = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | ALPHA: (1604) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | (1605) all_58_13 = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | (1606) all_56_10 = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (25), (1606) imply:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | (1607) all_10_2 = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | SIMP: (1607) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | (1608) all_10_2 = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | REDUCE: (143), (1608) imply:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | (1609) ~ (all_52_1 = e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | REDUCE: (79), (1608) imply:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | (1610) ~ (all_52_4 = e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | REDUCE: (64), (1608) imply:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | (1611) ~ (all_52_8 = e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | (1612) all_54_1 = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (1610), (1612) are inconsistent by sub-proof
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | #956.
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | (1613) ~ (all_54_1 = e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | (1614) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1614) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | (1615) all_54_1 = e2
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (1615) imply:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | (1616) all_52_4 = e2
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | SIMP: (1616) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | (1617) all_52_4 = e2
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (11), (1617) imply:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | (1618) ~ (all_52_7 = e2)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | SIMP: (1618) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | (1619) ~ (all_52_7 = e2)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | REDUCE: (1610), (1617) imply:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | (1620) ~ (e3 = e2)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | (1621) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1621) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | (1622) all_58_12 = e2 & op(e0, e3) = e2
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1622) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | (1623) op(e0, e3) = e2
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | (1624) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1624) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | (1625) all_58_4 = e3 & op(e3, e1) = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1625) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | (1626) op(e3, e1) = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (111), (1611), (1626) are inconsistent by
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #975.
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | (1627) all_58_5 = e3 & op(e2, e1) = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1627) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | (1628) op(e2, e1) = e3
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (1629) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1629) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1630) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (66), (111), (1606), (1609), (1630) are
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #988.
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1631) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1632) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1632) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1633) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (49), (1633) are inconsistent by sub-proof
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #34.
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1634) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1634) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1635) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1635) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1636) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (49), (1636) are inconsistent by sub-proof
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #34.
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1637) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1637) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1638) ~ (all_56_10 = e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1606), (1638) imply:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1639) $false
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1639) is inconsistent.
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (1640) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1640) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1641) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (111), (1606), (1628), (1641) are
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #685.
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1642) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1642) gives:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1643) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1643) implies:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1644) op(e2, e0) = e0
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (152), (1586), (1644) are
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #684.
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1645) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 168.09/25.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (28), (49), (55), (92), (111), (141), (153),
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1619), (1623), (1645) are inconsistent by
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #26.
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | (1646) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1646) gives:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1647) all_58_8 = e3 & op(e1, e1) = e3
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1647) implies:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1648) all_58_8 = e3
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1440), (1648) imply:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1649) e3 = e2
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1606), (1649) imply:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1650) all_56_10 = e2
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (49), (54), (55), (77), (89), (96),
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | (107), (111), (129), (132), (136), (148), (153),
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1428), (1650) are inconsistent by sub-proof #2.
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1651) all_58_14 = e3 & op(e0, e1) = e3
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1651) implies:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1652) all_58_14 = e3
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (1652) imply:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1653) e3 = e0
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1605), (1653) imply:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | (1654) all_58_13 = e0
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | (1655) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (111), (132), (1462), (1610), (1655) are
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #972.
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (40), (84), (1459), (1601), (1654) are
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #60.
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | (1656) all_58_13 = e2 & op(e0, e2) = e2
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1656) implies:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | (1657) op(e0, e2) = e2
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (111), (141), (1619), (1657) are inconsistent by
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #695.
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | (1658) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (99), (111), (114), (129), (1658) are
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #22.
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | (1659) all_54_1 = e1 | all_54_1 = e0
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (71), (1442), (1580), (1659) are inconsistent by
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | | sub-proof #596.
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | (1660) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.09/25.11 | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (1660) gives:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | (1661) all_56_12 = e2
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1579), (1661) imply:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | (1662) e2 = e0
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | REDUCE: (114), (1662) imply:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | (1663) $false
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | CLOSE: (1663) is inconsistent.
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | (1664) all_56_14 = e1 | all_56_15 = e0
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (55), (129), (1428), (1664) are inconsistent
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | | by sub-proof #3.
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | (1665) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 168.09/25.11 | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | BETA: splitting (1665) gives:
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | (1666) all_58_4 = e2 & op(e3, e1) = e2
% 168.09/25.11 | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | REF_CLOSE: (40), (55), (63), (67), (84), (99), (114), (129),
% 168.09/25.11 | | | | | | | | | | | | | | | | (147), (153), (1440), (1666) are inconsistent by
% 168.09/25.11 | | | | | | | | | | | | | | | | sub-proof #4.
% 168.09/25.11 | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | (1667) all_58_9 = e2 & op(e3, e0) = e2
% 168.09/25.11 | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | ALPHA: (1667) implies:
% 168.09/25.11 | | | | | | | | | | | | | | | | (1668) op(e3, e0) = e2
% 168.09/25.11 | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | | REF_CLOSE: (111), (114), (1593), (1668) are inconsistent by
% 168.09/25.11 | | | | | | | | | | | | | | | | sub-proof #699.
% 168.09/25.11 | | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | (1669) all_16_2 = e2
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | COMBINE_EQS: (12), (1669) imply:
% 168.09/25.11 | | | | | | | | | | (1670) all_10_2 = e2
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | SIMP: (1670) implies:
% 168.09/25.11 | | | | | | | | | | (1671) all_10_2 = e2
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | COMBINE_EQS: (25), (1671) imply:
% 168.09/25.11 | | | | | | | | | | (1672) all_56_10 = e2
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | REF_CLOSE: (11), (16), (49), (54), (55), (77), (89), (96),
% 168.09/25.11 | | | | | | | | | | (107), (111), (129), (132), (136), (148), (153),
% 168.09/25.11 | | | | | | | | | | (1428), (1672) are inconsistent by sub-proof #2.
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | (1673) all_14_2 = e3
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | COMBINE_EQS: (100), (1673) imply:
% 168.09/25.11 | | | | | | | | | (1674) all_8_2 = e3
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | SIMP: (1674) implies:
% 168.09/25.11 | | | | | | | | | (1675) all_8_2 = e3
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | COMBINE_EQS: (77), (1675) imply:
% 168.09/25.11 | | | | | | | | | (1676) all_56_12 = e3
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | REDUCE: (118), (1675) imply:
% 168.09/25.11 | | | | | | | | | (1677) ~ (all_52_9 = e3)
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | BETA: splitting (75) gives:
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | (1678) all_54_6 = e3
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | REF_CLOSE: (21), (1677), (1678) are inconsistent by sub-proof
% 168.09/25.11 | | | | | | | | | | #681.
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | (1679) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | BETA: splitting (1679) gives:
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | (1680) all_54_6 = e2
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | REF_CLOSE: (21), (1431), (1680) are inconsistent by sub-proof
% 168.09/25.11 | | | | | | | | | | | #680.
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | (1681) ~ (all_54_6 = e2)
% 168.09/25.11 | | | | | | | | | | | (1682) all_54_6 = e1 | all_54_6 = e0
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | BETA: splitting (1682) gives:
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | (1683) all_54_6 = e1
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | COMBINE_EQS: (21), (1683) imply:
% 168.09/25.11 | | | | | | | | | | | | (1684) all_52_9 = e1
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | SIMP: (1684) implies:
% 168.09/25.11 | | | | | | | | | | | | (1685) all_52_9 = e1
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | REDUCE: (104), (1685) imply:
% 168.09/25.11 | | | | | | | | | | | | (1686) ~ (all_52_8 = e1)
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | BETA: splitting (116) gives:
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | (1687) all_54_2 = e3
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | COMBINE_EQS: (5), (1687) imply:
% 168.09/25.11 | | | | | | | | | | | | | (1688) all_52_8 = e3
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | REDUCE: (64), (1688) imply:
% 168.09/25.11 | | | | | | | | | | | | | (1689) ~ (all_10_2 = e3)
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | SIMP: (1689) implies:
% 168.09/25.11 | | | | | | | | | | | | | (1690) ~ (all_10_2 = e3)
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | BETA: splitting (96) gives:
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | (1691) all_56_10 = e3
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | COMBINE_EQS: (25), (1691) imply:
% 168.09/25.11 | | | | | | | | | | | | | | (1692) all_10_2 = e3
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | SIMP: (1692) implies:
% 168.09/25.11 | | | | | | | | | | | | | | (1693) all_10_2 = e3
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | REDUCE: (1690), (1693) imply:
% 168.09/25.11 | | | | | | | | | | | | | | (1694) $false
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | CLOSE: (1694) is inconsistent.
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | (1695) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | BETA: splitting (1695) gives:
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | (1696) all_56_12 = e2
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | COMBINE_EQS: (1676), (1696) imply:
% 168.09/25.11 | | | | | | | | | | | | | | | (1697) e3 = e2
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | SIMP: (1697) implies:
% 168.09/25.11 | | | | | | | | | | | | | | | (1698) e3 = e2
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | REDUCE: (153), (1698) imply:
% 168.09/25.11 | | | | | | | | | | | | | | | (1699) $false
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | CLOSE: (1699) is inconsistent.
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | (1700) all_56_14 = e1 | all_56_15 = e0
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | | REF_CLOSE: (49), (55), (129), (1428), (1700) are inconsistent
% 168.09/25.11 | | | | | | | | | | | | | | | by sub-proof #3.
% 168.09/25.11 | | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | (1701) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | | REF_CLOSE: (5), (88), (1430), (1686), (1701) are inconsistent
% 168.09/25.11 | | | | | | | | | | | | | by sub-proof #84.
% 168.09/25.11 | | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | (1702) all_54_6 = e0
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | | REF_CLOSE: (21), (121), (1702) are inconsistent by sub-proof
% 168.09/25.11 | | | | | | | | | | | | #673.
% 168.09/25.11 | | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | End of split
% 168.09/25.11 | | | | | | | |
% 168.09/25.11 | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | |
% 168.09/25.11 | | | | | | | | (1703) all_10_2 = e0
% 168.09/25.11 | | | | | | | |
% 168.09/25.11 | | | | | | | | COMBINE_EQS: (25), (1703) imply:
% 168.09/25.11 | | | | | | | | (1704) all_56_10 = e0
% 168.09/25.11 | | | | | | | |
% 168.09/25.11 | | | | | | | | REDUCE: (79), (1703) imply:
% 168.09/25.11 | | | | | | | | (1705) ~ (all_52_4 = e0)
% 168.09/25.11 | | | | | | | |
% 168.09/25.11 | | | | | | | | BETA: splitting (96) gives:
% 168.09/25.11 | | | | | | | |
% 168.09/25.11 | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | (1706) all_56_10 = e3
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | REF_CLOSE: (84), (1704), (1706) are inconsistent by sub-proof
% 168.09/25.11 | | | | | | | | | #166.
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | (1707) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | BETA: splitting (1707) gives:
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | (1708) all_56_12 = e2
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | COMBINE_EQS: (77), (1708) imply:
% 168.09/25.11 | | | | | | | | | | (1709) all_8_2 = e2
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | SIMP: (1709) implies:
% 168.09/25.11 | | | | | | | | | | (1710) all_8_2 = e2
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | REDUCE: (112), (1710) imply:
% 168.09/25.11 | | | | | | | | | | (1711) ~ (all_52_4 = e2)
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | BETA: splitting (87) gives:
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | Case 1:
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | (1712) all_54_1 = e3
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | COMBINE_EQS: (71), (1712) imply:
% 168.09/25.11 | | | | | | | | | | | (1713) all_52_4 = e3
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | REDUCE: (110), (1713) imply:
% 168.09/25.11 | | | | | | | | | | | (1714) ~ (all_52_12 = e3)
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | SIMP: (1714) implies:
% 168.09/25.11 | | | | | | | | | | | (1715) ~ (all_52_12 = e3)
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | REF_CLOSE: (42), (93), (111), (1704), (1715) are inconsistent
% 168.09/25.11 | | | | | | | | | | | by sub-proof #145.
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | (1716) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | | REF_CLOSE: (71), (1442), (1705), (1711), (1716) are
% 168.09/25.11 | | | | | | | | | | | inconsistent by sub-proof #595.
% 168.09/25.11 | | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | Case 2:
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | (1717) all_56_14 = e1 | all_56_15 = e0
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | | REF_CLOSE: (49), (55), (129), (1428), (1717) are inconsistent
% 168.09/25.11 | | | | | | | | | | by sub-proof #3.
% 168.09/25.11 | | | | | | | | | |
% 168.09/25.11 | | | | | | | | | End of split
% 168.09/25.11 | | | | | | | | |
% 168.09/25.11 | | | | | | | | End of split
% 168.09/25.11 | | | | | | | |
% 168.09/25.11 | | | | | | | End of split
% 168.09/25.11 | | | | | | |
% 168.09/25.11 | | | | | | End of split
% 168.09/25.11 | | | | | |
% 168.09/25.11 | | | | | Case 2:
% 168.09/25.11 | | | | | |
% 168.09/25.11 | | | | | | (1718) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 168.09/25.11 | | | | | | op(e1, e0) = e1)
% 168.09/25.11 | | | | | |
% 168.09/25.11 | | | | | | BETA: splitting (1718) gives:
% 168.09/25.11 | | | | | |
% 168.09/25.11 | | | | | | Case 1:
% 168.09/25.11 | | | | | | |
% 168.09/25.11 | | | | | | | (1719) all_58_8 = e1 & op(e1, e1) = e1
% 168.09/25.11 | | | | | | |
% 168.09/25.11 | | | | | | | REF_CLOSE: (129), (1440), (1719) are inconsistent by sub-proof
% 168.09/25.11 | | | | | | | #397.
% 168.09/25.11 | | | | | | |
% 168.09/25.11 | | | | | | Case 2:
% 168.09/25.11 | | | | | | |
% 168.09/25.11 | | | | | | | (1720) all_58_11 = e1 & op(e1, e0) = e1
% 168.09/25.11 | | | | | | |
% 168.09/25.11 | | | | | | | REF_CLOSE: (4), (111), (115), (1720) are inconsistent by sub-proof
% 168.09/25.11 | | | | | | | #42.
% 168.09/25.11 | | | | | | |
% 168.09/25.11 | | | | | | End of split
% 168.09/25.11 | | | | | |
% 168.09/25.11 | | | | | End of split
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | Case 2:
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | | (1721) all_58_14 = e2 & op(e0, e1) = e2
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | | REF_CLOSE: (99), (114), (1721) are inconsistent by sub-proof #23.
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | End of split
% 168.09/25.11 | | | |
% 168.09/25.11 | | | End of split
% 168.09/25.11 | | |
% 168.09/25.11 | | End of split
% 168.09/25.11 | |
% 168.09/25.11 | End of split
% 168.09/25.11 |
% 168.09/25.11 End of proof
% 168.09/25.11
% 168.09/25.11 Sub-proof #2 shows that the following formulas are inconsistent:
% 168.09/25.11 ----------------------------------------------------------------
% 168.09/25.11 (1) ~ (all_52_4 = all_52_7)
% 168.09/25.11 (2) all_56_10 = e2
% 168.09/25.11 (3) all_56_14 = e2
% 168.09/25.11 (4) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 168.09/25.11 (5) all_56_15 = e1
% 168.09/25.11 (6) ~ (all_56_10 = e2) | (all_56_1 = e3 & op(e3, e2) = e3)
% 168.09/25.11 (7) ~ (e1 = e0)
% 168.09/25.11 (8) all_56_12 = all_8_2
% 168.09/25.11 (9) ~ (all_52_7 = all_8_2)
% 168.09/25.11 (10) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.09/25.11 (11) ~ (all_52_7 = e0)
% 168.09/25.11 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.09/25.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.09/25.11 (13) ~ (e2 = e1)
% 168.09/25.11 (14) op(e3, e2) = all_52_4
% 168.09/25.11 (15) ~ (all_52_7 = e1)
% 168.09/25.11 (16) all_54_13 = all_52_7
% 168.09/25.11 (17) ~ (e3 = e2)
% 168.09/25.11
% 168.09/25.11 Begin of proof
% 168.09/25.11 |
% 168.09/25.11 | BETA: splitting (10) gives:
% 168.09/25.11 |
% 168.09/25.11 | Case 1:
% 168.09/25.11 | |
% 168.09/25.11 | | (18) all_56_10 = e3
% 168.09/25.11 | |
% 168.09/25.11 | | REF_CLOSE: (2), (17), (18) are inconsistent by sub-proof #88.
% 168.09/25.11 | |
% 168.09/25.11 | Case 2:
% 168.09/25.11 | |
% 168.09/25.11 | | (19) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.09/25.11 | |
% 168.09/25.11 | | BETA: splitting (6) gives:
% 168.09/25.11 | |
% 168.09/25.11 | | Case 1:
% 168.09/25.11 | | |
% 168.09/25.11 | | | (20) ~ (all_56_10 = e2)
% 168.09/25.11 | | |
% 168.09/25.11 | | | REDUCE: (2), (20) imply:
% 168.09/25.11 | | | (21) $false
% 168.09/25.11 | | |
% 168.09/25.11 | | | CLOSE: (21) is inconsistent.
% 168.09/25.11 | | |
% 168.09/25.11 | | Case 2:
% 168.09/25.11 | | |
% 168.09/25.11 | | | (22) all_56_1 = e3 & op(e3, e2) = e3
% 168.09/25.11 | | |
% 168.09/25.11 | | | ALPHA: (22) implies:
% 168.09/25.11 | | | (23) op(e3, e2) = e3
% 168.09/25.11 | | |
% 168.09/25.11 | | | BETA: splitting (19) gives:
% 168.09/25.11 | | |
% 168.09/25.11 | | | Case 1:
% 168.09/25.11 | | | |
% 168.09/25.11 | | | | (24) all_56_12 = e2
% 168.09/25.11 | | | |
% 168.09/25.11 | | | | COMBINE_EQS: (8), (24) imply:
% 168.09/25.11 | | | | (25) all_8_2 = e2
% 168.09/25.11 | | | |
% 168.09/25.11 | | | | REDUCE: (9), (25) imply:
% 168.09/25.11 | | | | (26) ~ (all_52_7 = e2)
% 168.09/25.11 | | | |
% 168.09/25.11 | | | | BETA: splitting (4) gives:
% 168.09/25.11 | | | |
% 168.09/25.11 | | | | Case 1:
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | | (27) all_54_13 = e3
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | | COMBINE_EQS: (16), (27) imply:
% 168.09/25.11 | | | | | (28) all_52_7 = e3
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | | SIMP: (28) implies:
% 168.09/25.11 | | | | | (29) all_52_7 = e3
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | | REDUCE: (1), (29) imply:
% 168.09/25.11 | | | | | (30) ~ (all_52_4 = e3)
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | | REF_CLOSE: (12), (14), (23), (30) are inconsistent by sub-proof #974.
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | Case 2:
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | | (31) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | | REF_CLOSE: (11), (15), (16), (26), (31) are inconsistent by sub-proof
% 168.09/25.11 | | | | | #5.
% 168.09/25.11 | | | | |
% 168.09/25.11 | | | | End of split
% 168.09/25.11 | | | |
% 168.09/25.11 | | | Case 2:
% 168.09/25.11 | | | |
% 168.09/25.11 | | | | (32) all_56_14 = e1 | all_56_15 = e0
% 168.09/25.11 | | | |
% 168.09/25.11 | | | | REF_CLOSE: (3), (5), (7), (13), (32) are inconsistent by sub-proof #3.
% 168.09/25.11 | | | |
% 168.09/25.11 | | | End of split
% 168.09/25.11 | | |
% 168.09/25.11 | | End of split
% 168.09/25.11 | |
% 168.09/25.11 | End of split
% 168.09/25.11 |
% 168.09/25.11 End of proof
% 168.09/25.11
% 168.09/25.11 Sub-proof #3 shows that the following formulas are inconsistent:
% 168.09/25.11 ----------------------------------------------------------------
% 168.09/25.11 (1) all_56_14 = e2
% 168.09/25.11 (2) all_56_15 = e1
% 168.09/25.11 (3) ~ (e1 = e0)
% 168.09/25.11 (4) all_56_14 = e1 | all_56_15 = e0
% 168.09/25.11 (5) ~ (e2 = e1)
% 168.09/25.11
% 168.09/25.11 Begin of proof
% 168.09/25.11 |
% 168.09/25.11 | BETA: splitting (4) gives:
% 168.09/25.11 |
% 168.09/25.11 | Case 1:
% 168.09/25.11 | |
% 168.09/25.11 | | (6) all_56_14 = e1
% 168.09/25.11 | |
% 168.09/25.11 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #59.
% 168.09/25.11 | |
% 168.09/25.11 | Case 2:
% 168.09/25.11 | |
% 168.09/25.11 | | (7) all_56_15 = e0
% 168.09/25.11 | |
% 168.09/25.11 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #20.
% 168.09/25.11 | |
% 168.09/25.11 | End of split
% 168.09/25.11 |
% 168.09/25.11 End of proof
% 168.09/25.11
% 168.09/25.11 Sub-proof #4 shows that the following formulas are inconsistent:
% 168.09/25.11 ----------------------------------------------------------------
% 168.09/25.11 (1) ~ (e3 = e1)
% 168.09/25.11 (2) ~ (e1 = e0)
% 168.09/25.12 (3) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 168.09/25.12 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 168.09/25.12 (4) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 168.09/25.12 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 168.09/25.12 (5) ~ (e3 = e0)
% 168.09/25.12 (6) all_58_14 = e0
% 168.09/25.12 (7) all_58_4 = e2 & op(e3, e1) = e2
% 168.09/25.12 (8) all_58_8 = e2
% 168.09/25.12 (9) ~ (e2 = e0)
% 168.09/25.12 (10) ~ (e2 = e1)
% 168.09/25.12 (11) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 168.09/25.12 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 168.09/25.12 (12) ~ (e3 = e2)
% 168.09/25.12
% 168.09/25.12 Begin of proof
% 168.09/25.12 |
% 168.09/25.12 | ALPHA: (7) implies:
% 168.09/25.12 | (13) all_58_4 = e2
% 168.09/25.12 |
% 168.09/25.12 | BETA: splitting (11) gives:
% 168.09/25.12 |
% 168.09/25.12 | Case 1:
% 168.09/25.12 | |
% 168.09/25.12 | | (14) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 168.09/25.12 | | e1)
% 168.09/25.12 | |
% 168.09/25.12 | | BETA: splitting (14) gives:
% 168.09/25.12 | |
% 168.09/25.12 | | Case 1:
% 168.09/25.12 | | |
% 168.09/25.12 | | | (15) all_58_4 = e1 & op(e3, e1) = e1
% 168.09/25.12 | | |
% 168.09/25.12 | | | REF_CLOSE: (10), (13), (15) are inconsistent by sub-proof #943.
% 168.09/25.12 | | |
% 168.09/25.12 | | Case 2:
% 168.09/25.12 | | |
% 168.09/25.12 | | | (16) all_58_5 = e1 & op(e2, e1) = e1
% 168.09/25.12 | | |
% 168.09/25.12 | | | ALPHA: (16) implies:
% 168.09/25.12 | | | (17) all_58_5 = e1
% 168.09/25.12 | | |
% 168.09/25.12 | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (12), (13), (17) are
% 168.09/25.12 | | | inconsistent by sub-proof #270.
% 168.09/25.12 | | |
% 168.09/25.12 | | End of split
% 168.09/25.12 | |
% 168.09/25.12 | Case 2:
% 168.09/25.12 | |
% 168.09/25.12 | | (18) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 168.09/25.12 | | e1)
% 168.09/25.12 | |
% 168.09/25.12 | | BETA: splitting (18) gives:
% 168.09/25.12 | |
% 168.09/25.12 | | Case 1:
% 168.09/25.12 | | |
% 168.09/25.12 | | | (19) all_58_8 = e1 & op(e1, e1) = e1
% 168.09/25.12 | | |
% 168.09/25.12 | | | REF_CLOSE: (8), (10), (19) are inconsistent by sub-proof #397.
% 168.09/25.12 | | |
% 168.09/25.12 | | Case 2:
% 168.09/25.12 | | |
% 168.09/25.12 | | | (20) all_58_14 = e1 & op(e0, e1) = e1
% 168.09/25.12 | | |
% 168.09/25.12 | | | ALPHA: (20) implies:
% 168.09/25.12 | | | (21) all_58_14 = e1
% 168.09/25.12 | | |
% 168.09/25.12 | | | REF_CLOSE: (2), (6), (21) are inconsistent by sub-proof #586.
% 168.09/25.12 | | |
% 168.09/25.12 | | End of split
% 168.09/25.12 | |
% 168.09/25.12 | End of split
% 168.09/25.12 |
% 168.09/25.12 End of proof
% 168.09/25.12
% 168.09/25.12 Sub-proof #5 shows that the following formulas are inconsistent:
% 168.09/25.12 ----------------------------------------------------------------
% 168.09/25.12 (1) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 168.09/25.12 (2) ~ (all_52_7 = e0)
% 168.09/25.12 (3) ~ (all_52_7 = e2)
% 168.09/25.12 (4) ~ (all_52_7 = e1)
% 168.09/25.12 (5) all_54_13 = all_52_7
% 168.09/25.12
% 168.09/25.12 Begin of proof
% 168.09/25.12 |
% 168.09/25.12 | BETA: splitting (1) gives:
% 168.09/25.12 |
% 168.09/25.12 | Case 1:
% 168.09/25.12 | |
% 168.09/25.12 | | (6) all_54_13 = e2
% 168.09/25.12 | |
% 168.09/25.12 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #970.
% 168.09/25.12 | |
% 168.09/25.12 | Case 2:
% 168.09/25.12 | |
% 168.09/25.12 | | (7) all_54_13 = e1 | all_54_13 = e0
% 168.09/25.12 | |
% 168.09/25.12 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #256.
% 168.09/25.12 | |
% 168.09/25.12 | End of split
% 168.09/25.12 |
% 168.09/25.12 End of proof
% 168.09/25.12
% 168.09/25.12 Sub-proof #6 shows that the following formulas are inconsistent:
% 168.09/25.12 ----------------------------------------------------------------
% 168.09/25.12 (1) op(e1, e0) = e3
% 168.09/25.12 (2) op(e1, e0) = all_12_1
% 168.09/25.12 (3) op(e1, e0) = all_4_1
% 168.09/25.12 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.09/25.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.09/25.12 (5) ~ (all_4_1 = e3)
% 168.09/25.12
% 168.09/25.12 Begin of proof
% 168.09/25.12 |
% 168.09/25.12 | GROUND_INST: instantiating (4) with all_4_1, all_12_1, e0, e1, simplifying
% 168.09/25.12 | with (2), (3) gives:
% 168.09/25.12 | (6) all_12_1 = all_4_1
% 168.09/25.12 |
% 168.09/25.12 | GROUND_INST: instantiating (4) with e3, all_12_1, e0, e1, simplifying with
% 168.09/25.12 | (1), (2) gives:
% 168.09/25.12 | (7) all_12_1 = e3
% 168.09/25.12 |
% 168.09/25.12 | COMBINE_EQS: (6), (7) imply:
% 168.09/25.12 | (8) all_4_1 = e3
% 168.09/25.12 |
% 168.09/25.12 | REDUCE: (5), (8) imply:
% 168.09/25.12 | (9) $false
% 168.09/25.12 |
% 168.09/25.12 | CLOSE: (9) is inconsistent.
% 168.09/25.12 |
% 168.09/25.12 End of proof
% 168.09/25.12
% 168.09/25.12 Sub-proof #7 shows that the following formulas are inconsistent:
% 168.09/25.12 ----------------------------------------------------------------
% 168.09/25.12 (1) op(e1, e0) = e3
% 168.09/25.12 (2) op(e1, e0) = all_12_1
% 168.09/25.12 (3) op(e1, e0) = all_4_1
% 168.09/25.12 (4) op(e3, e0) = e2
% 168.09/25.12 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.09/25.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.09/25.12 (6) ~ (all_4_0 = e2)
% 168.09/25.12 (7) op(all_4_1, e0) = all_4_0
% 168.09/25.12
% 168.09/25.12 Begin of proof
% 168.09/25.12 |
% 168.09/25.12 | GROUND_INST: instantiating (5) with all_4_1, all_12_1, e0, e1, simplifying
% 168.09/25.12 | with (2), (3) gives:
% 168.09/25.12 | (8) all_12_1 = all_4_1
% 168.09/25.12 |
% 168.09/25.12 | GROUND_INST: instantiating (5) with e3, all_12_1, e0, e1, simplifying with
% 168.09/25.12 | (1), (2) gives:
% 168.09/25.12 | (9) all_12_1 = e3
% 168.09/25.12 |
% 168.09/25.12 | COMBINE_EQS: (8), (9) imply:
% 168.09/25.12 | (10) all_4_1 = e3
% 168.09/25.12 |
% 168.09/25.12 | REDUCE: (7), (10) imply:
% 168.09/25.12 | (11) op(e3, e0) = all_4_0
% 168.09/25.12 |
% 168.09/25.12 | GROUND_INST: instantiating (5) with e2, all_4_0, e0, e3, simplifying with (4),
% 168.09/25.12 | (11) gives:
% 168.09/25.12 | (12) all_4_0 = e2
% 168.09/25.12 |
% 168.09/25.12 | REDUCE: (6), (12) imply:
% 168.09/25.12 | (13) $false
% 168.09/25.12 |
% 168.09/25.12 | CLOSE: (13) is inconsistent.
% 168.09/25.12 |
% 168.09/25.12 End of proof
% 168.09/25.12
% 168.09/25.12 Sub-proof #8 shows that the following formulas are inconsistent:
% 168.09/25.12 ----------------------------------------------------------------
% 168.09/25.12 (1) op(e1, e2) = all_8_1
% 168.09/25.12 (2) op(e1, e2) = all_48_1
% 168.09/25.12 (3) ~ (all_8_1 = e0)
% 168.09/25.12 (4) op(e1, e2) = e0
% 168.09/25.12 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.09/25.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.09/25.12
% 168.09/25.12 Begin of proof
% 168.09/25.12 |
% 168.09/25.12 | GROUND_INST: instantiating (5) with e0, all_48_1, e2, e1, simplifying with
% 168.09/25.12 | (2), (4) gives:
% 168.09/25.12 | (6) all_48_1 = e0
% 168.09/25.12 |
% 168.09/25.12 | GROUND_INST: instantiating (5) with all_8_1, all_48_1, e2, e1, simplifying
% 168.09/25.12 | with (1), (2) gives:
% 168.09/25.12 | (7) all_48_1 = all_8_1
% 168.09/25.12 |
% 168.09/25.12 | COMBINE_EQS: (6), (7) imply:
% 168.09/25.12 | (8) all_8_1 = e0
% 168.09/25.12 |
% 168.09/25.12 | REDUCE: (3), (8) imply:
% 168.09/25.12 | (9) $false
% 168.09/25.12 |
% 168.09/25.12 | CLOSE: (9) is inconsistent.
% 168.09/25.12 |
% 168.09/25.12 End of proof
% 168.09/25.12
% 168.09/25.12 Sub-proof #9 shows that the following formulas are inconsistent:
% 168.09/25.12 ----------------------------------------------------------------
% 168.09/25.12 (1) op(e1, e2) = all_8_1
% 168.09/25.12 (2) op(e1, e2) = all_48_1
% 168.09/25.12 (3) op(e0, e2) = e3
% 168.09/25.12 (4) op(e1, e2) = e0
% 168.09/25.12 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.09/25.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.09/25.12 (6) ~ (all_8_0 = e3)
% 168.09/25.12 (7) op(all_8_1, e2) = all_8_0
% 168.09/25.12
% 168.09/25.12 Begin of proof
% 168.09/25.12 |
% 168.09/25.12 | GROUND_INST: instantiating (5) with e0, all_48_1, e2, e1, simplifying with
% 168.09/25.12 | (2), (4) gives:
% 168.09/25.12 | (8) all_48_1 = e0
% 168.09/25.12 |
% 168.09/25.12 | GROUND_INST: instantiating (5) with all_8_1, all_48_1, e2, e1, simplifying
% 168.09/25.12 | with (1), (2) gives:
% 168.09/25.12 | (9) all_48_1 = all_8_1
% 168.09/25.12 |
% 168.09/25.12 | COMBINE_EQS: (8), (9) imply:
% 168.09/25.12 | (10) all_8_1 = e0
% 168.09/25.12 |
% 168.09/25.12 | REDUCE: (7), (10) imply:
% 168.09/25.12 | (11) op(e0, e2) = all_8_0
% 168.09/25.12 |
% 168.09/25.12 | GROUND_INST: instantiating (5) with e3, all_8_0, e2, e0, simplifying with (3),
% 168.09/25.12 | (11) gives:
% 168.09/25.12 | (12) all_8_0 = e3
% 168.09/25.12 |
% 168.09/25.12 | REDUCE: (6), (12) imply:
% 168.09/25.12 | (13) $false
% 168.09/25.12 |
% 168.09/25.12 | CLOSE: (13) is inconsistent.
% 168.09/25.12 |
% 168.09/25.12 End of proof
% 168.09/25.12
% 168.09/25.12 Sub-proof #10 shows that the following formulas are inconsistent:
% 168.09/25.12 ----------------------------------------------------------------
% 168.09/25.12 (1) op(e3, e1) = all_52_8
% 168.09/25.12 (2) op(e3, e0) = e2
% 168.09/25.12 (3) ~ (all_52_8 = e0)
% 168.09/25.12 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.09/25.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.09/25.12 (5) ~ (e2 = e0)
% 168.09/25.12 (6) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 168.09/25.12
% 168.09/25.12 Begin of proof
% 168.09/25.12 |
% 168.09/25.12 | BETA: splitting (6) gives:
% 168.09/25.12 |
% 168.09/25.12 | Case 1:
% 168.09/25.12 | |
% 168.09/25.12 | | (7) all_58_4 = e0 & op(e3, e1) = e0
% 168.09/25.12 | |
% 168.09/25.12 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #178.
% 168.09/25.12 | |
% 168.09/25.12 | Case 2:
% 168.09/25.12 | |
% 168.09/25.12 | | (8) all_58_9 = e0 & op(e3, e0) = e0
% 168.09/25.12 | |
% 168.09/25.12 | | ALPHA: (8) implies:
% 168.09/25.12 | | (9) op(e3, e0) = e0
% 168.09/25.12 | |
% 168.09/25.12 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #699.
% 168.09/25.12 | |
% 168.09/25.12 | End of split
% 168.09/25.12 |
% 168.09/25.12 End of proof
% 168.09/25.12
% 168.09/25.12 Sub-proof #11 shows that the following formulas are inconsistent:
% 168.09/25.12 ----------------------------------------------------------------
% 168.09/25.12 (1) ~ (all_52_1 = all_52_13)
% 168.09/25.12 (2) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 168.09/25.12 (3) ~ (all_52_13 = e1)
% 168.09/25.12 (4) op(e2, e0) = e0
% 168.09/25.12 (5) all_54_4 = all_52_1
% 168.09/25.12 (6) ~ (all_52_1 = e1)
% 168.09/25.12 (7) ~ (all_52_13 = e2)
% 168.09/25.12 (8) all_54_4 = e1 | all_54_4 = e0
% 168.09/25.12 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.09/25.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.09/25.12 (10) all_54_7 = all_52_13
% 168.09/25.12 (11) op(e2, e0) = all_52_13
% 168.09/25.12
% 168.09/25.12 Begin of proof
% 168.09/25.12 |
% 168.09/25.12 | BETA: splitting (8) gives:
% 168.09/25.12 |
% 168.09/25.12 | Case 1:
% 168.09/25.12 | |
% 168.09/25.12 | | (12) all_54_4 = e1
% 168.09/25.12 | |
% 168.09/25.12 | | REF_CLOSE: (5), (6), (12) are inconsistent by sub-proof #617.
% 168.09/25.12 | |
% 168.09/25.12 | Case 2:
% 168.09/25.12 | |
% 168.09/25.12 | | (13) all_54_4 = e0
% 168.09/25.12 | |
% 168.09/25.12 | | COMBINE_EQS: (5), (13) imply:
% 168.09/25.12 | | (14) all_52_1 = e0
% 168.09/25.12 | |
% 168.09/25.12 | | SIMP: (14) implies:
% 168.09/25.12 | | (15) all_52_1 = e0
% 168.09/25.12 | |
% 168.09/25.12 | | REDUCE: (1), (15) imply:
% 168.09/25.12 | | (16) ~ (all_52_13 = e0)
% 168.09/25.12 | |
% 168.09/25.12 | | SIMP: (16) implies:
% 168.09/25.12 | | (17) ~ (all_52_13 = e0)
% 168.09/25.12 | |
% 168.09/25.12 | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (11), (17) are inconsistent by
% 168.09/25.12 | | sub-proof #122.
% 168.09/25.12 | |
% 168.09/25.12 | End of split
% 168.09/25.12 |
% 168.09/25.12 End of proof
% 168.09/25.12
% 168.09/25.12 Sub-proof #12 shows that the following formulas are inconsistent:
% 168.09/25.12 ----------------------------------------------------------------
% 168.09/25.12 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 168.09/25.12 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.09/25.12 (2) ~ (all_52_14 = e1)
% 168.09/25.12 (3) all_58_15 = e1
% 168.09/25.12 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 168.09/25.12 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 168.09/25.12 (5) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 168.09/25.12 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 168.09/25.12 (6) op(e0, e0) = e1
% 168.09/25.12 (7) ~ (all_52_12 = e1)
% 168.09/25.12 (8) ~ (e3 = e1)
% 168.09/25.12 (9) op(e3, e0) = all_52_12
% 168.09/25.12 (10) op(e1, e3) = all_52_2
% 168.09/25.12 (11) ~ (e1 = e0)
% 168.09/25.12 (12) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 168.09/25.12 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 168.09/25.12 e3)
% 168.09/25.12 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 168.09/25.12 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 168.09/25.12 (14) op(e1, e2) = all_52_6
% 168.09/25.12 (15) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 168.09/25.12 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 168.09/25.12 (16) all_58_3 = e1
% 168.09/25.12 (17) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 168.09/25.12 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 168.09/25.12 (18) ~ (all_6_2 = e2)
% 168.09/25.12 (19) op(e1, e1) = all_6_2
% 168.09/25.12 (20) ~ (e3 = e0)
% 168.09/25.12 (21) e2 = e1
% 168.09/25.12 (22) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.09/25.12 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.09/25.12 (23) ~ (all_52_6 = e1)
% 168.09/25.12 (24) all_58_14 = e0
% 168.09/25.12 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 168.09/25.12 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 168.09/25.12 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.09/25.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.09/25.12 (27) ~ (e2 = e0)
% 168.09/25.12 (28) op(e1, e0) = all_52_14
% 168.09/25.12 (29) op(e2, e1) = e2
% 168.09/25.13 (30) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 168.09/25.13 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 168.09/25.13 (31) all_58_5 = e2
% 168.09/25.13 (32) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.09/25.13 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.09/25.13 (33) ~ (e2 = e1)
% 168.09/25.13 (34) op(e3, e2) = all_52_4
% 168.09/25.13 (35) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.09/25.13 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 168.09/25.13 (36) ~ (all_52_4 = e1)
% 168.09/25.13 (37) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 168.09/25.13 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 168.09/25.13 (38) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 168.09/25.13 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 168.09/25.13 (39) ~ (e3 = e2)
% 168.09/25.13
% 168.09/25.13 Begin of proof
% 168.09/25.13 |
% 168.09/25.13 | SIMP: (21) implies:
% 168.09/25.13 | (40) e2 = e1
% 168.09/25.13 |
% 168.09/25.13 | COMBINE_EQS: (31), (40) imply:
% 168.09/25.13 | (41) all_58_5 = e1
% 168.09/25.13 |
% 168.09/25.13 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 168.09/25.13 | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 168.09/25.13 | (25), (26), (27), (28), (29), (30), (32), (33), (34), (35), (36),
% 168.09/25.13 | (37), (38), (39), (41) are inconsistent by sub-proof #17.
% 168.09/25.13 |
% 168.09/25.13 End of proof
% 168.09/25.13
% 168.09/25.13 Sub-proof #13 shows that the following formulas are inconsistent:
% 168.09/25.13 ----------------------------------------------------------------
% 168.09/25.13 (1) all_54_2 = all_52_8
% 168.09/25.13 (2) op(e3, e0) = all_52_12
% 168.09/25.13 (3) all_56_10 = e1
% 168.09/25.13 (4) all_58_3 = e0 & op(e2, e2) = e0
% 168.09/25.13 (5) all_58_3 = e1
% 168.09/25.13 (6) ~ (all_52_8 = e0)
% 168.09/25.13 (7) ~ (all_52_8 = e1)
% 168.09/25.13 (8) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 168.09/25.13 (9) ~ (all_52_8 = e2)
% 168.09/25.13 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.09/25.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.09/25.13 (11) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 168.09/25.13 (12) ~ (all_52_8 = all_52_12)
% 168.09/25.13
% 168.09/25.13 Begin of proof
% 168.09/25.13 |
% 168.09/25.13 | ALPHA: (4) implies:
% 168.09/25.13 | (13) all_58_3 = e0
% 168.09/25.13 |
% 168.09/25.13 | COMBINE_EQS: (5), (13) imply:
% 168.09/25.13 | (14) e1 = e0
% 168.09/25.13 |
% 168.09/25.13 | COMBINE_EQS: (3), (14) imply:
% 168.09/25.13 | (15) all_56_10 = e0
% 168.09/25.13 |
% 168.09/25.13 | REF_CLOSE: (1), (2), (6), (7), (8), (9), (10), (11), (12), (15) are
% 168.09/25.13 | inconsistent by sub-proof #83.
% 168.09/25.13 |
% 168.09/25.13 End of proof
% 168.09/25.13
% 168.09/25.13 Sub-proof #14 shows that the following formulas are inconsistent:
% 168.09/25.13 ----------------------------------------------------------------
% 168.09/25.13 (1) op(e1, e2) = all_8_1
% 168.09/25.13 (2) ~ (all_48_1 = e3)
% 168.09/25.13 (3) op(e1, e2) = all_48_1
% 168.09/25.13 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.09/25.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.09/25.13 (5) op(e1, e2) = e3
% 168.09/25.13
% 168.09/25.13 Begin of proof
% 168.09/25.13 |
% 168.09/25.13 | GROUND_INST: instantiating (4) with all_8_1, all_48_1, e2, e1, simplifying
% 168.09/25.13 | with (1), (3) gives:
% 168.09/25.13 | (6) all_48_1 = all_8_1
% 168.09/25.13 |
% 168.09/25.13 | GROUND_INST: instantiating (4) with e3, all_48_1, e2, e1, simplifying with
% 168.09/25.13 | (3), (5) gives:
% 168.09/25.13 | (7) all_48_1 = e3
% 168.09/25.13 |
% 168.09/25.13 | COMBINE_EQS: (6), (7) imply:
% 168.09/25.13 | (8) all_8_1 = e3
% 168.09/25.13 |
% 168.09/25.13 | REDUCE: (2), (7) imply:
% 168.09/25.13 | (9) $false
% 168.09/25.13 |
% 168.09/25.13 | CLOSE: (9) is inconsistent.
% 168.09/25.13 |
% 168.09/25.13 End of proof
% 168.09/25.13
% 168.09/25.13 Sub-proof #15 shows that the following formulas are inconsistent:
% 168.09/25.13 ----------------------------------------------------------------
% 168.09/25.13 (1) all_56_10 = all_10_2
% 168.09/25.13 (2) all_56_4 = e3
% 168.09/25.13 (3) ~ (all_10_2 = e0)
% 168.09/25.13 (4) ~ (all_10_2 = e3)
% 168.09/25.13 (5) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 168.09/25.13 (6) all_54_0 = all_10_2
% 168.09/25.13 (7) e3 = e1
% 168.09/25.13 (8) all_54_0 = e1 | all_54_0 = e0
% 168.09/25.13
% 168.09/25.13 Begin of proof
% 168.09/25.13 |
% 168.09/25.13 | SIMP: (7) implies:
% 168.09/25.13 | (9) e3 = e1
% 168.09/25.13 |
% 168.09/25.13 | COMBINE_EQS: (2), (9) imply:
% 168.09/25.13 | (10) all_56_4 = e1
% 168.09/25.13 |
% 168.09/25.13 | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10) are inconsistent by sub-proof
% 168.09/25.13 | #16.
% 168.09/25.13 |
% 168.09/25.13 End of proof
% 168.09/25.13
% 168.09/25.13 Sub-proof #16 shows that the following formulas are inconsistent:
% 168.09/25.13 ----------------------------------------------------------------
% 168.09/25.13 (1) all_56_10 = all_10_2
% 168.09/25.13 (2) all_56_4 = e1
% 168.09/25.13 (3) ~ (all_10_2 = e0)
% 168.09/25.13 (4) ~ (all_10_2 = e3)
% 168.09/25.13 (5) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 168.09/25.13 (6) all_54_0 = all_10_2
% 168.09/25.13 (7) all_54_0 = e1 | all_54_0 = e0
% 168.09/25.13
% 168.09/25.13 Begin of proof
% 168.09/25.13 |
% 168.09/25.13 | BETA: splitting (7) gives:
% 168.09/25.13 |
% 168.09/25.13 | Case 1:
% 168.09/25.13 | |
% 168.09/25.13 | | (8) all_54_0 = e1
% 168.09/25.13 | |
% 168.09/25.13 | | COMBINE_EQS: (6), (8) imply:
% 168.09/25.13 | | (9) all_10_2 = e1
% 168.09/25.13 | |
% 168.09/25.13 | | COMBINE_EQS: (1), (9) imply:
% 168.09/25.13 | | (10) all_56_10 = e1
% 168.09/25.13 | |
% 168.09/25.13 | | REDUCE: (4), (9) imply:
% 168.09/25.13 | | (11) ~ (e3 = e1)
% 168.09/25.13 | |
% 168.09/25.13 | | SIMP: (11) implies:
% 168.09/25.13 | | (12) ~ (e3 = e1)
% 168.09/25.13 | |
% 168.09/25.13 | | BETA: splitting (5) gives:
% 168.09/25.13 | |
% 168.09/25.13 | | Case 1:
% 168.09/25.13 | | |
% 168.09/25.13 | | | (13) ~ (all_56_10 = e1)
% 168.09/25.13 | | |
% 168.09/25.13 | | | REDUCE: (10), (13) imply:
% 168.09/25.13 | | | (14) $false
% 168.09/25.13 | | |
% 168.09/25.13 | | | CLOSE: (14) is inconsistent.
% 168.09/25.13 | | |
% 168.09/25.13 | | Case 2:
% 168.09/25.13 | | |
% 168.09/25.13 | | | (15) all_56_4 = e3 & op(e3, e1) = e3
% 168.09/25.13 | | |
% 168.09/25.13 | | | ALPHA: (15) implies:
% 168.09/25.13 | | | (16) all_56_4 = e3
% 168.09/25.13 | | |
% 168.09/25.13 | | | COMBINE_EQS: (2), (16) imply:
% 168.09/25.13 | | | (17) e3 = e1
% 168.09/25.13 | | |
% 168.09/25.13 | | | REDUCE: (12), (17) imply:
% 168.09/25.13 | | | (18) $false
% 168.09/25.13 | | |
% 168.09/25.13 | | | CLOSE: (18) is inconsistent.
% 168.09/25.13 | | |
% 168.09/25.13 | | End of split
% 168.09/25.13 | |
% 168.09/25.13 | Case 2:
% 168.09/25.13 | |
% 168.09/25.13 | | (19) all_54_0 = e0
% 168.09/25.13 | |
% 168.09/25.13 | | COMBINE_EQS: (6), (19) imply:
% 168.09/25.13 | | (20) all_10_2 = e0
% 168.09/25.13 | |
% 168.09/25.13 | | REDUCE: (3), (20) imply:
% 168.09/25.13 | | (21) $false
% 168.09/25.13 | |
% 168.09/25.13 | | CLOSE: (21) is inconsistent.
% 168.09/25.13 | |
% 168.09/25.13 | End of split
% 168.09/25.13 |
% 168.09/25.13 End of proof
% 168.09/25.13
% 168.09/25.13 Sub-proof #17 shows that the following formulas are inconsistent:
% 168.09/25.13 ----------------------------------------------------------------
% 168.09/25.13 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 168.09/25.13 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.09/25.13 (2) ~ (all_52_14 = e1)
% 168.09/25.13 (3) all_58_15 = e1
% 168.09/25.13 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 168.09/25.13 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 168.09/25.13 (5) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 168.09/25.13 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 168.09/25.13 (6) op(e0, e0) = e1
% 168.09/25.13 (7) ~ (all_52_12 = e1)
% 168.33/25.13 (8) ~ (e3 = e1)
% 168.33/25.13 (9) op(e3, e0) = all_52_12
% 168.33/25.13 (10) op(e1, e3) = all_52_2
% 168.33/25.13 (11) ~ (e1 = e0)
% 168.33/25.13 (12) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 168.33/25.13 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 168.33/25.13 e3)
% 168.33/25.13 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 168.33/25.13 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 168.33/25.13 (14) op(e1, e2) = all_52_6
% 168.33/25.13 (15) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 168.33/25.13 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 168.33/25.13 (16) all_58_3 = e1
% 168.33/25.13 (17) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 168.33/25.13 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 168.33/25.13 (18) ~ (all_6_2 = e2)
% 168.33/25.13 (19) op(e1, e1) = all_6_2
% 168.33/25.13 (20) ~ (e3 = e0)
% 168.33/25.13 (21) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.33/25.13 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.33/25.13 (22) ~ (all_52_6 = e1)
% 168.33/25.13 (23) all_58_14 = e0
% 168.33/25.13 (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 168.33/25.13 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 168.33/25.13 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.33/25.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.33/25.13 (26) ~ (e2 = e0)
% 168.33/25.13 (27) op(e1, e0) = all_52_14
% 168.33/25.13 (28) op(e2, e1) = e2
% 168.33/25.13 (29) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 168.33/25.13 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 168.33/25.13 (30) all_58_5 = e1
% 168.33/25.13 (31) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.33/25.13 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.33/25.13 (32) ~ (e2 = e1)
% 168.33/25.13 (33) op(e3, e2) = all_52_4
% 168.33/25.13 (34) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.33/25.13 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 168.33/25.13 (35) ~ (all_52_4 = e1)
% 168.33/25.13 (36) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 168.33/25.13 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 168.33/25.13 (37) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 168.33/25.13 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 168.33/25.13 (38) ~ (e3 = e2)
% 168.33/25.13
% 168.33/25.13 Begin of proof
% 168.33/25.13 |
% 168.33/25.13 | BETA: splitting (37) gives:
% 168.33/25.13 |
% 168.33/25.13 | Case 1:
% 168.33/25.13 | |
% 168.33/25.13 | | (39) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 168.33/25.13 | | e2)
% 168.33/25.13 | |
% 168.33/25.13 | | BETA: splitting (39) gives:
% 168.33/25.13 | |
% 168.33/25.13 | | Case 1:
% 168.33/25.13 | | |
% 168.33/25.13 | | | (40) all_58_4 = e2 & op(e3, e1) = e2
% 168.33/25.13 | | |
% 168.33/25.13 | | | ALPHA: (40) implies:
% 168.33/25.13 | | | (41) all_58_4 = e2
% 168.33/25.13 | | | (42) op(e3, e1) = e2
% 168.33/25.13 | | |
% 168.33/25.13 | | | BETA: splitting (15) gives:
% 168.33/25.13 | | |
% 168.33/25.13 | | | Case 1:
% 168.33/25.13 | | | |
% 168.33/25.13 | | | | (43) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 168.33/25.13 | | | | = e3)
% 168.33/25.13 | | | |
% 168.33/25.13 | | | | BETA: splitting (43) gives:
% 168.33/25.13 | | | |
% 168.33/25.13 | | | | Case 1:
% 168.33/25.13 | | | | |
% 168.33/25.13 | | | | | (44) all_58_4 = e3 & op(e3, e1) = e3
% 168.33/25.13 | | | | |
% 168.33/25.13 | | | | | REF_CLOSE: (38), (41), (44) are inconsistent by sub-proof #952.
% 168.33/25.13 | | | | |
% 168.33/25.13 | | | | Case 2:
% 168.33/25.13 | | | | |
% 168.33/25.13 | | | | | (45) all_58_5 = e3 & op(e2, e1) = e3
% 168.33/25.13 | | | | |
% 168.33/25.13 | | | | | REF_CLOSE: (25), (28), (38), (45) are inconsistent by sub-proof #150.
% 168.33/25.13 | | | | |
% 168.33/25.13 | | | | End of split
% 168.33/25.13 | | | |
% 168.33/25.13 | | | Case 2:
% 168.33/25.13 | | | |
% 168.33/25.13 | | | | (46) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 168.33/25.13 | | | | = e3)
% 168.33/25.13 | | | |
% 168.33/25.13 | | | | BETA: splitting (46) gives:
% 168.33/25.13 | | | |
% 168.33/25.13 | | | | Case 1:
% 168.33/25.13 | | | | |
% 168.33/25.13 | | | | | (47) all_58_8 = e3 & op(e1, e1) = e3
% 168.33/25.13 | | | | |
% 168.33/25.13 | | | | | ALPHA: (47) implies:
% 168.33/25.13 | | | | | (48) all_58_8 = e3
% 168.33/25.13 | | | | |
% 168.33/25.13 | | | | | BETA: splitting (29) gives:
% 168.33/25.13 | | | | |
% 168.33/25.13 | | | | | Case 1:
% 168.33/25.13 | | | | | |
% 168.33/25.13 | | | | | | (49) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1,
% 168.33/25.13 | | | | | | e2) = e1)
% 168.33/25.13 | | | | | |
% 168.33/25.13 | | | | | | BETA: splitting (49) gives:
% 168.33/25.13 | | | | | |
% 168.33/25.13 | | | | | | Case 1:
% 168.33/25.13 | | | | | | |
% 168.33/25.13 | | | | | | | (50) all_58_6 = e1 & op(e1, e3) = e1
% 168.33/25.13 | | | | | | |
% 168.33/25.13 | | | | | | | ALPHA: (50) implies:
% 168.33/25.13 | | | | | | | (51) all_58_6 = e1
% 168.33/25.13 | | | | | | | (52) op(e1, e3) = e1
% 168.33/25.13 | | | | | | |
% 168.33/25.13 | | | | | | | BETA: splitting (24) gives:
% 168.33/25.13 | | | | | | |
% 168.33/25.13 | | | | | | | Case 1:
% 168.33/25.13 | | | | | | | |
% 168.33/25.13 | | | | | | | | (53) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 &
% 168.33/25.13 | | | | | | | | op(e3, e2) = e1)
% 168.33/25.13 | | | | | | | |
% 168.33/25.13 | | | | | | | | BETA: splitting (53) gives:
% 168.33/25.13 | | | | | | | |
% 168.33/25.13 | | | | | | | | Case 1:
% 168.33/25.13 | | | | | | | | |
% 168.33/25.13 | | | | | | | | | (54) all_58_0 = e1 & op(e3, e3) = e1
% 168.33/25.13 | | | | | | | | |
% 168.33/25.13 | | | | | | | | | ALPHA: (54) implies:
% 168.33/25.13 | | | | | | | | | (55) all_58_0 = e1
% 168.33/25.13 | | | | | | | | | (56) op(e3, e3) = e1
% 168.33/25.13 | | | | | | | | |
% 168.33/25.13 | | | | | | | | | BETA: splitting (4) gives:
% 168.33/25.13 | | | | | | | | |
% 168.33/25.13 | | | | | | | | | Case 1:
% 168.33/25.13 | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | (57) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 168.33/25.13 | | | | | | | | | | op(e2, e3) = e0)
% 168.33/25.13 | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | BETA: splitting (57) gives:
% 168.33/25.13 | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | Case 1:
% 168.33/25.13 | | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | | (58) all_58_0 = e0 & op(e3, e3) = e0
% 168.33/25.13 | | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | | ALPHA: (58) implies:
% 168.33/25.13 | | | | | | | | | | | (59) op(e3, e3) = e0
% 168.33/25.13 | | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | | REF_CLOSE: (11), (25), (56), (59) are inconsistent by
% 168.33/25.13 | | | | | | | | | | | sub-proof #907.
% 168.33/25.13 | | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | Case 2:
% 168.33/25.13 | | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | | (60) all_58_2 = e0 & op(e2, e3) = e0
% 168.33/25.13 | | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | | ALPHA: (60) implies:
% 168.33/25.13 | | | | | | | | | | | (61) all_58_2 = e0
% 168.33/25.13 | | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | | REF_CLOSE: (5), (8), (10), (11), (13), (16), (20), (21),
% 168.33/25.13 | | | | | | | | | | | (23), (25), (26), (30), (31), (32), (34), (36),
% 168.33/25.13 | | | | | | | | | | | (38), (41), (48), (51), (52), (55), (56), (61) are
% 168.33/25.13 | | | | | | | | | | | inconsistent by sub-proof #18.
% 168.33/25.13 | | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | End of split
% 168.33/25.13 | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | Case 2:
% 168.33/25.13 | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | (62) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0
% 168.33/25.13 | | | | | | | | | | & op(e0, e3) = e0)
% 168.33/25.13 | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | BETA: splitting (62) gives:
% 168.33/25.13 | | | | | | | | | |
% 168.33/25.13 | | | | | | | | | | Case 1:
% 168.33/25.13 | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | (63) all_58_6 = e0 & op(e1, e3) = e0
% 168.33/25.14 | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | ALPHA: (63) implies:
% 168.33/25.14 | | | | | | | | | | | (64) op(e1, e3) = e0
% 168.33/25.14 | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | REF_CLOSE: (10), (11), (25), (52), (64) are inconsistent by
% 168.33/25.14 | | | | | | | | | | | sub-proof #749.
% 168.33/25.14 | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | (65) all_58_12 = e0 & op(e0, e3) = e0
% 168.33/25.14 | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | ALPHA: (65) implies:
% 168.33/25.14 | | | | | | | | | | | (66) all_58_12 = e0
% 168.33/25.14 | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | BETA: splitting (1) gives:
% 168.33/25.14 | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | (67) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 168.33/25.14 | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 168.33/25.14 | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | BETA: splitting (67) gives:
% 168.33/25.14 | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | (68) all_58_12 = e2 & op(e0, e3) = e2
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | REF_CLOSE: (26), (66), (68) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | | | | | | | #807.
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | (69) all_58_13 = e2 & op(e0, e2) = e2
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | ALPHA: (69) implies:
% 168.33/25.14 | | | | | | | | | | | | | (70) all_58_13 = e2
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | BETA: splitting (13) gives:
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | (71) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 168.33/25.14 | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 168.33/25.14 | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 168.33/25.14 | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | (72) all_58_0 = e3 & op(e3, e3) = e3
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | REF_CLOSE: (8), (55), (72) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | | | | | | | | | #905.
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | (73) all_58_2 = e3 & op(e2, e3) = e3
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | ALPHA: (73) implies:
% 168.33/25.14 | | | | | | | | | | | | | | | (74) all_58_2 = e3
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | (75) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 168.33/25.14 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 168.33/25.14 | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 168.33/25.14 | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | (76) all_58_12 = e3 & op(e0, e3) = e3
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | ALPHA: (76) implies:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (77) all_58_12 = e3
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | COMBINE_EQS: (66), (77) imply:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (78) e3 = e0
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | SIMP: (78) implies:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (79) e3 = e0
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (79) imply:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (80) all_58_2 = e0
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (10), (11), (13), (16), (20), (21),
% 168.33/25.14 | | | | | | | | | | | | | | | | | (23), (25), (26), (30), (31), (32), (34), (36),
% 168.33/25.14 | | | | | | | | | | | | | | | | | (38), (41), (48), (51), (52), (55), (56), (80) are
% 168.33/25.14 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #18.
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | (81) all_58_13 = e3 & op(e0, e2) = e3
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | ALPHA: (81) implies:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (82) all_58_13 = e3
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (82) imply:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (83) e3 = e2
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | SIMP: (83) implies:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (84) e3 = e2
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (84) imply:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (85) all_58_2 = e2
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (20), (38), (51), (55), (66), (85) are
% 168.33/25.14 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #456.
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | (86) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 168.33/25.14 | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 168.33/25.14 | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 168.33/25.14 | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | (87) all_58_14 = e3 & op(e0, e1) = e3
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (88) all_58_14 = e3
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (17), (20), (26), (32), (36), (41),
% 168.33/25.14 | | | | | | | | | | | | | | | | | (48), (88) are inconsistent by sub-proof #422.
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | (89) all_58_15 = e3 & op(e0, e0) = e3
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (90) all_58_15 = e3
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (90) imply:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (91) e3 = e1
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (91) imply:
% 168.33/25.14 | | | | | | | | | | | | | | | | | (92) all_58_2 = e1
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (16), (20), (21), (25), (26), (28),
% 168.33/25.14 | | | | | | | | | | | | | | | | | (31), (38), (92) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | | | | | | | | | | | #106.
% 168.33/25.14 | | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | (93) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 168.33/25.14 | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 168.33/25.14 | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 168.33/25.14 | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | (94) all_58_6 = e3 & op(e1, e3) = e3
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 168.33/25.14 | | | | | | | | | | | | | | | (95) op(e1, e3) = e3
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | REF_CLOSE: (8), (10), (25), (52), (95) are inconsistent by
% 168.33/25.14 | | | | | | | | | | | | | | | sub-proof #750.
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | (96) all_58_12 = e3 & op(e0, e3) = e3
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | | REF_CLOSE: (20), (66), (96) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | | | | | | | | | #110.
% 168.33/25.14 | | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | (97) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 168.33/25.14 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 168.33/25.14 | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | BETA: splitting (97) gives:
% 168.33/25.14 | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | (98) all_58_14 = e2 & op(e0, e1) = e2
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | ALPHA: (98) implies:
% 168.33/25.14 | | | | | | | | | | | | | (99) all_58_14 = e2
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | REF_CLOSE: (11), (17), (20), (26), (30), (41), (48), (99) are
% 168.33/25.14 | | | | | | | | | | | | | inconsistent by sub-proof #322.
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | (100) all_58_15 = e2 & op(e0, e0) = e2
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | ALPHA: (100) implies:
% 168.33/25.14 | | | | | | | | | | | | | (101) op(e0, e0) = e2
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | | REF_CLOSE: (6), (25), (32), (101) are inconsistent by
% 168.33/25.14 | | | | | | | | | | | | | sub-proof #640.
% 168.33/25.14 | | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | | |
% 168.33/25.14 | | | | | | | | | End of split
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | (102) all_58_1 = e1 & op(e3, e2) = e1
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | REF_CLOSE: (25), (33), (35), (102) are inconsistent by
% 168.33/25.14 | | | | | | | | | sub-proof #863.
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | End of split
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | | (103) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 &
% 168.33/25.14 | | | | | | | | op(e3, e0) = e1)
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | | BETA: splitting (103) gives:
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | (104) all_58_4 = e1 & op(e3, e1) = e1
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | ALPHA: (104) implies:
% 168.33/25.14 | | | | | | | | | (105) op(e3, e1) = e1
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | REF_CLOSE: (25), (32), (42), (105) are inconsistent by
% 168.33/25.14 | | | | | | | | | sub-proof #212.
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | (106) all_58_9 = e1 & op(e3, e0) = e1
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | REF_CLOSE: (7), (9), (25), (106) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | | | #43.
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | End of split
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | End of split
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | Case 2:
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | (107) all_58_7 = e1 & op(e1, e2) = e1
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | REF_CLOSE: (14), (22), (25), (107) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | #80.
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | End of split
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | Case 2:
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | | (108) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 168.33/25.14 | | | | | | op(e1, e0) = e1)
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | | BETA: splitting (108) gives:
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | | Case 1:
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | (109) all_58_8 = e1 & op(e1, e1) = e1
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | REF_CLOSE: (8), (48), (109) are inconsistent by sub-proof #384.
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | Case 2:
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | (110) all_58_11 = e1 & op(e1, e0) = e1
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | REF_CLOSE: (2), (25), (27), (110) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | #42.
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | End of split
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | End of split
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | Case 2:
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | (111) all_58_14 = e3 & op(e0, e1) = e3
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | ALPHA: (111) implies:
% 168.33/25.14 | | | | | (112) all_58_14 = e3
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | REF_CLOSE: (20), (23), (112) are inconsistent by sub-proof #423.
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | End of split
% 168.33/25.14 | | | |
% 168.33/25.14 | | | End of split
% 168.33/25.14 | | |
% 168.33/25.14 | | Case 2:
% 168.33/25.14 | | |
% 168.33/25.14 | | | (113) all_58_5 = e2 & op(e2, e1) = e2
% 168.33/25.14 | | |
% 168.33/25.14 | | | ALPHA: (113) implies:
% 168.33/25.14 | | | (114) all_58_5 = e2
% 168.33/25.14 | | |
% 168.33/25.14 | | | REF_CLOSE: (30), (32), (114) are inconsistent by sub-proof #522.
% 168.33/25.14 | | |
% 168.33/25.14 | | End of split
% 168.33/25.14 | |
% 168.33/25.14 | Case 2:
% 168.33/25.14 | |
% 168.33/25.14 | | (115) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 168.33/25.14 | | e2)
% 168.33/25.14 | |
% 168.33/25.14 | | BETA: splitting (115) gives:
% 168.33/25.14 | |
% 168.33/25.14 | | Case 1:
% 168.33/25.14 | | |
% 168.33/25.14 | | | (116) all_58_8 = e2 & op(e1, e1) = e2
% 168.33/25.14 | | |
% 168.33/25.14 | | | REF_CLOSE: (18), (19), (25), (116) are inconsistent by sub-proof #845.
% 168.33/25.14 | | |
% 168.33/25.14 | | Case 2:
% 168.33/25.14 | | |
% 168.33/25.14 | | | (117) all_58_14 = e2 & op(e0, e1) = e2
% 168.33/25.14 | | |
% 168.33/25.14 | | | REF_CLOSE: (23), (26), (117) are inconsistent by sub-proof #23.
% 168.33/25.14 | | |
% 168.33/25.14 | | End of split
% 168.33/25.14 | |
% 168.33/25.14 | End of split
% 168.33/25.14 |
% 168.33/25.14 End of proof
% 168.33/25.14
% 168.33/25.14 Sub-proof #18 shows that the following formulas are inconsistent:
% 168.33/25.14 ----------------------------------------------------------------
% 168.33/25.14 (1) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 168.33/25.14 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 168.33/25.14 (2) all_58_0 = e1
% 168.33/25.14 (3) all_58_6 = e1
% 168.33/25.14 (4) ~ (e3 = e1)
% 168.33/25.14 (5) op(e3, e3) = e1
% 168.33/25.14 (6) op(e1, e3) = all_52_2
% 168.33/25.14 (7) ~ (e1 = e0)
% 168.33/25.14 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 168.33/25.14 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 168.33/25.14 (9) all_58_3 = e1
% 168.33/25.14 (10) ~ (e3 = e0)
% 168.33/25.14 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.33/25.14 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.33/25.14 (12) all_58_14 = e0
% 168.33/25.14 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.33/25.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.33/25.14 (14) ~ (e2 = e0)
% 168.33/25.14 (15) all_58_8 = e3
% 168.33/25.14 (16) all_58_5 = e1
% 168.33/25.14 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.33/25.14 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.33/25.14 (18) ~ (e2 = e1)
% 168.33/25.14 (19) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.33/25.14 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 168.33/25.14 (20) all_58_4 = e2
% 168.33/25.14 (21) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 168.33/25.14 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 168.33/25.14 (22) all_58_2 = e0
% 168.33/25.14 (23) op(e1, e3) = e1
% 168.33/25.14 (24) ~ (e3 = e2)
% 168.33/25.14
% 168.33/25.14 Begin of proof
% 168.33/25.14 |
% 168.33/25.14 | BETA: splitting (17) gives:
% 168.33/25.14 |
% 168.33/25.14 | Case 1:
% 168.33/25.14 | |
% 168.33/25.14 | | (25) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 168.33/25.14 | | e3)
% 168.33/25.14 | |
% 168.33/25.14 | | REF_CLOSE: (4), (9), (10), (22), (25) are inconsistent by sub-proof #101.
% 168.33/25.14 | |
% 168.33/25.14 | Case 2:
% 168.33/25.14 | |
% 168.33/25.14 | | (26) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 168.33/25.14 | | e3)
% 168.33/25.14 | |
% 168.33/25.14 | | BETA: splitting (26) gives:
% 168.33/25.14 | |
% 168.33/25.14 | | Case 1:
% 168.33/25.14 | | |
% 168.33/25.14 | | | (27) all_58_5 = e3 & op(e2, e1) = e3
% 168.33/25.14 | | |
% 168.33/25.14 | | | ALPHA: (27) implies:
% 168.33/25.14 | | | (28) all_58_5 = e3
% 168.33/25.14 | | |
% 168.33/25.14 | | | REF_CLOSE: (4), (7), (12), (15), (18), (20), (21), (28) are inconsistent
% 168.33/25.14 | | | by sub-proof #19.
% 168.33/25.14 | | |
% 168.33/25.14 | | Case 2:
% 168.33/25.14 | | |
% 168.33/25.14 | | | (29) all_58_10 = e3 & op(e2, e0) = e3
% 168.33/25.14 | | |
% 168.33/25.14 | | | ALPHA: (29) implies:
% 168.33/25.14 | | | (30) all_58_10 = e3
% 168.33/25.14 | | |
% 168.33/25.14 | | | BETA: splitting (8) gives:
% 168.33/25.14 | | |
% 168.33/25.14 | | | Case 1:
% 168.33/25.14 | | | |
% 168.33/25.14 | | | | (31) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 168.33/25.14 | | | | = e3)
% 168.33/25.14 | | | |
% 168.33/25.14 | | | | BETA: splitting (31) gives:
% 168.33/25.14 | | | |
% 168.33/25.14 | | | | Case 1:
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | (32) all_58_0 = e3 & op(e3, e3) = e3
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | ALPHA: (32) implies:
% 168.33/25.14 | | | | | (33) all_58_0 = e3
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | COMBINE_EQS: (2), (33) imply:
% 168.33/25.14 | | | | | (34) e3 = e1
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | REF_CLOSE: (4), (7), (9), (10), (11), (14), (17), (18), (19), (22),
% 168.33/25.14 | | | | | (24), (30), (34) are inconsistent by sub-proof #116.
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | Case 2:
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | (35) all_58_2 = e3 & op(e2, e3) = e3
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | ALPHA: (35) implies:
% 168.33/25.14 | | | | | (36) all_58_2 = e3
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | REF_CLOSE: (10), (22), (36) are inconsistent by sub-proof #913.
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | End of split
% 168.33/25.14 | | | |
% 168.33/25.14 | | | Case 2:
% 168.33/25.14 | | | |
% 168.33/25.14 | | | | (37) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 168.33/25.14 | | | | = e3)
% 168.33/25.14 | | | |
% 168.33/25.14 | | | | BETA: splitting (37) gives:
% 168.33/25.14 | | | |
% 168.33/25.14 | | | | Case 1:
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | (38) all_58_6 = e3 & op(e1, e3) = e3
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | ALPHA: (38) implies:
% 168.33/25.14 | | | | | (39) op(e1, e3) = e3
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | REF_CLOSE: (4), (6), (13), (23), (39) are inconsistent by sub-proof
% 168.33/25.14 | | | | | #750.
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | Case 2:
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | (40) all_58_12 = e3 & op(e0, e3) = e3
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | ALPHA: (40) implies:
% 168.33/25.14 | | | | | (41) op(e0, e3) = e3
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | BETA: splitting (1) gives:
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | | Case 1:
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | | (42) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 168.33/25.14 | | | | | | e3) = e2)
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | | BETA: splitting (42) gives:
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | | Case 1:
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | (43) all_58_0 = e2 & op(e3, e3) = e2
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | ALPHA: (43) implies:
% 168.33/25.14 | | | | | | | (44) op(e3, e3) = e2
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | REF_CLOSE: (5), (13), (18), (44) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | #957.
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | Case 2:
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | (45) all_58_2 = e2 & op(e2, e3) = e2
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | ALPHA: (45) implies:
% 168.33/25.14 | | | | | | | (46) all_58_2 = e2
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | BETA: splitting (11) gives:
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | | (47) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 &
% 168.33/25.14 | | | | | | | | op(e2, e2) = e0)
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | | BETA: splitting (47) gives:
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | (48) all_58_2 = e0 & op(e2, e3) = e0
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | REF_CLOSE: (14), (46), (48) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | | | #928.
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | (49) all_58_3 = e0 & op(e2, e2) = e0
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | REF_CLOSE: (7), (9), (49) are inconsistent by sub-proof #927.
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | End of split
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | | (50) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 &
% 168.33/25.14 | | | | | | | | op(e2, e0) = e0)
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | | BETA: splitting (50) gives:
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | | Case 1:
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | (51) all_58_5 = e0 & op(e2, e1) = e0
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | REF_CLOSE: (7), (16), (51) are inconsistent by sub-proof #781.
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | Case 2:
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | (52) all_58_10 = e0 & op(e2, e0) = e0
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | | REF_CLOSE: (10), (30), (52) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | | | #932.
% 168.33/25.14 | | | | | | | | |
% 168.33/25.14 | | | | | | | | End of split
% 168.33/25.14 | | | | | | | |
% 168.33/25.14 | | | | | | | End of split
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | End of split
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | Case 2:
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | | (53) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0,
% 168.33/25.14 | | | | | | e3) = e2)
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | | BETA: splitting (53) gives:
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | | Case 1:
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | (54) all_58_6 = e2 & op(e1, e3) = e2
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | REF_CLOSE: (3), (18), (54) are inconsistent by sub-proof #715.
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | Case 2:
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | (55) all_58_12 = e2 & op(e0, e3) = e2
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | ALPHA: (55) implies:
% 168.33/25.14 | | | | | | | (56) op(e0, e3) = e2
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | | REF_CLOSE: (13), (24), (41), (56) are inconsistent by sub-proof
% 168.33/25.14 | | | | | | | #38.
% 168.33/25.14 | | | | | | |
% 168.33/25.14 | | | | | | End of split
% 168.33/25.14 | | | | | |
% 168.33/25.14 | | | | | End of split
% 168.33/25.14 | | | | |
% 168.33/25.14 | | | | End of split
% 168.33/25.14 | | | |
% 168.33/25.14 | | | End of split
% 168.33/25.14 | | |
% 168.33/25.14 | | End of split
% 168.33/25.14 | |
% 168.33/25.14 | End of split
% 168.33/25.14 |
% 168.33/25.15 End of proof
% 168.33/25.15
% 168.33/25.15 Sub-proof #19 shows that the following formulas are inconsistent:
% 168.33/25.15 ----------------------------------------------------------------
% 168.33/25.15 (1) ~ (e3 = e1)
% 168.33/25.15 (2) ~ (e1 = e0)
% 168.33/25.15 (3) all_58_5 = e3
% 168.33/25.15 (4) all_58_14 = e0
% 168.33/25.15 (5) all_58_8 = e3
% 168.33/25.15 (6) ~ (e2 = e1)
% 168.33/25.15 (7) all_58_4 = e2
% 168.33/25.15 (8) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 168.33/25.15 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 168.33/25.15
% 168.33/25.15 Begin of proof
% 168.33/25.15 |
% 168.33/25.15 | BETA: splitting (8) gives:
% 168.33/25.15 |
% 168.33/25.15 | Case 1:
% 168.33/25.15 | |
% 168.33/25.15 | | (9) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 168.33/25.15 | |
% 168.33/25.15 | | BETA: splitting (9) gives:
% 168.33/25.15 | |
% 168.33/25.15 | | Case 1:
% 168.33/25.15 | | |
% 168.33/25.15 | | | (10) all_58_4 = e1 & op(e3, e1) = e1
% 168.33/25.15 | | |
% 168.33/25.15 | | | REF_CLOSE: (6), (7), (10) are inconsistent by sub-proof #943.
% 168.33/25.15 | | |
% 168.33/25.15 | | Case 2:
% 168.33/25.15 | | |
% 168.33/25.15 | | | (11) all_58_5 = e1 & op(e2, e1) = e1
% 168.33/25.15 | | |
% 168.33/25.15 | | | REF_CLOSE: (1), (3), (11) are inconsistent by sub-proof #828.
% 168.33/25.15 | | |
% 168.33/25.15 | | End of split
% 168.33/25.15 | |
% 168.33/25.15 | Case 2:
% 168.33/25.15 | |
% 168.33/25.15 | | (12) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 168.33/25.15 | | e1)
% 168.33/25.15 | |
% 168.33/25.15 | | BETA: splitting (12) gives:
% 168.33/25.15 | |
% 168.33/25.15 | | Case 1:
% 168.33/25.15 | | |
% 168.33/25.15 | | | (13) all_58_8 = e1 & op(e1, e1) = e1
% 168.33/25.15 | | |
% 168.33/25.15 | | | REF_CLOSE: (1), (5), (13) are inconsistent by sub-proof #478.
% 168.33/25.15 | | |
% 168.33/25.15 | | Case 2:
% 168.33/25.15 | | |
% 168.33/25.15 | | | (14) all_58_14 = e1 & op(e0, e1) = e1
% 168.33/25.15 | | |
% 168.33/25.15 | | | ALPHA: (14) implies:
% 168.33/25.15 | | | (15) all_58_14 = e1
% 168.33/25.15 | | |
% 168.33/25.15 | | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #586.
% 168.33/25.15 | | |
% 168.33/25.15 | | End of split
% 168.33/25.15 | |
% 168.33/25.15 | End of split
% 168.33/25.15 |
% 168.33/25.15 End of proof
% 168.33/25.15
% 168.33/25.15 Sub-proof #20 shows that the following formulas are inconsistent:
% 168.33/25.15 ----------------------------------------------------------------
% 168.33/25.15 (1) all_56_15 = e1
% 168.33/25.15 (2) all_56_15 = e0
% 168.33/25.15 (3) ~ (e1 = e0)
% 168.33/25.15
% 168.33/25.15 Begin of proof
% 168.33/25.15 |
% 168.33/25.15 | COMBINE_EQS: (1), (2) imply:
% 168.33/25.15 | (4) e1 = e0
% 168.33/25.15 |
% 168.33/25.15 | SIMP: (4) implies:
% 168.33/25.15 | (5) e1 = e0
% 168.33/25.15 |
% 168.33/25.15 | REDUCE: (3), (5) imply:
% 168.33/25.15 | (6) $false
% 168.33/25.15 |
% 168.33/25.15 | CLOSE: (6) is inconsistent.
% 168.33/25.15 |
% 168.33/25.15 End of proof
% 168.33/25.15
% 168.33/25.15 Sub-proof #21 shows that the following formulas are inconsistent:
% 168.33/25.15 ----------------------------------------------------------------
% 168.33/25.15 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 168.33/25.15 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.33/25.15 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 168.33/25.15 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 168.33/25.15 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 168.33/25.15 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 168.33/25.15 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 168.33/25.15 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 168.33/25.15 (5) op(e0, e0) = e1
% 168.33/25.15 (6) all_22_2 = e3
% 168.33/25.15 (7) ~ (e3 = e1)
% 168.33/25.15 (8) ~ (e1 = e0)
% 168.33/25.15 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 168.33/25.15 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 168.33/25.15 (10) op(e1, e2) = all_52_6
% 168.33/25.15 (11) op(e2, e3) = all_52_1
% 168.33/25.15 (12) op(e0, e2) = e2
% 168.33/25.15 (13) op(e2, e2) = all_8_2
% 168.33/25.15 (14) op(e2, e3) = e2
% 168.33/25.15 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 168.33/25.15 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 168.33/25.15 (16) ~ (e3 = e0)
% 168.33/25.15 (17) ~ (all_22_2 = e3) | ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 &
% 168.33/25.15 op(e3, e2) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 =
% 168.33/25.15 e0) & op(e3, e2) = all_22_1 & $i(all_22_1))
% 168.33/25.15 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.33/25.15 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.33/25.15 (19) ~ (all_52_6 = e1)
% 168.33/25.15 (20) all_58_14 = e0
% 168.33/25.15 (21) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.33/25.15 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 168.33/25.15 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.33/25.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.33/25.15 (23) ~ (e2 = e0)
% 168.33/25.15 (24) all_58_3 = e3
% 168.33/25.15 (25) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.33/25.15 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.33/25.15 (26) ~ (e2 = e1)
% 168.33/25.15 (27) op(e3, e2) = all_52_4
% 168.33/25.15 (28) ~ (all_8_2 = e1)
% 168.33/25.15 (29) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.33/25.15 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 168.33/25.15 (30) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 168.33/25.15 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 168.33/25.15 e2) = all_14_1 & $i(all_14_1))
% 168.33/25.15 (31) ~ (e3 = e2)
% 168.33/25.15
% 168.33/25.15 Begin of proof
% 168.33/25.15 |
% 168.33/25.15 | BETA: splitting (17) gives:
% 168.33/25.15 |
% 168.33/25.15 | Case 1:
% 168.33/25.15 | |
% 168.33/25.15 | | (32) ~ (all_22_2 = e3)
% 168.33/25.15 | |
% 168.33/25.15 | | REDUCE: (6), (32) imply:
% 168.33/25.15 | | (33) $false
% 168.33/25.15 | |
% 168.33/25.15 | | CLOSE: (33) is inconsistent.
% 168.33/25.15 | |
% 168.33/25.15 | Case 2:
% 168.33/25.15 | |
% 168.33/25.15 | | (34) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 168.33/25.15 | | all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) &
% 168.33/25.15 | | op(e3, e2) = all_22_1 & $i(all_22_1))
% 168.33/25.15 | |
% 168.33/25.15 | | BETA: splitting (4) gives:
% 168.33/25.15 | |
% 168.33/25.15 | | Case 1:
% 168.33/25.15 | | |
% 168.33/25.15 | | | (35) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 168.33/25.15 | | | e1)
% 168.33/25.15 | | |
% 168.33/25.15 | | | BETA: splitting (35) gives:
% 168.33/25.15 | | |
% 168.33/25.15 | | | Case 1:
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | (36) all_58_1 = e1 & op(e3, e2) = e1
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | ALPHA: (36) implies:
% 168.33/25.15 | | | | (37) all_58_1 = e1
% 168.33/25.15 | | | | (38) op(e3, e2) = e1
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | BETA: splitting (1) gives:
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | Case 1:
% 168.33/25.15 | | | | |
% 168.33/25.15 | | | | | (39) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 168.33/25.15 | | | | | e2) = e2)
% 168.33/25.15 | | | | |
% 168.33/25.15 | | | | | BETA: splitting (39) gives:
% 168.33/25.15 | | | | |
% 168.33/25.15 | | | | | Case 1:
% 168.33/25.15 | | | | | |
% 168.33/25.15 | | | | | | (40) all_58_12 = e2 & op(e0, e3) = e2
% 168.33/25.15 | | | | | |
% 168.33/25.15 | | | | | | REF_CLOSE: (2), (3), (7), (8), (9), (11), (14), (15), (16), (18),
% 168.33/25.15 | | | | | | (22), (23), (24), (25), (26), (29), (31), (40) are
% 168.33/25.15 | | | | | | inconsistent by sub-proof #156.
% 168.33/25.15 | | | | | |
% 168.33/25.15 | | | | | Case 2:
% 168.33/25.15 | | | | | |
% 168.33/25.15 | | | | | | (41) all_58_13 = e2 & op(e0, e2) = e2
% 168.33/25.15 | | | | | |
% 168.33/25.15 | | | | | | ALPHA: (41) implies:
% 168.33/25.15 | | | | | | (42) all_58_13 = e2
% 168.33/25.15 | | | | | |
% 168.33/25.15 | | | | | | REF_CLOSE: (8), (10), (16), (21), (22), (23), (24), (27), (30),
% 168.33/25.15 | | | | | | (34), (37), (38), (42) are inconsistent by sub-proof
% 168.33/25.15 | | | | | | #429.
% 168.33/25.15 | | | | | |
% 168.33/25.15 | | | | | End of split
% 168.33/25.15 | | | | |
% 168.33/25.15 | | | | Case 2:
% 168.33/25.15 | | | | |
% 168.33/25.15 | | | | | (43) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 168.33/25.15 | | | | | e0) = e2)
% 168.33/25.15 | | | | |
% 168.33/25.15 | | | | | REF_CLOSE: (5), (20), (22), (23), (26), (43) are inconsistent by
% 168.33/25.15 | | | | | sub-proof #22.
% 168.33/25.15 | | | | |
% 168.33/25.15 | | | | End of split
% 168.33/25.15 | | | |
% 168.33/25.15 | | | Case 2:
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | (44) all_58_3 = e1 & op(e2, e2) = e1
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | REF_CLOSE: (13), (22), (28), (44) are inconsistent by sub-proof #498.
% 168.33/25.15 | | | |
% 168.33/25.15 | | | End of split
% 168.33/25.15 | | |
% 168.33/25.15 | | Case 2:
% 168.33/25.15 | | |
% 168.33/25.15 | | | (45) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 168.33/25.15 | | | e1)
% 168.33/25.15 | | |
% 168.33/25.15 | | | BETA: splitting (45) gives:
% 168.33/25.15 | | |
% 168.33/25.15 | | | Case 1:
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | (46) all_58_7 = e1 & op(e1, e2) = e1
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | REF_CLOSE: (10), (19), (22), (46) are inconsistent by sub-proof #80.
% 168.33/25.15 | | | |
% 168.33/25.15 | | | Case 2:
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | (47) all_58_13 = e1 & op(e0, e2) = e1
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | ALPHA: (47) implies:
% 168.33/25.15 | | | | (48) op(e0, e2) = e1
% 168.33/25.15 | | | |
% 168.33/25.15 | | | | REF_CLOSE: (12), (22), (26), (48) are inconsistent by sub-proof #968.
% 168.33/25.15 | | | |
% 168.33/25.15 | | | End of split
% 168.33/25.15 | | |
% 168.33/25.15 | | End of split
% 168.33/25.15 | |
% 168.33/25.15 | End of split
% 168.33/25.15 |
% 168.33/25.15 End of proof
% 168.33/25.15
% 168.33/25.15 Sub-proof #22 shows that the following formulas are inconsistent:
% 168.33/25.15 ----------------------------------------------------------------
% 168.33/25.15 (1) op(e0, e0) = e1
% 168.33/25.15 (2) all_58_14 = e0
% 168.33/25.15 (3) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.33/25.15 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.33/25.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.33/25.15 (5) ~ (e2 = e0)
% 168.33/25.15 (6) ~ (e2 = e1)
% 168.33/25.15
% 168.33/25.15 Begin of proof
% 168.33/25.15 |
% 168.33/25.15 | BETA: splitting (3) gives:
% 168.33/25.15 |
% 168.33/25.15 | Case 1:
% 168.33/25.15 | |
% 168.33/25.15 | | (7) all_58_14 = e2 & op(e0, e1) = e2
% 168.33/25.15 | |
% 168.33/25.15 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #23.
% 168.33/25.15 | |
% 168.33/25.15 | Case 2:
% 168.33/25.15 | |
% 168.33/25.15 | | (8) all_58_15 = e2 & op(e0, e0) = e2
% 168.33/25.15 | |
% 168.33/25.15 | | ALPHA: (8) implies:
% 168.33/25.15 | | (9) op(e0, e0) = e2
% 168.33/25.15 | |
% 168.33/25.15 | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #640.
% 168.33/25.15 | |
% 168.33/25.15 | End of split
% 168.33/25.15 |
% 168.33/25.15 End of proof
% 168.33/25.15
% 168.33/25.15 Sub-proof #23 shows that the following formulas are inconsistent:
% 168.33/25.15 ----------------------------------------------------------------
% 168.33/25.15 (1) all_58_14 = e2 & op(e0, e1) = e2
% 168.33/25.15 (2) all_58_14 = e0
% 168.33/25.15 (3) ~ (e2 = e0)
% 168.33/25.15
% 168.33/25.15 Begin of proof
% 168.33/25.15 |
% 168.33/25.15 | ALPHA: (1) implies:
% 168.33/25.15 | (4) all_58_14 = e2
% 168.33/25.15 |
% 168.33/25.15 | COMBINE_EQS: (2), (4) imply:
% 168.33/25.15 | (5) e2 = e0
% 168.33/25.15 |
% 168.33/25.15 | REDUCE: (3), (5) imply:
% 168.33/25.15 | (6) $false
% 168.33/25.15 |
% 168.33/25.15 | CLOSE: (6) is inconsistent.
% 168.33/25.15 |
% 168.33/25.15 End of proof
% 168.33/25.15
% 168.33/25.15 Sub-proof #24 shows that the following formulas are inconsistent:
% 168.33/25.15 ----------------------------------------------------------------
% 168.33/25.15 (1) all_54_5 = all_8_2
% 168.33/25.15 (2) all_54_5 = e1
% 168.33/25.15 (3) ~ (all_8_2 = e1)
% 168.33/25.15
% 168.33/25.15 Begin of proof
% 168.33/25.15 |
% 168.33/25.15 | COMBINE_EQS: (1), (2) imply:
% 168.33/25.15 | (4) all_8_2 = e1
% 168.33/25.15 |
% 168.33/25.15 | SIMP: (4) implies:
% 168.33/25.15 | (5) all_8_2 = e1
% 168.33/25.15 |
% 168.33/25.15 | REDUCE: (3), (5) imply:
% 168.33/25.15 | (6) $false
% 168.33/25.15 |
% 168.33/25.15 | CLOSE: (6) is inconsistent.
% 168.33/25.15 |
% 168.33/25.15 End of proof
% 168.33/25.15
% 168.33/25.15 Sub-proof #25 shows that the following formulas are inconsistent:
% 168.33/25.15 ----------------------------------------------------------------
% 168.33/25.15 (1) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 168.33/25.15 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 168.33/25.15 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.33/25.15 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.33/25.15 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.33/25.15 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 168.33/25.15 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.33/25.15 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.33/25.15 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.33/25.15 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 168.33/25.15 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 168.33/25.15 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.33/25.15 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.33/25.15 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.33/25.15 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.33/25.15 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 168.33/25.15 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.33/25.15 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.33/25.15 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.33/25.15 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.33/25.15 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 168.33/25.15 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.33/25.15 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.33/25.15 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.33/25.15 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 168.33/25.15 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 168.33/25.15 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.33/25.15 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.33/25.15 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.33/25.15 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.33/25.15 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 168.33/25.15 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.33/25.15 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.33/25.15 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.33/25.15 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 168.33/25.15 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 168.33/25.15 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.33/25.15 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.33/25.15 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.33/25.15 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.33/25.15 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 168.33/25.15 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.33/25.15 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.33/25.15 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.33/25.15 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 168.33/25.15 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.33/25.15 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.33/25.15 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 168.33/25.15 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.33/25.15 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 168.33/25.15 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.33/25.15 (2) op(e0, e1) = all_52_11
% 168.33/25.15 (3) all_56_2 = e1
% 168.33/25.15 (4) all_56_8 = e0
% 168.33/25.15 (5) all_56_14 = e3
% 168.33/25.15 (6) all_56_15 = e1
% 168.33/25.15 (7) ~ (e1 = e0)
% 168.33/25.15 (8) op(e0, e3) = e2
% 168.33/25.15 (9) all_56_12 = e2
% 168.33/25.15 (10) op(e0, e1) = e0
% 168.33/25.15 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.33/25.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.33/25.15 (12) ~ (all_52_7 = e2)
% 168.33/25.15 (13) op(e0, e2) = all_52_7
% 168.33/25.15 (14) ~ (e3 = e2)
% 168.33/25.15
% 168.33/25.15 Begin of proof
% 168.33/25.15 |
% 168.33/25.15 | BETA: splitting (1) gives:
% 168.33/25.15 |
% 168.33/25.15 | Case 1:
% 168.33/25.15 | |
% 168.33/25.16 | | (15) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 168.33/25.16 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 168.33/25.16 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 168.33/25.16 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2)
% 168.33/25.16 | | | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7))))
% 168.33/25.16 | | | (all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.33/25.16 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 168.33/25.16 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.33/25.16 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 168.33/25.16 | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.33/25.16 | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 168.33/25.16 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.33/25.16 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.33/25.16 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 168.33/25.16 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8))))
% 168.33/25.16 | | | (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.33/25.16 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.33/25.16 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.33/25.16 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 168.33/25.16 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8))))
% 168.33/25.16 | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.33/25.16 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 168.33/25.16 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.33/25.16 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 168.33/25.16 | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.33/25.16 | |
% 168.33/25.16 | | BETA: splitting (15) gives:
% 168.33/25.16 | |
% 168.33/25.16 | | Case 1:
% 168.33/25.16 | | |
% 168.33/25.16 | | | (16) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 168.33/25.16 | | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1
% 168.33/25.16 | | | & $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 =
% 168.33/25.16 | | | e1) & op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.33/25.16 | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 168.33/25.16 | | | & $i(all_56_7)))) | (all_56_1 = e2 & ~ (all_56_10 = e3) &
% 168.33/25.16 | | | op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.33/25.16 | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~ (all_56_14 =
% 168.33/25.16 | | | e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.33/25.16 | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0)
% 168.33/25.16 | | | & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.33/25.16 | | |
% 168.33/25.16 | | | REF_CLOSE: (3), (5), (9), (16) are inconsistent by sub-proof #176.
% 168.33/25.16 | | |
% 168.33/25.16 | | Case 2:
% 168.33/25.16 | | |
% 168.33/25.16 | | | (17) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 168.33/25.16 | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4
% 168.33/25.16 | | | & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 =
% 168.33/25.16 | | | e2) & op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.33/25.16 | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8
% 168.33/25.16 | | | & $i(all_56_8)))) | (all_56_3 = e2 & ~ (all_56_14 = e1) &
% 168.33/25.16 | | | op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.33/25.16 | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~ (all_56_12 =
% 168.33/25.16 | | | e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.33/25.16 | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0)
% 168.33/25.16 | | | & op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 &
% 168.33/25.16 | | | ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | (
% 168.33/25.16 | | | ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) &
% 168.33/25.16 | | | ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) =
% 168.33/25.16 | | | all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 168.33/25.16 | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.33/25.16 | | |
% 168.33/25.16 | | | BETA: splitting (17) gives:
% 168.33/25.16 | | |
% 168.33/25.16 | | | Case 1:
% 168.33/25.16 | | | |
% 168.33/25.16 | | | | (18) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 168.33/25.16 | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4
% 168.33/25.16 | | | | & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 =
% 168.33/25.16 | | | | e2) & op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.33/25.16 | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8
% 168.33/25.16 | | | | & $i(all_56_8)))
% 168.33/25.16 | | | |
% 168.33/25.16 | | | | ALPHA: (18) implies:
% 168.33/25.16 | | | | (19) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) =
% 168.33/25.16 | | | | all_56_8 & $i(all_56_8))
% 168.33/25.16 | | | |
% 168.33/25.16 | | | | REF_CLOSE: (4), (6), (19) are inconsistent by sub-proof #34.
% 168.33/25.16 | | | |
% 168.33/25.16 | | | Case 2:
% 168.33/25.16 | | | |
% 168.33/25.16 | | | | (20) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.33/25.16 | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) =
% 168.33/25.16 | | | | all_56_4 & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.33/25.16 | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 & $i(all_56_5))) &
% 168.33/25.16 | | | | ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) =
% 168.33/25.16 | | | | all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.33/25.16 | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | (
% 168.33/25.16 | | | | ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0)))
% 168.33/25.16 | | | | & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) =
% 168.33/25.16 | | | | all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 168.33/25.16 | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.33/25.16 | | | |
% 168.33/25.16 | | | | BETA: splitting (20) gives:
% 168.33/25.16 | | | |
% 168.33/25.16 | | | | Case 1:
% 168.33/25.16 | | | | |
% 168.33/25.16 | | | | | (21) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.33/25.16 | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) =
% 168.33/25.16 | | | | | all_56_4 & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.33/25.16 | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 & $i(all_56_5))) &
% 168.33/25.16 | | | | | ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) =
% 168.33/25.16 | | | | | all_56_8 & $i(all_56_8)))
% 168.33/25.16 | | | | |
% 168.33/25.16 | | | | | ALPHA: (21) implies:
% 168.33/25.16 | | | | | (22) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) =
% 168.33/25.16 | | | | | all_56_8 & $i(all_56_8))
% 168.33/25.16 | | | | |
% 168.33/25.16 | | | | | REF_CLOSE: (4), (6), (22) are inconsistent by sub-proof #34.
% 168.33/25.16 | | | | |
% 168.33/25.16 | | | | Case 2:
% 168.33/25.16 | | | | |
% 168.33/25.16 | | | | | (23) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.33/25.16 | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) =
% 168.33/25.16 | | | | | all_56_0 & $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 168.33/25.16 | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 & $i(all_56_2))) &
% 168.33/25.16 | | | | | ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0, e3) =
% 168.33/25.16 | | | | | all_56_6 & $i(all_56_6)))
% 168.33/25.16 | | | | |
% 168.33/25.16 | | | | | ALPHA: (23) implies:
% 168.33/25.16 | | | | | (24) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) =
% 168.33/25.16 | | | | | all_56_2 & $i(all_56_2))
% 168.33/25.16 | | | | |
% 168.33/25.16 | | | | | REF_CLOSE: (3), (5), (24) are inconsistent by sub-proof #485.
% 168.33/25.16 | | | | |
% 168.33/25.16 | | | | End of split
% 168.33/25.16 | | | |
% 168.33/25.16 | | | End of split
% 168.33/25.16 | | |
% 168.33/25.16 | | End of split
% 168.33/25.16 | |
% 168.33/25.16 | Case 2:
% 168.33/25.16 | |
% 168.33/25.16 | | (25) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~
% 168.33/25.16 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 168.33/25.16 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 168.33/25.16 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2)
% 168.33/25.16 | | | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7))))
% 168.33/25.16 | | | (all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 168.33/25.16 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 168.33/25.16 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.33/25.16 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 168.33/25.16 | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.33/25.16 | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) = e0 & ( ~
% 168.33/25.16 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 168.33/25.16 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 168.33/25.16 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2)
% 168.33/25.16 | | | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7))))
% 168.33/25.16 | | | (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.33/25.16 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.33/25.16 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.33/25.16 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 168.33/25.16 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8))))
% 168.33/25.16 | | | ( ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3)
% 168.33/25.16 | | & op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 =
% 168.33/25.16 | | e0) | ( ~ (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.33/25.16 | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1)
% 168.33/25.16 | | & op(e1, e0) = all_56_13 & $i(all_56_13))) & ((all_56_6 = e3 &
% 168.33/25.16 | | op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 168.33/25.16 | | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.33/25.16 | |
% 168.45/25.16 | | BETA: splitting (25) gives:
% 168.45/25.16 | |
% 168.45/25.16 | | Case 1:
% 168.45/25.16 | | |
% 168.45/25.16 | | | (26) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~
% 168.45/25.16 | | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1
% 168.45/25.16 | | | & $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 =
% 168.45/25.16 | | | e1) & op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.45/25.16 | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 168.45/25.16 | | | & $i(all_56_7)))) | (all_56_9 = e0 & ~ (all_56_10 = e3) &
% 168.45/25.16 | | | op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.45/25.16 | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~ (all_56_14 =
% 168.45/25.16 | | | e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.45/25.16 | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0)
% 168.45/25.16 | | | & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.45/25.16 | | |
% 168.45/25.16 | | | BETA: splitting (26) gives:
% 168.45/25.16 | | |
% 168.45/25.16 | | | Case 1:
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | (27) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~
% 168.45/25.16 | | | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1
% 168.45/25.16 | | | | & $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 =
% 168.45/25.16 | | | | e1) & op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.45/25.16 | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 168.45/25.16 | | | | & $i(all_56_7)))
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | ALPHA: (27) implies:
% 168.45/25.16 | | | | (28) ~ (all_56_12 = e2)
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | REDUCE: (9), (28) imply:
% 168.45/25.16 | | | | (29) $false
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | CLOSE: (29) is inconsistent.
% 168.45/25.16 | | | |
% 168.45/25.16 | | | Case 2:
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | (30) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 168.45/25.16 | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0
% 168.45/25.16 | | | | & $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 =
% 168.45/25.16 | | | | e1) & op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.45/25.16 | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6
% 168.45/25.16 | | | | & $i(all_56_6)))
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | ALPHA: (30) implies:
% 168.45/25.16 | | | | (31) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) =
% 168.45/25.16 | | | | all_56_2 & $i(all_56_2))
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | REF_CLOSE: (3), (5), (31) are inconsistent by sub-proof #485.
% 168.45/25.16 | | | |
% 168.45/25.16 | | | End of split
% 168.45/25.16 | | |
% 168.45/25.16 | | Case 2:
% 168.45/25.16 | | |
% 168.45/25.16 | | | (32) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) = e0 & ( ~
% 168.45/25.16 | | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1
% 168.45/25.16 | | | & $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 =
% 168.45/25.16 | | | e1) & op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.45/25.16 | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 168.45/25.16 | | | & $i(all_56_7)))) | (all_56_13 = e0 & ~ (all_56_14 = e1) &
% 168.45/25.16 | | | op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.45/25.16 | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~ (all_56_12 =
% 168.45/25.16 | | | e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.45/25.16 | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0)
% 168.45/25.16 | | | & op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 =
% 168.45/25.16 | | | e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0)
% 168.45/25.16 | | | = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.45/25.16 | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11)))
% 168.45/25.16 | | | & ( ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) =
% 168.45/25.16 | | | all_56_13 & $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) =
% 168.45/25.16 | | | e3) | (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 168.45/25.16 | | | op(e0, e1) = e1)))
% 168.45/25.16 | | |
% 168.45/25.16 | | | BETA: splitting (32) gives:
% 168.45/25.16 | | |
% 168.45/25.16 | | | Case 1:
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | (33) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) = e0 & ( ~
% 168.45/25.16 | | | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1
% 168.45/25.16 | | | | & $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 =
% 168.45/25.16 | | | | e1) & op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.45/25.16 | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 168.45/25.16 | | | | & $i(all_56_7)))
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | ALPHA: (33) implies:
% 168.45/25.16 | | | | (34) ~ (all_56_12 = e2)
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | REDUCE: (9), (34) imply:
% 168.45/25.16 | | | | (35) $false
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | CLOSE: (35) is inconsistent.
% 168.45/25.16 | | | |
% 168.45/25.16 | | | Case 2:
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | (36) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.45/25.16 | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) =
% 168.45/25.16 | | | | all_56_4 & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.45/25.16 | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 & $i(all_56_5))) &
% 168.45/25.16 | | | | ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) =
% 168.45/25.16 | | | | all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 168.45/25.16 | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) =
% 168.45/25.16 | | | | all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.45/25.16 | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.45/25.16 | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~ (all_56_13 =
% 168.45/25.16 | | | | e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.45/25.16 | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0,
% 168.45/25.16 | | | | e2) = e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.45/25.16 | | | |
% 168.45/25.16 | | | | REF_CLOSE: (2), (4), (6), (7), (8), (10), (11), (12), (13), (14), (36)
% 168.45/25.16 | | | | are inconsistent by sub-proof #26.
% 168.45/25.16 | | | |
% 168.45/25.16 | | | End of split
% 168.45/25.16 | | |
% 168.45/25.16 | | End of split
% 168.45/25.16 | |
% 168.45/25.16 | End of split
% 168.45/25.16 |
% 168.45/25.16 End of proof
% 168.45/25.16
% 168.45/25.16 Sub-proof #26 shows that the following formulas are inconsistent:
% 168.45/25.16 ----------------------------------------------------------------
% 168.45/25.16 (1) op(e0, e1) = all_52_11
% 168.45/25.16 (2) all_56_8 = e0
% 168.45/25.16 (3) all_56_15 = e1
% 168.45/25.16 (4) ~ (e1 = e0)
% 168.45/25.16 (5) op(e0, e3) = e2
% 168.45/25.16 (6) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10
% 168.45/25.16 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.45/25.16 $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.45/25.16 op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.45/25.16 (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~
% 168.45/25.16 (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3,
% 168.45/25.16 e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.45/25.16 (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~
% 168.45/25.16 (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.45/25.16 $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 168.45/25.16 e2 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.45/25.16 (7) op(e0, e1) = e0
% 168.45/25.16 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.16 (9) ~ (all_52_7 = e2)
% 168.45/25.16 (10) op(e0, e2) = all_52_7
% 168.45/25.16 (11) ~ (e3 = e2)
% 168.45/25.16
% 168.45/25.16 Begin of proof
% 168.45/25.16 |
% 168.45/25.16 | BETA: splitting (6) gives:
% 168.45/25.16 |
% 168.45/25.16 | Case 1:
% 168.45/25.16 | |
% 168.45/25.16 | | (12) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.45/25.16 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.45/25.16 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.45/25.16 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) |
% 168.45/25.16 | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 168.45/25.16 | |
% 168.45/25.16 | | ALPHA: (12) implies:
% 168.45/25.16 | | (13) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.45/25.16 | | $i(all_56_8))
% 168.45/25.16 | |
% 168.45/25.16 | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #34.
% 168.45/25.16 | |
% 168.45/25.16 | Case 2:
% 168.45/25.16 | |
% 168.45/25.16 | | (14) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 168.45/25.16 | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) |
% 168.45/25.16 | | ( ~ (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11))) &
% 168.45/25.16 | | ( ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) = all_56_13
% 168.45/25.16 | | & $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) = e3) |
% 168.45/25.16 | | (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) =
% 168.45/25.16 | | e1))
% 168.45/25.16 | |
% 168.45/25.16 | | ALPHA: (14) implies:
% 168.45/25.16 | | (15) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.45/25.16 | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)
% 168.45/25.16 | |
% 168.45/25.16 | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (15) are inconsistent
% 168.45/25.16 | | by sub-proof #27.
% 168.45/25.16 | |
% 168.45/25.16 | End of split
% 168.45/25.16 |
% 168.45/25.16 End of proof
% 168.45/25.16
% 168.45/25.16 Sub-proof #27 shows that the following formulas are inconsistent:
% 168.45/25.16 ----------------------------------------------------------------
% 168.45/25.17 (1) op(e0, e1) = all_52_11
% 168.45/25.17 (2) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 168.45/25.17 (all_56_8 = e1 & op(e0, e1) = e1)
% 168.45/25.17 (3) ~ (e1 = e0)
% 168.45/25.17 (4) op(e0, e3) = e2
% 168.45/25.17 (5) op(e0, e1) = e0
% 168.45/25.17 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.17 (7) ~ (all_52_7 = e2)
% 168.45/25.17 (8) op(e0, e2) = all_52_7
% 168.45/25.17 (9) ~ (e3 = e2)
% 168.45/25.17
% 168.45/25.17 Begin of proof
% 168.45/25.17 |
% 168.45/25.17 | BETA: splitting (2) gives:
% 168.45/25.17 |
% 168.45/25.17 | Case 1:
% 168.45/25.17 | |
% 168.45/25.17 | | (10) all_56_6 = e3 & op(e0, e3) = e3
% 168.45/25.17 | |
% 168.45/25.17 | | ALPHA: (10) implies:
% 168.45/25.17 | | (11) op(e0, e3) = e3
% 168.45/25.17 | |
% 168.45/25.17 | | GROUND_INST: instantiating (6) with e2, e3, e3, e0, simplifying with (4),
% 168.45/25.17 | | (11) gives:
% 168.45/25.17 | | (12) e3 = e2
% 168.45/25.17 | |
% 168.45/25.17 | | REDUCE: (9), (12) imply:
% 168.45/25.17 | | (13) $false
% 168.45/25.17 | |
% 168.45/25.17 | | CLOSE: (13) is inconsistent.
% 168.45/25.17 | |
% 168.45/25.17 | Case 2:
% 168.45/25.17 | |
% 168.45/25.17 | | (14) (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) =
% 168.45/25.17 | | e1)
% 168.45/25.17 | |
% 168.45/25.17 | | BETA: splitting (14) gives:
% 168.45/25.17 | |
% 168.45/25.17 | | Case 1:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (15) all_56_7 = e2 & op(e0, e2) = e2
% 168.45/25.17 | | |
% 168.45/25.17 | | | ALPHA: (15) implies:
% 168.45/25.17 | | | (16) op(e0, e2) = e2
% 168.45/25.17 | | |
% 168.45/25.17 | | | REF_CLOSE: (6), (7), (8), (16) are inconsistent by sub-proof #695.
% 168.45/25.17 | | |
% 168.45/25.17 | | Case 2:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (17) all_56_8 = e1 & op(e0, e1) = e1
% 168.45/25.17 | | |
% 168.45/25.17 | | | ALPHA: (17) implies:
% 168.45/25.17 | | | (18) op(e0, e1) = e1
% 168.45/25.17 | | |
% 168.45/25.17 | | | REF_CLOSE: (1), (3), (5), (6), (18) are inconsistent by sub-proof #28.
% 168.45/25.17 | | |
% 168.45/25.17 | | End of split
% 168.45/25.17 | |
% 168.45/25.17 | End of split
% 168.45/25.17 |
% 168.45/25.17 End of proof
% 168.45/25.17
% 168.45/25.17 Sub-proof #28 shows that the following formulas are inconsistent:
% 168.45/25.17 ----------------------------------------------------------------
% 168.45/25.17 (1) op(e0, e1) = all_52_11
% 168.45/25.17 (2) op(e0, e1) = e1
% 168.45/25.17 (3) ~ (e1 = e0)
% 168.45/25.17 (4) op(e0, e1) = e0
% 168.45/25.17 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.17
% 168.45/25.17 Begin of proof
% 168.45/25.17 |
% 168.45/25.17 | GROUND_INST: instantiating (5) with all_52_11, e0, e1, e0, simplifying with
% 168.45/25.17 | (1), (4) gives:
% 168.45/25.17 | (6) all_52_11 = e0
% 168.45/25.17 |
% 168.45/25.17 | GROUND_INST: instantiating (5) with all_52_11, e1, e1, e0, simplifying with
% 168.45/25.17 | (1), (2) gives:
% 168.45/25.17 | (7) all_52_11 = e1
% 168.45/25.17 |
% 168.45/25.17 | COMBINE_EQS: (6), (7) imply:
% 168.45/25.17 | (8) e1 = e0
% 168.45/25.17 |
% 168.45/25.17 | REDUCE: (3), (8) imply:
% 168.45/25.17 | (9) $false
% 168.45/25.17 |
% 168.45/25.17 | CLOSE: (9) is inconsistent.
% 168.45/25.17 |
% 168.45/25.17 End of proof
% 168.45/25.17
% 168.45/25.17 Sub-proof #29 shows that the following formulas are inconsistent:
% 168.45/25.17 ----------------------------------------------------------------
% 168.45/25.17 (1) op(e0, e0) = e1
% 168.45/25.17 (2) ~ (e1 = e0)
% 168.45/25.17 (3) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 168.45/25.17 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.45/25.17 (4) ~ (e3 = e0)
% 168.45/25.17 (5) op(e2, e0) = e1
% 168.45/25.17 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.17 (7) ~ (e2 = e0)
% 168.45/25.17 (8) all_58_9 = e3
% 168.45/25.17 (9) ~ (e2 = e1)
% 168.45/25.17 (10) all_58_10 = e1
% 168.45/25.17 (11) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 168.45/25.17 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 168.45/25.17 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 168.45/25.17 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 168.45/25.17 (12) ~ (e3 = e2)
% 168.45/25.17
% 168.45/25.17 Begin of proof
% 168.45/25.17 |
% 168.45/25.17 | BETA: splitting (3) gives:
% 168.45/25.17 |
% 168.45/25.17 | Case 1:
% 168.45/25.17 | |
% 168.45/25.17 | | (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 168.45/25.17 | | e2)
% 168.45/25.17 | |
% 168.45/25.17 | | BETA: splitting (13) gives:
% 168.45/25.17 | |
% 168.45/25.17 | | Case 1:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (14) all_58_9 = e2 & op(e3, e0) = e2
% 168.45/25.17 | | |
% 168.45/25.17 | | | ALPHA: (14) implies:
% 168.45/25.17 | | | (15) all_58_9 = e2
% 168.45/25.17 | | |
% 168.45/25.17 | | | REF_CLOSE: (8), (12), (15) are inconsistent by sub-proof #790.
% 168.45/25.17 | | |
% 168.45/25.17 | | Case 2:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (16) all_58_10 = e2 & op(e2, e0) = e2
% 168.45/25.17 | | |
% 168.45/25.17 | | | ALPHA: (16) implies:
% 168.45/25.17 | | | (17) op(e2, e0) = e2
% 168.45/25.17 | | |
% 168.45/25.17 | | | REF_CLOSE: (5), (6), (9), (17) are inconsistent by sub-proof #526.
% 168.45/25.17 | | |
% 168.45/25.17 | | End of split
% 168.45/25.17 | |
% 168.45/25.17 | Case 2:
% 168.45/25.17 | |
% 168.45/25.17 | | (18) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 168.45/25.17 | | e2)
% 168.45/25.17 | |
% 168.45/25.17 | | BETA: splitting (18) gives:
% 168.45/25.17 | |
% 168.45/25.17 | | Case 1:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (19) all_58_11 = e2 & op(e1, e0) = e2
% 168.45/25.17 | | |
% 168.45/25.17 | | | ALPHA: (19) implies:
% 168.45/25.17 | | | (20) all_58_11 = e2
% 168.45/25.17 | | |
% 168.45/25.17 | | | BETA: splitting (11) gives:
% 168.45/25.17 | | |
% 168.45/25.17 | | | Case 1:
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | (21) all_58_15 = e0 & op(e0, e0) = e0
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | ALPHA: (21) implies:
% 168.45/25.17 | | | | (22) op(e0, e0) = e0
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | REF_CLOSE: (1), (2), (6), (22) are inconsistent by sub-proof #204.
% 168.45/25.17 | | | |
% 168.45/25.17 | | | Case 2:
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | (23) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 168.45/25.17 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 168.45/25.17 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 168.45/25.17 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | ALPHA: (23) implies:
% 168.45/25.17 | | | | (24) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 168.45/25.17 | | | | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | REF_CLOSE: (2), (4), (7), (8), (10), (20), (24) are inconsistent by
% 168.45/25.17 | | | | sub-proof #833.
% 168.45/25.17 | | | |
% 168.45/25.17 | | | End of split
% 168.45/25.17 | | |
% 168.45/25.17 | | Case 2:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (25) all_58_15 = e2 & op(e0, e0) = e2
% 168.45/25.17 | | |
% 168.45/25.17 | | | ALPHA: (25) implies:
% 168.45/25.17 | | | (26) op(e0, e0) = e2
% 168.45/25.17 | | |
% 168.45/25.17 | | | REF_CLOSE: (1), (6), (9), (26) are inconsistent by sub-proof #640.
% 168.45/25.17 | | |
% 168.45/25.17 | | End of split
% 168.45/25.17 | |
% 168.45/25.17 | End of split
% 168.45/25.17 |
% 168.45/25.17 End of proof
% 168.45/25.17
% 168.45/25.17 Sub-proof #30 shows that the following formulas are inconsistent:
% 168.45/25.17 ----------------------------------------------------------------
% 168.45/25.17 (1) ~ (e3 = e1)
% 168.45/25.17 (2) ~ (e1 = e0)
% 168.45/25.17 (3) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 168.45/25.17 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 168.45/25.17 (4) ~ (e3 = e0)
% 168.45/25.17 (5) all_58_14 = e0
% 168.45/25.17 (6) all_58_5 = e2
% 168.45/25.17 (7) ~ (e2 = e1)
% 168.45/25.17 (8) all_58_4 = e2
% 168.45/25.17 (9) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 168.45/25.17 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 168.45/25.17 (10) ~ (e3 = e2)
% 168.45/25.17
% 168.45/25.17 Begin of proof
% 168.45/25.17 |
% 168.45/25.17 | BETA: splitting (3) gives:
% 168.45/25.17 |
% 168.45/25.17 | Case 1:
% 168.45/25.17 | |
% 168.45/25.17 | | (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 168.45/25.17 | | e3)
% 168.45/25.17 | |
% 168.45/25.17 | | BETA: splitting (11) gives:
% 168.45/25.17 | |
% 168.45/25.17 | | Case 1:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (12) all_58_4 = e3 & op(e3, e1) = e3
% 168.45/25.17 | | |
% 168.45/25.17 | | | REF_CLOSE: (8), (10), (12) are inconsistent by sub-proof #952.
% 168.45/25.17 | | |
% 168.45/25.17 | | Case 2:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (13) all_58_5 = e3 & op(e2, e1) = e3
% 168.45/25.17 | | |
% 168.45/25.17 | | | REF_CLOSE: (6), (10), (13) are inconsistent by sub-proof #561.
% 168.45/25.17 | | |
% 168.45/25.17 | | End of split
% 168.45/25.17 | |
% 168.45/25.17 | Case 2:
% 168.45/25.17 | |
% 168.45/25.17 | | (14) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 168.45/25.17 | | e3)
% 168.45/25.17 | |
% 168.45/25.17 | | BETA: splitting (14) gives:
% 168.45/25.17 | |
% 168.45/25.17 | | Case 1:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (15) all_58_8 = e3 & op(e1, e1) = e3
% 168.45/25.17 | | |
% 168.45/25.17 | | | ALPHA: (15) implies:
% 168.45/25.17 | | | (16) all_58_8 = e3
% 168.45/25.17 | | |
% 168.45/25.17 | | | BETA: splitting (9) gives:
% 168.45/25.17 | | |
% 168.45/25.17 | | | Case 1:
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | (17) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 168.45/25.17 | | | | = e1)
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | BETA: splitting (17) gives:
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | Case 1:
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | | (18) all_58_4 = e1 & op(e3, e1) = e1
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | | REF_CLOSE: (7), (8), (18) are inconsistent by sub-proof #943.
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | Case 2:
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | | (19) all_58_5 = e1 & op(e2, e1) = e1
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | | REF_CLOSE: (6), (7), (19) are inconsistent by sub-proof #852.
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | End of split
% 168.45/25.17 | | | |
% 168.45/25.17 | | | Case 2:
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | (20) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 168.45/25.17 | | | | = e1)
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | BETA: splitting (20) gives:
% 168.45/25.17 | | | |
% 168.45/25.17 | | | | Case 1:
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | | (21) all_58_8 = e1 & op(e1, e1) = e1
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | | REF_CLOSE: (1), (16), (21) are inconsistent by sub-proof #384.
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | Case 2:
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | | (22) all_58_14 = e1 & op(e0, e1) = e1
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | | ALPHA: (22) implies:
% 168.45/25.17 | | | | | (23) all_58_14 = e1
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | | REF_CLOSE: (2), (5), (23) are inconsistent by sub-proof #586.
% 168.45/25.17 | | | | |
% 168.45/25.17 | | | | End of split
% 168.45/25.17 | | | |
% 168.45/25.17 | | | End of split
% 168.45/25.17 | | |
% 168.45/25.17 | | Case 2:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (24) all_58_14 = e3 & op(e0, e1) = e3
% 168.45/25.17 | | |
% 168.45/25.17 | | | ALPHA: (24) implies:
% 168.45/25.17 | | | (25) all_58_14 = e3
% 168.45/25.17 | | |
% 168.45/25.17 | | | REF_CLOSE: (4), (5), (25) are inconsistent by sub-proof #423.
% 168.45/25.17 | | |
% 168.45/25.17 | | End of split
% 168.45/25.17 | |
% 168.45/25.17 | End of split
% 168.45/25.17 |
% 168.45/25.17 End of proof
% 168.45/25.17
% 168.45/25.17 Sub-proof #31 shows that the following formulas are inconsistent:
% 168.45/25.17 ----------------------------------------------------------------
% 168.45/25.17 (1) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 168.45/25.17 (2) ~ (all_6_2 = e2)
% 168.45/25.17 (3) op(e1, e1) = all_6_2
% 168.45/25.17 (4) all_58_14 = e0
% 168.45/25.17 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.17 (6) ~ (e2 = e0)
% 168.45/25.17
% 168.45/25.17 Begin of proof
% 168.45/25.17 |
% 168.45/25.17 | BETA: splitting (1) gives:
% 168.45/25.17 |
% 168.45/25.17 | Case 1:
% 168.45/25.17 | |
% 168.45/25.17 | | (7) all_58_8 = e2 & op(e1, e1) = e2
% 168.45/25.17 | |
% 168.45/25.17 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #845.
% 168.45/25.17 | |
% 168.45/25.17 | Case 2:
% 168.45/25.17 | |
% 168.45/25.17 | | (8) all_58_14 = e2 & op(e0, e1) = e2
% 168.45/25.17 | |
% 168.45/25.17 | | ALPHA: (8) implies:
% 168.45/25.17 | | (9) all_58_14 = e2
% 168.45/25.17 | |
% 168.45/25.17 | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #806.
% 168.45/25.17 | |
% 168.45/25.17 | End of split
% 168.45/25.17 |
% 168.45/25.17 End of proof
% 168.45/25.17
% 168.45/25.17 Sub-proof #32 shows that the following formulas are inconsistent:
% 168.45/25.17 ----------------------------------------------------------------
% 168.45/25.17 (1) all_58_14 = e3 & op(e0, e1) = e3
% 168.45/25.17 (2) all_58_14 = e0
% 168.45/25.17 (3) ~ (e3 = e0)
% 168.45/25.17
% 168.45/25.17 Begin of proof
% 168.45/25.17 |
% 168.45/25.17 | ALPHA: (1) implies:
% 168.45/25.17 | (4) all_58_14 = e3
% 168.45/25.17 |
% 168.45/25.17 | COMBINE_EQS: (2), (4) imply:
% 168.45/25.17 | (5) e3 = e0
% 168.45/25.17 |
% 168.45/25.17 | REDUCE: (3), (5) imply:
% 168.45/25.17 | (6) $false
% 168.45/25.17 |
% 168.45/25.17 | CLOSE: (6) is inconsistent.
% 168.45/25.17 |
% 168.45/25.17 End of proof
% 168.45/25.17
% 168.45/25.17 Sub-proof #33 shows that the following formulas are inconsistent:
% 168.45/25.17 ----------------------------------------------------------------
% 168.45/25.17 (1) all_56_8 = e0
% 168.45/25.17 (2) all_56_15 = e1
% 168.45/25.17 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.17 (4) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 =
% 168.45/25.17 e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4)))
% 168.45/25.17 & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.45/25.17 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.45/25.17 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.45/25.17 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 168.45/25.17 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.45/25.17 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.45/25.17 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.45/25.17 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.45/25.17 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 168.45/25.17 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.45/25.17 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.45/25.17 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.45/25.17 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.45/25.17 (5) ~ (e2 = e1)
% 168.45/25.17 (6) op(e3, e1) = e2
% 168.45/25.17
% 168.45/25.17 Begin of proof
% 168.45/25.17 |
% 168.45/25.17 | BETA: splitting (4) gives:
% 168.45/25.17 |
% 168.45/25.17 | Case 1:
% 168.45/25.17 | |
% 168.45/25.17 | | (7) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 168.45/25.17 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.45/25.17 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.45/25.17 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | (
% 168.45/25.17 | | ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 168.45/25.17 | |
% 168.45/25.17 | | ALPHA: (7) implies:
% 168.45/25.17 | | (8) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.45/25.17 | | $i(all_56_8))
% 168.45/25.17 | |
% 168.45/25.17 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #34.
% 168.45/25.17 | |
% 168.45/25.17 | Case 2:
% 168.45/25.17 | |
% 168.45/25.17 | | (9) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.45/25.17 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.45/25.17 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.45/25.17 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) |
% 168.45/25.17 | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 168.45/25.17 | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.45/25.17 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 168.45/25.17 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.45/25.17 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) |
% 168.45/25.17 | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.45/25.17 | |
% 168.45/25.17 | | BETA: splitting (9) gives:
% 168.45/25.17 | |
% 168.45/25.17 | | Case 1:
% 168.45/25.17 | | |
% 168.45/25.17 | | | (10) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.45/25.17 | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.45/25.17 | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.45/25.17 | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 168.45/25.17 | | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 168.45/25.17 | | |
% 168.45/25.18 | | | ALPHA: (10) implies:
% 168.45/25.18 | | | (11) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8
% 168.45/25.18 | | | & $i(all_56_8))
% 168.45/25.18 | | |
% 168.45/25.18 | | | REF_CLOSE: (1), (2), (11) are inconsistent by sub-proof #34.
% 168.45/25.18 | | |
% 168.45/25.18 | | Case 2:
% 168.45/25.18 | | |
% 168.45/25.18 | | | (12) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.45/25.18 | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 168.45/25.18 | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.45/25.18 | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 168.45/25.18 | | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 168.45/25.18 | | |
% 168.45/25.18 | | | ALPHA: (12) implies:
% 168.45/25.18 | | | (13) op(e3, e1) = e1
% 168.45/25.18 | | |
% 168.45/25.18 | | | REF_CLOSE: (3), (5), (6), (13) are inconsistent by sub-proof #212.
% 168.45/25.18 | | |
% 168.45/25.18 | | End of split
% 168.45/25.18 | |
% 168.45/25.18 | End of split
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #34 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.45/25.18 $i(all_56_8))
% 168.45/25.18 (2) all_56_15 = e1
% 168.45/25.18 (3) all_56_8 = e0
% 168.45/25.18
% 168.45/25.18 Begin of proof
% 168.45/25.18 |
% 168.45/25.18 | BETA: splitting (1) gives:
% 168.45/25.18 |
% 168.45/25.18 | Case 1:
% 168.45/25.18 | |
% 168.45/25.18 | | (4) ~ (all_56_15 = e1)
% 168.45/25.18 | |
% 168.45/25.18 | | REDUCE: (2), (4) imply:
% 168.45/25.18 | | (5) $false
% 168.45/25.18 | |
% 168.45/25.18 | | CLOSE: (5) is inconsistent.
% 168.45/25.18 | |
% 168.45/25.18 | Case 2:
% 168.45/25.18 | |
% 168.45/25.18 | | (6) ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)
% 168.45/25.18 | |
% 168.45/25.18 | | ALPHA: (6) implies:
% 168.45/25.18 | | (7) ~ (all_56_8 = e0)
% 168.45/25.18 | |
% 168.45/25.18 | | REDUCE: (3), (7) imply:
% 168.45/25.18 | | (8) $false
% 168.45/25.18 | |
% 168.45/25.18 | | CLOSE: (8) is inconsistent.
% 168.45/25.18 | |
% 168.45/25.18 | End of split
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #35 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.18 (2) op(e2, e3) = e3
% 168.45/25.18 (3) op(e2, e3) = e1
% 168.45/25.18 (4) ~ (e3 = e1)
% 168.45/25.18
% 168.45/25.18 Begin of proof
% 168.45/25.18 |
% 168.45/25.18 | GROUND_INST: instantiating (1) with e1, e3, e3, e2, simplifying with (2), (3)
% 168.45/25.18 | gives:
% 168.45/25.18 | (5) e3 = e1
% 168.45/25.18 |
% 168.45/25.18 | REDUCE: (4), (5) imply:
% 168.45/25.18 | (6) $false
% 168.45/25.18 |
% 168.45/25.18 | CLOSE: (6) is inconsistent.
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #36 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) all_58_4 = e3 & op(e3, e1) = e3
% 168.45/25.18 (2) all_58_4 = e2
% 168.45/25.18 (3) ~ (e3 = e2)
% 168.45/25.18
% 168.45/25.18 Begin of proof
% 168.45/25.18 |
% 168.45/25.18 | ALPHA: (1) implies:
% 168.45/25.18 | (4) all_58_4 = e3
% 168.45/25.18 |
% 168.45/25.18 | COMBINE_EQS: (2), (4) imply:
% 168.45/25.18 | (5) e3 = e2
% 168.45/25.18 |
% 168.45/25.18 | REDUCE: (3), (5) imply:
% 168.45/25.18 | (6) $false
% 168.45/25.18 |
% 168.45/25.18 | CLOSE: (6) is inconsistent.
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #37 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) op(e3, e2) = e1
% 168.45/25.18 (2) op(e3, e3) = all_10_2
% 168.45/25.18 (3) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 168.45/25.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.18 (5) ~ (all_10_2 = e2)
% 168.45/25.18 (6) ~ (e2 = e1)
% 168.45/25.18
% 168.45/25.18 Begin of proof
% 168.45/25.18 |
% 168.45/25.18 | BETA: splitting (3) gives:
% 168.45/25.18 |
% 168.45/25.18 | Case 1:
% 168.45/25.18 | |
% 168.45/25.18 | | (7) all_58_0 = e2 & op(e3, e3) = e2
% 168.45/25.18 | |
% 168.45/25.18 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #666.
% 168.45/25.18 | |
% 168.45/25.18 | Case 2:
% 168.45/25.18 | |
% 168.45/25.18 | | (8) all_58_1 = e2 & op(e3, e2) = e2
% 168.45/25.18 | |
% 168.45/25.18 | | ALPHA: (8) implies:
% 168.45/25.18 | | (9) op(e3, e2) = e2
% 168.45/25.18 | |
% 168.45/25.18 | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #180.
% 168.45/25.18 | |
% 168.45/25.18 | End of split
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #38 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.18 (2) op(e0, e3) = e3
% 168.45/25.18 (3) op(e0, e3) = e2
% 168.45/25.18 (4) ~ (e3 = e2)
% 168.45/25.18
% 168.45/25.18 Begin of proof
% 168.45/25.18 |
% 168.45/25.18 | GROUND_INST: instantiating (1) with e2, e3, e3, e0, simplifying with (2), (3)
% 168.45/25.18 | gives:
% 168.45/25.18 | (5) e3 = e2
% 168.45/25.18 |
% 168.45/25.18 | REDUCE: (4), (5) imply:
% 168.45/25.18 | (6) $false
% 168.45/25.18 |
% 168.45/25.18 | CLOSE: (6) is inconsistent.
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #39 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 168.45/25.18 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.45/25.18 (2) all_58_15 = e1
% 168.45/25.18 (3) op(e0, e0) = e1
% 168.45/25.18 (4) ~ (e3 = e1)
% 168.45/25.18 (5) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 168.45/25.18 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 168.45/25.18 (6) ~ (e3 = e0)
% 168.45/25.18 (7) all_58_12 = e0
% 168.45/25.18 (8) all_58_14 = e0
% 168.45/25.18 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.18 (10) ~ (e2 = e0)
% 168.45/25.18 (11) ~ (e2 = e1)
% 168.45/25.18 (12) ~ (e3 = e2)
% 168.45/25.18
% 168.45/25.18 Begin of proof
% 168.45/25.18 |
% 168.45/25.18 | BETA: splitting (5) gives:
% 168.45/25.18 |
% 168.45/25.18 | Case 1:
% 168.45/25.18 | |
% 168.45/25.18 | | (13) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 168.45/25.18 | | e3)
% 168.45/25.18 | |
% 168.45/25.18 | | BETA: splitting (13) gives:
% 168.45/25.18 | |
% 168.45/25.18 | | Case 1:
% 168.45/25.18 | | |
% 168.45/25.18 | | | (14) all_58_12 = e3 & op(e0, e3) = e3
% 168.45/25.18 | | |
% 168.45/25.18 | | | ALPHA: (14) implies:
% 168.45/25.18 | | | (15) all_58_12 = e3
% 168.45/25.18 | | |
% 168.45/25.18 | | | REF_CLOSE: (6), (7), (15) are inconsistent by sub-proof #608.
% 168.45/25.18 | | |
% 168.45/25.18 | | Case 2:
% 168.45/25.18 | | |
% 168.45/25.18 | | | (16) all_58_13 = e3 & op(e0, e2) = e3
% 168.45/25.18 | | |
% 168.45/25.18 | | | ALPHA: (16) implies:
% 168.45/25.18 | | | (17) all_58_13 = e3
% 168.45/25.18 | | |
% 168.45/25.18 | | | BETA: splitting (1) gives:
% 168.45/25.18 | | |
% 168.45/25.18 | | | Case 1:
% 168.45/25.18 | | | |
% 168.45/25.18 | | | | (18) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 168.45/25.18 | | | | e2) = e2)
% 168.45/25.18 | | | |
% 168.45/25.18 | | | | BETA: splitting (18) gives:
% 168.45/25.18 | | | |
% 168.45/25.18 | | | | Case 1:
% 168.45/25.18 | | | | |
% 168.45/25.18 | | | | | (19) all_58_12 = e2 & op(e0, e3) = e2
% 168.45/25.18 | | | | |
% 168.45/25.18 | | | | | ALPHA: (19) implies:
% 168.45/25.18 | | | | | (20) all_58_12 = e2
% 168.45/25.18 | | | | |
% 168.45/25.18 | | | | | REF_CLOSE: (7), (10), (20) are inconsistent by sub-proof #729.
% 168.45/25.18 | | | | |
% 168.45/25.18 | | | | Case 2:
% 168.45/25.18 | | | | |
% 168.45/25.18 | | | | | (21) all_58_13 = e2 & op(e0, e2) = e2
% 168.45/25.18 | | | | |
% 168.45/25.18 | | | | | ALPHA: (21) implies:
% 168.45/25.18 | | | | | (22) all_58_13 = e2
% 168.45/25.18 | | | | |
% 168.45/25.18 | | | | | REF_CLOSE: (12), (17), (22) are inconsistent by sub-proof #192.
% 168.45/25.18 | | | | |
% 168.45/25.18 | | | | End of split
% 168.45/25.18 | | | |
% 168.45/25.18 | | | Case 2:
% 168.45/25.18 | | | |
% 168.45/25.18 | | | | (23) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 168.45/25.18 | | | | e0) = e2)
% 168.45/25.18 | | | |
% 168.45/25.18 | | | | REF_CLOSE: (3), (8), (9), (10), (11), (23) are inconsistent by sub-proof
% 168.45/25.18 | | | | #41.
% 168.45/25.18 | | | |
% 168.45/25.18 | | | End of split
% 168.45/25.18 | | |
% 168.45/25.18 | | End of split
% 168.45/25.18 | |
% 168.45/25.18 | Case 2:
% 168.45/25.18 | |
% 168.45/25.18 | | (24) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 168.45/25.18 | | e3)
% 168.45/25.18 | |
% 168.45/25.18 | | REF_CLOSE: (2), (4), (6), (8), (24) are inconsistent by sub-proof #40.
% 168.45/25.18 | |
% 168.45/25.18 | End of split
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #40 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) all_58_15 = e1
% 168.45/25.18 (2) ~ (e3 = e1)
% 168.45/25.18 (3) ~ (e3 = e0)
% 168.45/25.18 (4) all_58_14 = e0
% 168.45/25.18 (5) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 168.45/25.18
% 168.45/25.18 Begin of proof
% 168.45/25.18 |
% 168.45/25.18 | BETA: splitting (5) gives:
% 168.45/25.18 |
% 168.45/25.18 | Case 1:
% 168.45/25.18 | |
% 168.45/25.18 | | (6) all_58_14 = e3 & op(e0, e1) = e3
% 168.45/25.18 | |
% 168.45/25.18 | | ALPHA: (6) implies:
% 168.45/25.18 | | (7) all_58_14 = e3
% 168.45/25.18 | |
% 168.45/25.18 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #423.
% 168.45/25.18 | |
% 168.45/25.18 | Case 2:
% 168.45/25.18 | |
% 168.45/25.18 | | (8) all_58_15 = e3 & op(e0, e0) = e3
% 168.45/25.18 | |
% 168.45/25.18 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #878.
% 168.45/25.18 | |
% 168.45/25.18 | End of split
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #41 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) op(e0, e0) = e1
% 168.45/25.18 (2) all_58_14 = e0
% 168.45/25.18 (3) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.45/25.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.18 (5) ~ (e2 = e0)
% 168.45/25.18 (6) ~ (e2 = e1)
% 168.45/25.18
% 168.45/25.18 Begin of proof
% 168.45/25.18 |
% 168.45/25.18 | BETA: splitting (3) gives:
% 168.45/25.18 |
% 168.45/25.18 | Case 1:
% 168.45/25.18 | |
% 168.45/25.18 | | (7) all_58_14 = e2 & op(e0, e1) = e2
% 168.45/25.18 | |
% 168.45/25.18 | | ALPHA: (7) implies:
% 168.45/25.18 | | (8) all_58_14 = e2
% 168.45/25.18 | |
% 168.45/25.18 | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #806.
% 168.45/25.18 | |
% 168.45/25.18 | Case 2:
% 168.45/25.18 | |
% 168.45/25.18 | | (9) all_58_15 = e2 & op(e0, e0) = e2
% 168.45/25.18 | |
% 168.45/25.18 | | ALPHA: (9) implies:
% 168.45/25.18 | | (10) op(e0, e0) = e2
% 168.45/25.18 | |
% 168.45/25.18 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #640.
% 168.45/25.18 | |
% 168.45/25.18 | End of split
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #42 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) all_58_11 = e1 & op(e1, e0) = e1
% 168.45/25.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.18 (3) op(e1, e0) = all_52_14
% 168.45/25.18 (4) ~ (all_52_14 = e1)
% 168.45/25.18
% 168.45/25.18 Begin of proof
% 168.45/25.18 |
% 168.45/25.18 | ALPHA: (1) implies:
% 168.45/25.18 | (5) op(e1, e0) = e1
% 168.45/25.18 |
% 168.45/25.18 | GROUND_INST: instantiating (2) with all_52_14, e1, e0, e1, simplifying with
% 168.45/25.18 | (3), (5) gives:
% 168.45/25.18 | (6) all_52_14 = e1
% 168.45/25.18 |
% 168.45/25.18 | REDUCE: (4), (6) imply:
% 168.45/25.18 | (7) $false
% 168.45/25.18 |
% 168.45/25.18 | CLOSE: (7) is inconsistent.
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #43 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) all_58_9 = e1 & op(e3, e0) = e1
% 168.45/25.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.18 (3) op(e3, e0) = all_52_12
% 168.45/25.18 (4) ~ (all_52_12 = e1)
% 168.45/25.18
% 168.45/25.18 Begin of proof
% 168.45/25.18 |
% 168.45/25.18 | ALPHA: (1) implies:
% 168.45/25.18 | (5) op(e3, e0) = e1
% 168.45/25.18 |
% 168.45/25.18 | GROUND_INST: instantiating (2) with all_52_12, e1, e0, e3, simplifying with
% 168.45/25.18 | (3), (5) gives:
% 168.45/25.18 | (6) all_52_12 = e1
% 168.45/25.18 |
% 168.45/25.18 | REDUCE: (4), (6) imply:
% 168.45/25.18 | (7) $false
% 168.45/25.18 |
% 168.45/25.18 | CLOSE: (7) is inconsistent.
% 168.45/25.18 |
% 168.45/25.18 End of proof
% 168.45/25.18
% 168.45/25.18 Sub-proof #44 shows that the following formulas are inconsistent:
% 168.45/25.18 ----------------------------------------------------------------
% 168.45/25.18 (1) op(e2, e1) = all_52_9
% 168.45/25.18 (2) ~ (all_52_14 = e1)
% 168.45/25.18 (3) all_54_2 = all_52_8
% 168.45/25.18 (4) ~ (all_52_1 = e3)
% 168.45/25.18 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 168.45/25.18 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 168.45/25.18 (6) ~ (all_52_14 = all_4_2)
% 168.45/25.18 (7) ~ (all_52_1 = e0)
% 168.45/25.18 (8) all_54_12 = all_52_3
% 168.45/25.18 (9) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 168.45/25.18 (10) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 168.45/25.18 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 168.45/25.18 (11) ~ (all_52_1 = all_8_2)
% 168.45/25.18 (12) ~ (all_52_3 = e3)
% 168.45/25.18 (13) op(e3, e3) = e0
% 168.45/25.18 (14) ~ (all_52_13 = all_8_2)
% 168.45/25.18 (15) ~ (all_4_2 = e1)
% 168.45/25.18 (16) all_56_14 = all_6_2
% 168.45/25.18 (17) op(e3, e0) = all_52_12
% 168.45/25.18 (18) ~ (all_52_1 = all_52_3)
% 168.45/25.18 (19) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 168.45/25.18 (20) op(e1, e3) = all_52_2
% 168.45/25.18 (21) ~ (all_24_2 = e0) | ( ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0 &
% 168.45/25.18 op(e0, e3) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 168.45/25.18 e1) & op(e0, e3) = all_24_1 & $i(all_24_1))
% 168.45/25.18 (22) ~ (all_52_6 = all_8_2)
% 168.45/25.18 (23) ~ (all_52_14 = e3)
% 168.45/25.18 (24) ~ (all_56_12 = e0) | (all_56_11 = e2 & op(e2, e0) = e2)
% 168.45/25.18 (25) op(e1, e2) = all_52_6
% 168.45/25.18 (26) ~ (all_52_3 = all_4_2)
% 168.45/25.18 (27) op(e2, e3) = all_52_1
% 168.45/25.18 (28) ( ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 & op(e0, e3) =
% 168.45/25.18 all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e0,
% 168.45/25.18 e3) = all_10_1 & $i(all_10_1))
% 168.45/25.18 (29) all_58_6 = e3 & op(e1, e3) = e3
% 168.45/25.18 (30) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 168.45/25.18 (31) all_54_15 = all_4_2
% 168.45/25.18 (32) all_56_10 = e0
% 168.45/25.18 (33) all_56_12 = all_8_2
% 168.45/25.19 (34) all_54_4 = all_52_1
% 168.45/25.19 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 168.45/25.19 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 168.45/25.19 (36) all_56_15 = all_4_2
% 168.45/25.19 (37) ~ (all_52_8 = e0)
% 168.45/25.19 (38) ~ (all_52_7 = all_8_2)
% 168.45/25.19 (39) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.45/25.19 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.45/25.19 (40) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 168.45/25.19 (41) ~ (all_52_8 = e2)
% 168.45/25.19 (42) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.45/25.19 (43) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 168.45/25.19 (44) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.45/25.19 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 168.45/25.19 (45) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 168.45/25.19 (46) all_54_11 = all_52_14
% 168.45/25.19 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.19 (48) ~ (all_52_4 = all_8_2)
% 168.45/25.19 (49) ~ (all_52_8 = all_6_2)
% 168.45/25.19 (50) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 168.45/25.19 (51) ~ (all_52_13 = all_4_2)
% 168.45/25.19 (52) ~ (all_52_9 = all_8_2)
% 168.45/25.19 (53) ~ (all_52_14 = e2)
% 168.45/25.19 (54) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.45/25.19 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.45/25.19 (55) all_54_5 = all_8_2
% 168.45/25.19 (56) ~ (all_52_8 = all_52_12)
% 168.45/25.19 (57) op(e3, e2) = all_52_4
% 168.45/25.19 (58) ~ (all_4_2 = e3)
% 168.45/25.19 (59) ~ (all_52_3 = e0)
% 168.45/25.19 (60) ~ (all_8_2 = e1)
% 168.45/25.19 (61) all_24_2 = e0
% 168.45/25.19 (62) op(e0, e2) = all_52_7
% 168.45/25.19 (63) op(e2, e0) = all_52_13
% 168.45/25.19 (64) all_58_0 = e0
% 168.45/25.19
% 168.45/25.19 Begin of proof
% 168.45/25.19 |
% 168.45/25.19 | ALPHA: (29) implies:
% 168.45/25.19 | (65) all_58_6 = e3
% 168.45/25.19 | (66) op(e1, e3) = e3
% 168.45/25.19 |
% 168.45/25.19 | BETA: splitting (19) gives:
% 168.45/25.19 |
% 168.45/25.19 | Case 1:
% 168.45/25.19 | |
% 168.45/25.19 | | (67) all_54_11 = e2
% 168.45/25.19 | |
% 168.45/25.19 | | REF_CLOSE: (46), (53), (67) are inconsistent by sub-proof #622.
% 168.45/25.19 | |
% 168.45/25.19 | Case 2:
% 168.45/25.19 | |
% 168.45/25.19 | | (68) all_54_11 = e1 | all_54_11 = e0
% 168.45/25.19 | |
% 168.45/25.19 | | BETA: splitting (68) gives:
% 168.45/25.19 | |
% 168.45/25.19 | | Case 1:
% 168.45/25.19 | | |
% 168.45/25.19 | | | (69) all_54_11 = e1
% 168.45/25.19 | | |
% 168.45/25.19 | | | REF_CLOSE: (2), (46), (69) are inconsistent by sub-proof #734.
% 168.45/25.19 | | |
% 168.45/25.19 | | Case 2:
% 168.45/25.19 | | |
% 168.45/25.19 | | | (70) all_54_11 = e0
% 168.45/25.19 | | |
% 168.45/25.19 | | | COMBINE_EQS: (46), (70) imply:
% 168.45/25.19 | | | (71) all_52_14 = e0
% 168.45/25.19 | | |
% 168.45/25.19 | | | SIMP: (71) implies:
% 168.45/25.19 | | | (72) all_52_14 = e0
% 168.45/25.19 | | |
% 168.45/25.19 | | | REDUCE: (6), (72) imply:
% 168.45/25.19 | | | (73) ~ (all_4_2 = e0)
% 168.45/25.19 | | |
% 168.45/25.19 | | | SIMP: (73) implies:
% 168.45/25.19 | | | (74) ~ (all_4_2 = e0)
% 168.45/25.19 | | |
% 168.45/25.19 | | | REDUCE: (23), (72) imply:
% 168.45/25.19 | | | (75) ~ (e3 = e0)
% 168.45/25.19 | | |
% 168.45/25.19 | | | SIMP: (75) implies:
% 168.45/25.19 | | | (76) ~ (e3 = e0)
% 168.45/25.19 | | |
% 168.45/25.19 | | | BETA: splitting (42) gives:
% 168.45/25.19 | | |
% 168.45/25.19 | | | Case 1:
% 168.45/25.19 | | | |
% 168.45/25.19 | | | | (77) all_56_10 = e3
% 168.45/25.19 | | | |
% 168.45/25.19 | | | | REF_CLOSE: (32), (76), (77) are inconsistent by sub-proof #166.
% 168.45/25.19 | | | |
% 168.45/25.19 | | | Case 2:
% 168.45/25.19 | | | |
% 168.45/25.19 | | | | (78) ~ (all_56_10 = e3)
% 168.45/25.19 | | | | (79) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.45/25.19 | | | |
% 168.45/25.19 | | | | BETA: splitting (30) gives:
% 168.45/25.19 | | | |
% 168.45/25.19 | | | | Case 1:
% 168.45/25.19 | | | | |
% 168.45/25.19 | | | | | (80) all_54_15 = e3
% 168.45/25.19 | | | | |
% 168.45/25.19 | | | | | REF_CLOSE: (31), (58), (80) are inconsistent by sub-proof #992.
% 168.45/25.19 | | | | |
% 168.45/25.19 | | | | Case 2:
% 168.45/25.19 | | | | |
% 168.45/25.19 | | | | | (81) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 168.45/25.19 | | | | |
% 168.45/25.19 | | | | | BETA: splitting (81) gives:
% 168.45/25.19 | | | | |
% 168.45/25.19 | | | | | Case 1:
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | | (82) all_54_15 = e2
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | | COMBINE_EQS: (31), (82) imply:
% 168.45/25.19 | | | | | | (83) all_4_2 = e2
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | | SIMP: (83) implies:
% 168.45/25.19 | | | | | | (84) all_4_2 = e2
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | | REDUCE: (26), (84) imply:
% 168.45/25.19 | | | | | | (85) ~ (all_52_3 = e2)
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | | REDUCE: (51), (84) imply:
% 168.45/25.19 | | | | | | (86) ~ (all_52_13 = e2)
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | | BETA: splitting (24) gives:
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | | Case 1:
% 168.45/25.19 | | | | | | |
% 168.45/25.19 | | | | | | | (87) ~ (all_56_12 = e0)
% 168.45/25.19 | | | | | | |
% 168.45/25.19 | | | | | | | REDUCE: (33), (87) imply:
% 168.45/25.19 | | | | | | | (88) ~ (all_8_2 = e0)
% 168.45/25.19 | | | | | | |
% 168.45/25.19 | | | | | | | BETA: splitting (43) gives:
% 168.45/25.19 | | | | | | |
% 168.45/25.19 | | | | | | | Case 1:
% 168.45/25.19 | | | | | | | |
% 168.45/25.19 | | | | | | | | (89) all_54_12 = e3
% 168.45/25.19 | | | | | | | |
% 168.45/25.19 | | | | | | | | REF_CLOSE: (8), (12), (89) are inconsistent by sub-proof #738.
% 168.45/25.19 | | | | | | | |
% 168.45/25.19 | | | | | | | Case 2:
% 168.45/25.19 | | | | | | | |
% 168.45/25.19 | | | | | | | | (90) ~ (all_54_12 = e3)
% 168.45/25.19 | | | | | | | | (91) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 168.45/25.19 | | | | | | | |
% 168.45/25.19 | | | | | | | | BETA: splitting (91) gives:
% 168.45/25.19 | | | | | | | |
% 168.45/25.19 | | | | | | | | Case 1:
% 168.45/25.19 | | | | | | | | |
% 168.45/25.19 | | | | | | | | | (92) all_54_12 = e2
% 168.45/25.19 | | | | | | | | |
% 168.45/25.19 | | | | | | | | | REF_CLOSE: (8), (85), (92) are inconsistent by sub-proof #676.
% 168.45/25.19 | | | | | | | | |
% 168.45/25.19 | | | | | | | | Case 2:
% 168.45/25.19 | | | | | | | | |
% 168.45/25.19 | | | | | | | | | (93) all_54_12 = e1 | all_54_12 = e0
% 168.45/25.19 | | | | | | | | |
% 168.45/25.19 | | | | | | | | | BETA: splitting (93) gives:
% 168.45/25.19 | | | | | | | | |
% 168.45/25.19 | | | | | | | | | Case 1:
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | (94) all_54_12 = e1
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | COMBINE_EQS: (8), (94) imply:
% 168.45/25.19 | | | | | | | | | | (95) all_52_3 = e1
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | SIMP: (95) implies:
% 168.45/25.19 | | | | | | | | | | (96) all_52_3 = e1
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | REDUCE: (18), (96) imply:
% 168.45/25.19 | | | | | | | | | | (97) ~ (all_52_1 = e1)
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | REDUCE: (12), (96) imply:
% 168.45/25.19 | | | | | | | | | | (98) ~ (e3 = e1)
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | SIMP: (98) implies:
% 168.45/25.19 | | | | | | | | | | (99) ~ (e3 = e1)
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | REDUCE: (59), (96) imply:
% 168.45/25.19 | | | | | | | | | | (100) ~ (e1 = e0)
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | BETA: splitting (45) gives:
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | Case 1:
% 168.45/25.19 | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | (101) all_54_4 = e3
% 168.45/25.19 | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | COMBINE_EQS: (34), (101) imply:
% 168.45/25.19 | | | | | | | | | | | (102) all_52_1 = e3
% 168.45/25.19 | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | REDUCE: (4), (102) imply:
% 168.45/25.19 | | | | | | | | | | | (103) $false
% 168.45/25.19 | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | CLOSE: (103) is inconsistent.
% 168.45/25.19 | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | Case 2:
% 168.45/25.19 | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | (104) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 168.45/25.19 | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | BETA: splitting (104) gives:
% 168.45/25.19 | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | Case 1:
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | (105) all_54_4 = e2
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | COMBINE_EQS: (34), (105) imply:
% 168.45/25.19 | | | | | | | | | | | | (106) all_52_1 = e2
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | REDUCE: (11), (106) imply:
% 168.45/25.19 | | | | | | | | | | | | (107) ~ (all_8_2 = e2)
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | SIMP: (107) implies:
% 168.45/25.19 | | | | | | | | | | | | (108) ~ (all_8_2 = e2)
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | REDUCE: (97), (106) imply:
% 168.45/25.19 | | | | | | | | | | | | (109) ~ (e2 = e1)
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | REDUCE: (7), (106) imply:
% 168.45/25.19 | | | | | | | | | | | | (110) ~ (e2 = e0)
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | REDUCE: (27), (106) imply:
% 168.45/25.19 | | | | | | | | | | | | (111) op(e2, e3) = e2
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | BETA: splitting (21) gives:
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | Case 1:
% 168.45/25.19 | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | (112) ~ (all_24_2 = e0)
% 168.45/25.19 | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | REDUCE: (61), (112) imply:
% 168.45/25.19 | | | | | | | | | | | | | (113) $false
% 168.45/25.19 | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | CLOSE: (113) is inconsistent.
% 168.45/25.19 | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | Case 2:
% 168.45/25.19 | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | (114) ( ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0
% 168.45/25.19 | | | | | | | | | | | | | & op(e0, e3) = all_24_1 & $i(all_24_0) &
% 168.45/25.19 | | | | | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0, e3)
% 168.45/25.19 | | | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 168.45/25.19 | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | BETA: splitting (9) gives:
% 168.45/25.19 | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | Case 1:
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | (115) all_54_5 = e3
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | COMBINE_EQS: (55), (115) imply:
% 168.45/25.19 | | | | | | | | | | | | | | (116) all_8_2 = e3
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | COMBINE_EQS: (33), (116) imply:
% 168.45/25.19 | | | | | | | | | | | | | | (117) all_56_12 = e3
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | REDUCE: (52), (116) imply:
% 168.45/25.19 | | | | | | | | | | | | | | (118) ~ (all_52_9 = e3)
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | REDUCE: (14), (116) imply:
% 168.45/25.19 | | | | | | | | | | | | | | (119) ~ (all_52_13 = e3)
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | REDUCE: (108), (116) imply:
% 168.45/25.19 | | | | | | | | | | | | | | (120) ~ (e3 = e2)
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | BETA: splitting (54) gives:
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | Case 1:
% 168.45/25.19 | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | (121) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 168.45/25.19 | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 168.45/25.19 | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 168.45/25.19 | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | Case 1:
% 168.45/25.19 | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | (122) all_58_2 = e3 & op(e2, e3) = e3
% 168.45/25.19 | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 168.45/25.19 | | | | | | | | | | | | | | | | (123) op(e2, e3) = e3
% 168.45/25.19 | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (47), (111), (120), (123) are inconsistent
% 168.45/25.19 | | | | | | | | | | | | | | | | by sub-proof #462.
% 168.45/25.19 | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | Case 2:
% 168.45/25.19 | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | (124) all_58_3 = e3 & op(e2, e2) = e3
% 168.45/25.19 | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 168.45/25.19 | | | | | | | | | | | | | | | | (125) all_58_3 = e3
% 168.45/25.19 | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | BETA: splitting (79) gives:
% 168.45/25.19 | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | Case 1:
% 168.45/25.19 | | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | | (126) all_56_12 = e2
% 168.45/25.19 | | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | | COMBINE_EQS: (117), (126) imply:
% 168.45/25.19 | | | | | | | | | | | | | | | | | (127) e3 = e2
% 168.45/25.19 | | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (127) imply:
% 168.45/25.19 | | | | | | | | | | | | | | | | | (128) all_58_3 = e2
% 168.45/25.19 | | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (27), (39), (47), (54), (76), (99), (100),
% 168.45/25.19 | | | | | | | | | | | | | | | | | (109), (110), (111), (120), (128) are inconsistent
% 168.45/25.19 | | | | | | | | | | | | | | | | | by sub-proof #665.
% 168.45/25.19 | | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | Case 2:
% 168.45/25.19 | | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | | (129) all_56_14 = e1 | all_56_15 = e0
% 168.45/25.19 | | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (16), (17), (32), (36), (37), (40), (41),
% 168.45/25.19 | | | | | | | | | | | | | | | | | (47), (49), (50), (56), (74), (129) are
% 168.45/25.19 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #82.
% 168.45/25.19 | | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | | End of split
% 168.45/25.19 | | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | End of split
% 168.45/25.19 | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | Case 2:
% 168.45/25.19 | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | (130) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 168.45/25.19 | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 168.45/25.19 | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | | REF_CLOSE: (1), (47), (63), (118), (119), (130) are
% 168.45/25.19 | | | | | | | | | | | | | | | inconsistent by sub-proof #218.
% 168.45/25.19 | | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | End of split
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | Case 2:
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | (131) ~ (all_54_5 = e3)
% 168.45/25.19 | | | | | | | | | | | | | | (132) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | REDUCE: (55), (131) imply:
% 168.45/25.19 | | | | | | | | | | | | | | (133) ~ (all_8_2 = e3)
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (13), (20), (22), (25), (27), (28),
% 168.45/25.19 | | | | | | | | | | | | | | (35), (38), (39), (44), (47), (48), (54), (55),
% 168.45/25.19 | | | | | | | | | | | | | | (57), (60), (62), (64), (65), (66), (76), (88),
% 168.45/25.19 | | | | | | | | | | | | | | (99), (100), (114), (132), (133) are inconsistent
% 168.45/25.19 | | | | | | | | | | | | | | by sub-proof #207.
% 168.45/25.19 | | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | | End of split
% 168.45/25.19 | | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | End of split
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | Case 2:
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | (134) all_54_4 = e1 | all_54_4 = e0
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | | REF_CLOSE: (7), (34), (97), (134) are inconsistent by
% 168.45/25.19 | | | | | | | | | | | | sub-proof #672.
% 168.45/25.19 | | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | | End of split
% 168.45/25.19 | | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | End of split
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | Case 2:
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | (135) all_54_12 = e0
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | | REF_CLOSE: (8), (59), (135) are inconsistent by sub-proof
% 168.45/25.19 | | | | | | | | | | #653.
% 168.45/25.19 | | | | | | | | | |
% 168.45/25.19 | | | | | | | | | End of split
% 168.45/25.19 | | | | | | | | |
% 168.45/25.19 | | | | | | | | End of split
% 168.45/25.19 | | | | | | | |
% 168.45/25.19 | | | | | | | End of split
% 168.45/25.19 | | | | | | |
% 168.45/25.19 | | | | | | Case 2:
% 168.45/25.19 | | | | | | |
% 168.45/25.19 | | | | | | | (136) all_56_11 = e2 & op(e2, e0) = e2
% 168.45/25.19 | | | | | | |
% 168.45/25.19 | | | | | | | ALPHA: (136) implies:
% 168.45/25.19 | | | | | | | (137) op(e2, e0) = e2
% 168.45/25.19 | | | | | | |
% 168.45/25.19 | | | | | | | REF_CLOSE: (47), (63), (86), (137) are inconsistent by sub-proof
% 168.45/25.19 | | | | | | | #662.
% 168.45/25.19 | | | | | | |
% 168.45/25.19 | | | | | | End of split
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | Case 2:
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | | (138) all_54_15 = e1 | all_54_15 = e0
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | | REF_CLOSE: (15), (31), (74), (138) are inconsistent by sub-proof
% 168.45/25.19 | | | | | | #698.
% 168.45/25.19 | | | | | |
% 168.45/25.19 | | | | | End of split
% 168.45/25.19 | | | | |
% 168.45/25.19 | | | | End of split
% 168.45/25.19 | | | |
% 168.45/25.19 | | | End of split
% 168.45/25.19 | | |
% 168.45/25.19 | | End of split
% 168.45/25.19 | |
% 168.45/25.19 | End of split
% 168.45/25.19 |
% 168.45/25.19 End of proof
% 168.45/25.19
% 168.45/25.19 Sub-proof #45 shows that the following formulas are inconsistent:
% 168.45/25.19 ----------------------------------------------------------------
% 168.45/25.19 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 168.45/25.19 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 168.45/25.19 (2) ~ (e3 = e1)
% 168.45/25.19 (3) ~ (e1 = e0)
% 168.45/25.19 (4) op(e2, e3) = all_52_1
% 168.45/25.19 (5) op(e2, e3) = e2
% 168.45/25.19 (6) ~ (e3 = e0)
% 168.45/25.19 (7) all_58_8 = e3 & op(e1, e1) = e3
% 168.45/25.19 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.45/25.19 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.45/25.19 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.19 (10) all_58_8 = e2
% 168.45/25.19 (11) ~ (e2 = e0)
% 168.45/25.19 (12) all_58_3 = e3
% 168.45/25.19 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.45/25.19 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.45/25.19 (14) ~ (e2 = e1)
% 168.45/25.19 (15) ~ (e3 = e2)
% 168.45/25.19
% 168.45/25.19 Begin of proof
% 168.45/25.19 |
% 168.45/25.19 | ALPHA: (7) implies:
% 168.45/25.19 | (16) all_58_8 = e3
% 168.45/25.19 |
% 168.45/25.19 | COMBINE_EQS: (10), (16) imply:
% 168.45/25.19 | (17) e3 = e2
% 168.45/25.19 |
% 168.45/25.19 | COMBINE_EQS: (12), (17) imply:
% 168.45/25.19 | (18) all_58_3 = e2
% 168.45/25.19 |
% 168.45/25.19 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (13), (14), (15),
% 168.45/25.19 | (18) are inconsistent by sub-proof #665.
% 168.45/25.19 |
% 168.45/25.19 End of proof
% 168.45/25.19
% 168.45/25.19 Sub-proof #46 shows that the following formulas are inconsistent:
% 168.45/25.19 ----------------------------------------------------------------
% 168.45/25.19 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 168.45/25.19 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 168.45/25.19 (2) ~ (all_4_2 = e2)
% 168.45/25.19 (3) all_58_2 = e2
% 168.45/25.19 (4) ~ (e3 = e1)
% 168.45/25.19 (5) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 168.45/25.19 (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) =
% 168.45/25.19 e0) | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 168.45/25.19 e1) = e0))
% 168.45/25.19 (6) ~ (e1 = e0)
% 168.45/25.19 (7) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 168.45/25.19 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.45/25.19 (8) op(e2, e3) = all_52_1
% 168.45/25.19 (9) op(e2, e3) = e2
% 168.45/25.19 (10) ~ (e3 = e0)
% 168.45/25.19 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.45/25.19 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.45/25.19 (12) op(e0, e0) = all_4_2
% 168.45/25.19 (13) all_58_11 = e3
% 168.45/25.19 (14) op(e2, e0) = e1
% 168.45/25.19 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.20 (16) ~ (e2 = e0)
% 168.45/25.20 (17) all_58_3 = e3
% 168.45/25.20 (18) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.45/25.20 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.45/25.20 (19) ~ (e2 = e1)
% 168.45/25.20 (20) ~ (e3 = e2)
% 168.45/25.20
% 168.45/25.20 Begin of proof
% 168.45/25.20 |
% 168.45/25.20 | ALPHA: (5) implies:
% 168.45/25.20 | (21) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.45/25.20 | | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.45/25.20 |
% 168.45/25.20 | BETA: splitting (7) gives:
% 168.45/25.20 |
% 168.45/25.20 | Case 1:
% 168.45/25.20 | |
% 168.45/25.20 | | (22) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 168.45/25.20 | | e2)
% 168.45/25.20 | |
% 168.45/25.20 | | BETA: splitting (22) gives:
% 168.45/25.20 | |
% 168.45/25.20 | | Case 1:
% 168.45/25.20 | | |
% 168.45/25.20 | | | (23) all_58_9 = e2 & op(e3, e0) = e2
% 168.45/25.20 | | |
% 168.45/25.20 | | | ALPHA: (23) implies:
% 168.45/25.20 | | | (24) all_58_9 = e2
% 168.45/25.20 | | |
% 168.45/25.20 | | | REF_CLOSE: (6), (10), (13), (14), (15), (16), (21), (24) are inconsistent
% 168.45/25.20 | | | by sub-proof #722.
% 168.45/25.20 | | |
% 168.45/25.20 | | Case 2:
% 168.45/25.20 | | |
% 168.45/25.20 | | | (25) all_58_10 = e2 & op(e2, e0) = e2
% 168.45/25.20 | | |
% 168.45/25.20 | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (11), (15), (16), (17), (19),
% 168.45/25.20 | | | (25) are inconsistent by sub-proof #447.
% 168.45/25.20 | | |
% 168.45/25.20 | | End of split
% 168.45/25.20 | |
% 168.45/25.20 | Case 2:
% 168.45/25.20 | |
% 168.45/25.20 | | (26) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 168.45/25.20 | | e2)
% 168.45/25.20 | |
% 168.45/25.20 | | BETA: splitting (26) gives:
% 168.45/25.20 | |
% 168.45/25.20 | | Case 1:
% 168.45/25.20 | | |
% 168.45/25.20 | | | (27) all_58_11 = e2 & op(e1, e0) = e2
% 168.45/25.20 | | |
% 168.45/25.20 | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (11), (13), (15), (16),
% 168.45/25.20 | | | (17), (18), (19), (20), (27) are inconsistent by sub-proof
% 168.45/25.20 | | | #419.
% 168.45/25.20 | | |
% 168.45/25.20 | | Case 2:
% 168.45/25.20 | | |
% 168.45/25.20 | | | (28) all_58_15 = e2 & op(e0, e0) = e2
% 168.45/25.20 | | |
% 168.45/25.20 | | | REF_CLOSE: (2), (12), (15), (28) are inconsistent by sub-proof #854.
% 168.45/25.20 | | |
% 168.45/25.20 | | End of split
% 168.45/25.20 | |
% 168.45/25.20 | End of split
% 168.45/25.20 |
% 168.45/25.20 End of proof
% 168.45/25.20
% 168.45/25.20 Sub-proof #47 shows that the following formulas are inconsistent:
% 168.45/25.20 ----------------------------------------------------------------
% 168.45/25.20 (1) all_56_0 = e2
% 168.45/25.20 (2) op(e1, e3) = all_52_2
% 168.45/25.20 (3) op(e1, e2) = all_52_6
% 168.45/25.20 (4) op(e2, e3) = all_52_1
% 168.45/25.20 (5) ~ (all_52_6 = e2)
% 168.45/25.20 (6) op(e2, e3) = e2
% 168.45/25.20 (7) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 168.45/25.20 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 168.45/25.20 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.45/25.20 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.45/25.20 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.45/25.20 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 168.45/25.20 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.45/25.20 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.45/25.20 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.45/25.20 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 168.45/25.20 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 168.45/25.20 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.45/25.20 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.45/25.20 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.45/25.20 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.45/25.20 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 168.45/25.20 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.45/25.20 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.45/25.20 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.45/25.20 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.45/25.20 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 168.45/25.20 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.45/25.20 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.45/25.20 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.45/25.20 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.45/25.20 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.20 (9) all_56_12 = e3
% 168.45/25.20 (10) ~ (all_52_2 = e3)
% 168.45/25.20 (11) ~ (e3 = e2)
% 168.45/25.20
% 168.45/25.20 Begin of proof
% 168.45/25.20 |
% 168.45/25.20 | BETA: splitting (7) gives:
% 168.45/25.20 |
% 168.45/25.20 | Case 1:
% 168.45/25.20 | |
% 168.45/25.20 | | (12) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 168.45/25.20 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 168.45/25.20 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 168.45/25.20 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2)
% 168.45/25.20 | | | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7))))
% 168.45/25.20 | | | (all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.45/25.20 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 168.45/25.20 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.45/25.20 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 168.45/25.20 | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.45/25.20 | |
% 168.45/25.20 | | REF_CLOSE: (1), (4), (6), (8), (9), (11), (12) are inconsistent by sub-proof
% 168.45/25.20 | | #367.
% 168.45/25.20 | |
% 168.45/25.20 | Case 2:
% 168.45/25.20 | |
% 168.45/25.20 | | (13) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 168.45/25.20 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.45/25.20 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.45/25.20 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 168.45/25.20 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8))))
% 168.45/25.20 | | | (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.45/25.20 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.45/25.20 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.45/25.20 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 168.45/25.20 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8))))
% 168.45/25.20 | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.45/25.20 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 168.45/25.20 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.45/25.20 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 168.45/25.20 | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.45/25.20 | |
% 168.45/25.20 | | BETA: splitting (13) gives:
% 168.45/25.20 | |
% 168.45/25.20 | | Case 1:
% 168.45/25.20 | | |
% 168.45/25.20 | | | (14) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 168.45/25.20 | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.45/25.20 | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.45/25.20 | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 168.45/25.20 | | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 168.45/25.20 | | |
% 168.45/25.20 | | | ALPHA: (14) implies:
% 168.45/25.20 | | | (15) op(e1, e3) = e3
% 168.45/25.20 | | |
% 168.45/25.20 | | | REF_CLOSE: (2), (8), (10), (15) are inconsistent by sub-proof #987.
% 168.45/25.20 | | |
% 168.45/25.20 | | Case 2:
% 168.45/25.20 | | |
% 168.45/25.20 | | | (16) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.45/25.20 | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4
% 168.45/25.20 | | | & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 =
% 168.45/25.20 | | | e2) & op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.45/25.20 | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8
% 168.45/25.20 | | | & $i(all_56_8)))) | (all_56_4 = e1 & ~ (all_56_10 = e3) &
% 168.45/25.20 | | | op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.45/25.20 | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~ (all_56_14 =
% 168.45/25.20 | | | e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.45/25.20 | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0)
% 168.45/25.20 | | | & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.45/25.20 | | |
% 168.45/25.20 | | | REF_CLOSE: (1), (3), (5), (8), (9), (16) are inconsistent by sub-proof
% 168.45/25.20 | | | #167.
% 168.45/25.20 | | |
% 168.45/25.20 | | End of split
% 168.45/25.20 | |
% 168.45/25.20 | End of split
% 168.45/25.20 |
% 168.45/25.20 End of proof
% 168.45/25.20
% 168.45/25.20 Sub-proof #48 shows that the following formulas are inconsistent:
% 168.45/25.20 ----------------------------------------------------------------
% 168.45/25.20 (1) all_54_8 = all_52_2
% 168.45/25.20 (2) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 168.45/25.20 (3) ~ (all_52_2 = e1)
% 168.45/25.20 (4) ~ (all_52_2 = e2)
% 168.45/25.20 (5) ~ (all_52_2 = e0)
% 168.45/25.20
% 168.45/25.20 Begin of proof
% 168.45/25.20 |
% 168.45/25.20 | BETA: splitting (2) gives:
% 168.45/25.20 |
% 168.45/25.20 | Case 1:
% 168.45/25.20 | |
% 168.45/25.20 | | (6) all_54_8 = e2
% 168.45/25.20 | |
% 168.45/25.20 | | COMBINE_EQS: (1), (6) imply:
% 168.45/25.20 | | (7) all_52_2 = e2
% 168.45/25.20 | |
% 168.45/25.20 | | REDUCE: (4), (7) imply:
% 168.45/25.20 | | (8) $false
% 168.45/25.20 | |
% 168.45/25.20 | | CLOSE: (8) is inconsistent.
% 168.45/25.20 | |
% 168.45/25.20 | Case 2:
% 168.45/25.20 | |
% 168.45/25.20 | | (9) all_54_8 = e1 | all_54_8 = e0
% 168.45/25.20 | |
% 168.45/25.20 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #688.
% 168.45/25.20 | |
% 168.45/25.20 | End of split
% 168.45/25.20 |
% 168.45/25.20 End of proof
% 168.45/25.20
% 168.45/25.20 Sub-proof #49 shows that the following formulas are inconsistent:
% 168.45/25.20 ----------------------------------------------------------------
% 168.45/25.20 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 168.45/25.20 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.45/25.20 (2) all_58_15 = e2
% 168.45/25.20 (3) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.45/25.20 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 168.45/25.20 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 168.45/25.20 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 168.45/25.20 (5) op(e0, e0) = e2
% 168.45/25.20 (6) ~ (all_8_2 = e3)
% 168.45/25.20 (7) all_58_7 = e1
% 168.45/25.20 (8) ~ (e3 = e1)
% 168.45/25.20 (9) all_58_6 = e3
% 168.45/25.20 (10) all_58_13 = e0
% 168.45/25.20 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 168.45/25.20 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 168.45/25.20 e1)
% 168.45/25.20 (12) ~ (e1 = e0)
% 168.45/25.20 (13) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 168.45/25.20 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 168.45/25.20 e3)
% 168.45/25.20 (14) op(e0, e2) = e0
% 168.45/25.20 (15) op(e2, e2) = all_8_2
% 168.45/25.20 (16) ~ (e3 = e0)
% 168.45/25.20 (17) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 168.45/25.20 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.45/25.20 (18) all_58_11 = e3
% 168.45/25.20 (19) all_58_1 = e3
% 168.45/25.20 (20) all_58_3 = e2
% 168.45/25.20 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.20 (22) all_58_8 = e2
% 168.45/25.20 (23) ~ (e2 = e0)
% 168.45/25.20 (24) ~ (e2 = e1)
% 168.45/25.20 (25) op(e0, e2) = all_52_7
% 168.45/25.20 (26) ~ (e3 = e2)
% 168.45/25.20
% 168.45/25.20 Begin of proof
% 168.45/25.20 |
% 168.45/25.20 | BETA: splitting (17) gives:
% 168.45/25.20 |
% 168.45/25.20 | Case 1:
% 168.45/25.20 | |
% 168.45/25.20 | | (27) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 168.45/25.20 | | e0)
% 168.45/25.20 | |
% 168.45/25.20 | | BETA: splitting (27) gives:
% 168.45/25.20 | |
% 168.45/25.20 | | Case 1:
% 168.45/25.20 | | |
% 168.45/25.20 | | | (28) all_58_6 = e0 & op(e1, e3) = e0
% 168.45/25.20 | | |
% 168.45/25.20 | | | ALPHA: (28) implies:
% 168.45/25.20 | | | (29) all_58_6 = e0
% 168.45/25.20 | | |
% 168.45/25.20 | | | COMBINE_EQS: (9), (29) imply:
% 168.45/25.20 | | | (30) e3 = e0
% 168.45/25.20 | | |
% 168.45/25.20 | | | REF_CLOSE: (3), (4), (6), (8), (10), (12), (14), (15), (16), (19), (20),
% 168.45/25.20 | | | (21), (24), (25), (30) are inconsistent by sub-proof #590.
% 168.45/25.20 | | |
% 168.45/25.20 | | Case 2:
% 168.45/25.20 | | |
% 168.45/25.20 | | | (31) all_58_7 = e0 & op(e1, e2) = e0
% 168.45/25.20 | | |
% 168.45/25.20 | | | REF_CLOSE: (7), (12), (31) are inconsistent by sub-proof #727.
% 168.45/25.20 | | |
% 168.45/25.20 | | End of split
% 168.45/25.20 | |
% 168.45/25.20 | Case 2:
% 168.45/25.20 | |
% 168.45/25.20 | | (32) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 168.45/25.20 | | e0)
% 168.45/25.20 | |
% 168.45/25.20 | | BETA: splitting (32) gives:
% 168.45/25.20 | |
% 168.45/25.20 | | Case 1:
% 168.45/25.20 | | |
% 168.45/25.20 | | | (33) all_58_8 = e0 & op(e1, e1) = e0
% 168.45/25.20 | | |
% 168.45/25.20 | | | REF_CLOSE: (1), (2), (5), (8), (10), (11), (12), (13), (14), (16), (21),
% 168.45/25.20 | | | (22), (23), (24), (25), (26), (33) are inconsistent by
% 168.45/25.20 | | | sub-proof #52.
% 168.45/25.20 | | |
% 168.45/25.20 | | Case 2:
% 168.45/25.20 | | |
% 168.45/25.20 | | | (34) all_58_11 = e0 & op(e1, e0) = e0
% 168.45/25.20 | | |
% 168.45/25.20 | | | ALPHA: (34) implies:
% 168.45/25.20 | | | (35) all_58_11 = e0
% 168.45/25.20 | | |
% 168.45/25.20 | | | COMBINE_EQS: (18), (35) imply:
% 168.45/25.20 | | | (36) e3 = e0
% 168.45/25.20 | | |
% 168.45/25.20 | | | REF_CLOSE: (3), (4), (6), (8), (10), (12), (14), (15), (16), (19), (20),
% 168.45/25.20 | | | (21), (24), (25), (36) are inconsistent by sub-proof #590.
% 168.45/25.20 | | |
% 168.45/25.20 | | End of split
% 168.45/25.20 | |
% 168.45/25.20 | End of split
% 168.45/25.20 |
% 168.45/25.20 End of proof
% 168.45/25.20
% 168.45/25.20 Sub-proof #50 shows that the following formulas are inconsistent:
% 168.45/25.20 ----------------------------------------------------------------
% 168.45/25.20 (1) op(e2, e0) = e3
% 168.45/25.20 (2) op(e2, e0) = all_26_1
% 168.45/25.20 (3) ~ (all_20_1 = e3)
% 168.45/25.20 (4) op(e2, e0) = all_20_1
% 168.45/25.20 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.20
% 168.45/25.20 Begin of proof
% 168.45/25.20 |
% 168.45/25.20 | GROUND_INST: instantiating (5) with all_20_1, all_26_1, e0, e2, simplifying
% 168.45/25.20 | with (2), (4) gives:
% 168.45/25.20 | (6) all_26_1 = all_20_1
% 168.45/25.20 |
% 168.45/25.20 | GROUND_INST: instantiating (5) with e3, all_26_1, e0, e2, simplifying with
% 168.45/25.20 | (1), (2) gives:
% 168.45/25.20 | (7) all_26_1 = e3
% 168.45/25.20 |
% 168.45/25.20 | COMBINE_EQS: (6), (7) imply:
% 168.45/25.20 | (8) all_20_1 = e3
% 168.45/25.20 |
% 168.45/25.20 | SIMP: (8) implies:
% 168.45/25.20 | (9) all_20_1 = e3
% 168.45/25.20 |
% 168.45/25.20 | REDUCE: (3), (9) imply:
% 168.45/25.20 | (10) $false
% 168.45/25.20 |
% 168.45/25.20 | CLOSE: (10) is inconsistent.
% 168.45/25.20 |
% 168.45/25.20 End of proof
% 168.45/25.20
% 168.45/25.20 Sub-proof #51 shows that the following formulas are inconsistent:
% 168.45/25.20 ----------------------------------------------------------------
% 168.45/25.20 (1) op(e2, e0) = e3
% 168.45/25.20 (2) op(e2, e0) = all_26_1
% 168.45/25.20 (3) op(e2, e0) = all_20_1
% 168.45/25.20 (4) op(e3, e0) = e1
% 168.45/25.20 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.20 (6) op(all_20_1, e0) = all_20_0
% 168.45/25.20 (7) ~ (all_20_0 = e1)
% 168.45/25.20
% 168.45/25.20 Begin of proof
% 168.45/25.20 |
% 168.45/25.20 | GROUND_INST: instantiating (5) with all_20_1, all_26_1, e0, e2, simplifying
% 168.45/25.20 | with (2), (3) gives:
% 168.45/25.20 | (8) all_26_1 = all_20_1
% 168.45/25.20 |
% 168.45/25.20 | GROUND_INST: instantiating (5) with e3, all_26_1, e0, e2, simplifying with
% 168.45/25.20 | (1), (2) gives:
% 168.45/25.20 | (9) all_26_1 = e3
% 168.45/25.20 |
% 168.45/25.20 | COMBINE_EQS: (8), (9) imply:
% 168.45/25.20 | (10) all_20_1 = e3
% 168.45/25.20 |
% 168.45/25.20 | SIMP: (10) implies:
% 168.45/25.20 | (11) all_20_1 = e3
% 168.45/25.20 |
% 168.45/25.20 | REDUCE: (6), (11) imply:
% 168.45/25.20 | (12) op(e3, e0) = all_20_0
% 168.45/25.20 |
% 168.45/25.20 | GROUND_INST: instantiating (5) with e1, all_20_0, e0, e3, simplifying with
% 168.45/25.20 | (4), (12) gives:
% 168.45/25.20 | (13) all_20_0 = e1
% 168.45/25.20 |
% 168.45/25.20 | REDUCE: (7), (13) imply:
% 168.45/25.20 | (14) $false
% 168.45/25.20 |
% 168.45/25.20 | CLOSE: (14) is inconsistent.
% 168.45/25.20 |
% 168.45/25.21 End of proof
% 168.45/25.21
% 168.45/25.21 Sub-proof #52 shows that the following formulas are inconsistent:
% 168.45/25.21 ----------------------------------------------------------------
% 168.45/25.21 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 168.45/25.21 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.45/25.21 (2) all_58_15 = e2
% 168.45/25.21 (3) op(e0, e0) = e2
% 168.45/25.21 (4) ~ (e3 = e1)
% 168.45/25.21 (5) all_58_13 = e0
% 168.45/25.21 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 168.45/25.21 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 168.45/25.21 (7) ~ (e1 = e0)
% 168.45/25.21 (8) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 168.45/25.21 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 168.45/25.21 (9) op(e0, e2) = e0
% 168.45/25.21 (10) ~ (e3 = e0)
% 168.45/25.21 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.21 (12) all_58_8 = e2
% 168.45/25.21 (13) ~ (e2 = e0)
% 168.45/25.21 (14) ~ (e2 = e1)
% 168.45/25.21 (15) all_58_8 = e0 & op(e1, e1) = e0
% 168.45/25.21 (16) op(e0, e2) = all_52_7
% 168.45/25.21 (17) ~ (e3 = e2)
% 168.45/25.21
% 168.45/25.21 Begin of proof
% 168.45/25.21 |
% 168.45/25.21 | ALPHA: (15) implies:
% 168.45/25.21 | (18) all_58_8 = e0
% 168.45/25.21 |
% 168.45/25.21 | COMBINE_EQS: (12), (18) imply:
% 168.45/25.21 | (19) e2 = e0
% 168.45/25.21 |
% 168.45/25.21 | COMBINE_EQS: (2), (19) imply:
% 168.45/25.21 | (20) all_58_15 = e0
% 168.45/25.21 |
% 168.45/25.21 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 168.45/25.21 | (16), (17), (20) are inconsistent by sub-proof #628.
% 168.45/25.21 |
% 168.45/25.21 End of proof
% 168.45/25.21
% 168.45/25.21 Sub-proof #53 shows that the following formulas are inconsistent:
% 168.45/25.21 ----------------------------------------------------------------
% 168.45/25.21 (1) op(e0, e1) = e3
% 168.45/25.21 (2) op(e0, e0) = e2
% 168.45/25.21 (3) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 168.45/25.21 (all_56_8 = e1 & op(e0, e1) = e1)
% 168.45/25.21 (4) ~ (e3 = e1)
% 168.45/25.21 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 168.45/25.21 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 168.45/25.21 (6) ~ (e1 = e0)
% 168.45/25.21 (7) op(e0, e2) = e0
% 168.45/25.21 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.21 (9) ~ (e2 = e0)
% 168.45/25.21 (10) ~ (e2 = e1)
% 168.45/25.21 (11) op(e0, e2) = all_52_7
% 168.45/25.21
% 168.45/25.21 Begin of proof
% 168.45/25.21 |
% 168.45/25.21 | BETA: splitting (3) gives:
% 168.45/25.21 |
% 168.45/25.21 | Case 1:
% 168.45/25.21 | |
% 168.45/25.21 | | (12) all_56_6 = e3 & op(e0, e3) = e3
% 168.45/25.21 | |
% 168.45/25.21 | | ALPHA: (12) implies:
% 168.45/25.21 | | (13) op(e0, e3) = e3
% 168.45/25.21 | |
% 168.45/25.21 | | BETA: splitting (5) gives:
% 168.45/25.21 | |
% 168.45/25.21 | | Case 1:
% 168.45/25.21 | | |
% 168.45/25.21 | | | (14) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2)
% 168.45/25.21 | | | = e1)
% 168.45/25.21 | | |
% 168.45/25.21 | | | REF_CLOSE: (4), (6), (7), (8), (11), (13), (14) are inconsistent by
% 168.45/25.21 | | | sub-proof #54.
% 168.45/25.21 | | |
% 168.45/25.21 | | Case 2:
% 168.45/25.21 | | |
% 168.45/25.21 | | | (15) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0)
% 168.45/25.21 | | | = e1)
% 168.45/25.21 | | |
% 168.45/25.21 | | | REF_CLOSE: (1), (2), (4), (8), (10), (15) are inconsistent by sub-proof
% 168.45/25.21 | | | #107.
% 168.45/25.21 | | |
% 168.45/25.21 | | End of split
% 168.45/25.21 | |
% 168.45/25.21 | Case 2:
% 168.45/25.21 | |
% 168.45/25.21 | | (16) (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) =
% 168.45/25.21 | | e1)
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (1), (4), (7), (8), (9), (11), (16) are inconsistent by sub-proof
% 168.45/25.21 | | #99.
% 168.45/25.21 | |
% 168.45/25.21 | End of split
% 168.45/25.21 |
% 168.45/25.21 End of proof
% 168.45/25.21
% 168.45/25.21 Sub-proof #54 shows that the following formulas are inconsistent:
% 168.45/25.21 ----------------------------------------------------------------
% 168.45/25.21 (1) op(e0, e3) = e3
% 168.45/25.21 (2) ~ (e3 = e1)
% 168.45/25.21 (3) ~ (e1 = e0)
% 168.45/25.21 (4) op(e0, e2) = e0
% 168.45/25.21 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 168.45/25.21 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.21 (7) op(e0, e2) = all_52_7
% 168.45/25.21
% 168.45/25.21 Begin of proof
% 168.45/25.21 |
% 168.45/25.21 | BETA: splitting (5) gives:
% 168.45/25.21 |
% 168.45/25.21 | Case 1:
% 168.45/25.21 | |
% 168.45/25.21 | | (8) all_58_12 = e1 & op(e0, e3) = e1
% 168.45/25.21 | |
% 168.45/25.21 | | ALPHA: (8) implies:
% 168.45/25.21 | | (9) op(e0, e3) = e1
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #125.
% 168.45/25.21 | |
% 168.45/25.21 | Case 2:
% 168.45/25.21 | |
% 168.45/25.21 | | (10) all_58_13 = e1 & op(e0, e2) = e1
% 168.45/25.21 | |
% 168.45/25.21 | | ALPHA: (10) implies:
% 168.45/25.21 | | (11) op(e0, e2) = e1
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (3), (4), (6), (7), (11) are inconsistent by sub-proof #889.
% 168.45/25.21 | |
% 168.45/25.21 | End of split
% 168.45/25.21 |
% 168.45/25.21 End of proof
% 168.45/25.21
% 168.45/25.21 Sub-proof #55 shows that the following formulas are inconsistent:
% 168.45/25.21 ----------------------------------------------------------------
% 168.45/25.21 (1) all_54_12 = all_52_3
% 168.45/25.21 (2) all_54_12 = e1 | all_54_12 = e0
% 168.45/25.21 (3) op(e0, e3) = e3
% 168.45/25.21 (4) ~ (all_52_3 = e3)
% 168.45/25.21 (5) op(e0, e3) = all_52_3
% 168.45/25.21 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.21 (7) ~ (all_52_3 = e0)
% 168.45/25.21
% 168.45/25.21 Begin of proof
% 168.45/25.21 |
% 168.45/25.21 | BETA: splitting (2) gives:
% 168.45/25.21 |
% 168.45/25.21 | Case 1:
% 168.45/25.21 | |
% 168.45/25.21 | | (8) all_54_12 = e1
% 168.45/25.21 | |
% 168.45/25.21 | | COMBINE_EQS: (1), (8) imply:
% 168.45/25.21 | | (9) all_52_3 = e1
% 168.45/25.21 | |
% 168.45/25.21 | | SIMP: (9) implies:
% 168.45/25.21 | | (10) all_52_3 = e1
% 168.45/25.21 | |
% 168.45/25.21 | | REDUCE: (4), (10) imply:
% 168.45/25.21 | | (11) ~ (e3 = e1)
% 168.45/25.21 | |
% 168.45/25.21 | | SIMP: (11) implies:
% 168.45/25.21 | | (12) ~ (e3 = e1)
% 168.45/25.21 | |
% 168.45/25.21 | | REDUCE: (5), (10) imply:
% 168.45/25.21 | | (13) op(e0, e3) = e1
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (3), (6), (12), (13) are inconsistent by sub-proof #125.
% 168.45/25.21 | |
% 168.45/25.21 | Case 2:
% 168.45/25.21 | |
% 168.45/25.21 | | (14) all_54_12 = e0
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (1), (7), (14) are inconsistent by sub-proof #653.
% 168.45/25.21 | |
% 168.45/25.21 | End of split
% 168.45/25.21 |
% 168.45/25.21 End of proof
% 168.45/25.21
% 168.45/25.21 Sub-proof #56 shows that the following formulas are inconsistent:
% 168.45/25.21 ----------------------------------------------------------------
% 168.45/25.21 (1) ( ~ (all_16_0 = e0) & op(all_16_1, e3) = all_16_0 & op(e2, e3) = all_16_1
% 168.45/25.21 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e2, e3) =
% 168.45/25.21 all_16_1 & $i(all_16_1))
% 168.45/25.21 (2) op(e2, e3) = all_38_1
% 168.45/25.21 (3) op(e2, e3) = e1
% 168.45/25.21 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.21 (5) op(e1, e3) = e0
% 168.45/25.21
% 168.45/25.21 Begin of proof
% 168.45/25.21 |
% 168.45/25.21 | BETA: splitting (1) gives:
% 168.45/25.21 |
% 168.45/25.21 | Case 1:
% 168.45/25.21 | |
% 168.45/25.21 | | (6) ~ (all_16_0 = e0) & op(all_16_1, e3) = all_16_0 & op(e2, e3) =
% 168.45/25.21 | | all_16_1 & $i(all_16_0) & $i(all_16_1)
% 168.45/25.21 | |
% 168.45/25.21 | | ALPHA: (6) implies:
% 168.45/25.21 | | (7) ~ (all_16_0 = e0)
% 168.45/25.21 | | (8) op(e2, e3) = all_16_1
% 168.45/25.21 | | (9) op(all_16_1, e3) = all_16_0
% 168.45/25.21 | |
% 168.45/25.21 | | GROUND_INST: instantiating (4) with all_16_1, all_38_1, e3, e2, simplifying
% 168.45/25.21 | | with (2), (8) gives:
% 168.45/25.21 | | (10) all_38_1 = all_16_1
% 168.45/25.21 | |
% 168.45/25.21 | | GROUND_INST: instantiating (4) with e1, all_38_1, e3, e2, simplifying with
% 168.45/25.21 | | (2), (3) gives:
% 168.45/25.21 | | (11) all_38_1 = e1
% 168.45/25.21 | |
% 168.45/25.21 | | COMBINE_EQS: (10), (11) imply:
% 168.45/25.21 | | (12) all_16_1 = e1
% 168.45/25.21 | |
% 168.45/25.21 | | REDUCE: (9), (12) imply:
% 168.45/25.21 | | (13) op(e1, e3) = all_16_0
% 168.45/25.21 | |
% 168.45/25.21 | | GROUND_INST: instantiating (4) with e0, all_16_0, e3, e1, simplifying with
% 168.45/25.21 | | (5), (13) gives:
% 168.45/25.21 | | (14) all_16_0 = e0
% 168.45/25.21 | |
% 168.45/25.21 | | REDUCE: (7), (14) imply:
% 168.45/25.21 | | (15) $false
% 168.45/25.21 | |
% 168.45/25.21 | | CLOSE: (15) is inconsistent.
% 168.45/25.21 | |
% 168.45/25.21 | Case 2:
% 168.45/25.21 | |
% 168.45/25.21 | | (16) ~ (all_16_1 = e1) & op(e2, e3) = all_16_1 & $i(all_16_1)
% 168.45/25.21 | |
% 168.45/25.21 | | ALPHA: (16) implies:
% 168.45/25.21 | | (17) ~ (all_16_1 = e1)
% 168.45/25.21 | | (18) op(e2, e3) = all_16_1
% 168.45/25.21 | |
% 168.45/25.21 | | GROUND_INST: instantiating (4) with all_16_1, all_38_1, e3, e2, simplifying
% 168.45/25.21 | | with (2), (18) gives:
% 168.45/25.21 | | (19) all_38_1 = all_16_1
% 168.45/25.21 | |
% 168.45/25.21 | | GROUND_INST: instantiating (4) with e1, all_38_1, e3, e2, simplifying with
% 168.45/25.21 | | (2), (3) gives:
% 168.45/25.21 | | (20) all_38_1 = e1
% 168.45/25.21 | |
% 168.45/25.21 | | COMBINE_EQS: (19), (20) imply:
% 168.45/25.21 | | (21) all_16_1 = e1
% 168.45/25.21 | |
% 168.45/25.21 | | REDUCE: (17), (21) imply:
% 168.45/25.21 | | (22) $false
% 168.45/25.21 | |
% 168.45/25.21 | | CLOSE: (22) is inconsistent.
% 168.45/25.21 | |
% 168.45/25.21 | End of split
% 168.45/25.21 |
% 168.45/25.21 End of proof
% 168.45/25.21
% 168.45/25.21 Sub-proof #57 shows that the following formulas are inconsistent:
% 168.45/25.21 ----------------------------------------------------------------
% 168.45/25.21 (1) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 168.45/25.21 (2) all_58_7 = e1
% 168.45/25.21 (3) ~ (e1 = e0)
% 168.45/25.21 (4) op(e0, e2) = e2
% 168.45/25.21 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.21 (6) ~ (e2 = e0)
% 168.45/25.21 (7) op(e0, e2) = all_52_7
% 168.45/25.21
% 168.45/25.21 Begin of proof
% 168.45/25.21 |
% 168.45/25.21 | BETA: splitting (1) gives:
% 168.45/25.21 |
% 168.45/25.21 | Case 1:
% 168.45/25.21 | |
% 168.45/25.21 | | (8) all_58_7 = e0 & op(e1, e2) = e0
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #727.
% 168.45/25.21 | |
% 168.45/25.21 | Case 2:
% 168.45/25.21 | |
% 168.45/25.21 | | (9) all_58_13 = e0 & op(e0, e2) = e0
% 168.45/25.21 | |
% 168.45/25.21 | | ALPHA: (9) implies:
% 168.45/25.21 | | (10) op(e0, e2) = e0
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (4), (5), (6), (7), (10) are inconsistent by sub-proof #631.
% 168.45/25.21 | |
% 168.45/25.21 | End of split
% 168.45/25.21 |
% 168.45/25.21 End of proof
% 168.45/25.21
% 168.45/25.21 Sub-proof #58 shows that the following formulas are inconsistent:
% 168.45/25.21 ----------------------------------------------------------------
% 168.45/25.21 (1) all_54_8 = all_52_2
% 168.45/25.21 (2) op(e1, e0) = e3
% 168.45/25.21 (3) all_58_7 = e1
% 168.45/25.21 (4) all_54_8 = e1 | all_54_8 = e0
% 168.45/25.21 (5) ~ (e3 = e1)
% 168.45/25.21 (6) op(e1, e3) = all_52_2
% 168.45/25.21 (7) all_58_11 = e3
% 168.45/25.21 (8) ~ (all_52_2 = e1)
% 168.45/25.21 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.21 (10) all_58_8 = e2
% 168.45/25.21 (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 168.45/25.21 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 168.45/25.21 (12) op(e1, e0) = e0
% 168.45/25.21 (13) ~ (all_52_2 = e3)
% 168.45/25.21 (14) ~ (e3 = e2)
% 168.45/25.21
% 168.45/25.21 Begin of proof
% 168.45/25.21 |
% 168.45/25.21 | BETA: splitting (4) gives:
% 168.45/25.21 |
% 168.45/25.21 | Case 1:
% 168.45/25.21 | |
% 168.45/25.21 | | (15) all_54_8 = e1
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #689.
% 168.45/25.21 | |
% 168.45/25.21 | Case 2:
% 168.45/25.21 | |
% 168.45/25.21 | | (16) all_54_8 = e0
% 168.45/25.21 | |
% 168.45/25.21 | | COMBINE_EQS: (1), (16) imply:
% 168.45/25.21 | | (17) all_52_2 = e0
% 168.45/25.21 | |
% 168.45/25.21 | | SIMP: (17) implies:
% 168.45/25.21 | | (18) all_52_2 = e0
% 168.45/25.21 | |
% 168.45/25.21 | | REDUCE: (13), (18) imply:
% 168.45/25.21 | | (19) ~ (e3 = e0)
% 168.45/25.21 | |
% 168.45/25.21 | | SIMP: (19) implies:
% 168.45/25.21 | | (20) ~ (e3 = e0)
% 168.45/25.21 | |
% 168.45/25.21 | | GROUND_INST: instantiating (9) with e0, e3, e0, e1, simplifying with (2),
% 168.45/25.21 | | (12) gives:
% 168.45/25.21 | | (21) e3 = e0
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (3), (5), (6), (7), (9), (10), (11), (13), (14), (20), (21) are
% 168.45/25.21 | | inconsistent by sub-proof #73.
% 168.45/25.21 | |
% 168.45/25.21 | End of split
% 168.45/25.21 |
% 168.45/25.21 End of proof
% 168.45/25.21
% 168.45/25.21 Sub-proof #59 shows that the following formulas are inconsistent:
% 168.45/25.21 ----------------------------------------------------------------
% 168.45/25.21 (1) all_56_14 = e2
% 168.45/25.21 (2) all_56_14 = e1
% 168.45/25.21 (3) ~ (e2 = e1)
% 168.45/25.21
% 168.45/25.21 Begin of proof
% 168.45/25.21 |
% 168.45/25.21 | COMBINE_EQS: (1), (2) imply:
% 168.45/25.21 | (4) e2 = e1
% 168.45/25.21 |
% 168.45/25.21 | SIMP: (4) implies:
% 168.45/25.21 | (5) e2 = e1
% 168.45/25.21 |
% 168.45/25.21 | REDUCE: (3), (5) imply:
% 168.45/25.21 | (6) $false
% 168.45/25.21 |
% 168.45/25.21 | CLOSE: (6) is inconsistent.
% 168.45/25.21 |
% 168.45/25.21 End of proof
% 168.45/25.21
% 168.45/25.21 Sub-proof #60 shows that the following formulas are inconsistent:
% 168.45/25.21 ----------------------------------------------------------------
% 168.45/25.21 (1) all_58_7 = e1
% 168.45/25.21 (2) ~ (e3 = e1)
% 168.45/25.21 (3) all_58_13 = e0
% 168.45/25.21 (4) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 168.45/25.21 (5) ~ (e3 = e0)
% 168.45/25.21
% 168.45/25.21 Begin of proof
% 168.45/25.21 |
% 168.45/25.21 | BETA: splitting (4) gives:
% 168.45/25.21 |
% 168.45/25.21 | Case 1:
% 168.45/25.21 | |
% 168.45/25.21 | | (6) all_58_7 = e3 & op(e1, e2) = e3
% 168.45/25.21 | |
% 168.45/25.21 | | ALPHA: (6) implies:
% 168.45/25.21 | | (7) all_58_7 = e3
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #821.
% 168.45/25.21 | |
% 168.45/25.21 | Case 2:
% 168.45/25.21 | |
% 168.45/25.21 | | (8) all_58_13 = e3 & op(e0, e2) = e3
% 168.45/25.21 | |
% 168.45/25.21 | | ALPHA: (8) implies:
% 168.45/25.21 | | (9) all_58_13 = e3
% 168.45/25.21 | |
% 168.45/25.21 | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #708.
% 168.45/25.21 | |
% 168.45/25.21 | End of split
% 168.45/25.21 |
% 168.45/25.22 End of proof
% 168.45/25.22
% 168.45/25.22 Sub-proof #61 shows that the following formulas are inconsistent:
% 168.45/25.22 ----------------------------------------------------------------
% 168.45/25.22 (1) all_58_14 = e2 & op(e0, e1) = e2
% 168.45/25.22 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.22 (3) op(e0, e1) = all_52_11
% 168.45/25.22 (4) ~ (all_52_11 = e2)
% 168.45/25.22
% 168.45/25.22 Begin of proof
% 168.45/25.22 |
% 168.45/25.22 | ALPHA: (1) implies:
% 168.45/25.22 | (5) op(e0, e1) = e2
% 168.45/25.22 |
% 168.45/25.22 | GROUND_INST: instantiating (2) with all_52_11, e2, e1, e0, simplifying with
% 168.45/25.22 | (3), (5) gives:
% 168.45/25.22 | (6) all_52_11 = e2
% 168.45/25.22 |
% 168.45/25.22 | REDUCE: (4), (6) imply:
% 168.45/25.22 | (7) $false
% 168.45/25.22 |
% 168.45/25.22 | CLOSE: (7) is inconsistent.
% 168.45/25.22 |
% 168.45/25.22 End of proof
% 168.45/25.22
% 168.45/25.22 Sub-proof #62 shows that the following formulas are inconsistent:
% 168.45/25.22 ----------------------------------------------------------------
% 168.45/25.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.22 (2) op(e1, e0) = e3
% 168.45/25.22 (3) op(e1, e0) = e0
% 168.45/25.22 (4) ~ (e3 = e0)
% 168.45/25.22
% 168.45/25.22 Begin of proof
% 168.45/25.22 |
% 168.45/25.22 | GROUND_INST: instantiating (1) with e3, e0, e0, e1, simplifying with (2), (3)
% 168.45/25.22 | gives:
% 168.45/25.22 | (5) e3 = e0
% 168.45/25.22 |
% 168.45/25.22 | REDUCE: (4), (5) imply:
% 168.45/25.22 | (6) $false
% 168.45/25.22 |
% 168.45/25.22 | CLOSE: (6) is inconsistent.
% 168.45/25.22 |
% 168.45/25.22 End of proof
% 168.45/25.22
% 168.45/25.22 Sub-proof #63 shows that the following formulas are inconsistent:
% 168.45/25.22 ----------------------------------------------------------------
% 168.45/25.22 (1) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 =
% 168.45/25.22 e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4)))
% 168.45/25.22 & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.45/25.22 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.45/25.22 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.45/25.22 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 168.45/25.22 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.45/25.22 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.45/25.22 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.45/25.22 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.45/25.22 (2) op(e3, e1) = e0
% 168.45/25.22 (3) ~ (e1 = e0)
% 168.45/25.22 (4) op(e1, e2) = all_52_6
% 168.45/25.22 (5) ~ (all_52_6 = e2)
% 168.45/25.22 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.22
% 168.45/25.22 Begin of proof
% 168.45/25.22 |
% 168.45/25.22 | BETA: splitting (1) gives:
% 168.45/25.22 |
% 168.45/25.22 | Case 1:
% 168.45/25.22 | |
% 168.45/25.22 | | (7) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.45/25.22 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.45/25.22 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.45/25.22 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | (
% 168.45/25.22 | | ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 168.45/25.22 | |
% 168.45/25.22 | | ALPHA: (7) implies:
% 168.45/25.22 | | (8) op(e1, e2) = e2
% 168.45/25.22 | |
% 168.45/25.22 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #986.
% 168.45/25.22 | |
% 168.45/25.22 | Case 2:
% 168.45/25.22 | |
% 168.45/25.22 | | (9) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.45/25.22 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 168.45/25.22 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.45/25.22 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 168.45/25.22 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 168.45/25.22 | |
% 168.45/25.22 | | ALPHA: (9) implies:
% 168.45/25.22 | | (10) op(e3, e1) = e1
% 168.45/25.22 | |
% 168.45/25.22 | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #569.
% 168.45/25.22 | |
% 168.45/25.22 | End of split
% 168.45/25.22 |
% 168.45/25.22 End of proof
% 168.45/25.22
% 168.45/25.22 Sub-proof #64 shows that the following formulas are inconsistent:
% 168.45/25.22 ----------------------------------------------------------------
% 168.45/25.22 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.22 (2) op(e1, e3) = e3
% 168.45/25.22 (3) op(e1, e3) = e0
% 168.45/25.22 (4) ~ (e3 = e0)
% 168.45/25.22
% 168.45/25.22 Begin of proof
% 168.45/25.22 |
% 168.45/25.22 | GROUND_INST: instantiating (1) with e0, e3, e3, e1, simplifying with (2), (3)
% 168.45/25.22 | gives:
% 168.45/25.22 | (5) e3 = e0
% 168.45/25.22 |
% 168.45/25.22 | REDUCE: (4), (5) imply:
% 168.45/25.22 | (6) $false
% 168.45/25.22 |
% 168.45/25.22 | CLOSE: (6) is inconsistent.
% 168.45/25.22 |
% 168.45/25.22 End of proof
% 168.45/25.22
% 168.45/25.22 Sub-proof #65 shows that the following formulas are inconsistent:
% 168.45/25.22 ----------------------------------------------------------------
% 168.45/25.22 (1) ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.45/25.22 $i(all_56_3))
% 168.45/25.22 (2) all_56_14 = e2
% 168.45/25.22 (3) all_56_3 = e1
% 168.45/25.22
% 168.45/25.22 Begin of proof
% 168.45/25.22 |
% 168.45/25.22 | BETA: splitting (1) gives:
% 168.45/25.22 |
% 168.45/25.22 | Case 1:
% 168.45/25.22 | |
% 168.45/25.22 | | (4) ~ (all_56_14 = e2)
% 168.45/25.22 | |
% 168.45/25.22 | | REDUCE: (2), (4) imply:
% 168.45/25.22 | | (5) $false
% 168.45/25.22 | |
% 168.45/25.22 | | CLOSE: (5) is inconsistent.
% 168.45/25.22 | |
% 168.45/25.22 | Case 2:
% 168.45/25.22 | |
% 168.45/25.22 | | (6) ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 & $i(all_56_3)
% 168.45/25.22 | |
% 168.45/25.22 | | ALPHA: (6) implies:
% 168.45/25.22 | | (7) ~ (all_56_3 = e1)
% 168.45/25.22 | |
% 168.45/25.22 | | REDUCE: (3), (7) imply:
% 168.45/25.22 | | (8) $false
% 168.45/25.22 | |
% 168.45/25.22 | | CLOSE: (8) is inconsistent.
% 168.45/25.22 | |
% 168.45/25.22 | End of split
% 168.45/25.22 |
% 168.45/25.22 End of proof
% 168.45/25.22
% 168.45/25.22 Sub-proof #66 shows that the following formulas are inconsistent:
% 168.45/25.22 ----------------------------------------------------------------
% 168.45/25.22 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 168.45/25.22 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 168.45/25.22 (2) all_58_12 = e2
% 168.45/25.22 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 168.45/25.22 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 168.45/25.22 (4) all_58_7 = e1
% 168.45/25.22 (5) ~ (all_4_2 = e1)
% 168.45/25.22 (6) ~ (e3 = e1)
% 168.45/25.22 (7) op(e1, e3) = all_52_2
% 168.45/25.22 (8) op(e3, e1) = all_52_8
% 168.45/25.22 (9) ~ (e1 = e0)
% 168.45/25.22 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 168.45/25.22 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 168.45/25.22 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 168.45/25.22 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 168.45/25.22 (12) ~ (e3 = e0)
% 168.45/25.22 (13) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 168.45/25.22 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.45/25.22 (14) op(e0, e0) = all_4_2
% 168.45/25.22 (15) ~ (all_52_8 = e2)
% 168.45/25.22 (16) all_58_1 = e3
% 168.45/25.22 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.45/25.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.45/25.22 (18) all_58_8 = e2
% 168.45/25.22 (19) ~ (e2 = e0)
% 168.45/25.22 (20) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 168.45/25.22 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 168.45/25.22 (21) ~ (e2 = e1)
% 168.45/25.22 (22) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 168.45/25.22 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 168.45/25.22 (23) op(e2, e0) = e2
% 168.45/25.22 (24) ~ (e3 = e2)
% 168.45/25.22
% 168.45/25.22 Begin of proof
% 168.45/25.22 |
% 168.45/25.22 | BETA: splitting (22) gives:
% 168.45/25.22 |
% 168.45/25.22 | Case 1:
% 168.45/25.22 | |
% 168.45/25.22 | | (25) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 168.45/25.22 | | e2)
% 168.45/25.22 | |
% 168.45/25.22 | | BETA: splitting (25) gives:
% 168.45/25.22 | |
% 168.45/25.22 | | Case 1:
% 168.45/25.22 | | |
% 168.45/25.22 | | | (26) all_58_0 = e2 & op(e3, e3) = e2
% 168.45/25.22 | | |
% 168.45/25.22 | | | ALPHA: (26) implies:
% 168.45/25.22 | | | (27) all_58_0 = e2
% 168.45/25.22 | | | (28) op(e3, e3) = e2
% 168.45/25.22 | | |
% 168.45/25.22 | | | REF_CLOSE: (2), (3), (6), (7), (9), (10), (11), (12), (17), (19), (21),
% 168.45/25.22 | | | (24), (27), (28) are inconsistent by sub-proof #138.
% 168.45/25.22 | | |
% 168.45/25.22 | | Case 2:
% 168.45/25.22 | | |
% 168.45/25.22 | | | (29) all_58_1 = e2 & op(e3, e2) = e2
% 168.45/25.22 | | |
% 168.45/25.22 | | | ALPHA: (29) implies:
% 168.45/25.22 | | | (30) all_58_1 = e2
% 168.45/25.22 | | |
% 168.45/25.22 | | | COMBINE_EQS: (16), (30) imply:
% 168.45/25.22 | | | (31) e3 = e2
% 168.45/25.22 | | |
% 168.45/25.22 | | | REDUCE: (24), (31) imply:
% 168.45/25.22 | | | (32) $false
% 168.45/25.22 | | |
% 168.45/25.22 | | | CLOSE: (32) is inconsistent.
% 168.45/25.22 | | |
% 168.45/25.22 | | End of split
% 168.45/25.22 | |
% 168.45/25.22 | Case 2:
% 168.45/25.22 | |
% 168.45/25.22 | | (33) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 168.45/25.22 | | e2)
% 168.45/25.22 | |
% 168.45/25.22 | | BETA: splitting (33) gives:
% 168.45/25.22 | |
% 168.45/25.22 | | Case 1:
% 168.45/25.22 | | |
% 168.45/25.22 | | | (34) all_58_4 = e2 & op(e3, e1) = e2
% 168.45/25.22 | | |
% 168.45/25.22 | | | REF_CLOSE: (8), (15), (17), (34) are inconsistent by sub-proof #572.
% 168.45/25.22 | | |
% 168.45/25.22 | | Case 2:
% 168.45/25.22 | | |
% 168.45/25.22 | | | (35) all_58_9 = e2 & op(e3, e0) = e2
% 168.45/25.22 | | |
% 168.45/25.22 | | | ALPHA: (35) implies:
% 168.45/25.22 | | | (36) all_58_9 = e2
% 168.45/25.22 | | |
% 168.45/25.22 | | | BETA: splitting (1) gives:
% 168.45/25.22 | | |
% 168.45/25.22 | | | Case 1:
% 168.45/25.22 | | | |
% 168.45/25.22 | | | | (37) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 168.45/25.22 | | | | = e1)
% 168.45/25.22 | | | |
% 168.45/25.22 | | | | BETA: splitting (37) gives:
% 168.45/25.22 | | | |
% 168.45/25.22 | | | | Case 1:
% 168.45/25.22 | | | | |
% 168.45/25.22 | | | | | (38) all_58_9 = e1 & op(e3, e0) = e1
% 168.45/25.22 | | | | |
% 168.45/25.22 | | | | | ALPHA: (38) implies:
% 168.45/25.22 | | | | | (39) all_58_9 = e1
% 168.45/25.22 | | | | |
% 168.45/25.22 | | | | | REF_CLOSE: (21), (36), (39) are inconsistent by sub-proof #942.
% 168.45/25.22 | | | | |
% 168.45/25.22 | | | | Case 2:
% 168.45/25.22 | | | | |
% 168.45/25.22 | | | | | (40) all_58_10 = e1 & op(e2, e0) = e1
% 168.45/25.22 | | | | |
% 168.45/25.22 | | | | | ALPHA: (40) implies:
% 168.45/25.22 | | | | | (41) op(e2, e0) = e1
% 168.45/25.22 | | | | |
% 168.45/25.22 | | | | | REF_CLOSE: (17), (21), (23), (41) are inconsistent by sub-proof #526.
% 168.45/25.22 | | | | |
% 168.45/25.22 | | | | End of split
% 168.45/25.22 | | | |
% 168.45/25.22 | | | Case 2:
% 168.45/25.22 | | | |
% 168.45/25.22 | | | | (42) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 168.45/25.22 | | | | e0) = e1)
% 168.45/25.22 | | | |
% 168.45/25.22 | | | | REF_CLOSE: (4), (5), (6), (9), (12), (13), (14), (17), (18), (19), (20),
% 168.45/25.22 | | | | (24), (42) are inconsistent by sub-proof #68.
% 168.45/25.22 | | | |
% 168.45/25.22 | | | End of split
% 168.45/25.22 | | |
% 168.45/25.22 | | End of split
% 168.45/25.22 | |
% 168.45/25.22 | End of split
% 168.45/25.22 |
% 168.45/25.22 End of proof
% 168.45/25.22
% 168.45/25.22 Sub-proof #67 shows that the following formulas are inconsistent:
% 168.45/25.22 ----------------------------------------------------------------
% 168.45/25.22 (1) op(e2, e1) = all_52_9
% 168.45/25.22 (2) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 168.45/25.22 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 168.45/25.22 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.45/25.22 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.45/25.22 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.45/25.22 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 168.45/25.22 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.45/25.22 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.45/25.22 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.45/25.22 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 168.45/25.22 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 168.45/25.22 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.45/25.22 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.45/25.22 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.45/25.22 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.45/25.22 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 168.45/25.22 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.45/25.22 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.45/25.22 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.45/25.22 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.45/25.22 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 168.45/25.22 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.45/25.22 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.45/25.22 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.45/25.22 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 168.45/25.22 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 168.45/25.22 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.45/25.22 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.45/25.22 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.45/25.22 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.45/25.22 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 168.45/25.22 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.45/25.22 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.45/25.22 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.45/25.22 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 168.45/25.22 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 168.45/25.22 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.45/25.22 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.45/25.22 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.45/25.22 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.45/25.22 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 168.45/25.22 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.45/25.22 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.45/25.22 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.45/25.22 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 168.45/25.22 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.45/25.22 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.45/25.22 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 168.45/25.22 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.45/25.22 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 168.45/25.22 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.45/25.22 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 168.45/25.22 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 168.45/25.22 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 168.45/25.22 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 168.45/25.22 (5) op(e0, e1) = all_52_11
% 168.45/25.22 (6) ~ (all_52_4 = all_52_7)
% 168.45/25.22 (7) ~ (all_52_14 = all_4_2)
% 168.45/25.22 (8) ~ (all_52_1 = all_52_2)
% 168.45/25.22 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 168.45/25.22 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 168.45/25.23 (10) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 168.45/25.23 (11) all_54_8 = all_52_2
% 168.45/25.23 (12) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 168.45/25.23 (13) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 168.45/25.23 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 168.45/25.23 (14) ~ (all_8_2 = e3)
% 168.45/25.23 (15) all_58_7 = e1
% 168.71/25.23 (16) ( ~ (all_18_0 = e0) & op(all_18_1, e1) = all_18_0 & op(e2, e1) =
% 168.71/25.23 all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e2,
% 168.71/25.23 e1) = all_18_1 & $i(all_18_1))
% 168.71/25.23 (17) all_56_10 = all_10_2
% 168.71/25.23 (18) ~ (all_52_13 = all_8_2)
% 168.71/25.23 (19) ~ (all_4_2 = e1)
% 168.71/25.23 (20) op(e3, e3) = all_10_2
% 168.71/25.23 (21) all_32_2 = all_10_2
% 168.71/25.23 (22) ~ (all_52_1 = all_52_13)
% 168.71/25.23 (23) ~ (all_34_2 = e3) | ( ~ (all_34_0 = e1) & op(all_34_1, e0) = all_34_0 &
% 168.71/25.23 op(e3, e0) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 168.71/25.23 e2) & op(e3, e0) = all_34_1 & $i(all_34_1))
% 168.71/25.23 (24) ~ (e3 = e1)
% 168.71/25.23 (25) op(e3, e0) = all_52_12
% 168.71/25.23 (26) ~ (all_52_1 = all_52_3)
% 168.71/25.23 (27) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 168.71/25.23 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 168.71/25.23 e1)
% 168.71/25.23 (28) op(e0, e3) = all_52_3
% 168.71/25.23 (29) op(e1, e3) = all_52_2
% 168.71/25.23 (30) ~ (all_10_2 = e0)
% 168.71/25.23 (31) op(e3, e1) = all_52_8
% 168.71/25.23 (32) ~ (e1 = e0)
% 168.71/25.23 (33) ~ (all_32_2 = e1) | ( ~ (all_32_0 = e2) & op(all_32_1, e3) = all_32_0 &
% 168.71/25.23 op(e1, e3) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 168.71/25.23 e0) & op(e1, e3) = all_32_1 & $i(all_32_1))
% 168.71/25.23 (34) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 168.71/25.23 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 168.71/25.23 e3)
% 168.71/25.23 (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 168.71/25.23 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 168.71/25.23 (36) op(e1, e2) = all_52_6
% 168.71/25.23 (37) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 168.71/25.23 (38) op(e2, e3) = all_52_1
% 168.71/25.23 (39) all_34_2 = all_4_2
% 168.71/25.23 (40) ~ (all_52_7 = all_4_2)
% 168.71/25.23 (41) ~ (all_52_12 = all_4_2)
% 168.71/25.23 (42) ( ~ (all_6_0 = e3) & op(all_6_1, e1) = all_6_0 & op(e2, e1) = all_6_1 &
% 168.71/25.23 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e2, e1) = all_6_1
% 168.71/25.23 & $i(all_6_1))
% 168.71/25.23 (43) ~ (all_52_3 = all_52_7)
% 168.71/25.23 (44) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 168.71/25.23 (45) all_54_1 = all_52_4
% 168.71/25.23 (46) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 168.71/25.23 (47) all_54_15 = all_4_2
% 168.71/25.23 (48) op(e2, e2) = all_8_2
% 168.71/25.23 (49) all_56_12 = all_8_2
% 168.71/25.23 (50) ~ (all_52_6 = e2)
% 168.71/25.23 (51) ~ (all_8_2 = e0)
% 168.71/25.23 (52) ~ (all_52_4 = all_10_2)
% 168.71/25.23 (53) ~ (all_52_12 = all_52_14)
% 168.71/25.23 (54) all_54_4 = all_52_1
% 168.71/25.23 (55) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 168.71/25.23 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 168.71/25.23 (56) all_56_15 = all_4_2
% 168.71/25.23 (57) ~ (e3 = e0)
% 168.71/25.23 (58) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 168.71/25.23 (59) ~ (all_52_7 = all_8_2)
% 168.71/25.23 (60) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.71/25.23 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.71/25.23 (61) ~ (all_52_13 = all_52_14)
% 168.71/25.23 (62) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 168.71/25.23 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.71/25.23 (63) ~ (all_52_2 = all_52_14)
% 168.71/25.23 (64) op(e0, e0) = all_4_2
% 168.71/25.23 (65) ~ (all_52_8 = e2)
% 168.71/25.23 (66) ~ (all_52_2 = e1)
% 168.71/25.23 (67) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.71/25.23 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 168.71/25.23 (68) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.71/25.23 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 168.71/25.23 (69) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 168.71/25.23 (70) all_54_11 = all_52_14
% 168.71/25.23 (71) ~ (all_52_7 = all_52_11)
% 168.71/25.23 (72) ~ (all_52_4 = all_52_12)
% 168.71/25.23 (73) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.71/25.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.71/25.23 (74) ~ (all_52_4 = all_8_2)
% 168.71/25.23 (75) all_58_8 = e2
% 168.71/25.23 (76) ~ (all_52_13 = all_4_2)
% 168.71/25.23 (77) ~ (all_10_2 = e2)
% 168.71/25.23 (78) ~ (all_52_9 = all_8_2)
% 168.71/25.23 (79) ~ (all_52_12 = all_10_2)
% 168.71/25.23 (80) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 168.71/25.23 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 168.71/25.23 (81) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 168.71/25.23 (82) ~ (all_52_4 = all_52_8)
% 168.71/25.23 (83) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.71/25.23 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.71/25.23 (84) all_54_5 = all_8_2
% 168.71/25.23 (85) op(e3, e2) = all_52_4
% 168.71/25.23 (86) ~ (all_52_2 = all_10_2)
% 168.71/25.23 (87) ~ (all_52_7 = e1)
% 168.71/25.23 (88) ~ (all_8_2 = e1)
% 168.71/25.23 (89) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 168.71/25.23 (90) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.71/25.23 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 168.71/25.23 (91) all_54_0 = all_10_2
% 168.71/25.23 (92) op(e0, e2) = all_52_7
% 168.71/25.23 (93) ~ (all_52_4 = e1)
% 168.71/25.23 (94) ~ (all_52_1 = all_10_2)
% 168.71/25.23 (95) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 168.71/25.23 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 168.71/25.23 (96) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 168.71/25.23 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 168.71/25.23 (97) all_54_13 = all_52_7
% 168.71/25.23 (98) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 168.71/25.23 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 168.71/25.23 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 168.71/25.23 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 168.71/25.23 (99) ~ (all_52_2 = all_52_3)
% 168.71/25.23 (100) op(e2, e0) = all_52_13
% 168.71/25.23
% 168.71/25.23 Begin of proof
% 168.71/25.23 |
% 168.71/25.23 | BETA: splitting (12) gives:
% 168.71/25.23 |
% 168.71/25.23 | Case 1:
% 168.71/25.23 | |
% 168.71/25.23 | | (101) all_54_5 = e3
% 168.71/25.23 | |
% 168.71/25.23 | | COMBINE_EQS: (84), (101) imply:
% 168.71/25.23 | | (102) all_8_2 = e3
% 168.71/25.23 | |
% 168.71/25.23 | | REDUCE: (14), (102) imply:
% 168.71/25.23 | | (103) $false
% 168.71/25.23 | |
% 168.71/25.23 | | CLOSE: (103) is inconsistent.
% 168.71/25.23 | |
% 168.71/25.23 | Case 2:
% 168.71/25.23 | |
% 168.71/25.23 | | (104) ~ (all_54_5 = e3)
% 168.71/25.23 | | (105) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 168.71/25.23 | |
% 168.71/25.23 | | BETA: splitting (105) gives:
% 168.71/25.23 | |
% 168.71/25.23 | | Case 1:
% 168.71/25.23 | | |
% 168.71/25.23 | | | (106) all_54_5 = e2
% 168.71/25.23 | | |
% 168.71/25.23 | | | COMBINE_EQS: (84), (106) imply:
% 168.71/25.23 | | | (107) all_8_2 = e2
% 168.71/25.23 | | |
% 168.71/25.23 | | | COMBINE_EQS: (49), (107) imply:
% 168.71/25.23 | | | (108) all_56_12 = e2
% 168.71/25.23 | | |
% 168.71/25.23 | | | REDUCE: (74), (107) imply:
% 168.71/25.23 | | | (109) ~ (all_52_4 = e2)
% 168.71/25.23 | | |
% 168.71/25.23 | | | REDUCE: (59), (107) imply:
% 168.71/25.23 | | | (110) ~ (all_52_7 = e2)
% 168.71/25.23 | | |
% 168.71/25.23 | | | REDUCE: (78), (107) imply:
% 168.71/25.23 | | | (111) ~ (all_52_9 = e2)
% 168.71/25.23 | | |
% 168.71/25.23 | | | REDUCE: (18), (107) imply:
% 168.71/25.23 | | | (112) ~ (all_52_13 = e2)
% 168.71/25.23 | | |
% 168.71/25.23 | | | REDUCE: (14), (107) imply:
% 168.71/25.23 | | | (113) ~ (e3 = e2)
% 168.71/25.23 | | |
% 168.71/25.23 | | | SIMP: (113) implies:
% 168.71/25.23 | | | (114) ~ (e3 = e2)
% 168.71/25.23 | | |
% 168.71/25.23 | | | REDUCE: (88), (107) imply:
% 168.71/25.23 | | | (115) ~ (e2 = e1)
% 168.71/25.23 | | |
% 168.71/25.23 | | | REDUCE: (51), (107) imply:
% 168.71/25.23 | | | (116) ~ (e2 = e0)
% 168.71/25.23 | | |
% 168.71/25.23 | | | BETA: splitting (96) gives:
% 168.71/25.23 | | |
% 168.71/25.23 | | | Case 1:
% 168.71/25.23 | | | |
% 168.71/25.23 | | | | (117) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 168.71/25.23 | | | | = e2)
% 168.71/25.23 | | | |
% 168.71/25.23 | | | | REF_CLOSE: (20), (73), (77), (85), (109), (117) are inconsistent by
% 168.71/25.23 | | | | sub-proof #659.
% 168.71/25.23 | | | |
% 168.71/25.23 | | | Case 2:
% 168.71/25.23 | | | |
% 168.71/25.23 | | | | (118) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 168.71/25.23 | | | | = e2)
% 168.71/25.23 | | | |
% 168.71/25.23 | | | | BETA: splitting (118) gives:
% 168.71/25.23 | | | |
% 168.71/25.23 | | | | Case 1:
% 168.71/25.23 | | | | |
% 168.71/25.23 | | | | | (119) all_58_4 = e2 & op(e3, e1) = e2
% 168.71/25.23 | | | | |
% 168.71/25.23 | | | | | REF_CLOSE: (31), (65), (73), (119) are inconsistent by sub-proof #572.
% 168.71/25.23 | | | | |
% 168.71/25.23 | | | | Case 2:
% 168.71/25.23 | | | | |
% 168.71/25.23 | | | | | (120) all_58_9 = e2 & op(e3, e0) = e2
% 168.71/25.23 | | | | |
% 168.71/25.23 | | | | | ALPHA: (120) implies:
% 168.71/25.23 | | | | | (121) all_58_9 = e2
% 168.71/25.23 | | | | | (122) op(e3, e0) = e2
% 168.71/25.23 | | | | |
% 168.71/25.23 | | | | | BETA: splitting (3) gives:
% 168.71/25.23 | | | | |
% 168.71/25.23 | | | | | Case 1:
% 168.71/25.23 | | | | | |
% 168.71/25.23 | | | | | | (123) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 &
% 168.71/25.23 | | | | | | op(e2, e0) = e1)
% 168.71/25.23 | | | | | |
% 168.71/25.23 | | | | | | BETA: splitting (123) gives:
% 168.71/25.23 | | | | | |
% 168.71/25.23 | | | | | | Case 1:
% 168.71/25.23 | | | | | | |
% 168.71/25.23 | | | | | | | (124) all_58_9 = e1 & op(e3, e0) = e1
% 168.71/25.23 | | | | | | |
% 168.71/25.23 | | | | | | | REF_CLOSE: (115), (121), (124) are inconsistent by sub-proof #701.
% 168.71/25.23 | | | | | | |
% 168.71/25.23 | | | | | | Case 2:
% 168.71/25.23 | | | | | | |
% 168.71/25.23 | | | | | | | (125) all_58_10 = e1 & op(e2, e0) = e1
% 168.71/25.23 | | | | | | |
% 168.71/25.23 | | | | | | | ALPHA: (125) implies:
% 168.71/25.23 | | | | | | | (126) all_58_10 = e1
% 168.71/25.23 | | | | | | | (127) op(e2, e0) = e1
% 168.71/25.23 | | | | | | |
% 168.71/25.23 | | | | | | | BETA: splitting (67) gives:
% 168.71/25.23 | | | | | | |
% 168.71/25.23 | | | | | | | Case 1:
% 168.71/25.23 | | | | | | | |
% 168.71/25.23 | | | | | | | | (128) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 &
% 168.71/25.23 | | | | | | | | op(e2, e2) = e2)
% 168.71/25.23 | | | | | | | |
% 168.71/25.23 | | | | | | | | BETA: splitting (128) gives:
% 168.71/25.23 | | | | | | | |
% 168.71/25.23 | | | | | | | | Case 1:
% 168.71/25.23 | | | | | | | | |
% 168.71/25.23 | | | | | | | | | (129) all_58_1 = e2 & op(e3, e2) = e2
% 168.71/25.23 | | | | | | | | |
% 168.71/25.23 | | | | | | | | | ALPHA: (129) implies:
% 168.71/25.23 | | | | | | | | | (130) op(e3, e2) = e2
% 168.71/25.23 | | | | | | | | |
% 168.71/25.23 | | | | | | | | | REF_CLOSE: (73), (85), (109), (130) are inconsistent by
% 168.71/25.23 | | | | | | | | | sub-proof #993.
% 168.71/25.23 | | | | | | | | |
% 168.71/25.23 | | | | | | | | Case 2:
% 168.71/25.23 | | | | | | | | |
% 168.71/25.23 | | | | | | | | | (131) all_58_3 = e2 & op(e2, e2) = e2
% 168.71/25.23 | | | | | | | | |
% 168.71/25.23 | | | | | | | | | ALPHA: (131) implies:
% 168.71/25.23 | | | | | | | | | (132) all_58_3 = e2
% 168.71/25.23 | | | | | | | | |
% 168.71/25.23 | | | | | | | | | BETA: splitting (13) gives:
% 168.71/25.23 | | | | | | | | |
% 168.71/25.23 | | | | | | | | | Case 1:
% 168.71/25.23 | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | (133) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 168.71/25.23 | | | | | | | | | | & op(e2, e3) = e2)
% 168.71/25.23 | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | BETA: splitting (133) gives:
% 168.71/25.23 | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | Case 1:
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | (134) all_58_0 = e2 & op(e3, e3) = e2
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | REF_CLOSE: (20), (73), (77), (134) are inconsistent by
% 168.71/25.23 | | | | | | | | | | | sub-proof #666.
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | Case 2:
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | (135) all_58_2 = e2 & op(e2, e3) = e2
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | ALPHA: (135) implies:
% 168.71/25.23 | | | | | | | | | | | (136) all_58_2 = e2
% 168.71/25.23 | | | | | | | | | | | (137) op(e2, e3) = e2
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | REF_CLOSE: (4), (24), (32), (38), (57), (60), (73), (83),
% 168.71/25.23 | | | | | | | | | | | (114), (115), (116), (132), (136), (137) are
% 168.71/25.23 | | | | | | | | | | | inconsistent by sub-proof #779.
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | End of split
% 168.71/25.23 | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | Case 2:
% 168.71/25.23 | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | (138) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2
% 168.71/25.23 | | | | | | | | | | & op(e0, e3) = e2)
% 168.71/25.23 | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | BETA: splitting (138) gives:
% 168.71/25.23 | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | Case 1:
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | (139) all_58_6 = e2 & op(e1, e3) = e2
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | ALPHA: (139) implies:
% 168.71/25.23 | | | | | | | | | | | (140) all_58_6 = e2
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | REF_CLOSE: (15), (24), (32), (57), (62), (75), (80), (114),
% 168.71/25.23 | | | | | | | | | | | (116), (140) are inconsistent by sub-proof #158.
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | Case 2:
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | (141) all_58_12 = e2 & op(e0, e3) = e2
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | ALPHA: (141) implies:
% 168.71/25.23 | | | | | | | | | | | (142) all_58_12 = e2
% 168.71/25.23 | | | | | | | | | | | (143) op(e0, e3) = e2
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | BETA: splitting (27) gives:
% 168.71/25.23 | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | Case 1:
% 168.71/25.23 | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | (144) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 168.71/25.23 | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 168.71/25.23 | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | REF_CLOSE: (73), (87), (92), (115), (142), (144) are
% 168.71/25.23 | | | | | | | | | | | | inconsistent by sub-proof #79.
% 168.71/25.23 | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | Case 2:
% 168.71/25.23 | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | (145) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 168.71/25.23 | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 168.71/25.23 | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | BETA: splitting (145) gives:
% 168.71/25.23 | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | Case 1:
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | (146) all_58_14 = e1 & op(e0, e1) = e1
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | ALPHA: (146) implies:
% 168.71/25.23 | | | | | | | | | | | | | (147) all_58_14 = e1
% 168.71/25.23 | | | | | | | | | | | | | (148) op(e0, e1) = e1
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | GROUND_INST: instantiating (73) with all_52_11, e1, e1, e0,
% 168.71/25.23 | | | | | | | | | | | | | simplifying with (5), (148) gives:
% 168.71/25.23 | | | | | | | | | | | | | (149) all_52_11 = e1
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | GROUND_INST: instantiating (73) with all_52_3, e2, e3, e0,
% 168.71/25.23 | | | | | | | | | | | | | simplifying with (28), (143) gives:
% 168.71/25.23 | | | | | | | | | | | | | (150) all_52_3 = e2
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | GROUND_INST: instantiating (73) with all_52_13, e1, e0, e2,
% 168.71/25.23 | | | | | | | | | | | | | simplifying with (100), (127) gives:
% 168.71/25.23 | | | | | | | | | | | | | (151) all_52_13 = e1
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | GROUND_INST: instantiating (73) with all_52_12, e2, e0, e3,
% 168.71/25.23 | | | | | | | | | | | | | simplifying with (25), (122) gives:
% 168.71/25.23 | | | | | | | | | | | | | (152) all_52_12 = e2
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | REDUCE: (26), (150) imply:
% 168.71/25.23 | | | | | | | | | | | | | (153) ~ (all_52_1 = e2)
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | REDUCE: (22), (151) imply:
% 168.71/25.23 | | | | | | | | | | | | | (154) ~ (all_52_1 = e1)
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | REDUCE: (99), (150) imply:
% 168.71/25.23 | | | | | | | | | | | | | (155) ~ (all_52_2 = e2)
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | REDUCE: (43), (150) imply:
% 168.71/25.23 | | | | | | | | | | | | | (156) ~ (all_52_7 = e2)
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | REDUCE: (53), (152) imply:
% 168.71/25.23 | | | | | | | | | | | | | (157) ~ (all_52_14 = e2)
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | SIMP: (157) implies:
% 168.71/25.23 | | | | | | | | | | | | | (158) ~ (all_52_14 = e2)
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | REDUCE: (79), (152) imply:
% 168.71/25.23 | | | | | | | | | | | | | (159) ~ (all_10_2 = e2)
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | REDUCE: (41), (152) imply:
% 168.71/25.23 | | | | | | | | | | | | | (160) ~ (all_4_2 = e2)
% 168.71/25.23 | | | | | | | | | | | | |
% 168.71/25.23 | | | | | | | | | | | | | SIMP: (160) implies:
% 168.71/25.24 | | | | | | | | | | | | | (161) ~ (all_4_2 = e2)
% 168.71/25.24 | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | REDUCE: (61), (151) imply:
% 168.71/25.24 | | | | | | | | | | | | | (162) ~ (all_52_14 = e1)
% 168.71/25.24 | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | SIMP: (162) implies:
% 168.71/25.24 | | | | | | | | | | | | | (163) ~ (all_52_14 = e1)
% 168.71/25.24 | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | REDUCE: (76), (151) imply:
% 168.71/25.24 | | | | | | | | | | | | | (164) ~ (all_4_2 = e1)
% 168.71/25.24 | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | REDUCE: (112), (151) imply:
% 168.71/25.24 | | | | | | | | | | | | | (165) ~ (e2 = e1)
% 168.71/25.24 | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | BETA: splitting (23) gives:
% 168.71/25.24 | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | (166) ~ (all_34_2 = e3)
% 168.71/25.24 | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | REDUCE: (39), (166) imply:
% 168.71/25.24 | | | | | | | | | | | | | | (167) ~ (all_4_2 = e3)
% 168.71/25.24 | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 168.71/25.24 | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | (168) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 168.71/25.24 | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 168.71/25.24 | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 168.71/25.24 | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | (169) all_58_0 = e1 & op(e3, e3) = e1
% 168.71/25.24 | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | (170) all_58_0 = e1
% 168.71/25.24 | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | (171) all_54_15 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (167), (171) are inconsistent by sub-proof
% 168.71/25.24 | | | | | | | | | | | | | | | | | #992.
% 168.71/25.24 | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | (172) ~ (all_54_15 = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | (173) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | (174) all_54_15 = e2
% 168.71/25.24 | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (161), (174) are inconsistent by sub-proof
% 168.71/25.24 | | | | | | | | | | | | | | | | | | #991.
% 168.71/25.24 | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | (175) ~ (all_54_15 = e2)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | (176) all_54_15 = e1 | all_54_15 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | (177) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | (178) all_58_9 = e3 & op(e3, e0) = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (121), (178) are inconsistent by sub-proof
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | #940.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | (179) all_58_10 = e3 & op(e2, e0) = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (126), (179) are inconsistent by sub-proof
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | #813.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.24 | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | (180) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | (181) all_58_11 = e3 & op(e1, e0) = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | (182) all_58_11 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | (183) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | (184) all_58_6 = e0 & op(e1, e3) = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | (185) all_58_6 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | (186) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | (187) all_58_0 = e3 & op(e3, e3) = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | (188) all_58_0 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (170), (188) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | (189) e3 = e1
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (189) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | (190) e3 = e1
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (190) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | (191) all_58_11 = e1
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (24), (32), (57), (62), (75), (80), (114),
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | (116), (191) are inconsistent by sub-proof #76.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | (192) all_58_2 = e3 & op(e2, e3) = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | (193) all_58_2 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_54_15 = e1
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (47), (194) are inconsistent by sub-proof
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | #990.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_54_15 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (195) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_4_2 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (196) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_4_2 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (197) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_56_15 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (197) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | (199) ~ (all_52_14 = e0)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (197) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | (200) ~ (e3 = e0)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (197) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | (201) ~ (e2 = e0)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (197) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | (202) ~ (e1 = e0)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (64), (197) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | (203) op(e0, e0) = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (204) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_58_2 = e0 & op(e2, e3) = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_2 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (193), (206) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) e3 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (207) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_58_11 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_54_11 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (209) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_52_14 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (210) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_52_14 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (211) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) ~ (all_52_2 = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (24), (29), (73), (212), (213) are
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #75.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (75), (114), (208), (214) are inconsistent
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #159.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (158), (163), (199), (215) are inconsistent
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #602.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) all_58_3 = e0 & op(e2, e2) = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_58_3 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (24), (32), (36), (38), (50), (57),
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (67), (73), (83), (85), (90), (92), (109),
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (114), (115), (116), (127), (217)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #215.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (218) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_5 = e0 & op(e2, e1) = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) op(e2, e1) = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_54_11 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (221) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_52_14 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (222) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_52_14 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (223) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) ~ (all_52_2 = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_58_12 = e3 & op(e0, e3) = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_58_12 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (142), (227) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) e3 = e2
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) e3 = e2
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (193), (229) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_58_2 = e2
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (24), (32), (35), (57), (114), (116), (142),
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (230) are inconsistent by sub-proof #435.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_58_13 = e3 & op(e0, e2) = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_58_13 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_54_8 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (224), (233) are inconsistent by sub-proof
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #690.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_54_8 = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_54_8 = e2
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (155), (236) are inconsistent by sub-proof
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #259.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) ~ (all_54_8 = e2)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_54_8 = e1 | all_54_8 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_54_8 = e1
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (66), (239) are inconsistent by sub-proof
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #689.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_54_8 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (240) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_52_2 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (241) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_52_2 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (242) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) ~ (all_52_1 = e0)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (242) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) ~ (all_10_2 = e0)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) ~ (all_32_2 = e1)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (21), (245) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) ~ (all_10_2 = e1)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_54_4 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (54), (247) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_52_1 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (248) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_52_1 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (94), (249) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) ~ (all_10_2 = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (250) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) ~ (all_10_2 = e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (77), (89), (91), (246), (251) are
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #74.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (54), (153), (154), (243), (252) are inconsistent
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #671.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_32_2 = e1
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (253) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_10_2 = e1
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (17), (254) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_56_10 = e1
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) ~ (all_56_10 = e1)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (255), (256) imply:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) $false
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (257) is inconsistent.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_56_4 = e3 & op(e3, e1) = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_56_4 = e3
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (68) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_58_1 = e0 & op(e3, e2) = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) op(e3, e2) = e0
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (108), (116), (262), (264) are inconsistent
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #796.
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (265) gives:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (259), (267) are inconsistent by sub-proof
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #795.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (268) gives:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (270) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (255), (259), (270) are inconsistent by sub-proof
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #795.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (271) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_56_4 = e1
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (272) imply:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) e3 = e1
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (182), (273) imply:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) all_58_11 = e1
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (24), (32), (57), (62), (75), (80), (114),
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (116), (274) are inconsistent by sub-proof #76.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (275) gives:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (277) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) op(e2, e1) = e1
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (73), (220), (278) are inconsistent by
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #911.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) op(e3, e0) = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (116), (122), (280) are inconsistent by
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #699.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) op(e2, e0) = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (73), (127), (283) are inconsistent by
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #849.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (198), (255), (259), (284) are inconsistent by
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #353.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_58_3 = e0 & op(e2, e2) = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (285) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_58_3 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (24), (32), (36), (38), (50), (57),
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (67), (73), (83), (85), (90), (92), (109),
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (111), (114), (115), (116), (127), (286)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #215.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (287) gives:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_58_7 = e0 & op(e1, e2) = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_58_7 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (289) imply:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) e1 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (147), (290) imply:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_58_14 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (32), (73), (115), (142), (203),
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (291) are inconsistent by sub-proof #173.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) all_58_13 = e0 & op(e0, e2) = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (292) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_58_13 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (232), (293) imply:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) e3 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (24), (29), (57), (73), (75), (80), (114),
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182), (224), (294) are inconsistent by sub-proof
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #73.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_58_14 = e3 & op(e0, e1) = e3
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) op(e0, e1) = e3
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (42), (73), (220), (297) are
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #70.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_58_15 = e3 & op(e0, e0) = e3
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_58_15 = e3
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (24), (32), (57), (98), (115), (116), (121),
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (182), (299) are inconsistent by sub-proof #374.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (70), (158), (163), (199), (300) are inconsistent
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #602.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) all_58_10 = e0 & op(e2, e0) = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (301) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) op(e2, e0) = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (73), (127), (302) are inconsistent by
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #849.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | (303) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (303) gives:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | (304) all_58_6 = e3 & op(e1, e3) = e3
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (304) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | (305) all_58_6 = e3
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (185), (305) imply:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | (306) e3 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (306) imply:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | (307) $false
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (307) is inconsistent.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | (308) all_58_12 = e3 & op(e0, e3) = e3
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | (309) all_58_12 = e3
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (114), (142), (309) are inconsistent by sub-proof
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | | #635.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | (310) all_58_7 = e0 & op(e1, e2) = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | (311) all_58_7 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (32), (311) are inconsistent by sub-proof
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | #710.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | (312) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | (313) all_58_8 = e0 & op(e1, e1) = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | (314) all_58_8 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (75), (314) imply:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | (315) e2 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (315) imply:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | (316) all_58_3 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (24), (32), (36), (38), (50), (57),
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | (60), (67), (73), (83), (85), (90), (92), (109),
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | (110), (111), (114), (115), (116), (127), (316)
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #215.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | (317) all_58_11 = e0 & op(e1, e0) = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | (318) all_58_11 = e0
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (182), (318) are inconsistent by sub-proof
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | | #474.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | (319) all_58_15 = e3 & op(e0, e0) = e3
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (73), (167), (319) are inconsistent by
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | | sub-proof #161.
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | End of split
% 168.71/25.25 | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | (320) all_58_2 = e1 & op(e2, e3) = e1
% 168.71/25.25 | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 168.71/25.25 | | | | | | | | | | | | | | | | (321) all_58_2 = e1
% 168.71/25.25 | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 168.71/25.25 | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.25 | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | (322) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 168.71/25.25 | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 168.71/25.25 | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (48), (73), (321), (322) are
% 168.71/25.25 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #937.
% 168.71/25.25 | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.25 | | | | | | | | | | | | | | | | |
% 168.71/25.25 | | | | | | | | | | | | | | | | | (323) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 168.71/25.26 | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (324) all_58_5 = e3 & op(e2, e1) = e3
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (325) all_58_5 = e3
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (57), (60), (73), (116), (127), (132),
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (321), (325) are inconsistent by sub-proof #549.
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (326) all_58_10 = e3 & op(e2, e0) = e3
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (126), (326) are inconsistent by sub-proof
% 168.71/25.26 | | | | | | | | | | | | | | | | | | #813.
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | (327) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 168.71/25.26 | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | Case 1:
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | (328) all_58_6 = e1 & op(e1, e3) = e1
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | ALPHA: (328) implies:
% 168.71/25.26 | | | | | | | | | | | | | | | | (329) op(e1, e3) = e1
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | REF_CLOSE: (15), (24), (29), (32), (57), (62), (73), (75),
% 168.71/25.26 | | | | | | | | | | | | | | | | (80), (114), (116), (329) are inconsistent by
% 168.71/25.26 | | | | | | | | | | | | | | | | sub-proof #69.
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | (330) all_58_12 = e1 & op(e0, e3) = e1
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 168.71/25.26 | | | | | | | | | | | | | | | | (331) all_58_12 = e1
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | REF_CLOSE: (115), (142), (331) are inconsistent by sub-proof
% 168.71/25.26 | | | | | | | | | | | | | | | | #862.
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | (332) all_34_2 = e3
% 168.71/25.26 | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | COMBINE_EQS: (39), (332) imply:
% 168.71/25.26 | | | | | | | | | | | | | | (333) all_4_2 = e3
% 168.71/25.26 | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | SIMP: (333) implies:
% 168.71/25.26 | | | | | | | | | | | | | | (334) all_4_2 = e3
% 168.71/25.26 | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | REDUCE: (40), (334) imply:
% 168.71/25.26 | | | | | | | | | | | | | | (335) ~ (all_52_7 = e3)
% 168.71/25.26 | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 168.71/25.26 | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | Case 1:
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | (336) all_54_13 = e3
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | REF_CLOSE: (97), (335), (336) are inconsistent by sub-proof
% 168.71/25.26 | | | | | | | | | | | | | | | #971.
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | (337) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | BETA: splitting (337) gives:
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | Case 1:
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | (338) all_54_13 = e2
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | REF_CLOSE: (97), (110), (338) are inconsistent by sub-proof
% 168.71/25.26 | | | | | | | | | | | | | | | | #970.
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | (339) all_54_13 = e1 | all_54_13 = e0
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | BETA: splitting (339) gives:
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | (340) all_54_13 = e1
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (87), (97), (340) are inconsistent by sub-proof
% 168.71/25.26 | | | | | | | | | | | | | | | | | #257.
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | (341) all_54_13 = e0
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (341) imply:
% 168.71/25.26 | | | | | | | | | | | | | | | | | (342) all_52_7 = e0
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | SIMP: (342) implies:
% 168.71/25.26 | | | | | | | | | | | | | | | | | (343) all_52_7 = e0
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | REDUCE: (6), (343) imply:
% 168.71/25.26 | | | | | | | | | | | | | | | | | (344) ~ (all_52_4 = e0)
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | BETA: splitting (58) gives:
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (345) all_54_1 = e3
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (45), (345) imply:
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (346) all_52_4 = e3
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | REDUCE: (82), (346) imply:
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (347) ~ (all_52_8 = e3)
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | SIMP: (347) implies:
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (348) ~ (all_52_8 = e3)
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | REDUCE: (52), (346) imply:
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (349) ~ (all_10_2 = e3)
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | SIMP: (349) implies:
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (350) ~ (all_10_2 = e3)
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | Case 1:
% 168.71/25.26 | | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | | (351) ~ (all_56_10 = e1)
% 168.71/25.26 | | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | | REDUCE: (17), (351) imply:
% 168.71/25.26 | | | | | | | | | | | | | | | | | | | (352) ~ (all_10_2 = e1)
% 168.71/25.26 | | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (77), (89), (91), (350), (352) are
% 168.71/25.26 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #74.
% 168.71/25.26 | | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | | (353) all_56_4 = e3 & op(e3, e1) = e3
% 168.71/25.26 | | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 168.71/25.26 | | | | | | | | | | | | | | | | | | | (354) op(e3, e1) = e3
% 168.71/25.26 | | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (73), (348), (354) are inconsistent by
% 168.71/25.26 | | | | | | | | | | | | | | | | | | | sub-proof #975.
% 168.71/25.26 | | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | (355) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (93), (109), (344), (355) are inconsistent
% 168.71/25.26 | | | | | | | | | | | | | | | | | | by sub-proof #595.
% 168.71/25.26 | | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | (356) all_58_15 = e1 & op(e0, e0) = e1
% 168.71/25.26 | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | | REF_CLOSE: (19), (64), (73), (356) are inconsistent by
% 168.71/25.26 | | | | | | | | | | | | | sub-proof #130.
% 168.71/25.26 | | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | | |
% 168.71/25.26 | | | | | | | | | End of split
% 168.71/25.26 | | | | | | | | |
% 168.71/25.26 | | | | | | | | End of split
% 168.71/25.26 | | | | | | | |
% 168.71/25.26 | | | | | | | Case 2:
% 168.71/25.26 | | | | | | | |
% 168.71/25.26 | | | | | | | | (357) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 &
% 168.71/25.26 | | | | | | | | op(e0, e2) = e2)
% 168.71/25.26 | | | | | | | |
% 168.71/25.26 | | | | | | | | REF_CLOSE: (36), (50), (73), (92), (110), (357) are inconsistent
% 168.71/25.26 | | | | | | | | by sub-proof #694.
% 168.71/25.26 | | | | | | | |
% 168.71/25.26 | | | | | | | End of split
% 168.71/25.26 | | | | | | |
% 168.71/25.26 | | | | | | End of split
% 168.71/25.26 | | | | | |
% 168.71/25.26 | | | | | Case 2:
% 168.71/25.26 | | | | | |
% 168.71/25.26 | | | | | | (358) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 168.71/25.26 | | | | | | op(e0, e0) = e1)
% 168.71/25.26 | | | | | |
% 168.71/25.26 | | | | | | REF_CLOSE: (15), (19), (24), (32), (57), (62), (64), (73), (75),
% 168.71/25.26 | | | | | | (80), (114), (116), (358) are inconsistent by sub-proof
% 168.71/25.26 | | | | | | #68.
% 168.71/25.26 | | | | | |
% 168.71/25.26 | | | | | End of split
% 168.71/25.26 | | | | |
% 168.71/25.26 | | | | End of split
% 168.71/25.26 | | | |
% 168.71/25.26 | | | End of split
% 168.71/25.26 | | |
% 168.71/25.26 | | Case 2:
% 168.71/25.26 | | |
% 168.71/25.26 | | | (359) all_54_5 = e1 | all_54_5 = e0
% 168.71/25.26 | | |
% 168.71/25.26 | | | REF_CLOSE: (51), (84), (88), (359) are inconsistent by sub-proof #735.
% 168.71/25.26 | | |
% 168.71/25.26 | | End of split
% 168.71/25.26 | |
% 168.71/25.26 | End of split
% 168.71/25.26 |
% 168.71/25.26 End of proof
% 168.71/25.26
% 168.71/25.26 Sub-proof #68 shows that the following formulas are inconsistent:
% 168.71/25.26 ----------------------------------------------------------------
% 168.71/25.26 (1) all_58_7 = e1
% 168.71/25.26 (2) ~ (all_4_2 = e1)
% 168.71/25.26 (3) ~ (e3 = e1)
% 168.71/25.26 (4) ~ (e1 = e0)
% 168.71/25.26 (5) ~ (e3 = e0)
% 168.71/25.26 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 168.71/25.26 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.71/25.26 (7) op(e0, e0) = all_4_2
% 168.71/25.26 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.71/25.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.71/25.26 (9) all_58_8 = e2
% 168.71/25.26 (10) ~ (e2 = e0)
% 168.71/25.26 (11) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 168.71/25.26 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 168.71/25.26 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 168.71/25.26 (13) ~ (e3 = e2)
% 168.71/25.26
% 168.71/25.26 Begin of proof
% 168.71/25.26 |
% 168.71/25.26 | BETA: splitting (11) gives:
% 168.71/25.26 |
% 168.71/25.26 | Case 1:
% 168.71/25.26 | |
% 168.71/25.26 | | (14) all_58_11 = e1 & op(e1, e0) = e1
% 168.71/25.26 | |
% 168.71/25.26 | | ALPHA: (14) implies:
% 168.71/25.26 | | (15) all_58_11 = e1
% 168.71/25.26 | |
% 168.71/25.26 | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (12), (13), (15) are
% 168.71/25.26 | | inconsistent by sub-proof #76.
% 168.71/25.26 | |
% 168.71/25.26 | Case 2:
% 168.71/25.26 | |
% 168.71/25.26 | | (16) all_58_15 = e1 & op(e0, e0) = e1
% 168.71/25.26 | |
% 168.71/25.26 | | REF_CLOSE: (2), (7), (8), (16) are inconsistent by sub-proof #130.
% 168.71/25.26 | |
% 168.71/25.26 | End of split
% 168.71/25.26 |
% 168.71/25.26 End of proof
% 168.71/25.26
% 168.71/25.26 Sub-proof #69 shows that the following formulas are inconsistent:
% 168.71/25.26 ----------------------------------------------------------------
% 168.71/25.26 (1) all_58_7 = e1
% 168.71/25.26 (2) ~ (e3 = e1)
% 168.71/25.26 (3) op(e1, e3) = all_52_2
% 168.71/25.26 (4) ~ (e1 = e0)
% 168.71/25.26 (5) ~ (e3 = e0)
% 168.71/25.26 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 168.71/25.26 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.71/25.26 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.71/25.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.71/25.26 (8) all_58_8 = e2
% 168.71/25.26 (9) ~ (e2 = e0)
% 168.71/25.26 (10) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 168.71/25.26 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 168.71/25.26 (11) op(e1, e3) = e1
% 168.71/25.26 (12) ~ (e3 = e2)
% 168.71/25.26
% 168.71/25.26 Begin of proof
% 168.71/25.26 |
% 168.71/25.26 | BETA: splitting (10) gives:
% 168.71/25.26 |
% 168.71/25.26 | Case 1:
% 168.71/25.26 | |
% 168.71/25.26 | | (13) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 168.71/25.26 | | e3)
% 168.71/25.26 | |
% 168.71/25.26 | | BETA: splitting (13) gives:
% 168.71/25.26 | |
% 168.71/25.26 | | Case 1:
% 168.71/25.26 | | |
% 168.71/25.26 | | | (14) all_58_6 = e3 & op(e1, e3) = e3
% 168.71/25.26 | | |
% 168.71/25.26 | | | ALPHA: (14) implies:
% 168.71/25.26 | | | (15) op(e1, e3) = e3
% 168.71/25.26 | | |
% 168.71/25.26 | | | REF_CLOSE: (2), (3), (7), (11), (15) are inconsistent by sub-proof #750.
% 168.71/25.26 | | |
% 168.71/25.26 | | Case 2:
% 168.71/25.26 | | |
% 168.71/25.26 | | | (16) all_58_7 = e3 & op(e1, e2) = e3
% 168.71/25.26 | | |
% 168.71/25.26 | | | ALPHA: (16) implies:
% 168.71/25.26 | | | (17) all_58_7 = e3
% 168.71/25.26 | | |
% 168.71/25.26 | | | REF_CLOSE: (1), (2), (17) are inconsistent by sub-proof #821.
% 168.71/25.26 | | |
% 168.71/25.26 | | End of split
% 168.71/25.26 | |
% 168.71/25.26 | Case 2:
% 168.71/25.26 | |
% 168.71/25.26 | | (18) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 168.71/25.26 | | e3)
% 168.71/25.26 | |
% 168.71/25.26 | | BETA: splitting (18) gives:
% 168.71/25.26 | |
% 168.71/25.26 | | Case 1:
% 168.71/25.26 | | |
% 168.71/25.26 | | | (19) all_58_8 = e3 & op(e1, e1) = e3
% 168.71/25.26 | | |
% 168.71/25.26 | | | REF_CLOSE: (8), (12), (19) are inconsistent by sub-proof #272.
% 168.71/25.26 | | |
% 168.71/25.26 | | Case 2:
% 168.71/25.26 | | |
% 168.71/25.26 | | | (20) all_58_11 = e3 & op(e1, e0) = e3
% 168.71/25.26 | | |
% 168.71/25.26 | | | ALPHA: (20) implies:
% 168.71/25.26 | | | (21) all_58_11 = e3
% 168.71/25.26 | | |
% 168.71/25.26 | | | BETA: splitting (6) gives:
% 168.71/25.26 | | |
% 168.71/25.26 | | | Case 1:
% 168.71/25.26 | | | |
% 168.71/25.26 | | | | (22) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2)
% 168.71/25.26 | | | | = e0)
% 168.71/25.26 | | | |
% 168.71/25.26 | | | | REF_CLOSE: (1), (3), (4), (7), (11), (22) are inconsistent by sub-proof
% 168.71/25.26 | | | | #497.
% 168.71/25.26 | | | |
% 168.71/25.26 | | | Case 2:
% 168.71/25.26 | | | |
% 168.71/25.26 | | | | (23) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0)
% 168.71/25.26 | | | | = e0)
% 168.71/25.26 | | | |
% 168.71/25.26 | | | | BETA: splitting (23) gives:
% 168.71/25.26 | | | |
% 168.71/25.26 | | | | Case 1:
% 168.71/25.26 | | | | |
% 168.71/25.26 | | | | | (24) all_58_8 = e0 & op(e1, e1) = e0
% 168.71/25.26 | | | | |
% 168.71/25.26 | | | | | REF_CLOSE: (8), (9), (24) are inconsistent by sub-proof #271.
% 168.71/25.26 | | | | |
% 168.71/25.26 | | | | Case 2:
% 168.71/25.26 | | | | |
% 168.71/25.26 | | | | | (25) all_58_11 = e0 & op(e1, e0) = e0
% 168.71/25.26 | | | | |
% 168.71/25.26 | | | | | ALPHA: (25) implies:
% 168.71/25.26 | | | | | (26) all_58_11 = e0
% 168.71/25.26 | | | | |
% 168.71/25.26 | | | | | REF_CLOSE: (5), (21), (26) are inconsistent by sub-proof #474.
% 168.71/25.26 | | | | |
% 168.71/25.26 | | | | End of split
% 168.71/25.26 | | | |
% 168.71/25.26 | | | End of split
% 168.71/25.26 | | |
% 168.71/25.26 | | End of split
% 168.71/25.26 | |
% 168.71/25.26 | End of split
% 168.71/25.26 |
% 168.71/25.26 End of proof
% 168.71/25.26
% 168.81/25.26 Sub-proof #70 shows that the following formulas are inconsistent:
% 168.81/25.26 ----------------------------------------------------------------
% 168.81/25.26 (1) op(e2, e1) = all_52_9
% 168.81/25.26 (2) op(e0, e1) = e3
% 168.81/25.26 (3) ( ~ (all_18_0 = e0) & op(all_18_1, e1) = all_18_0 & op(e2, e1) = all_18_1
% 168.81/25.26 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e2, e1) =
% 168.81/25.26 all_18_1 & $i(all_18_1))
% 168.81/25.26 (4) ( ~ (all_6_0 = e3) & op(all_6_1, e1) = all_6_0 & op(e2, e1) = all_6_1 &
% 168.81/25.26 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e2, e1) = all_6_1
% 168.81/25.26 & $i(all_6_1))
% 168.81/25.26 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.26 (6) op(e2, e1) = e0
% 168.81/25.26
% 168.81/25.26 Begin of proof
% 168.81/25.26 |
% 168.81/25.26 | GROUND_INST: instantiating (5) with all_52_9, e0, e1, e2, simplifying with
% 168.81/25.26 | (1), (6) gives:
% 168.81/25.26 | (7) all_52_9 = e0
% 168.81/25.26 |
% 168.81/25.26 | BETA: splitting (4) gives:
% 168.81/25.26 |
% 168.81/25.26 | Case 1:
% 168.81/25.26 | |
% 168.81/25.26 | | (8) ~ (all_6_0 = e3) & op(all_6_1, e1) = all_6_0 & op(e2, e1) = all_6_1
% 168.81/25.26 | | & $i(all_6_0) & $i(all_6_1)
% 168.81/25.26 | |
% 168.81/25.26 | | ALPHA: (8) implies:
% 168.81/25.26 | | (9) ~ (all_6_0 = e3)
% 168.81/25.26 | | (10) op(e2, e1) = all_6_1
% 168.81/25.26 | | (11) op(all_6_1, e1) = all_6_0
% 168.81/25.26 | |
% 168.81/25.26 | | BETA: splitting (3) gives:
% 168.81/25.26 | |
% 168.81/25.26 | | Case 1:
% 168.81/25.26 | | |
% 168.81/25.26 | | | (12) ~ (all_18_0 = e0) & op(all_18_1, e1) = all_18_0 & op(e2, e1) =
% 168.81/25.26 | | | all_18_1 & $i(all_18_0) & $i(all_18_1)
% 168.81/25.26 | | |
% 168.81/25.26 | | | ALPHA: (12) implies:
% 168.81/25.26 | | | (13) op(e2, e1) = all_18_1
% 168.81/25.26 | | |
% 168.81/25.26 | | | REF_CLOSE: (2), (5), (6), (9), (10), (11), (13) are inconsistent by
% 168.81/25.26 | | | sub-proof #72.
% 168.81/25.26 | | |
% 168.81/25.26 | | Case 2:
% 168.81/25.26 | | |
% 168.81/25.26 | | | (14) ~ (all_18_1 = e3) & op(e2, e1) = all_18_1 & $i(all_18_1)
% 168.81/25.26 | | |
% 168.81/25.26 | | | ALPHA: (14) implies:
% 168.81/25.26 | | | (15) op(e2, e1) = all_18_1
% 168.81/25.26 | | |
% 168.81/25.26 | | | REF_CLOSE: (2), (5), (6), (9), (10), (11), (15) are inconsistent by
% 168.81/25.26 | | | sub-proof #72.
% 168.81/25.26 | | |
% 168.81/25.26 | | End of split
% 168.81/25.26 | |
% 168.81/25.26 | Case 2:
% 168.81/25.26 | |
% 168.81/25.26 | | (16) ~ (all_6_1 = e0) & op(e2, e1) = all_6_1 & $i(all_6_1)
% 168.81/25.26 | |
% 168.81/25.26 | | ALPHA: (16) implies:
% 168.81/25.26 | | (17) ~ (all_6_1 = e0)
% 168.81/25.26 | | (18) op(e2, e1) = all_6_1
% 168.81/25.26 | |
% 168.81/25.26 | | BETA: splitting (3) gives:
% 168.81/25.26 | |
% 168.81/25.26 | | Case 1:
% 168.81/25.26 | | |
% 168.81/25.26 | | | (19) ~ (all_18_0 = e0) & op(all_18_1, e1) = all_18_0 & op(e2, e1) =
% 168.81/25.26 | | | all_18_1 & $i(all_18_0) & $i(all_18_1)
% 168.81/25.26 | | |
% 168.81/25.26 | | | ALPHA: (19) implies:
% 168.81/25.26 | | | (20) op(e2, e1) = all_18_1
% 168.81/25.26 | | |
% 168.81/25.26 | | | REF_CLOSE: (5), (6), (17), (18), (20) are inconsistent by sub-proof #71.
% 168.81/25.26 | | |
% 168.81/25.26 | | Case 2:
% 168.81/25.26 | | |
% 168.81/25.26 | | | (21) ~ (all_18_1 = e3) & op(e2, e1) = all_18_1 & $i(all_18_1)
% 168.81/25.26 | | |
% 168.81/25.26 | | | ALPHA: (21) implies:
% 168.81/25.26 | | | (22) op(e2, e1) = all_18_1
% 168.81/25.26 | | |
% 168.81/25.26 | | | REF_CLOSE: (5), (6), (17), (18), (22) are inconsistent by sub-proof #71.
% 168.81/25.26 | | |
% 168.81/25.26 | | End of split
% 168.81/25.26 | |
% 168.81/25.26 | End of split
% 168.81/25.26 |
% 168.81/25.26 End of proof
% 168.81/25.26
% 168.81/25.26 Sub-proof #71 shows that the following formulas are inconsistent:
% 168.81/25.26 ----------------------------------------------------------------
% 168.81/25.26 (1) op(e2, e1) = all_6_1
% 168.81/25.26 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.26 (3) op(e2, e1) = e0
% 168.81/25.26 (4) ~ (all_6_1 = e0)
% 168.81/25.26 (5) op(e2, e1) = all_18_1
% 168.81/25.26
% 168.81/25.26 Begin of proof
% 168.81/25.26 |
% 168.81/25.26 | GROUND_INST: instantiating (2) with e0, all_18_1, e1, e2, simplifying with
% 168.81/25.26 | (3), (5) gives:
% 168.81/25.26 | (6) all_18_1 = e0
% 168.81/25.26 |
% 168.81/25.26 | GROUND_INST: instantiating (2) with all_6_1, all_18_1, e1, e2, simplifying
% 168.81/25.26 | with (1), (5) gives:
% 168.81/25.26 | (7) all_18_1 = all_6_1
% 168.81/25.26 |
% 168.81/25.26 | COMBINE_EQS: (6), (7) imply:
% 168.81/25.26 | (8) all_6_1 = e0
% 168.81/25.26 |
% 168.81/25.26 | SIMP: (8) implies:
% 168.81/25.26 | (9) all_6_1 = e0
% 168.81/25.26 |
% 168.81/25.26 | REDUCE: (4), (9) imply:
% 168.81/25.26 | (10) $false
% 168.81/25.26 |
% 168.81/25.26 | CLOSE: (10) is inconsistent.
% 168.81/25.26 |
% 168.81/25.26 End of proof
% 168.81/25.26
% 168.81/25.26 Sub-proof #72 shows that the following formulas are inconsistent:
% 168.81/25.26 ----------------------------------------------------------------
% 168.81/25.27 (1) op(e0, e1) = e3
% 168.81/25.27 (2) ~ (all_6_0 = e3)
% 168.81/25.27 (3) op(e2, e1) = all_6_1
% 168.81/25.27 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.27 (5) op(e2, e1) = e0
% 168.81/25.27 (6) op(all_6_1, e1) = all_6_0
% 168.81/25.27 (7) op(e2, e1) = all_18_1
% 168.81/25.27
% 168.81/25.27 Begin of proof
% 168.81/25.27 |
% 168.81/25.27 | GROUND_INST: instantiating (4) with e0, all_18_1, e1, e2, simplifying with
% 168.81/25.27 | (5), (7) gives:
% 168.81/25.27 | (8) all_18_1 = e0
% 168.81/25.27 |
% 168.81/25.27 | GROUND_INST: instantiating (4) with all_6_1, all_18_1, e1, e2, simplifying
% 168.81/25.27 | with (3), (7) gives:
% 168.81/25.27 | (9) all_18_1 = all_6_1
% 168.81/25.27 |
% 168.81/25.27 | COMBINE_EQS: (8), (9) imply:
% 168.81/25.27 | (10) all_6_1 = e0
% 168.81/25.27 |
% 168.81/25.27 | SIMP: (10) implies:
% 168.81/25.27 | (11) all_6_1 = e0
% 168.81/25.27 |
% 168.81/25.27 | REDUCE: (6), (11) imply:
% 168.81/25.27 | (12) op(e0, e1) = all_6_0
% 168.81/25.27 |
% 168.81/25.27 | GROUND_INST: instantiating (4) with e3, all_6_0, e1, e0, simplifying with (1),
% 168.81/25.27 | (12) gives:
% 168.81/25.27 | (13) all_6_0 = e3
% 168.81/25.27 |
% 168.81/25.27 | REDUCE: (2), (13) imply:
% 168.81/25.27 | (14) $false
% 168.81/25.27 |
% 168.81/25.27 | CLOSE: (14) is inconsistent.
% 168.81/25.27 |
% 168.81/25.27 End of proof
% 168.81/25.27
% 168.81/25.27 Sub-proof #73 shows that the following formulas are inconsistent:
% 168.81/25.27 ----------------------------------------------------------------
% 168.81/25.27 (1) all_58_7 = e1
% 168.81/25.27 (2) ~ (e3 = e1)
% 168.81/25.27 (3) op(e1, e3) = all_52_2
% 168.81/25.27 (4) ~ (e3 = e0)
% 168.81/25.27 (5) e3 = e0
% 168.81/25.27 (6) all_58_11 = e3
% 168.81/25.27 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.27 (8) all_58_8 = e2
% 168.81/25.27 (9) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 168.81/25.27 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 168.81/25.27 (10) ~ (all_52_2 = e3)
% 168.81/25.27 (11) ~ (e3 = e2)
% 168.81/25.27
% 168.81/25.27 Begin of proof
% 168.81/25.27 |
% 168.81/25.27 | COMBINE_EQS: (5), (6) imply:
% 168.81/25.27 | (12) all_58_11 = e0
% 168.81/25.27 |
% 168.81/25.27 | BETA: splitting (9) gives:
% 168.81/25.27 |
% 168.81/25.27 | Case 1:
% 168.81/25.27 | |
% 168.81/25.27 | | (13) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 168.81/25.27 | | e3)
% 168.81/25.27 | |
% 168.81/25.27 | | REF_CLOSE: (1), (2), (3), (7), (10), (13) are inconsistent by sub-proof #75.
% 168.81/25.27 | |
% 168.81/25.27 | Case 2:
% 168.81/25.27 | |
% 168.81/25.27 | | (14) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 168.81/25.27 | | e3)
% 168.81/25.27 | |
% 168.81/25.27 | | REF_CLOSE: (4), (8), (11), (12), (14) are inconsistent by sub-proof #159.
% 168.81/25.27 | |
% 168.81/25.27 | End of split
% 168.81/25.27 |
% 168.81/25.27 End of proof
% 168.81/25.27
% 168.81/25.27 Sub-proof #74 shows that the following formulas are inconsistent:
% 168.81/25.27 ----------------------------------------------------------------
% 168.81/25.27 (1) ~ (all_10_2 = e0)
% 168.81/25.27 (2) ~ (all_10_2 = e1)
% 168.81/25.27 (3) ~ (all_10_2 = e2)
% 168.81/25.27 (4) ~ (all_10_2 = e3)
% 168.81/25.27 (5) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 168.81/25.27 (6) all_54_0 = all_10_2
% 168.81/25.27
% 168.81/25.27 Begin of proof
% 168.81/25.27 |
% 168.81/25.27 | BETA: splitting (5) gives:
% 168.81/25.27 |
% 168.81/25.27 | Case 1:
% 168.81/25.27 | |
% 168.81/25.27 | | (7) all_54_0 = e3
% 168.81/25.27 | |
% 168.81/25.27 | | COMBINE_EQS: (6), (7) imply:
% 168.81/25.27 | | (8) all_10_2 = e3
% 168.81/25.27 | |
% 168.81/25.27 | | REDUCE: (4), (8) imply:
% 168.81/25.27 | | (9) $false
% 168.81/25.27 | |
% 168.81/25.27 | | CLOSE: (9) is inconsistent.
% 168.81/25.27 | |
% 168.81/25.27 | Case 2:
% 168.81/25.27 | |
% 168.81/25.27 | | (10) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 168.81/25.27 | |
% 168.81/25.27 | | REF_CLOSE: (1), (2), (3), (6), (10) are inconsistent by sub-proof #958.
% 168.81/25.27 | |
% 168.81/25.27 | End of split
% 168.81/25.27 |
% 168.81/25.27 End of proof
% 168.81/25.27
% 168.81/25.27 Sub-proof #75 shows that the following formulas are inconsistent:
% 168.81/25.27 ----------------------------------------------------------------
% 168.81/25.27 (1) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 168.81/25.27 (2) all_58_7 = e1
% 168.81/25.27 (3) ~ (e3 = e1)
% 168.81/25.27 (4) op(e1, e3) = all_52_2
% 168.81/25.27 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.27 (6) ~ (all_52_2 = e3)
% 168.81/25.27
% 168.81/25.27 Begin of proof
% 168.81/25.27 |
% 168.81/25.27 | BETA: splitting (1) gives:
% 168.81/25.27 |
% 168.81/25.27 | Case 1:
% 168.81/25.27 | |
% 168.81/25.27 | | (7) all_58_6 = e3 & op(e1, e3) = e3
% 168.81/25.27 | |
% 168.81/25.27 | | ALPHA: (7) implies:
% 168.81/25.27 | | (8) op(e1, e3) = e3
% 168.81/25.27 | |
% 168.81/25.27 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #987.
% 168.81/25.27 | |
% 168.81/25.27 | Case 2:
% 168.81/25.27 | |
% 168.81/25.27 | | (9) all_58_7 = e3 & op(e1, e2) = e3
% 168.81/25.27 | |
% 168.81/25.27 | | ALPHA: (9) implies:
% 168.81/25.27 | | (10) all_58_7 = e3
% 168.81/25.27 | |
% 168.81/25.27 | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #821.
% 168.81/25.27 | |
% 168.81/25.27 | End of split
% 168.81/25.27 |
% 168.81/25.27 End of proof
% 168.81/25.27
% 168.81/25.27 Sub-proof #76 shows that the following formulas are inconsistent:
% 168.81/25.27 ----------------------------------------------------------------
% 168.81/25.27 (1) all_58_7 = e1
% 168.81/25.27 (2) ~ (e3 = e1)
% 168.81/25.27 (3) ~ (e1 = e0)
% 168.81/25.27 (4) all_58_11 = e1
% 168.81/25.27 (5) ~ (e3 = e0)
% 168.81/25.27 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 168.81/25.27 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.81/25.27 (7) all_58_8 = e2
% 168.81/25.27 (8) ~ (e2 = e0)
% 168.81/25.27 (9) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 168.81/25.27 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 168.81/25.27 (10) ~ (e3 = e2)
% 168.81/25.27
% 168.81/25.27 Begin of proof
% 168.81/25.27 |
% 168.81/25.27 | BETA: splitting (9) gives:
% 168.81/25.27 |
% 168.81/25.27 | Case 1:
% 168.81/25.27 | |
% 168.81/25.27 | | (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 168.81/25.27 | | e3)
% 168.81/25.27 | |
% 168.81/25.27 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11) are inconsistent by
% 168.81/25.27 | | sub-proof #77.
% 168.81/25.27 | |
% 168.81/25.27 | Case 2:
% 168.81/25.27 | |
% 168.81/25.27 | | (12) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 168.81/25.27 | | e3)
% 168.81/25.27 | |
% 168.81/25.27 | | BETA: splitting (12) gives:
% 168.81/25.27 | |
% 168.81/25.27 | | Case 1:
% 168.81/25.27 | | |
% 168.81/25.27 | | | (13) all_58_8 = e3 & op(e1, e1) = e3
% 168.81/25.27 | | |
% 168.81/25.27 | | | REF_CLOSE: (7), (10), (13) are inconsistent by sub-proof #475.
% 168.81/25.27 | | |
% 168.81/25.27 | | Case 2:
% 168.81/25.27 | | |
% 168.81/25.27 | | | (14) all_58_11 = e3 & op(e1, e0) = e3
% 168.81/25.27 | | |
% 168.81/25.27 | | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #115.
% 168.81/25.27 | | |
% 168.81/25.27 | | End of split
% 168.81/25.27 | |
% 168.81/25.27 | End of split
% 168.81/25.27 |
% 168.81/25.27 End of proof
% 168.81/25.27
% 168.81/25.27 Sub-proof #77 shows that the following formulas are inconsistent:
% 168.81/25.27 ----------------------------------------------------------------
% 168.81/25.27 (1) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 168.81/25.27 (2) all_58_7 = e1
% 168.81/25.27 (3) ~ (e3 = e1)
% 168.81/25.27 (4) ~ (e1 = e0)
% 168.81/25.27 (5) all_58_11 = e1
% 168.81/25.27 (6) ~ (e3 = e0)
% 168.81/25.27 (7) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 168.81/25.27 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.81/25.27 (8) all_58_8 = e2
% 168.81/25.27 (9) ~ (e2 = e0)
% 168.81/25.27
% 168.81/25.27 Begin of proof
% 168.81/25.27 |
% 168.81/25.27 | BETA: splitting (1) gives:
% 168.81/25.27 |
% 168.81/25.27 | Case 1:
% 168.81/25.27 | |
% 168.81/25.27 | | (10) all_58_6 = e3 & op(e1, e3) = e3
% 168.81/25.27 | |
% 168.81/25.27 | | ALPHA: (10) implies:
% 168.81/25.27 | | (11) all_58_6 = e3
% 168.81/25.27 | |
% 168.81/25.27 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (11) are inconsistent by
% 168.81/25.27 | | sub-proof #78.
% 168.81/25.27 | |
% 168.81/25.27 | Case 2:
% 168.81/25.27 | |
% 168.81/25.27 | | (12) all_58_7 = e3 & op(e1, e2) = e3
% 168.81/25.27 | |
% 168.81/25.27 | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #183.
% 168.81/25.27 | |
% 168.81/25.27 | End of split
% 168.81/25.27 |
% 168.81/25.27 End of proof
% 168.81/25.27
% 168.81/25.27 Sub-proof #78 shows that the following formulas are inconsistent:
% 168.81/25.27 ----------------------------------------------------------------
% 168.81/25.27 (1) all_58_7 = e1
% 168.81/25.27 (2) all_58_6 = e3
% 168.81/25.27 (3) ~ (e1 = e0)
% 168.81/25.27 (4) all_58_11 = e1
% 168.81/25.27 (5) ~ (e3 = e0)
% 168.81/25.27 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 168.81/25.27 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.81/25.27 (7) all_58_8 = e2
% 168.81/25.27 (8) ~ (e2 = e0)
% 168.81/25.27
% 168.81/25.27 Begin of proof
% 168.81/25.27 |
% 168.81/25.27 | BETA: splitting (6) gives:
% 168.81/25.27 |
% 168.81/25.27 | Case 1:
% 168.81/25.27 | |
% 168.81/25.27 | | (9) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 168.81/25.27 | |
% 168.81/25.27 | | BETA: splitting (9) gives:
% 168.81/25.27 | |
% 168.81/25.27 | | Case 1:
% 168.81/25.27 | | |
% 168.81/25.27 | | | (10) all_58_6 = e0 & op(e1, e3) = e0
% 168.81/25.27 | | |
% 168.81/25.27 | | | ALPHA: (10) implies:
% 168.81/25.27 | | | (11) all_58_6 = e0
% 168.81/25.27 | | |
% 168.81/25.27 | | | REF_CLOSE: (2), (5), (11) are inconsistent by sub-proof #537.
% 168.81/25.27 | | |
% 168.81/25.27 | | Case 2:
% 168.81/25.27 | | |
% 168.81/25.27 | | | (12) all_58_7 = e0 & op(e1, e2) = e0
% 168.81/25.27 | | |
% 168.81/25.27 | | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #727.
% 168.81/25.27 | | |
% 168.81/25.27 | | End of split
% 168.81/25.27 | |
% 168.81/25.27 | Case 2:
% 168.81/25.27 | |
% 168.81/25.27 | | (13) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 168.81/25.27 | | e0)
% 168.81/25.27 | |
% 168.81/25.27 | | BETA: splitting (13) gives:
% 168.81/25.27 | |
% 168.81/25.27 | | Case 1:
% 168.81/25.27 | | |
% 168.81/25.27 | | | (14) all_58_8 = e0 & op(e1, e1) = e0
% 168.81/25.27 | | |
% 168.81/25.27 | | | REF_CLOSE: (7), (8), (14) are inconsistent by sub-proof #271.
% 168.81/25.27 | | |
% 168.81/25.27 | | Case 2:
% 168.81/25.27 | | |
% 168.81/25.27 | | | (15) all_58_11 = e0 & op(e1, e0) = e0
% 168.81/25.27 | | |
% 168.81/25.27 | | | ALPHA: (15) implies:
% 168.81/25.27 | | | (16) all_58_11 = e0
% 168.81/25.27 | | |
% 168.81/25.27 | | | REF_CLOSE: (3), (4), (16) are inconsistent by sub-proof #491.
% 168.81/25.27 | | |
% 168.81/25.27 | | End of split
% 168.81/25.27 | |
% 168.81/25.27 | End of split
% 168.81/25.27 |
% 168.81/25.27 End of proof
% 168.81/25.27
% 168.81/25.27 Sub-proof #79 shows that the following formulas are inconsistent:
% 168.81/25.27 ----------------------------------------------------------------
% 168.81/25.27 (1) all_58_12 = e2
% 168.81/25.27 (2) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 168.81/25.27 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.27 (4) ~ (e2 = e1)
% 168.81/25.27 (5) ~ (all_52_7 = e1)
% 168.81/25.27 (6) op(e0, e2) = all_52_7
% 168.81/25.27
% 168.81/25.27 Begin of proof
% 168.81/25.27 |
% 168.81/25.27 | BETA: splitting (2) gives:
% 168.81/25.27 |
% 168.81/25.27 | Case 1:
% 168.81/25.27 | |
% 168.81/25.27 | | (7) all_58_12 = e1 & op(e0, e3) = e1
% 168.81/25.27 | |
% 168.81/25.27 | | ALPHA: (7) implies:
% 168.81/25.27 | | (8) all_58_12 = e1
% 168.81/25.27 | |
% 168.81/25.27 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #862.
% 168.81/25.27 | |
% 168.81/25.27 | Case 2:
% 168.81/25.27 | |
% 168.81/25.27 | | (9) all_58_13 = e1 & op(e0, e2) = e1
% 168.81/25.27 | |
% 168.81/25.27 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #114.
% 168.81/25.27 | |
% 168.81/25.27 | End of split
% 168.81/25.27 |
% 168.81/25.27 End of proof
% 168.81/25.27
% 168.81/25.27 Sub-proof #80 shows that the following formulas are inconsistent:
% 168.81/25.27 ----------------------------------------------------------------
% 168.81/25.27 (1) all_58_7 = e1 & op(e1, e2) = e1
% 168.81/25.27 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.27 (3) op(e1, e2) = all_52_6
% 168.81/25.27 (4) ~ (all_52_6 = e1)
% 168.81/25.27
% 168.81/25.27 Begin of proof
% 168.81/25.27 |
% 168.81/25.27 | ALPHA: (1) implies:
% 168.81/25.27 | (5) op(e1, e2) = e1
% 168.81/25.27 |
% 168.81/25.27 | GROUND_INST: instantiating (2) with all_52_6, e1, e2, e1, simplifying with
% 168.81/25.27 | (3), (5) gives:
% 168.81/25.27 | (6) all_52_6 = e1
% 168.81/25.27 |
% 168.81/25.27 | REDUCE: (4), (6) imply:
% 168.81/25.27 | (7) $false
% 168.81/25.27 |
% 168.81/25.27 | CLOSE: (7) is inconsistent.
% 168.81/25.27 |
% 168.81/25.27 End of proof
% 168.81/25.27
% 168.81/25.27 Sub-proof #81 shows that the following formulas are inconsistent:
% 168.81/25.27 ----------------------------------------------------------------
% 168.81/25.27 (1) all_54_2 = all_52_8
% 168.81/25.27 (2) ~ (all_52_1 = e0)
% 168.81/25.27 (3) ~ (all_52_1 = all_52_13)
% 168.81/25.27 (4) all_56_14 = all_6_2
% 168.81/25.27 (5) op(e3, e0) = all_52_12
% 168.81/25.27 (6) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 168.81/25.27 (7) ~ (all_52_1 = e2)
% 168.81/25.27 (8) ~ (all_52_13 = e1)
% 168.81/25.27 (9) all_56_10 = e0
% 168.81/25.27 (10) all_54_4 = all_52_1
% 168.81/25.27 (11) all_56_15 = all_4_2
% 168.81/25.27 (12) ~ (all_52_8 = e0)
% 168.81/25.27 (13) ~ (all_52_1 = e1)
% 168.81/25.27 (14) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 168.81/25.27 (15) all_56_12 = e1
% 168.81/25.27 (16) ~ (all_52_8 = e2)
% 168.81/25.27 (17) ~ (all_52_13 = e2)
% 168.81/25.27 (18) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.81/25.27 (19) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 168.81/25.27 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.27 (21) ~ (all_52_8 = all_6_2)
% 168.81/25.27 (22) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 168.81/25.27 (23) ~ (all_52_13 = all_4_2)
% 168.81/25.27 (24) ~ (all_52_8 = all_52_12)
% 168.81/25.27 (25) ~ (e2 = e1)
% 168.81/25.27 (26) all_54_7 = all_52_13
% 168.81/25.27
% 168.81/25.27 Begin of proof
% 168.81/25.27 |
% 168.81/25.27 | BETA: splitting (19) gives:
% 168.81/25.27 |
% 168.81/25.27 | Case 1:
% 168.81/25.27 | |
% 168.81/25.27 | | (27) all_54_4 = e3
% 168.81/25.27 | |
% 168.81/25.27 | | COMBINE_EQS: (10), (27) imply:
% 168.81/25.27 | | (28) all_52_1 = e3
% 168.81/25.27 | |
% 168.81/25.27 | | SIMP: (28) implies:
% 168.81/25.27 | | (29) all_52_1 = e3
% 168.81/25.27 | |
% 168.81/25.27 | | REDUCE: (3), (29) imply:
% 168.81/25.27 | | (30) ~ (all_52_13 = e3)
% 168.81/25.27 | |
% 168.81/25.27 | | SIMP: (30) implies:
% 168.81/25.28 | | (31) ~ (all_52_13 = e3)
% 168.81/25.28 | |
% 168.81/25.28 | | BETA: splitting (6) gives:
% 168.81/25.28 | |
% 168.81/25.28 | | Case 1:
% 168.81/25.28 | | |
% 168.81/25.28 | | | (32) all_54_7 = e3
% 168.81/25.28 | | |
% 168.81/25.28 | | | REF_CLOSE: (26), (31), (32) are inconsistent by sub-proof #533.
% 168.81/25.28 | | |
% 168.81/25.28 | | Case 2:
% 168.81/25.28 | | |
% 168.81/25.28 | | | (33) ~ (all_54_7 = e3)
% 168.81/25.28 | | | (34) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 168.81/25.28 | | |
% 168.81/25.28 | | | BETA: splitting (34) gives:
% 168.81/25.28 | | |
% 168.81/25.28 | | | Case 1:
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | (35) all_54_7 = e2
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | REF_CLOSE: (17), (26), (35) are inconsistent by sub-proof #532.
% 168.81/25.28 | | | |
% 168.81/25.28 | | | Case 2:
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | (36) all_54_7 = e1 | all_54_7 = e0
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | BETA: splitting (36) gives:
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | Case 1:
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | (37) all_54_7 = e1
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | REF_CLOSE: (8), (26), (37) are inconsistent by sub-proof #172.
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | Case 2:
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | (38) all_54_7 = e0
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | COMBINE_EQS: (26), (38) imply:
% 168.81/25.28 | | | | | (39) all_52_13 = e0
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | SIMP: (39) implies:
% 168.81/25.28 | | | | | (40) all_52_13 = e0
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | REDUCE: (23), (40) imply:
% 168.81/25.28 | | | | | (41) ~ (all_4_2 = e0)
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | SIMP: (41) implies:
% 168.81/25.28 | | | | | (42) ~ (all_4_2 = e0)
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | REDUCE: (31), (40) imply:
% 168.81/25.28 | | | | | (43) ~ (e3 = e0)
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | SIMP: (43) implies:
% 168.81/25.28 | | | | | (44) ~ (e3 = e0)
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | BETA: splitting (18) gives:
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | | Case 1:
% 168.81/25.28 | | | | | |
% 168.81/25.28 | | | | | | (45) all_56_10 = e3
% 168.81/25.28 | | | | | |
% 168.81/25.28 | | | | | | REF_CLOSE: (9), (44), (45) are inconsistent by sub-proof #166.
% 168.81/25.28 | | | | | |
% 168.81/25.28 | | | | | Case 2:
% 168.81/25.28 | | | | | |
% 168.81/25.28 | | | | | | (46) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.81/25.28 | | | | | |
% 168.81/25.28 | | | | | | BETA: splitting (46) gives:
% 168.81/25.28 | | | | | |
% 168.81/25.28 | | | | | | Case 1:
% 168.81/25.28 | | | | | | |
% 168.81/25.28 | | | | | | | (47) all_56_12 = e2
% 168.81/25.28 | | | | | | |
% 168.81/25.28 | | | | | | | COMBINE_EQS: (15), (47) imply:
% 168.81/25.28 | | | | | | | (48) e2 = e1
% 168.81/25.28 | | | | | | |
% 168.81/25.28 | | | | | | | REDUCE: (25), (48) imply:
% 168.81/25.28 | | | | | | | (49) $false
% 168.81/25.28 | | | | | | |
% 168.81/25.28 | | | | | | | CLOSE: (49) is inconsistent.
% 168.81/25.28 | | | | | | |
% 168.81/25.28 | | | | | | Case 2:
% 168.81/25.28 | | | | | | |
% 168.81/25.28 | | | | | | | (50) all_56_14 = e1 | all_56_15 = e0
% 168.81/25.28 | | | | | | |
% 168.81/25.28 | | | | | | | REF_CLOSE: (1), (4), (5), (9), (11), (12), (14), (16), (20), (21),
% 168.81/25.28 | | | | | | | (22), (24), (42), (50) are inconsistent by sub-proof
% 168.81/25.28 | | | | | | | #82.
% 168.81/25.28 | | | | | | |
% 168.81/25.28 | | | | | | End of split
% 168.81/25.28 | | | | | |
% 168.81/25.28 | | | | | End of split
% 168.81/25.28 | | | | |
% 168.81/25.28 | | | | End of split
% 168.81/25.28 | | | |
% 168.81/25.28 | | | End of split
% 168.81/25.28 | | |
% 168.81/25.28 | | End of split
% 168.81/25.28 | |
% 168.81/25.28 | Case 2:
% 168.81/25.28 | |
% 168.81/25.28 | | (51) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (2), (7), (10), (13), (51) are inconsistent by sub-proof #671.
% 168.81/25.28 | |
% 168.81/25.28 | End of split
% 168.81/25.28 |
% 168.81/25.28 End of proof
% 168.81/25.28
% 168.81/25.28 Sub-proof #82 shows that the following formulas are inconsistent:
% 168.81/25.28 ----------------------------------------------------------------
% 168.81/25.28 (1) all_54_2 = all_52_8
% 168.81/25.28 (2) all_56_14 = all_6_2
% 168.81/25.28 (3) op(e3, e0) = all_52_12
% 168.81/25.28 (4) all_56_10 = e0
% 168.81/25.28 (5) all_56_14 = e1 | all_56_15 = e0
% 168.81/25.28 (6) all_56_15 = all_4_2
% 168.81/25.28 (7) ~ (all_52_8 = e0)
% 168.81/25.28 (8) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 168.81/25.28 (9) ~ (all_52_8 = e2)
% 168.81/25.28 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.28 (11) ~ (all_52_8 = all_6_2)
% 168.81/25.28 (12) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 168.81/25.28 (13) ~ (all_52_8 = all_52_12)
% 168.81/25.28 (14) ~ (all_4_2 = e0)
% 168.81/25.28
% 168.81/25.28 Begin of proof
% 168.81/25.28 |
% 168.81/25.28 | BETA: splitting (5) gives:
% 168.81/25.28 |
% 168.81/25.28 | Case 1:
% 168.81/25.28 | |
% 168.81/25.28 | | (15) all_56_14 = e1
% 168.81/25.28 | |
% 168.81/25.28 | | COMBINE_EQS: (2), (15) imply:
% 168.81/25.28 | | (16) all_6_2 = e1
% 168.81/25.28 | |
% 168.81/25.28 | | SIMP: (16) implies:
% 168.81/25.28 | | (17) all_6_2 = e1
% 168.81/25.28 | |
% 168.81/25.28 | | REDUCE: (11), (17) imply:
% 168.81/25.28 | | (18) ~ (all_52_8 = e1)
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (12), (13), (18) are
% 168.81/25.28 | | inconsistent by sub-proof #83.
% 168.81/25.28 | |
% 168.81/25.28 | Case 2:
% 168.81/25.28 | |
% 168.81/25.28 | | (19) all_56_15 = e0
% 168.81/25.28 | |
% 168.81/25.28 | | COMBINE_EQS: (6), (19) imply:
% 168.81/25.28 | | (20) all_4_2 = e0
% 168.81/25.28 | |
% 168.81/25.28 | | REDUCE: (14), (20) imply:
% 168.81/25.28 | | (21) $false
% 168.81/25.28 | |
% 168.81/25.28 | | CLOSE: (21) is inconsistent.
% 168.81/25.28 | |
% 168.81/25.28 | End of split
% 168.81/25.28 |
% 168.81/25.28 End of proof
% 168.81/25.28
% 168.81/25.28 Sub-proof #83 shows that the following formulas are inconsistent:
% 168.81/25.28 ----------------------------------------------------------------
% 168.81/25.28 (1) all_54_2 = all_52_8
% 168.81/25.28 (2) op(e3, e0) = all_52_12
% 168.81/25.28 (3) all_56_10 = e0
% 168.81/25.28 (4) ~ (all_52_8 = e0)
% 168.81/25.28 (5) ~ (all_52_8 = e1)
% 168.81/25.28 (6) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 168.81/25.28 (7) ~ (all_52_8 = e2)
% 168.81/25.28 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.28 (9) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 168.81/25.28 (10) ~ (all_52_8 = all_52_12)
% 168.81/25.28
% 168.81/25.28 Begin of proof
% 168.81/25.28 |
% 168.81/25.28 | BETA: splitting (9) gives:
% 168.81/25.28 |
% 168.81/25.28 | Case 1:
% 168.81/25.28 | |
% 168.81/25.28 | | (11) all_54_2 = e3
% 168.81/25.28 | |
% 168.81/25.28 | | COMBINE_EQS: (1), (11) imply:
% 168.81/25.28 | | (12) all_52_8 = e3
% 168.81/25.28 | |
% 168.81/25.28 | | SIMP: (12) implies:
% 168.81/25.28 | | (13) all_52_8 = e3
% 168.81/25.28 | |
% 168.81/25.28 | | REDUCE: (10), (13) imply:
% 168.81/25.28 | | (14) ~ (all_52_12 = e3)
% 168.81/25.28 | |
% 168.81/25.28 | | SIMP: (14) implies:
% 168.81/25.28 | | (15) ~ (all_52_12 = e3)
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (2), (3), (6), (8), (15) are inconsistent by sub-proof #145.
% 168.81/25.28 | |
% 168.81/25.28 | Case 2:
% 168.81/25.28 | |
% 168.81/25.28 | | (16) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (1), (4), (5), (7), (16) are inconsistent by sub-proof #84.
% 168.81/25.28 | |
% 168.81/25.28 | End of split
% 168.81/25.28 |
% 168.81/25.28 End of proof
% 168.81/25.28
% 168.81/25.28 Sub-proof #84 shows that the following formulas are inconsistent:
% 168.81/25.28 ----------------------------------------------------------------
% 168.81/25.28 (1) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 168.81/25.28 (2) all_54_2 = all_52_8
% 168.81/25.28 (3) ~ (all_52_8 = e0)
% 168.81/25.28 (4) ~ (all_52_8 = e1)
% 168.81/25.28 (5) ~ (all_52_8 = e2)
% 168.81/25.28
% 168.81/25.28 Begin of proof
% 168.81/25.28 |
% 168.81/25.28 | BETA: splitting (1) gives:
% 168.81/25.28 |
% 168.81/25.28 | Case 1:
% 168.81/25.28 | |
% 168.81/25.28 | | (6) all_54_2 = e2
% 168.81/25.28 | |
% 168.81/25.28 | | COMBINE_EQS: (2), (6) imply:
% 168.81/25.28 | | (7) all_52_8 = e2
% 168.81/25.28 | |
% 168.81/25.28 | | SIMP: (7) implies:
% 168.81/25.28 | | (8) all_52_8 = e2
% 168.81/25.28 | |
% 168.81/25.28 | | REDUCE: (5), (8) imply:
% 168.81/25.28 | | (9) $false
% 168.81/25.28 | |
% 168.81/25.28 | | CLOSE: (9) is inconsistent.
% 168.81/25.28 | |
% 168.81/25.28 | Case 2:
% 168.81/25.28 | |
% 168.81/25.28 | | (10) all_54_2 = e1 | all_54_2 = e0
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #253.
% 168.81/25.28 | |
% 168.81/25.28 | End of split
% 168.81/25.28 |
% 168.81/25.28 End of proof
% 168.81/25.28
% 168.81/25.28 Sub-proof #85 shows that the following formulas are inconsistent:
% 168.81/25.28 ----------------------------------------------------------------
% 168.81/25.28 (1) all_58_7 = e2
% 168.81/25.28 (2) all_58_15 = e2
% 168.81/25.28 (3) all_58_6 = e1
% 168.81/25.28 (4) ~ (e3 = e1)
% 168.81/25.28 (5) op(e1, e3) = all_52_2
% 168.81/25.28 (6) ~ (e1 = e0)
% 168.81/25.28 (7) all_58_11 = e0
% 168.81/25.28 (8) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 168.81/25.28 (9) ~ (e3 = e0)
% 168.81/25.28 (10) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 168.81/25.28 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.81/25.28 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.28 (12) ~ (e2 = e0)
% 168.81/25.28 (13) all_58_8 = e3
% 168.81/25.28 (14) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 168.81/25.28 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 168.81/25.28 (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 168.81/25.28 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 168.81/25.28 (16) ~ (e2 = e1)
% 168.81/25.28 (17) ~ (e3 = e2)
% 168.81/25.28
% 168.81/25.28 Begin of proof
% 168.81/25.28 |
% 168.81/25.28 | BETA: splitting (8) gives:
% 168.81/25.28 |
% 168.81/25.28 | Case 1:
% 168.81/25.28 | |
% 168.81/25.28 | | (18) all_58_11 = e3 & op(e1, e0) = e3
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (1), (4), (5), (6), (9), (10), (11), (12), (13), (14), (16), (18)
% 168.81/25.28 | | are inconsistent by sub-proof #477.
% 168.81/25.28 | |
% 168.81/25.28 | Case 2:
% 168.81/25.28 | |
% 168.81/25.28 | | (19) all_58_15 = e3 & op(e0, e0) = e3
% 168.81/25.28 | |
% 168.81/25.28 | | ALPHA: (19) implies:
% 168.81/25.28 | | (20) all_58_15 = e3
% 168.81/25.28 | |
% 168.81/25.28 | | COMBINE_EQS: (2), (20) imply:
% 168.81/25.28 | | (21) e3 = e2
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (1), (3), (4), (7), (9), (13), (15), (17), (21) are inconsistent
% 168.81/25.28 | | by sub-proof #473.
% 168.81/25.28 | |
% 168.81/25.28 | End of split
% 168.81/25.28 |
% 168.81/25.28 End of proof
% 168.81/25.28
% 168.81/25.28 Sub-proof #86 shows that the following formulas are inconsistent:
% 168.81/25.28 ----------------------------------------------------------------
% 168.81/25.28 (1) all_58_9 = e3 & op(e3, e0) = e3
% 168.81/25.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.28 (3) op(e3, e0) = all_52_12
% 168.81/25.28 (4) ~ (all_52_12 = e3)
% 168.81/25.28
% 168.81/25.28 Begin of proof
% 168.81/25.28 |
% 168.81/25.28 | ALPHA: (1) implies:
% 168.81/25.28 | (5) op(e3, e0) = e3
% 168.81/25.28 |
% 168.81/25.28 | GROUND_INST: instantiating (2) with all_52_12, e3, e0, e3, simplifying with
% 168.81/25.28 | (3), (5) gives:
% 168.81/25.28 | (6) all_52_12 = e3
% 168.81/25.28 |
% 168.81/25.28 | REDUCE: (4), (6) imply:
% 168.81/25.28 | (7) $false
% 168.81/25.28 |
% 168.81/25.28 | CLOSE: (7) is inconsistent.
% 168.81/25.28 |
% 168.81/25.28 End of proof
% 168.81/25.28
% 168.81/25.28 Sub-proof #87 shows that the following formulas are inconsistent:
% 168.81/25.28 ----------------------------------------------------------------
% 168.81/25.28 (1) all_54_2 = all_52_8
% 168.81/25.28 (2) op(e3, e1) = all_52_8
% 168.81/25.28 (3) ~ (all_52_8 = e1)
% 168.81/25.28 (4) ~ (all_52_8 = e2)
% 168.81/25.28 (5) ~ (all_52_8 = e3)
% 168.81/25.28 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.28 (7) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 168.81/25.28 (8) all_58_5 = e2
% 168.81/25.28 (9) ~ (e2 = e1)
% 168.81/25.28 (10) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 168.81/25.28
% 168.81/25.28 Begin of proof
% 168.81/25.28 |
% 168.81/25.28 | BETA: splitting (10) gives:
% 168.81/25.28 |
% 168.81/25.28 | Case 1:
% 168.81/25.28 | |
% 168.81/25.28 | | (11) all_58_4 = e1 & op(e3, e1) = e1
% 168.81/25.28 | |
% 168.81/25.28 | | ALPHA: (11) implies:
% 168.81/25.28 | | (12) op(e3, e1) = e1
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (12) are inconsistent by
% 168.81/25.28 | | sub-proof #567.
% 168.81/25.28 | |
% 168.81/25.28 | Case 2:
% 168.81/25.28 | |
% 168.81/25.28 | | (13) all_58_5 = e1 & op(e2, e1) = e1
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (8), (9), (13) are inconsistent by sub-proof #852.
% 168.81/25.28 | |
% 168.81/25.28 | End of split
% 168.81/25.28 |
% 168.81/25.28 End of proof
% 168.81/25.28
% 168.81/25.28 Sub-proof #88 shows that the following formulas are inconsistent:
% 168.81/25.28 ----------------------------------------------------------------
% 168.81/25.28 (1) all_56_10 = e3
% 168.81/25.28 (2) all_56_10 = e2
% 168.81/25.28 (3) ~ (e3 = e2)
% 168.81/25.28
% 168.81/25.28 Begin of proof
% 168.81/25.28 |
% 168.81/25.28 | COMBINE_EQS: (1), (2) imply:
% 168.81/25.28 | (4) e3 = e2
% 168.81/25.28 |
% 168.81/25.28 | SIMP: (4) implies:
% 168.81/25.28 | (5) e3 = e2
% 168.81/25.28 |
% 168.81/25.28 | REDUCE: (3), (5) imply:
% 168.81/25.28 | (6) $false
% 168.81/25.28 |
% 168.81/25.28 | CLOSE: (6) is inconsistent.
% 168.81/25.28 |
% 168.81/25.28 End of proof
% 168.81/25.28
% 168.81/25.28 Sub-proof #89 shows that the following formulas are inconsistent:
% 168.81/25.28 ----------------------------------------------------------------
% 168.81/25.28 (1) all_58_14 = e2
% 168.81/25.28 (2) all_56_10 = e2
% 168.81/25.28 (3) ~ (e3 = e1)
% 168.81/25.28 (4) op(e3, e0) = all_52_12
% 168.81/25.28 (5) op(e1, e3) = all_52_2
% 168.81/25.28 (6) ~ (all_52_12 = e3)
% 168.81/25.28 (7) ~ (e1 = e0)
% 168.81/25.28 (8) all_58_11 = e2
% 168.81/25.28 (9) all_58_3 = e1
% 168.81/25.28 (10) ~ (e3 = e0)
% 168.81/25.28 (11) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 168.81/25.28 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 168.81/25.28 (12) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 168.81/25.28 (13) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.81/25.28 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 168.81/25.28 (14) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 168.81/25.28 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.28 (16) ~ (e2 = e0)
% 168.81/25.28 (17) all_58_8 = e3
% 168.81/25.28 (18) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 168.81/25.28 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 168.81/25.28 (19) ~ (e2 = e1)
% 168.81/25.28 (20) ~ (all_52_4 = e2)
% 168.81/25.28 (21) op(e3, e2) = all_52_4
% 168.81/25.28 (22) op(e0, e2) = all_52_7
% 168.81/25.28
% 168.81/25.28 Begin of proof
% 168.81/25.28 |
% 168.81/25.28 | BETA: splitting (14) gives:
% 168.81/25.28 |
% 168.81/25.28 | Case 1:
% 168.81/25.28 | |
% 168.81/25.28 | | (23) all_58_13 = e0 & op(e0, e2) = e0
% 168.81/25.28 | |
% 168.81/25.28 | | ALPHA: (23) implies:
% 168.81/25.28 | | (24) op(e0, e2) = e0
% 168.81/25.28 | |
% 168.81/25.28 | | BETA: splitting (13) gives:
% 168.81/25.28 | |
% 168.81/25.28 | | Case 1:
% 168.81/25.28 | | |
% 168.81/25.28 | | | (25) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 168.81/25.28 | | | e2)
% 168.81/25.28 | | |
% 168.81/25.28 | | | REF_CLOSE: (9), (15), (19), (20), (21), (25) are inconsistent by sub-proof
% 168.81/25.28 | | | #90.
% 168.81/25.28 | | |
% 168.81/25.28 | | Case 2:
% 168.81/25.28 | | |
% 168.81/25.28 | | | (26) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 168.81/25.28 | | | e2)
% 168.81/25.28 | | |
% 168.81/25.28 | | | BETA: splitting (26) gives:
% 168.81/25.28 | | |
% 168.81/25.28 | | | Case 1:
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | (27) all_58_7 = e2 & op(e1, e2) = e2
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | ALPHA: (27) implies:
% 168.81/25.28 | | | | (28) all_58_7 = e2
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | REF_CLOSE: (3), (5), (7), (8), (10), (11), (15), (16), (17), (18), (19),
% 168.81/25.28 | | | | (28) are inconsistent by sub-proof #228.
% 168.81/25.28 | | | |
% 168.81/25.28 | | | Case 2:
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | (29) all_58_13 = e2 & op(e0, e2) = e2
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | ALPHA: (29) implies:
% 168.81/25.28 | | | | (30) op(e0, e2) = e2
% 168.81/25.28 | | | |
% 168.81/25.28 | | | | REF_CLOSE: (15), (16), (22), (24), (30) are inconsistent by sub-proof
% 168.81/25.28 | | | | #631.
% 168.81/25.28 | | | |
% 168.81/25.28 | | | End of split
% 168.81/25.28 | | |
% 168.81/25.28 | | End of split
% 168.81/25.28 | |
% 168.81/25.28 | Case 2:
% 168.81/25.28 | |
% 168.81/25.28 | | (31) all_58_14 = e0 & op(e0, e1) = e0
% 168.81/25.28 | |
% 168.81/25.28 | | ALPHA: (31) implies:
% 168.81/25.28 | | (32) all_58_14 = e0
% 168.81/25.28 | |
% 168.81/25.28 | | COMBINE_EQS: (1), (32) imply:
% 168.81/25.28 | | (33) e2 = e0
% 168.81/25.28 | |
% 168.81/25.28 | | COMBINE_EQS: (2), (33) imply:
% 168.81/25.28 | | (34) all_56_10 = e0
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (4), (6), (12), (15), (34) are inconsistent by sub-proof #145.
% 168.81/25.28 | |
% 168.81/25.28 | End of split
% 168.81/25.28 |
% 168.81/25.28 End of proof
% 168.81/25.28
% 168.81/25.28 Sub-proof #90 shows that the following formulas are inconsistent:
% 168.81/25.28 ----------------------------------------------------------------
% 168.81/25.28 (1) all_58_3 = e1
% 168.81/25.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.28 (3) ~ (e2 = e1)
% 168.81/25.28 (4) ~ (all_52_4 = e2)
% 168.81/25.28 (5) op(e3, e2) = all_52_4
% 168.81/25.28 (6) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 168.81/25.28
% 168.81/25.28 Begin of proof
% 168.81/25.28 |
% 168.81/25.28 | BETA: splitting (6) gives:
% 168.81/25.28 |
% 168.81/25.28 | Case 1:
% 168.81/25.28 | |
% 168.81/25.28 | | (7) all_58_1 = e2 & op(e3, e2) = e2
% 168.81/25.28 | |
% 168.81/25.28 | | ALPHA: (7) implies:
% 168.81/25.28 | | (8) op(e3, e2) = e2
% 168.81/25.28 | |
% 168.81/25.28 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #993.
% 168.81/25.28 | |
% 168.81/25.28 | Case 2:
% 168.81/25.28 | |
% 168.81/25.28 | | (9) all_58_3 = e2 & op(e2, e2) = e2
% 168.81/25.28 | |
% 168.81/25.28 | | ALPHA: (9) implies:
% 168.81/25.28 | | (10) all_58_3 = e2
% 168.81/25.28 | |
% 168.81/25.28 | | COMBINE_EQS: (1), (10) imply:
% 168.81/25.28 | | (11) e2 = e1
% 168.81/25.28 | |
% 168.81/25.28 | | REDUCE: (3), (11) imply:
% 168.81/25.28 | | (12) $false
% 168.81/25.28 | |
% 168.81/25.28 | | CLOSE: (12) is inconsistent.
% 168.81/25.28 | |
% 168.81/25.28 | End of split
% 168.81/25.29 |
% 168.81/25.29 End of proof
% 168.81/25.29
% 168.81/25.29 Sub-proof #91 shows that the following formulas are inconsistent:
% 168.81/25.29 ----------------------------------------------------------------
% 168.81/25.29 (1) op(e3, e1) = all_52_8
% 168.81/25.29 (2) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 168.81/25.29 (3) ~ (all_52_8 = e3)
% 168.81/25.29 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.29 (5) op(e2, e1) = e2
% 168.81/25.29 (6) ~ (e3 = e2)
% 168.81/25.29
% 168.81/25.29 Begin of proof
% 168.81/25.29 |
% 168.81/25.29 | BETA: splitting (2) gives:
% 168.81/25.29 |
% 168.81/25.29 | Case 1:
% 168.81/25.29 | |
% 168.81/25.29 | | (7) all_58_4 = e3 & op(e3, e1) = e3
% 168.81/25.29 | |
% 168.81/25.29 | | ALPHA: (7) implies:
% 168.81/25.29 | | (8) op(e3, e1) = e3
% 168.81/25.29 | |
% 168.81/25.29 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #975.
% 168.81/25.29 | |
% 168.81/25.29 | Case 2:
% 168.81/25.29 | |
% 168.81/25.29 | | (9) all_58_5 = e3 & op(e2, e1) = e3
% 168.81/25.29 | |
% 168.81/25.29 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #150.
% 168.81/25.29 | |
% 168.81/25.29 | End of split
% 168.81/25.29 |
% 168.81/25.29 End of proof
% 168.81/25.29
% 168.81/25.29 Sub-proof #92 shows that the following formulas are inconsistent:
% 168.81/25.29 ----------------------------------------------------------------
% 168.81/25.29 (1) all_54_14 = all_52_11
% 168.81/25.29 (2) all_56_14 = all_6_2
% 168.81/25.29 (3) all_56_14 = e1 | all_56_15 = e0
% 168.81/25.29 (4) ~ (e3 = e0)
% 168.81/25.29 (5) ~ (all_52_11 = all_6_2)
% 168.81/25.29 (6) all_54_14 = e1 | all_54_14 = e0
% 168.81/25.29 (7) ~ (all_52_11 = e0)
% 168.81/25.29 (8) all_56_15 = e3
% 168.81/25.29
% 168.81/25.29 Begin of proof
% 168.81/25.29 |
% 168.81/25.29 | BETA: splitting (6) gives:
% 168.81/25.29 |
% 168.81/25.29 | Case 1:
% 168.81/25.29 | |
% 168.81/25.29 | | (9) all_54_14 = e1
% 168.81/25.29 | |
% 168.81/25.29 | | COMBINE_EQS: (1), (9) imply:
% 168.81/25.29 | | (10) all_52_11 = e1
% 168.81/25.29 | |
% 168.81/25.29 | | SIMP: (10) implies:
% 168.81/25.29 | | (11) all_52_11 = e1
% 168.81/25.29 | |
% 168.81/25.29 | | REDUCE: (5), (11) imply:
% 168.81/25.29 | | (12) ~ (all_6_2 = e1)
% 168.81/25.29 | |
% 168.81/25.29 | | SIMP: (12) implies:
% 168.81/25.29 | | (13) ~ (all_6_2 = e1)
% 168.81/25.29 | |
% 168.81/25.29 | | BETA: splitting (3) gives:
% 168.81/25.29 | |
% 168.81/25.29 | | Case 1:
% 168.81/25.29 | | |
% 168.81/25.29 | | | (14) all_56_14 = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | COMBINE_EQS: (2), (14) imply:
% 168.81/25.29 | | | (15) all_6_2 = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | REDUCE: (13), (15) imply:
% 168.81/25.29 | | | (16) $false
% 168.81/25.29 | | |
% 168.81/25.29 | | | CLOSE: (16) is inconsistent.
% 168.81/25.29 | | |
% 168.81/25.29 | | Case 2:
% 168.81/25.29 | | |
% 168.81/25.29 | | | (17) all_56_15 = e0
% 168.81/25.29 | | |
% 168.81/25.29 | | | COMBINE_EQS: (8), (17) imply:
% 168.81/25.29 | | | (18) e3 = e0
% 168.81/25.29 | | |
% 168.81/25.29 | | | REDUCE: (4), (18) imply:
% 168.81/25.29 | | | (19) $false
% 168.81/25.29 | | |
% 168.81/25.29 | | | CLOSE: (19) is inconsistent.
% 168.81/25.29 | | |
% 168.81/25.29 | | End of split
% 168.81/25.29 | |
% 168.81/25.29 | Case 2:
% 168.81/25.29 | |
% 168.81/25.29 | | (20) all_54_14 = e0
% 168.81/25.29 | |
% 168.81/25.29 | | REF_CLOSE: (1), (7), (20) are inconsistent by sub-proof #965.
% 168.81/25.29 | |
% 168.81/25.29 | End of split
% 168.81/25.29 |
% 168.81/25.29 End of proof
% 168.81/25.29
% 168.81/25.29 Sub-proof #93 shows that the following formulas are inconsistent:
% 168.81/25.29 ----------------------------------------------------------------
% 168.81/25.29 (1) op(e3, e1) = e0
% 168.81/25.29 (2) op(e3, e0) = e0
% 168.81/25.29 (3) ~ (e1 = e0)
% 168.81/25.29 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 168.81/25.29 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 168.81/25.29 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.29 (6) op(e3, e3) = e2
% 168.81/25.29 (7) ~ (e2 = e1)
% 168.81/25.29 (8) op(e3, e2) = all_52_4
% 168.81/25.29 (9) ~ (all_52_4 = e1)
% 168.81/25.29
% 168.81/25.29 Begin of proof
% 168.81/25.29 |
% 168.81/25.29 | BETA: splitting (4) gives:
% 168.81/25.29 |
% 168.81/25.29 | Case 1:
% 168.81/25.29 | |
% 168.81/25.29 | | (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 168.81/25.29 | | e1)
% 168.81/25.29 | |
% 168.81/25.29 | | REF_CLOSE: (5), (6), (7), (8), (9), (10) are inconsistent by sub-proof #94.
% 168.81/25.29 | |
% 168.81/25.29 | Case 2:
% 168.81/25.29 | |
% 168.81/25.29 | | (11) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 168.81/25.29 | | e1)
% 168.81/25.29 | |
% 168.81/25.29 | | BETA: splitting (11) gives:
% 168.81/25.29 | |
% 168.81/25.29 | | Case 1:
% 168.81/25.29 | | |
% 168.81/25.29 | | | (12) all_58_4 = e1 & op(e3, e1) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | ALPHA: (12) implies:
% 168.81/25.29 | | | (13) op(e3, e1) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | REF_CLOSE: (1), (3), (5), (13) are inconsistent by sub-proof #569.
% 168.81/25.29 | | |
% 168.81/25.29 | | Case 2:
% 168.81/25.29 | | |
% 168.81/25.29 | | | (14) all_58_9 = e1 & op(e3, e0) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | ALPHA: (14) implies:
% 168.81/25.29 | | | (15) op(e3, e0) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | REF_CLOSE: (2), (3), (5), (15) are inconsistent by sub-proof #553.
% 168.81/25.29 | | |
% 168.81/25.29 | | End of split
% 168.81/25.29 | |
% 168.81/25.29 | End of split
% 168.81/25.29 |
% 168.81/25.29 End of proof
% 168.81/25.29
% 168.81/25.29 Sub-proof #94 shows that the following formulas are inconsistent:
% 168.81/25.29 ----------------------------------------------------------------
% 168.81/25.29 (1) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 168.81/25.29 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.29 (3) op(e3, e3) = e2
% 168.81/25.29 (4) ~ (e2 = e1)
% 168.81/25.29 (5) op(e3, e2) = all_52_4
% 168.81/25.29 (6) ~ (all_52_4 = e1)
% 168.81/25.29
% 168.81/25.29 Begin of proof
% 168.81/25.29 |
% 168.81/25.29 | BETA: splitting (1) gives:
% 168.81/25.29 |
% 168.81/25.29 | Case 1:
% 168.81/25.29 | |
% 168.81/25.29 | | (7) all_58_0 = e1 & op(e3, e3) = e1
% 168.81/25.29 | |
% 168.81/25.29 | | ALPHA: (7) implies:
% 168.81/25.29 | | (8) op(e3, e3) = e1
% 168.81/25.29 | |
% 168.81/25.29 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #957.
% 168.81/25.29 | |
% 168.81/25.29 | Case 2:
% 168.81/25.29 | |
% 168.81/25.29 | | (9) all_58_1 = e1 & op(e3, e2) = e1
% 168.81/25.29 | |
% 168.81/25.29 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #863.
% 168.81/25.29 | |
% 168.81/25.29 | End of split
% 168.81/25.29 |
% 168.81/25.29 End of proof
% 168.81/25.29
% 168.81/25.29 Sub-proof #95 shows that the following formulas are inconsistent:
% 168.81/25.29 ----------------------------------------------------------------
% 168.81/25.29 (1) ~ (e1 = e0)
% 168.81/25.29 (2) all_58_3 = e1
% 168.81/25.29 (3) ~ (e3 = e0)
% 168.81/25.29 (4) all_58_1 = e3
% 168.81/25.29 (5) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 168.81/25.29
% 168.81/25.29 Begin of proof
% 168.81/25.29 |
% 168.81/25.29 | BETA: splitting (5) gives:
% 168.81/25.29 |
% 168.81/25.29 | Case 1:
% 168.81/25.29 | |
% 168.81/25.29 | | (6) all_58_1 = e0 & op(e3, e2) = e0
% 168.81/25.29 | |
% 168.81/25.29 | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #794.
% 168.81/25.29 | |
% 168.81/25.29 | Case 2:
% 168.81/25.29 | |
% 168.81/25.29 | | (7) all_58_3 = e0 & op(e2, e2) = e0
% 168.81/25.29 | |
% 168.81/25.29 | | ALPHA: (7) implies:
% 168.81/25.29 | | (8) all_58_3 = e0
% 168.81/25.29 | |
% 168.81/25.29 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #523.
% 168.81/25.29 | |
% 168.81/25.29 | End of split
% 168.81/25.29 |
% 168.81/25.29 End of proof
% 168.81/25.29
% 168.81/25.29 Sub-proof #96 shows that the following formulas are inconsistent:
% 168.81/25.29 ----------------------------------------------------------------
% 168.81/25.29 (1) all_58_15 = e2
% 168.81/25.29 (2) op(e0, e0) = e2
% 168.81/25.29 (3) ~ (e3 = e1)
% 168.81/25.29 (4) all_58_13 = e0
% 168.81/25.29 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 168.81/25.29 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 168.81/25.29 (6) ~ (e1 = e0)
% 168.81/25.29 (7) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 168.81/25.29 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 168.81/25.29 (8) op(e0, e2) = e0
% 168.81/25.29 (9) op(e0, e3) = e0
% 168.81/25.29 (10) ~ (e3 = e0)
% 168.81/25.29 (11) all_58_12 = e0
% 168.81/25.29 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.29 (13) ~ (e2 = e1)
% 168.81/25.29 (14) op(e0, e2) = all_52_7
% 168.81/25.29 (15) ~ (e3 = e2)
% 168.81/25.29
% 168.81/25.29 Begin of proof
% 168.81/25.29 |
% 168.81/25.29 | BETA: splitting (5) gives:
% 168.81/25.29 |
% 168.81/25.29 | Case 1:
% 168.81/25.29 | |
% 168.81/25.29 | | (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 168.81/25.29 | | e1)
% 168.81/25.29 | |
% 168.81/25.29 | | BETA: splitting (16) gives:
% 168.81/25.29 | |
% 168.81/25.29 | | Case 1:
% 168.81/25.29 | | |
% 168.81/25.29 | | | (17) all_58_12 = e1 & op(e0, e3) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | ALPHA: (17) implies:
% 168.81/25.29 | | | (18) op(e0, e3) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | REF_CLOSE: (6), (9), (12), (18) are inconsistent by sub-proof #531.
% 168.81/25.29 | | |
% 168.81/25.29 | | Case 2:
% 168.81/25.29 | | |
% 168.81/25.29 | | | (19) all_58_13 = e1 & op(e0, e2) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | ALPHA: (19) implies:
% 168.81/25.29 | | | (20) op(e0, e2) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | REF_CLOSE: (6), (8), (12), (14), (20) are inconsistent by sub-proof #889.
% 168.81/25.29 | | |
% 168.81/25.29 | | End of split
% 168.81/25.29 | |
% 168.81/25.29 | Case 2:
% 168.81/25.29 | |
% 168.81/25.29 | | (21) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 168.81/25.29 | | e1)
% 168.81/25.29 | |
% 168.81/25.29 | | BETA: splitting (21) gives:
% 168.81/25.29 | |
% 168.81/25.29 | | Case 1:
% 168.81/25.29 | | |
% 168.81/25.29 | | | (22) all_58_14 = e1 & op(e0, e1) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | ALPHA: (22) implies:
% 168.81/25.29 | | | (23) op(e0, e1) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | REF_CLOSE: (1), (3), (4), (7), (10), (11), (12), (15), (23) are
% 168.81/25.29 | | | inconsistent by sub-proof #108.
% 168.81/25.29 | | |
% 168.81/25.29 | | Case 2:
% 168.81/25.29 | | |
% 168.81/25.29 | | | (24) all_58_15 = e1 & op(e0, e0) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | ALPHA: (24) implies:
% 168.81/25.29 | | | (25) op(e0, e0) = e1
% 168.81/25.29 | | |
% 168.81/25.29 | | | REF_CLOSE: (2), (12), (13), (25) are inconsistent by sub-proof #640.
% 168.81/25.29 | | |
% 168.81/25.29 | | End of split
% 168.81/25.29 | |
% 168.81/25.29 | End of split
% 168.81/25.29 |
% 168.81/25.29 End of proof
% 168.81/25.29
% 168.81/25.29 Sub-proof #97 shows that the following formulas are inconsistent:
% 168.81/25.29 ----------------------------------------------------------------
% 168.81/25.29 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 168.81/25.29 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 168.81/25.29 (2) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 168.81/25.29 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 168.81/25.29 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.81/25.29 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.81/25.29 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.81/25.29 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 168.81/25.29 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.29 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.81/25.29 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.81/25.29 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 168.81/25.29 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 168.81/25.29 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.81/25.29 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.81/25.29 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.81/25.29 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.81/25.29 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 168.81/25.29 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.81/25.29 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.81/25.29 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.81/25.29 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.81/25.29 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 168.81/25.29 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.29 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.81/25.29 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.81/25.29 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 168.81/25.29 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 168.81/25.29 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.81/25.29 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.81/25.29 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.81/25.29 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.81/25.29 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 168.81/25.29 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.29 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.81/25.29 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.81/25.29 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 168.81/25.29 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 168.81/25.29 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.81/25.29 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.81/25.29 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.81/25.29 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.81/25.29 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 168.81/25.29 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.81/25.29 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.81/25.29 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.81/25.29 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 168.81/25.29 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.81/25.29 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.81/25.29 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 168.81/25.29 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.81/25.29 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 168.81/25.29 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.81/25.29 (3) all_54_14 = all_52_11
% 168.81/25.29 (4) all_58_15 = e2
% 168.81/25.29 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 168.81/25.29 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 168.81/25.29 (6) all_54_12 = all_52_3
% 168.81/25.29 (7) op(e0, e0) = e2
% 168.81/25.29 (8) all_56_10 = all_10_2
% 168.81/25.29 (9) ~ (all_6_2 = e3)
% 168.81/25.29 (10) ~ (all_52_3 = e2)
% 168.81/25.29 (11) ~ (e3 = e1)
% 168.81/25.29 (12) all_56_14 = all_6_2
% 168.81/25.29 (13) op(e3, e0) = all_52_12
% 168.81/25.29 (14) all_58_13 = e0
% 168.81/25.29 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 168.81/25.29 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 168.81/25.29 e1)
% 168.81/25.29 (16) ~ (all_10_2 = e0)
% 168.81/25.29 (17) op(e3, e1) = all_52_8
% 168.81/25.29 (18) ~ (e1 = e0)
% 168.81/25.29 (19) all_56_7 = e0
% 168.81/25.29 (20) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 168.81/25.29 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 168.81/25.29 e3)
% 168.81/25.29 (21) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 168.81/25.29 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 168.81/25.29 (22) all_50_2 = all_10_2
% 168.81/25.29 (23) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 168.81/25.29 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 168.81/25.29 (24) ~ (all_52_8 = all_10_2)
% 168.81/25.29 (25) all_58_3 = e1
% 168.81/25.29 (26) op(e0, e2) = e0
% 168.81/25.29 (27) all_58_6 = e2
% 168.81/25.29 (28) op(e1, e1) = all_6_2
% 168.81/25.29 (29) ~ (all_52_11 = e2)
% 168.81/25.29 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 168.81/25.29 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 168.81/25.29 (31) ~ (e3 = e0)
% 168.81/25.29 (32) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.81/25.29 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.81/25.29 (33) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 168.81/25.29 (34) all_56_12 = e1
% 168.81/25.29 (35) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.81/25.29 (36) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 168.81/25.29 (37) ~ (all_52_3 = all_10_2)
% 168.81/25.29 (38) ~ (all_52_3 = all_52_11)
% 168.81/25.29 (39) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 168.81/25.29 (40) ~ (all_52_11 = all_6_2)
% 168.81/25.29 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.29 (42) ~ (e2 = e0)
% 168.81/25.29 (43) op(e2, e1) = e2
% 168.81/25.29 (44) ~ (all_10_2 = e2)
% 168.81/25.29 (45) ~ (all_52_12 = all_10_2)
% 168.81/25.29 (46) all_56_5 = e2
% 168.81/25.29 (47) ~ (all_50_2 = e1) | ( ~ (all_50_0 = e0) & op(all_50_1, e3) = all_50_0 &
% 168.81/25.29 op(e1, e3) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 168.81/25.29 e2) & op(e1, e3) = all_50_1 & $i(all_50_1))
% 168.81/25.30 (48) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.81/25.30 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.81/25.30 (49) ~ (e2 = e1)
% 168.81/25.30 (50) ~ (all_52_3 = e0)
% 168.81/25.30 (51) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 168.81/25.30 (52) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.81/25.30 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 168.81/25.30 (53) all_54_0 = all_10_2
% 168.81/25.30 (54) op(e0, e2) = all_52_7
% 168.81/25.30 (55) ~ (all_52_11 = e0)
% 168.81/25.30 (56) all_58_2 = e0
% 168.81/25.30 (57) all_56_15 = e2
% 168.81/25.30 (58) ~ (e3 = e2)
% 168.81/25.30
% 168.81/25.30 Begin of proof
% 168.81/25.30 |
% 168.81/25.30 | BETA: splitting (48) gives:
% 168.81/25.30 |
% 168.81/25.30 | Case 1:
% 168.81/25.30 | |
% 168.81/25.30 | | (59) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 168.81/25.30 | | e3)
% 168.81/25.30 | |
% 168.81/25.30 | | REF_CLOSE: (11), (25), (31), (56), (59) are inconsistent by sub-proof #101.
% 168.81/25.30 | |
% 168.81/25.30 | Case 2:
% 168.81/25.30 | |
% 168.81/25.30 | | (60) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 168.81/25.30 | | e3)
% 168.81/25.30 | |
% 168.81/25.30 | | BETA: splitting (60) gives:
% 168.81/25.30 | |
% 168.81/25.30 | | Case 1:
% 168.81/25.30 | | |
% 168.81/25.30 | | | (61) all_58_5 = e3 & op(e2, e1) = e3
% 168.81/25.30 | | |
% 168.81/25.30 | | | REF_CLOSE: (41), (43), (58), (61) are inconsistent by sub-proof #150.
% 168.81/25.30 | | |
% 168.81/25.30 | | Case 2:
% 168.81/25.30 | | |
% 168.81/25.30 | | | (62) all_58_10 = e3 & op(e2, e0) = e3
% 168.81/25.30 | | |
% 168.81/25.30 | | | ALPHA: (62) implies:
% 168.81/25.30 | | | (63) all_58_10 = e3
% 168.81/25.30 | | | (64) op(e2, e0) = e3
% 168.81/25.30 | | |
% 168.81/25.30 | | | BETA: splitting (47) gives:
% 168.81/25.30 | | |
% 168.81/25.30 | | | Case 1:
% 168.81/25.30 | | | |
% 168.81/25.30 | | | | (65) ~ (all_50_2 = e1)
% 168.81/25.30 | | | |
% 168.81/25.30 | | | | REDUCE: (22), (65) imply:
% 168.81/25.30 | | | | (66) ~ (all_10_2 = e1)
% 168.81/25.30 | | | |
% 168.81/25.30 | | | | BETA: splitting (51) gives:
% 168.81/25.30 | | | |
% 168.81/25.30 | | | | Case 1:
% 168.81/25.30 | | | | |
% 168.81/25.30 | | | | | (67) all_54_0 = e3
% 168.81/25.30 | | | | |
% 168.81/25.30 | | | | | COMBINE_EQS: (53), (67) imply:
% 168.81/25.30 | | | | | (68) all_10_2 = e3
% 168.81/25.30 | | | | |
% 168.81/25.30 | | | | | COMBINE_EQS: (8), (68) imply:
% 168.81/25.30 | | | | | (69) all_56_10 = e3
% 168.81/25.30 | | | | |
% 168.81/25.30 | | | | | REDUCE: (24), (68) imply:
% 168.81/25.30 | | | | | (70) ~ (all_52_8 = e3)
% 168.81/25.30 | | | | |
% 168.81/25.30 | | | | | REDUCE: (45), (68) imply:
% 168.81/25.30 | | | | | (71) ~ (all_52_12 = e3)
% 168.81/25.30 | | | | |
% 168.81/25.30 | | | | | BETA: splitting (20) gives:
% 168.81/25.30 | | | | |
% 168.81/25.30 | | | | | Case 1:
% 168.81/25.30 | | | | | |
% 168.81/25.30 | | | | | | (72) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 168.81/25.30 | | | | | | op(e0, e2) = e3)
% 168.81/25.30 | | | | | |
% 168.81/25.30 | | | | | | BETA: splitting (72) gives:
% 168.81/25.30 | | | | | |
% 168.81/25.30 | | | | | | Case 1:
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | (73) all_58_12 = e3 & op(e0, e3) = e3
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | ALPHA: (73) implies:
% 168.81/25.30 | | | | | | | (74) all_58_12 = e3
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | BETA: splitting (23) gives:
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | (75) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 168.81/25.30 | | | | | | | | op(e2, e1) = e3)
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | BETA: splitting (75) gives:
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | (76) all_58_4 = e3 & op(e3, e1) = e3
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | ALPHA: (76) implies:
% 168.81/25.30 | | | | | | | | | (77) op(e3, e1) = e3
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | REF_CLOSE: (17), (41), (70), (77) are inconsistent by
% 168.81/25.30 | | | | | | | | | sub-proof #975.
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | (78) all_58_5 = e3 & op(e2, e1) = e3
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | ALPHA: (78) implies:
% 168.81/25.30 | | | | | | | | | (79) all_58_5 = e3
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | BETA: splitting (52) gives:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | (80) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 &
% 168.81/25.30 | | | | | | | | | | op(e2, e2) = e2)
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | BETA: splitting (80) gives:
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | (81) all_58_2 = e2 & op(e2, e3) = e2
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | ALPHA: (81) implies:
% 168.81/25.30 | | | | | | | | | | | (82) all_58_2 = e2
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | BETA: splitting (32) gives:
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | (83) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 168.81/25.30 | | | | | | | | | | | | & op(e2, e2) = e0)
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | BETA: splitting (83) gives:
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | | (84) all_58_2 = e0 & op(e2, e3) = e0
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | | REF_CLOSE: (42), (82), (84) are inconsistent by sub-proof
% 168.81/25.30 | | | | | | | | | | | | | #928.
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | | (85) all_58_3 = e0 & op(e2, e2) = e0
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | | REF_CLOSE: (18), (25), (85) are inconsistent by sub-proof
% 168.81/25.30 | | | | | | | | | | | | | #927.
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | End of split
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | (86) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 168.81/25.30 | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | BETA: splitting (86) gives:
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | | (87) all_58_5 = e0 & op(e2, e1) = e0
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | | REF_CLOSE: (31), (79), (87) are inconsistent by sub-proof
% 168.81/25.30 | | | | | | | | | | | | | #926.
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | | (88) all_58_10 = e0 & op(e2, e0) = e0
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | | REF_CLOSE: (31), (63), (88) are inconsistent by sub-proof
% 168.81/25.30 | | | | | | | | | | | | | #932.
% 168.81/25.30 | | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | End of split
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | End of split
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | (89) all_58_3 = e2 & op(e2, e2) = e2
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | ALPHA: (89) implies:
% 168.81/25.30 | | | | | | | | | | | (90) all_58_3 = e2
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | REF_CLOSE: (25), (49), (90) are inconsistent by sub-proof
% 168.81/25.30 | | | | | | | | | | | #924.
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | End of split
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | (91) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2
% 168.81/25.30 | | | | | | | | | | & op(e2, e0) = e2)
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | BETA: splitting (91) gives:
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | (92) all_58_5 = e2 & op(e2, e1) = e2
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | REF_CLOSE: (58), (79), (92) are inconsistent by sub-proof
% 168.81/25.30 | | | | | | | | | | | #923.
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | (93) all_58_10 = e2 & op(e2, e0) = e2
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | ALPHA: (93) implies:
% 168.81/25.30 | | | | | | | | | | | (94) all_58_10 = e2
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | COMBINE_EQS: (63), (94) imply:
% 168.81/25.30 | | | | | | | | | | | (95) e3 = e2
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | REDUCE: (58), (95) imply:
% 168.81/25.30 | | | | | | | | | | | (96) $false
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | CLOSE: (96) is inconsistent.
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | End of split
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | End of split
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | End of split
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | (97) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 168.81/25.30 | | | | | | | | op(e0, e1) = e3)
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | BETA: splitting (97) gives:
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | (98) all_58_8 = e3 & op(e1, e1) = e3
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | REF_CLOSE: (9), (28), (41), (98) are inconsistent by sub-proof
% 168.81/25.30 | | | | | | | | | #961.
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | (99) all_58_14 = e3 & op(e0, e1) = e3
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | ALPHA: (99) implies:
% 168.81/25.30 | | | | | | | | | (100) all_58_14 = e3
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | REF_CLOSE: (7), (11), (15), (18), (26), (41), (49), (54),
% 168.81/25.30 | | | | | | | | | (74), (100) are inconsistent by sub-proof #100.
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | End of split
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | End of split
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | Case 2:
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | (101) all_58_13 = e3 & op(e0, e2) = e3
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | ALPHA: (101) implies:
% 168.81/25.30 | | | | | | | (102) all_58_13 = e3
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | COMBINE_EQS: (14), (102) imply:
% 168.81/25.30 | | | | | | | (103) e3 = e0
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | SIMP: (103) implies:
% 168.81/25.30 | | | | | | | (104) e3 = e0
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | COMBINE_EQS: (69), (104) imply:
% 168.81/25.30 | | | | | | | (105) all_56_10 = e0
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | REF_CLOSE: (13), (33), (41), (71), (105) are inconsistent by
% 168.81/25.30 | | | | | | | sub-proof #145.
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | End of split
% 168.81/25.30 | | | | | |
% 168.81/25.30 | | | | | Case 2:
% 168.81/25.30 | | | | | |
% 168.81/25.30 | | | | | | (106) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 168.81/25.30 | | | | | | op(e0, e0) = e3)
% 168.81/25.30 | | | | | |
% 168.81/25.30 | | | | | | BETA: splitting (106) gives:
% 168.81/25.30 | | | | | |
% 168.81/25.30 | | | | | | Case 1:
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | (107) all_58_14 = e3 & op(e0, e1) = e3
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | ALPHA: (107) implies:
% 168.81/25.30 | | | | | | | (108) op(e0, e1) = e3
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | BETA: splitting (30) gives:
% 168.81/25.30 | | | | | | |
% 168.81/25.30 | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | (109) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 168.81/25.30 | | | | | | | | op(e2, e3) = e1)
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | BETA: splitting (109) gives:
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | (110) all_58_0 = e1 & op(e3, e3) = e1
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | ALPHA: (110) implies:
% 168.81/25.30 | | | | | | | | | (111) all_58_0 = e1
% 168.81/25.30 | | | | | | | | | (112) op(e3, e3) = e1
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | BETA: splitting (15) gives:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | (113) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 168.81/25.30 | | | | | | | | | | e1 & op(e0, e2) = e1)
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | REF_CLOSE: (5), (11), (18), (21), (26), (27), (31), (41),
% 168.81/25.30 | | | | | | | | | | (42), (54), (58), (111), (112), (113) are
% 168.81/25.30 | | | | | | | | | | inconsistent by sub-proof #111.
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | (114) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 168.81/25.30 | | | | | | | | | | e1 & op(e0, e0) = e1)
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | REF_CLOSE: (7), (11), (41), (49), (108), (114) are
% 168.81/25.30 | | | | | | | | | | inconsistent by sub-proof #107.
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | End of split
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | (115) all_58_2 = e1 & op(e2, e3) = e1
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | ALPHA: (115) implies:
% 168.81/25.30 | | | | | | | | | (116) all_58_2 = e1
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | REF_CLOSE: (18), (56), (116) are inconsistent by sub-proof
% 168.81/25.30 | | | | | | | | | #776.
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | End of split
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | (117) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 168.81/25.30 | | | | | | | | op(e0, e3) = e1)
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | BETA: splitting (117) gives:
% 168.81/25.30 | | | | | | | |
% 168.81/25.30 | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | (118) all_58_6 = e1 & op(e1, e3) = e1
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | REF_CLOSE: (27), (49), (118) are inconsistent by sub-proof
% 168.81/25.30 | | | | | | | | | #774.
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | (119) all_58_12 = e1 & op(e0, e3) = e1
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | ALPHA: (119) implies:
% 168.81/25.30 | | | | | | | | | (120) op(e0, e3) = e1
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | BETA: splitting (2) gives:
% 168.81/25.30 | | | | | | | | |
% 168.81/25.30 | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | (121) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 168.81/25.30 | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.81/25.30 | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.81/25.30 | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))) |
% 168.81/25.30 | | | | | | | | | | (all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 168.81/25.30 | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.81/25.30 | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.81/25.30 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))) |
% 168.81/25.30 | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 168.81/25.30 | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.81/25.30 | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.81/25.30 | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) |
% 168.81/25.30 | | | | | | | | | | (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 168.81/25.30 | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.81/25.30 | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.81/25.30 | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) |
% 168.81/25.30 | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 168.81/25.30 | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.81/25.30 | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.81/25.30 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | e3) = all_56_6 & $i(all_56_6))))
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | BETA: splitting (121) gives:
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | (122) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 168.81/25.30 | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.81/25.30 | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.81/25.30 | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.81/25.30 | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.81/25.30 | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.81/25.30 | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.81/25.30 | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.81/25.30 | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.81/25.30 | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | BETA: splitting (122) gives:
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | (123) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 168.81/25.30 | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.81/25.30 | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.81/25.30 | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.81/25.30 | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.81/25.30 | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | ALPHA: (123) implies:
% 168.81/25.30 | | | | | | | | | | | | (124) ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7))
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | REF_CLOSE: (19), (57), (124) are inconsistent by sub-proof
% 168.81/25.30 | | | | | | | | | | | | #164.
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | (125) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 168.81/25.30 | | | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.81/25.30 | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.30 | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.81/25.30 | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.81/25.30 | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | ALPHA: (125) implies:
% 168.81/25.30 | | | | | | | | | | | | (126) ~ (all_56_10 = e3)
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | REDUCE: (69), (126) imply:
% 168.81/25.30 | | | | | | | | | | | | (127) $false
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 168.81/25.30 | | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | End of split
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | (128) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 168.81/25.30 | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.81/25.30 | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.81/25.30 | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.81/25.30 | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.81/25.30 | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.81/25.30 | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.81/25.30 | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.81/25.30 | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.81/25.30 | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 168.81/25.30 | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 168.81/25.30 | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 168.81/25.30 | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 168.81/25.30 | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.81/25.30 | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 168.81/25.30 | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 168.81/25.30 | | | | | | | | | | | $i(all_56_6))))
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | | REF_CLOSE: (34), (46), (69), (128) are inconsistent by
% 168.81/25.30 | | | | | | | | | | | sub-proof #147.
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | End of split
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | Case 2:
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | (129) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 168.81/25.30 | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.81/25.30 | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.81/25.30 | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))) |
% 168.81/25.30 | | | | | | | | | | (all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 168.81/25.30 | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.81/25.30 | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.81/25.30 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))) |
% 168.81/25.30 | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.81/25.30 | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 168.81/25.30 | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & (
% 168.81/25.30 | | | | | | | | | | ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 168.81/25.30 | | | | | | | | | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))) |
% 168.81/25.30 | | | | | | | | | | (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 168.81/25.30 | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 168.81/25.30 | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & (
% 168.81/25.30 | | | | | | | | | | ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.81/25.30 | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.81/25.30 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) | ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.81/25.30 | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.81/25.30 | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.81/25.30 | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.81/25.30 | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 168.81/25.30 | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.81/25.30 | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | BETA: splitting (129) gives:
% 168.81/25.30 | | | | | | | | | |
% 168.81/25.30 | | | | | | | | | | Case 1:
% 168.81/25.30 | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | (130) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 168.81/25.31 | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.81/25.31 | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.81/25.31 | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.81/25.31 | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.81/25.31 | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.81/25.31 | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.81/25.31 | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.81/25.31 | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.81/25.31 | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.81/25.31 | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | BETA: splitting (130) gives:
% 168.81/25.31 | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | Case 1:
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | (131) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 168.81/25.31 | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.81/25.31 | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.81/25.31 | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.81/25.31 | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.81/25.31 | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.81/25.31 | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | ALPHA: (131) implies:
% 168.81/25.31 | | | | | | | | | | | | (132) ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.81/25.31 | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7))
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | REF_CLOSE: (19), (57), (132) are inconsistent by sub-proof
% 168.81/25.31 | | | | | | | | | | | | #164.
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | Case 2:
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | (133) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 168.81/25.31 | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.81/25.31 | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.31 | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.81/25.31 | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.81/25.31 | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.81/25.31 | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | ALPHA: (133) implies:
% 168.81/25.31 | | | | | | | | | | | | (134) ~ (all_56_10 = e3)
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | REDUCE: (69), (134) imply:
% 168.81/25.31 | | | | | | | | | | | | (135) $false
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | CLOSE: (135) is inconsistent.
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | End of split
% 168.81/25.31 | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | Case 2:
% 168.81/25.31 | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | (136) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.81/25.31 | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.81/25.31 | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.81/25.31 | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.81/25.31 | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.81/25.31 | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.81/25.31 | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.81/25.31 | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.81/25.31 | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.81/25.31 | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 168.81/25.31 | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.81/25.31 | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.81/25.31 | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.81/25.31 | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.81/25.31 | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 168.81/25.31 | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.81/25.31 | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.81/25.31 | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | BETA: splitting (136) gives:
% 168.81/25.31 | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | Case 1:
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | (137) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.81/25.31 | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 168.81/25.31 | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.81/25.31 | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.81/25.31 | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.81/25.31 | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.81/25.31 | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | ALPHA: (137) implies:
% 168.81/25.31 | | | | | | | | | | | | (138) op(e2, e0) = e0
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | REF_CLOSE: (31), (41), (64), (138) are inconsistent by
% 168.81/25.31 | | | | | | | | | | | | sub-proof #123.
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | Case 2:
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | (139) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 168.81/25.31 | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.81/25.31 | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.81/25.31 | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.81/25.31 | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.81/25.31 | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.81/25.31 | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.81/25.31 | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 168.81/25.31 | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 168.81/25.31 | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 168.81/25.31 | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.81/25.31 | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 168.81/25.31 | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 168.81/25.31 | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.81/25.31 | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 168.81/25.31 | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 168.81/25.31 | | | | | | | | | | | | op(e0, e1) = e1)))
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | BETA: splitting (139) gives:
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | Case 1:
% 168.81/25.31 | | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | | (140) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 168.81/25.31 | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 168.81/25.31 | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.81/25.31 | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.81/25.31 | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.81/25.31 | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.81/25.31 | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.81/25.31 | | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | | ALPHA: (140) implies:
% 168.81/25.31 | | | | | | | | | | | | | (141) ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.81/25.31 | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))
% 168.81/25.31 | | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | | REF_CLOSE: (34), (46), (141) are inconsistent by sub-proof
% 168.81/25.31 | | | | | | | | | | | | | #148.
% 168.81/25.31 | | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | Case 2:
% 168.81/25.31 | | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | | (142) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.81/25.31 | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.81/25.31 | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.81/25.31 | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.81/25.31 | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.81/25.31 | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.81/25.31 | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 168.81/25.31 | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 168.81/25.31 | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 168.81/25.31 | | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | | ALPHA: (142) implies:
% 168.81/25.31 | | | | | | | | | | | | | (143) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 168.81/25.31 | | | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 168.81/25.31 | | | | | | | | | | | | | = e1)
% 168.81/25.31 | | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | | REF_CLOSE: (11), (26), (41), (42), (54), (108), (120), (143)
% 168.81/25.31 | | | | | | | | | | | | | are inconsistent by sub-proof #98.
% 168.81/25.31 | | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | | End of split
% 168.81/25.31 | | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | | End of split
% 168.81/25.31 | | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | | End of split
% 168.81/25.31 | | | | | | | | | |
% 168.81/25.31 | | | | | | | | | End of split
% 168.81/25.31 | | | | | | | | |
% 168.81/25.31 | | | | | | | | End of split
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | End of split
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | Case 2:
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | | (144) all_58_15 = e3 & op(e0, e0) = e3
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | | ALPHA: (144) implies:
% 168.81/25.31 | | | | | | | (145) all_58_15 = e3
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | | REF_CLOSE: (4), (58), (145) are inconsistent by sub-proof #856.
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | End of split
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | End of split
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | Case 2:
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | (146) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | REF_CLOSE: (16), (44), (53), (66), (146) are inconsistent by sub-proof
% 168.81/25.31 | | | | | #958.
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | End of split
% 168.81/25.31 | | | |
% 168.81/25.31 | | | Case 2:
% 168.81/25.31 | | | |
% 168.81/25.31 | | | | (147) all_50_2 = e1
% 168.81/25.31 | | | |
% 168.81/25.31 | | | | COMBINE_EQS: (22), (147) imply:
% 168.81/25.31 | | | | (148) all_10_2 = e1
% 168.81/25.31 | | | |
% 168.81/25.31 | | | | SIMP: (148) implies:
% 168.81/25.31 | | | | (149) all_10_2 = e1
% 168.81/25.31 | | | |
% 168.81/25.31 | | | | COMBINE_EQS: (8), (149) imply:
% 168.81/25.31 | | | | (150) all_56_10 = e1
% 168.81/25.31 | | | |
% 168.81/25.31 | | | | REDUCE: (37), (149) imply:
% 168.81/25.31 | | | | (151) ~ (all_52_3 = e1)
% 168.81/25.31 | | | |
% 168.81/25.31 | | | | REDUCE: (44), (149) imply:
% 168.81/25.31 | | | | (152) ~ (e2 = e1)
% 168.81/25.31 | | | |
% 168.81/25.31 | | | | BETA: splitting (36) gives:
% 168.81/25.31 | | | |
% 168.81/25.31 | | | | Case 1:
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | (153) all_54_12 = e3
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | COMBINE_EQS: (6), (153) imply:
% 168.81/25.31 | | | | | (154) all_52_3 = e3
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | SIMP: (154) implies:
% 168.81/25.31 | | | | | (155) all_52_3 = e3
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | REDUCE: (38), (155) imply:
% 168.81/25.31 | | | | | (156) ~ (all_52_11 = e3)
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | SIMP: (156) implies:
% 168.81/25.31 | | | | | (157) ~ (all_52_11 = e3)
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | BETA: splitting (35) gives:
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | Case 1:
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | | (158) all_56_10 = e3
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | | COMBINE_EQS: (150), (158) imply:
% 168.81/25.31 | | | | | | (159) e3 = e1
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | | COMBINE_EQS: (63), (159) imply:
% 168.81/25.31 | | | | | | (160) all_58_10 = e1
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | | REF_CLOSE: (11), (18), (25), (31), (32), (42), (48), (49), (52),
% 168.81/25.31 | | | | | | (56), (58), (160) are inconsistent by sub-proof #128.
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | Case 2:
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | | (161) ~ (all_56_10 = e3)
% 168.81/25.31 | | | | | | (162) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | | REDUCE: (150), (161) imply:
% 168.81/25.31 | | | | | | (163) ~ (e3 = e1)
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | | BETA: splitting (162) gives:
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | | Case 1:
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | | (164) all_56_12 = e2
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | | COMBINE_EQS: (34), (164) imply:
% 168.81/25.31 | | | | | | | (165) e2 = e1
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | | REDUCE: (49), (165) imply:
% 168.81/25.31 | | | | | | | (166) $false
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | | CLOSE: (166) is inconsistent.
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | Case 2:
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | | (167) ~ (all_56_12 = e2)
% 168.81/25.31 | | | | | | | (168) all_56_14 = e1 | all_56_15 = e0
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | | BETA: splitting (168) gives:
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | | Case 1:
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | | (169) all_56_14 = e1
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | | COMBINE_EQS: (12), (169) imply:
% 168.81/25.31 | | | | | | | | (170) all_6_2 = e1
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | | REDUCE: (40), (170) imply:
% 168.81/25.31 | | | | | | | | (171) ~ (all_52_11 = e1)
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | | BETA: splitting (39) gives:
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | | Case 1:
% 168.81/25.31 | | | | | | | | |
% 168.81/25.31 | | | | | | | | | (172) all_54_14 = e3
% 168.81/25.31 | | | | | | | | |
% 168.81/25.31 | | | | | | | | | REF_CLOSE: (3), (157), (172) are inconsistent by sub-proof
% 168.81/25.31 | | | | | | | | | #969.
% 168.81/25.31 | | | | | | | | |
% 168.81/25.31 | | | | | | | | Case 2:
% 168.81/25.31 | | | | | | | | |
% 168.81/25.31 | | | | | | | | | (173) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 168.81/25.31 | | | | | | | | |
% 168.81/25.31 | | | | | | | | | REF_CLOSE: (3), (29), (55), (171), (173) are inconsistent by
% 168.81/25.31 | | | | | | | | | sub-proof #655.
% 168.81/25.31 | | | | | | | | |
% 168.81/25.31 | | | | | | | | End of split
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | Case 2:
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | | (174) all_56_15 = e0
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | | COMBINE_EQS: (57), (174) imply:
% 168.81/25.31 | | | | | | | | (175) e2 = e0
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | | COMBINE_EQS: (4), (175) imply:
% 168.81/25.31 | | | | | | | | (176) all_58_15 = e0
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | | REF_CLOSE: (1), (7), (11), (14), (15), (18), (20), (26), (31),
% 168.81/25.31 | | | | | | | | (41), (42), (49), (54), (58), (176) are inconsistent
% 168.81/25.31 | | | | | | | | by sub-proof #628.
% 168.81/25.31 | | | | | | | |
% 168.81/25.31 | | | | | | | End of split
% 168.81/25.31 | | | | | | |
% 168.81/25.31 | | | | | | End of split
% 168.81/25.31 | | | | | |
% 168.81/25.31 | | | | | End of split
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | Case 2:
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | (177) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | | REF_CLOSE: (6), (10), (50), (151), (177) are inconsistent by sub-proof
% 168.81/25.31 | | | | | #675.
% 168.81/25.31 | | | | |
% 168.81/25.31 | | | | End of split
% 168.81/25.31 | | | |
% 168.81/25.31 | | | End of split
% 168.81/25.31 | | |
% 168.81/25.31 | | End of split
% 168.81/25.31 | |
% 168.81/25.31 | End of split
% 168.81/25.31 |
% 168.81/25.31 End of proof
% 168.81/25.31
% 168.81/25.31 Sub-proof #98 shows that the following formulas are inconsistent:
% 168.81/25.31 ----------------------------------------------------------------
% 168.81/25.31 (1) op(e0, e1) = e3
% 168.81/25.31 (2) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 168.81/25.31 (all_56_8 = e1 & op(e0, e1) = e1)
% 168.81/25.31 (3) ~ (e3 = e1)
% 168.81/25.31 (4) op(e0, e3) = e1
% 168.81/25.31 (5) op(e0, e2) = e0
% 168.81/25.31 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.31 (7) ~ (e2 = e0)
% 168.81/25.31 (8) op(e0, e2) = all_52_7
% 168.81/25.31
% 168.81/25.31 Begin of proof
% 168.81/25.31 |
% 168.81/25.31 | BETA: splitting (2) gives:
% 168.81/25.31 |
% 168.81/25.31 | Case 1:
% 168.81/25.31 | |
% 168.81/25.31 | | (9) all_56_6 = e3 & op(e0, e3) = e3
% 168.81/25.31 | |
% 168.81/25.31 | | ALPHA: (9) implies:
% 168.81/25.31 | | (10) op(e0, e3) = e3
% 168.81/25.31 | |
% 168.81/25.31 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #125.
% 168.81/25.31 | |
% 168.81/25.31 | Case 2:
% 168.81/25.31 | |
% 168.81/25.31 | | (11) (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) =
% 168.81/25.31 | | e1)
% 168.81/25.31 | |
% 168.81/25.31 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (11) are inconsistent by sub-proof
% 168.81/25.31 | | #99.
% 168.81/25.31 | |
% 168.81/25.31 | End of split
% 168.81/25.31 |
% 168.81/25.31 End of proof
% 168.81/25.31
% 168.81/25.31 Sub-proof #99 shows that the following formulas are inconsistent:
% 168.81/25.31 ----------------------------------------------------------------
% 168.81/25.31 (1) op(e0, e1) = e3
% 168.81/25.31 (2) (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) = e1)
% 168.81/25.31 (3) ~ (e3 = e1)
% 168.81/25.31 (4) op(e0, e2) = e0
% 168.81/25.31 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.31 (6) ~ (e2 = e0)
% 168.81/25.31 (7) op(e0, e2) = all_52_7
% 168.81/25.31
% 168.81/25.31 Begin of proof
% 168.81/25.31 |
% 168.81/25.31 | BETA: splitting (2) gives:
% 168.81/25.31 |
% 168.81/25.31 | Case 1:
% 168.81/25.31 | |
% 168.81/25.31 | | (8) all_56_7 = e2 & op(e0, e2) = e2
% 168.81/25.31 | |
% 168.81/25.31 | | ALPHA: (8) implies:
% 168.81/25.31 | | (9) op(e0, e2) = e2
% 168.81/25.31 | |
% 168.81/25.31 | | REF_CLOSE: (4), (5), (6), (7), (9) are inconsistent by sub-proof #631.
% 168.81/25.31 | |
% 168.81/25.31 | Case 2:
% 168.81/25.31 | |
% 168.81/25.31 | | (10) all_56_8 = e1 & op(e0, e1) = e1
% 168.81/25.31 | |
% 168.81/25.31 | | ALPHA: (10) implies:
% 168.81/25.31 | | (11) op(e0, e1) = e1
% 168.81/25.31 | |
% 168.81/25.31 | | REF_CLOSE: (1), (3), (5), (11) are inconsistent by sub-proof #133.
% 168.81/25.31 | |
% 168.81/25.31 | End of split
% 168.81/25.31 |
% 168.81/25.31 End of proof
% 168.81/25.31
% 168.81/25.31 Sub-proof #100 shows that the following formulas are inconsistent:
% 168.81/25.31 ----------------------------------------------------------------
% 168.81/25.31 (1) op(e0, e0) = e2
% 168.81/25.31 (2) ~ (e3 = e1)
% 168.81/25.31 (3) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 168.81/25.31 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 168.81/25.31 (4) ~ (e1 = e0)
% 168.81/25.31 (5) op(e0, e2) = e0
% 168.81/25.31 (6) all_58_14 = e3
% 168.81/25.31 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.31 (8) all_58_12 = e3
% 168.81/25.31 (9) ~ (e2 = e1)
% 168.81/25.31 (10) op(e0, e2) = all_52_7
% 168.81/25.31
% 168.81/25.31 Begin of proof
% 168.81/25.31 |
% 168.81/25.31 | BETA: splitting (3) gives:
% 168.81/25.31 |
% 168.81/25.31 | Case 1:
% 168.81/25.31 | |
% 168.81/25.31 | | (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 168.81/25.31 | | e1)
% 168.81/25.31 | |
% 168.81/25.31 | | BETA: splitting (11) gives:
% 168.81/25.31 | |
% 168.81/25.31 | | Case 1:
% 168.81/25.31 | | |
% 168.81/25.31 | | | (12) all_58_12 = e1 & op(e0, e3) = e1
% 168.81/25.31 | | |
% 168.81/25.31 | | | ALPHA: (12) implies:
% 168.81/25.31 | | | (13) all_58_12 = e1
% 168.81/25.31 | | |
% 168.81/25.31 | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #600.
% 168.81/25.31 | | |
% 168.81/25.31 | | Case 2:
% 168.81/25.31 | | |
% 168.81/25.31 | | | (14) all_58_13 = e1 & op(e0, e2) = e1
% 168.81/25.31 | | |
% 168.81/25.31 | | | ALPHA: (14) implies:
% 168.81/25.31 | | | (15) op(e0, e2) = e1
% 168.81/25.31 | | |
% 168.81/25.31 | | | REF_CLOSE: (4), (5), (7), (10), (15) are inconsistent by sub-proof #889.
% 168.81/25.31 | | |
% 168.81/25.31 | | End of split
% 168.81/25.31 | |
% 168.81/25.31 | Case 2:
% 168.81/25.31 | |
% 168.81/25.31 | | (16) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 168.81/25.31 | | e1)
% 168.81/25.31 | |
% 168.81/25.31 | | BETA: splitting (16) gives:
% 168.81/25.31 | |
% 168.81/25.31 | | Case 1:
% 168.81/25.31 | | |
% 168.81/25.31 | | | (17) all_58_14 = e1 & op(e0, e1) = e1
% 168.81/25.31 | | |
% 168.81/25.31 | | | ALPHA: (17) implies:
% 168.81/25.31 | | | (18) all_58_14 = e1
% 168.81/25.31 | | |
% 168.81/25.31 | | | REF_CLOSE: (2), (6), (18) are inconsistent by sub-proof #626.
% 168.81/25.31 | | |
% 168.81/25.31 | | Case 2:
% 168.81/25.31 | | |
% 168.81/25.31 | | | (19) all_58_15 = e1 & op(e0, e0) = e1
% 168.81/25.31 | | |
% 168.81/25.31 | | | ALPHA: (19) implies:
% 168.81/25.31 | | | (20) op(e0, e0) = e1
% 168.81/25.31 | | |
% 168.81/25.31 | | | REF_CLOSE: (1), (7), (9), (20) are inconsistent by sub-proof #640.
% 168.81/25.31 | | |
% 168.81/25.31 | | End of split
% 168.81/25.31 | |
% 168.81/25.31 | End of split
% 168.81/25.31 |
% 168.81/25.31 End of proof
% 168.81/25.31
% 168.81/25.31 Sub-proof #101 shows that the following formulas are inconsistent:
% 168.81/25.31 ----------------------------------------------------------------
% 168.81/25.31 (1) ~ (e3 = e1)
% 168.81/25.31 (2) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 168.81/25.31 (3) all_58_3 = e1
% 168.81/25.31 (4) ~ (e3 = e0)
% 168.81/25.31 (5) all_58_2 = e0
% 168.81/25.31
% 168.81/25.31 Begin of proof
% 168.81/25.31 |
% 168.81/25.31 | BETA: splitting (2) gives:
% 168.81/25.31 |
% 168.81/25.31 | Case 1:
% 168.81/25.31 | |
% 168.81/25.31 | | (6) all_58_2 = e3 & op(e2, e3) = e3
% 168.81/25.31 | |
% 168.81/25.31 | | ALPHA: (6) implies:
% 168.81/25.31 | | (7) all_58_2 = e3
% 168.81/25.31 | |
% 168.81/25.31 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #913.
% 168.81/25.31 | |
% 168.81/25.31 | Case 2:
% 168.81/25.31 | |
% 168.81/25.31 | | (8) all_58_3 = e3 & op(e2, e2) = e3
% 168.81/25.31 | |
% 168.81/25.31 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #102.
% 168.81/25.31 | |
% 168.81/25.31 | End of split
% 168.81/25.31 |
% 168.81/25.31 End of proof
% 168.81/25.31
% 168.81/25.31 Sub-proof #102 shows that the following formulas are inconsistent:
% 168.81/25.31 ----------------------------------------------------------------
% 168.81/25.31 (1) all_58_3 = e3 & op(e2, e2) = e3
% 168.81/25.31 (2) all_58_3 = e1
% 168.81/25.32 (3) ~ (e3 = e1)
% 168.81/25.32
% 168.81/25.32 Begin of proof
% 168.81/25.32 |
% 168.81/25.32 | ALPHA: (1) implies:
% 168.81/25.32 | (4) all_58_3 = e3
% 168.81/25.32 |
% 168.81/25.32 | COMBINE_EQS: (2), (4) imply:
% 168.81/25.32 | (5) e3 = e1
% 168.81/25.32 |
% 168.81/25.32 | REDUCE: (3), (5) imply:
% 168.81/25.32 | (6) $false
% 168.81/25.32 |
% 168.81/25.32 | CLOSE: (6) is inconsistent.
% 168.81/25.32 |
% 168.81/25.32 End of proof
% 168.81/25.32
% 168.81/25.32 Sub-proof #103 shows that the following formulas are inconsistent:
% 168.81/25.32 ----------------------------------------------------------------
% 168.81/25.32 (1) all_58_0 = e0 & op(e3, e3) = e0
% 168.81/25.32 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.32 (3) op(e3, e3) = all_10_2
% 168.81/25.32 (4) ~ (all_10_2 = e0)
% 168.81/25.32
% 168.81/25.32 Begin of proof
% 168.81/25.32 |
% 168.81/25.32 | ALPHA: (1) implies:
% 168.81/25.32 | (5) op(e3, e3) = e0
% 168.81/25.32 |
% 168.81/25.32 | GROUND_INST: instantiating (2) with all_10_2, e0, e3, e3, simplifying with
% 168.81/25.32 | (3), (5) gives:
% 168.81/25.32 | (6) all_10_2 = e0
% 168.81/25.32 |
% 168.81/25.32 | REDUCE: (4), (6) imply:
% 168.81/25.32 | (7) $false
% 168.81/25.32 |
% 168.81/25.32 | CLOSE: (7) is inconsistent.
% 168.81/25.32 |
% 168.81/25.32 End of proof
% 168.81/25.32
% 168.81/25.32 Sub-proof #104 shows that the following formulas are inconsistent:
% 168.81/25.32 ----------------------------------------------------------------
% 168.81/25.32 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 168.81/25.32 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 168.81/25.32 (2) all_58_15 = e2
% 168.81/25.32 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 168.81/25.32 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 168.81/25.32 (4) op(e0, e0) = e2
% 168.81/25.32 (5) ~ (all_6_2 = e3)
% 168.81/25.32 (6) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 168.81/25.32 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 168.81/25.32 (7) ~ (e3 = e1)
% 168.81/25.32 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 168.81/25.32 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 168.81/25.32 (9) op(e3, e1) = all_52_8
% 168.81/25.32 (10) ~ (e1 = e0)
% 168.81/25.32 (11) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 168.81/25.32 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 168.81/25.32 e3)
% 168.81/25.32 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 168.81/25.32 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 168.81/25.32 (13) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 168.81/25.32 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 168.81/25.32 (14) all_58_3 = e1
% 168.81/25.32 (15) all_58_12 = e0 & op(e0, e3) = e0
% 168.81/25.32 (16) op(e0, e2) = e0
% 168.81/25.32 (17) all_58_6 = e2
% 168.81/25.32 (18) op(e1, e1) = all_6_2
% 168.81/25.32 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 168.81/25.32 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 168.81/25.32 (20) ~ (e3 = e0)
% 168.81/25.32 (21) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.81/25.32 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.81/25.32 (22) op(e3, e2) = e2
% 168.81/25.32 (23) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.81/25.32 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 168.81/25.32 (24) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 168.81/25.32 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 168.81/25.32 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.32 (26) ~ (e2 = e0)
% 168.81/25.32 (27) op(e2, e1) = e2
% 168.81/25.32 (28) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 168.81/25.32 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 168.81/25.32 (29) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.81/25.32 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.81/25.32 (30) ~ (e2 = e1)
% 168.81/25.32 (31) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.81/25.32 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 168.81/25.32 (32) op(e0, e2) = all_52_7
% 168.81/25.32 (33) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 168.81/25.32 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 168.81/25.32 (34) ~ (e3 = e2)
% 168.81/25.32
% 168.81/25.32 Begin of proof
% 168.81/25.32 |
% 168.81/25.32 | ALPHA: (15) implies:
% 168.81/25.32 | (35) all_58_12 = e0
% 168.81/25.32 | (36) op(e0, e3) = e0
% 168.81/25.32 |
% 168.81/25.32 | BETA: splitting (28) gives:
% 168.81/25.32 |
% 168.81/25.32 | Case 1:
% 168.81/25.32 | |
% 168.81/25.32 | | (37) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 168.81/25.32 | | e3)
% 168.81/25.32 | |
% 168.81/25.32 | | BETA: splitting (37) gives:
% 168.81/25.32 | |
% 168.81/25.32 | | Case 1:
% 168.81/25.32 | | |
% 168.81/25.32 | | | (38) all_58_6 = e3 & op(e1, e3) = e3
% 168.81/25.32 | | |
% 168.81/25.32 | | | ALPHA: (38) implies:
% 168.81/25.32 | | | (39) all_58_6 = e3
% 168.81/25.32 | | |
% 168.81/25.32 | | | REF_CLOSE: (17), (34), (39) are inconsistent by sub-proof #822.
% 168.81/25.32 | | |
% 168.81/25.32 | | Case 2:
% 168.81/25.32 | | |
% 168.81/25.32 | | | (40) all_58_7 = e3 & op(e1, e2) = e3
% 168.81/25.32 | | |
% 168.81/25.32 | | | ALPHA: (40) implies:
% 168.81/25.32 | | | (41) all_58_7 = e3
% 168.81/25.32 | | |
% 168.81/25.32 | | | BETA: splitting (19) gives:
% 168.81/25.32 | | |
% 168.81/25.32 | | | Case 1:
% 168.81/25.32 | | | |
% 168.81/25.32 | | | | (42) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 168.81/25.32 | | | | = e1)
% 168.81/25.32 | | | |
% 168.81/25.32 | | | | BETA: splitting (42) gives:
% 168.81/25.32 | | | |
% 168.81/25.32 | | | | Case 1:
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | (43) all_58_0 = e1 & op(e3, e3) = e1
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | ALPHA: (43) implies:
% 168.81/25.32 | | | | | (44) all_58_0 = e1
% 168.81/25.32 | | | | | (45) op(e3, e3) = e1
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | BETA: splitting (8) gives:
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | Case 1:
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | (46) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 168.81/25.32 | | | | | | op(e0, e2) = e1)
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | REF_CLOSE: (3), (7), (10), (12), (16), (17), (20), (25), (26), (32),
% 168.81/25.32 | | | | | | (34), (44), (45), (46) are inconsistent by sub-proof
% 168.81/25.32 | | | | | | #111.
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | Case 2:
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | (47) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 168.81/25.32 | | | | | | op(e0, e0) = e1)
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | BETA: splitting (47) gives:
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | Case 1:
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | (48) all_58_14 = e1 & op(e0, e1) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | ALPHA: (48) implies:
% 168.81/25.32 | | | | | | | (49) op(e0, e1) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | BETA: splitting (11) gives:
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | Case 1:
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | (50) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 168.81/25.32 | | | | | | | | op(e0, e2) = e3)
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | BETA: splitting (50) gives:
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | Case 1:
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | (51) all_58_12 = e3 & op(e0, e3) = e3
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | REF_CLOSE: (20), (35), (51) are inconsistent by sub-proof
% 168.81/25.32 | | | | | | | | | #110.
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | Case 2:
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | (52) all_58_13 = e3 & op(e0, e2) = e3
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | ALPHA: (52) implies:
% 168.81/25.32 | | | | | | | | | (53) all_58_13 = e3
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | BETA: splitting (23) gives:
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | Case 1:
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | (54) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 &
% 168.81/25.32 | | | | | | | | | | op(e2, e2) = e0)
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | REF_CLOSE: (10), (14), (22), (25), (26), (54) are
% 168.81/25.32 | | | | | | | | | | inconsistent by sub-proof #109.
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | Case 2:
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | (55) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0
% 168.81/25.32 | | | | | | | | | | & op(e0, e2) = e0)
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | BETA: splitting (55) gives:
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | Case 1:
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | | (56) all_58_7 = e0 & op(e1, e2) = e0
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | | ALPHA: (56) implies:
% 168.81/25.32 | | | | | | | | | | | (57) all_58_7 = e0
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | | COMBINE_EQS: (41), (57) imply:
% 168.81/25.32 | | | | | | | | | | | (58) e3 = e0
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | | SIMP: (58) implies:
% 168.81/25.32 | | | | | | | | | | | (59) e3 = e0
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | | COMBINE_EQS: (53), (59) imply:
% 168.81/25.32 | | | | | | | | | | | (60) all_58_13 = e0
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | | REF_CLOSE: (2), (7), (11), (20), (25), (34), (35), (49), (60)
% 168.81/25.32 | | | | | | | | | | | are inconsistent by sub-proof #108.
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | Case 2:
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | | (61) all_58_13 = e0 & op(e0, e2) = e0
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | | ALPHA: (61) implies:
% 168.81/25.32 | | | | | | | | | | | (62) all_58_13 = e0
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | | REF_CLOSE: (2), (7), (11), (20), (25), (34), (35), (49), (62)
% 168.81/25.32 | | | | | | | | | | | are inconsistent by sub-proof #108.
% 168.81/25.32 | | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | End of split
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | End of split
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | End of split
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | Case 2:
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | (63) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 168.81/25.32 | | | | | | | | op(e0, e0) = e3)
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | BETA: splitting (63) gives:
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | Case 1:
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | (64) all_58_14 = e3 & op(e0, e1) = e3
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | ALPHA: (64) implies:
% 168.81/25.32 | | | | | | | | | (65) op(e0, e1) = e3
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | BETA: splitting (8) gives:
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | Case 1:
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | (66) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1
% 168.81/25.32 | | | | | | | | | | & op(e0, e2) = e1)
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | REF_CLOSE: (3), (7), (10), (12), (16), (17), (20), (25),
% 168.81/25.32 | | | | | | | | | | (26), (32), (34), (44), (45), (66) are
% 168.81/25.32 | | | | | | | | | | inconsistent by sub-proof #111.
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | Case 2:
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | | REF_CLOSE: (4), (7), (25), (30), (47), (65) are inconsistent
% 168.81/25.32 | | | | | | | | | | by sub-proof #107.
% 168.81/25.32 | | | | | | | | | |
% 168.81/25.32 | | | | | | | | | End of split
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | Case 2:
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | (67) all_58_15 = e3 & op(e0, e0) = e3
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | ALPHA: (67) implies:
% 168.81/25.32 | | | | | | | | | (68) all_58_15 = e3
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | REF_CLOSE: (2), (34), (68) are inconsistent by sub-proof #856.
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | End of split
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | End of split
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | Case 2:
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | (69) all_58_15 = e1 & op(e0, e0) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | ALPHA: (69) implies:
% 168.81/25.32 | | | | | | | (70) op(e0, e0) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | REF_CLOSE: (4), (25), (30), (70) are inconsistent by sub-proof
% 168.81/25.32 | | | | | | | #640.
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | End of split
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | End of split
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | Case 2:
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | (71) all_58_2 = e1 & op(e2, e3) = e1
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | ALPHA: (71) implies:
% 168.81/25.32 | | | | | (72) all_58_2 = e1
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | REF_CLOSE: (7), (10), (14), (20), (21), (25), (26), (27), (29), (34),
% 168.81/25.32 | | | | | (72) are inconsistent by sub-proof #106.
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | End of split
% 168.81/25.32 | | | |
% 168.81/25.32 | | | Case 2:
% 168.81/25.32 | | | |
% 168.81/25.32 | | | | (73) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 168.81/25.32 | | | | = e1)
% 168.81/25.32 | | | |
% 168.81/25.32 | | | | REF_CLOSE: (10), (17), (25), (30), (36), (73) are inconsistent by
% 168.81/25.32 | | | | sub-proof #105.
% 168.81/25.32 | | | |
% 168.81/25.32 | | | End of split
% 168.81/25.32 | | |
% 168.81/25.32 | | End of split
% 168.81/25.32 | |
% 168.81/25.32 | Case 2:
% 168.81/25.32 | |
% 168.81/25.32 | | (74) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 168.81/25.32 | | e3)
% 168.81/25.32 | |
% 168.81/25.32 | | BETA: splitting (74) gives:
% 168.81/25.32 | |
% 168.81/25.32 | | Case 1:
% 168.81/25.32 | | |
% 168.81/25.32 | | | (75) all_58_8 = e3 & op(e1, e1) = e3
% 168.81/25.32 | | |
% 168.81/25.32 | | | REF_CLOSE: (5), (18), (25), (75) are inconsistent by sub-proof #961.
% 168.81/25.32 | | |
% 168.81/25.32 | | Case 2:
% 168.81/25.32 | | |
% 168.81/25.32 | | | (76) all_58_11 = e3 & op(e1, e0) = e3
% 168.81/25.32 | | |
% 168.81/25.32 | | | ALPHA: (76) implies:
% 168.81/25.32 | | | (77) all_58_11 = e3
% 168.81/25.32 | | |
% 168.81/25.32 | | | BETA: splitting (19) gives:
% 168.81/25.32 | | |
% 168.81/25.32 | | | Case 1:
% 168.81/25.32 | | | |
% 168.81/25.32 | | | | (78) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 168.81/25.32 | | | | = e1)
% 168.81/25.32 | | | |
% 168.81/25.32 | | | | BETA: splitting (78) gives:
% 168.81/25.32 | | | |
% 168.81/25.32 | | | | Case 1:
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | (79) all_58_0 = e1 & op(e3, e3) = e1
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | ALPHA: (79) implies:
% 168.81/25.32 | | | | | (80) all_58_0 = e1
% 168.81/25.32 | | | | | (81) op(e3, e3) = e1
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | BETA: splitting (1) gives:
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | Case 1:
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | (82) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 168.81/25.32 | | | | | | e0) = e1)
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | BETA: splitting (82) gives:
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | Case 1:
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | (83) all_58_9 = e1 & op(e3, e0) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | ALPHA: (83) implies:
% 168.81/25.32 | | | | | | | (84) all_58_9 = e1
% 168.81/25.32 | | | | | | | (85) op(e3, e0) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | BETA: splitting (8) gives:
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | Case 1:
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | (86) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 168.81/25.32 | | | | | | | | op(e0, e2) = e1)
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | REF_CLOSE: (3), (7), (10), (12), (16), (17), (20), (25), (26),
% 168.81/25.32 | | | | | | | | (32), (34), (80), (81), (86) are inconsistent by
% 168.81/25.32 | | | | | | | | sub-proof #111.
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | Case 2:
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | (87) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 168.81/25.32 | | | | | | | | op(e0, e0) = e1)
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | BETA: splitting (87) gives:
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | | Case 1:
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | (88) all_58_14 = e1 & op(e0, e1) = e1
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | REF_CLOSE: (5), (6), (7), (9), (10), (13), (18), (20), (24),
% 168.81/25.32 | | | | | | | | | (25), (26), (27), (30), (33), (34), (81), (84),
% 168.81/25.32 | | | | | | | | | (85), (88) are inconsistent by sub-proof #131.
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | Case 2:
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | (89) all_58_15 = e1 & op(e0, e0) = e1
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | ALPHA: (89) implies:
% 168.81/25.32 | | | | | | | | | (90) op(e0, e0) = e1
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | | REF_CLOSE: (4), (25), (30), (90) are inconsistent by sub-proof
% 168.81/25.32 | | | | | | | | | #640.
% 168.81/25.32 | | | | | | | | |
% 168.81/25.32 | | | | | | | | End of split
% 168.81/25.32 | | | | | | | |
% 168.81/25.32 | | | | | | | End of split
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | Case 2:
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | (91) all_58_10 = e1 & op(e2, e0) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | ALPHA: (91) implies:
% 168.81/25.32 | | | | | | | (92) all_58_10 = e1
% 168.81/25.32 | | | | | | | (93) op(e2, e0) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | REF_CLOSE: (7), (10), (14), (20), (21), (25), (26), (27), (29),
% 168.81/25.32 | | | | | | | (30), (31), (34), (92), (93) are inconsistent by
% 168.81/25.32 | | | | | | | sub-proof #127.
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | End of split
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | Case 2:
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | (94) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 168.81/25.32 | | | | | | op(e0, e0) = e1)
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | BETA: splitting (94) gives:
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | | Case 1:
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | (95) all_58_11 = e1 & op(e1, e0) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | REF_CLOSE: (7), (77), (95) are inconsistent by sub-proof #721.
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | Case 2:
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | (96) all_58_15 = e1 & op(e0, e0) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | ALPHA: (96) implies:
% 168.81/25.32 | | | | | | | (97) op(e0, e0) = e1
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | | REF_CLOSE: (4), (25), (30), (97) are inconsistent by sub-proof
% 168.81/25.32 | | | | | | | #640.
% 168.81/25.32 | | | | | | |
% 168.81/25.32 | | | | | | End of split
% 168.81/25.32 | | | | | |
% 168.81/25.32 | | | | | End of split
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | Case 2:
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | (98) all_58_2 = e1 & op(e2, e3) = e1
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | ALPHA: (98) implies:
% 168.81/25.32 | | | | | (99) all_58_2 = e1
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | | REF_CLOSE: (7), (10), (14), (20), (21), (25), (26), (27), (29), (34),
% 168.81/25.32 | | | | | (99) are inconsistent by sub-proof #106.
% 168.81/25.32 | | | | |
% 168.81/25.32 | | | | End of split
% 168.81/25.32 | | | |
% 168.81/25.32 | | | Case 2:
% 168.81/25.32 | | | |
% 168.81/25.32 | | | | (100) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 168.81/25.32 | | | | e3) = e1)
% 168.81/25.32 | | | |
% 168.81/25.32 | | | | REF_CLOSE: (10), (17), (25), (30), (36), (100) are inconsistent by
% 168.81/25.32 | | | | sub-proof #105.
% 168.81/25.32 | | | |
% 168.81/25.32 | | | End of split
% 168.81/25.32 | | |
% 168.81/25.32 | | End of split
% 168.81/25.32 | |
% 168.81/25.32 | End of split
% 168.81/25.32 |
% 168.81/25.32 End of proof
% 168.81/25.32
% 168.81/25.32 Sub-proof #105 shows that the following formulas are inconsistent:
% 168.81/25.32 ----------------------------------------------------------------
% 168.81/25.33 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 168.81/25.33 (2) ~ (e1 = e0)
% 168.81/25.33 (3) all_58_6 = e2
% 168.81/25.33 (4) op(e0, e3) = e0
% 168.81/25.33 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.33 (6) ~ (e2 = e1)
% 168.81/25.33
% 168.81/25.33 Begin of proof
% 168.81/25.33 |
% 168.81/25.33 | BETA: splitting (1) gives:
% 168.81/25.33 |
% 168.81/25.33 | Case 1:
% 168.81/25.33 | |
% 168.81/25.33 | | (7) all_58_6 = e1 & op(e1, e3) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #774.
% 168.81/25.33 | |
% 168.81/25.33 | Case 2:
% 168.81/25.33 | |
% 168.81/25.33 | | (8) all_58_12 = e1 & op(e0, e3) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | ALPHA: (8) implies:
% 168.81/25.33 | | (9) op(e0, e3) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #531.
% 168.81/25.33 | |
% 168.81/25.33 | End of split
% 168.81/25.33 |
% 168.81/25.33 End of proof
% 168.81/25.33
% 168.81/25.33 Sub-proof #106 shows that the following formulas are inconsistent:
% 168.81/25.33 ----------------------------------------------------------------
% 168.81/25.33 (1) ~ (e3 = e1)
% 168.81/25.33 (2) ~ (e1 = e0)
% 168.81/25.33 (3) all_58_3 = e1
% 168.81/25.33 (4) ~ (e3 = e0)
% 168.81/25.33 (5) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.81/25.33 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.81/25.33 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.33 (7) ~ (e2 = e0)
% 168.81/25.33 (8) op(e2, e1) = e2
% 168.81/25.33 (9) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.81/25.33 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.81/25.33 (10) all_58_2 = e1
% 168.81/25.33 (11) ~ (e3 = e2)
% 168.81/25.33
% 168.81/25.33 Begin of proof
% 168.81/25.33 |
% 168.81/25.33 | BETA: splitting (5) gives:
% 168.81/25.33 |
% 168.81/25.33 | Case 1:
% 168.81/25.33 | |
% 168.81/25.33 | | (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 168.81/25.33 | | e0)
% 168.81/25.33 | |
% 168.81/25.33 | | BETA: splitting (12) gives:
% 168.81/25.33 | |
% 168.81/25.33 | | Case 1:
% 168.81/25.33 | | |
% 168.81/25.33 | | | (13) all_58_2 = e0 & op(e2, e3) = e0
% 168.81/25.33 | | |
% 168.81/25.33 | | | REF_CLOSE: (2), (10), (13) are inconsistent by sub-proof #935.
% 168.81/25.33 | | |
% 168.81/25.33 | | Case 2:
% 168.81/25.33 | | |
% 168.81/25.33 | | | (14) all_58_3 = e0 & op(e2, e2) = e0
% 168.81/25.33 | | |
% 168.81/25.33 | | | ALPHA: (14) implies:
% 168.81/25.33 | | | (15) all_58_3 = e0
% 168.81/25.33 | | |
% 168.81/25.33 | | | REF_CLOSE: (2), (3), (15) are inconsistent by sub-proof #523.
% 168.81/25.33 | | |
% 168.81/25.33 | | End of split
% 168.81/25.33 | |
% 168.81/25.33 | Case 2:
% 168.81/25.33 | |
% 168.81/25.33 | | (16) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 168.81/25.33 | | e0)
% 168.81/25.33 | |
% 168.81/25.33 | | BETA: splitting (16) gives:
% 168.81/25.33 | |
% 168.81/25.33 | | Case 1:
% 168.81/25.33 | | |
% 168.81/25.33 | | | (17) all_58_5 = e0 & op(e2, e1) = e0
% 168.81/25.33 | | |
% 168.81/25.33 | | | REF_CLOSE: (6), (7), (8), (17) are inconsistent by sub-proof #151.
% 168.81/25.33 | | |
% 168.81/25.33 | | Case 2:
% 168.81/25.33 | | |
% 168.81/25.33 | | | (18) all_58_10 = e0 & op(e2, e0) = e0
% 168.81/25.33 | | |
% 168.81/25.33 | | | ALPHA: (18) implies:
% 168.81/25.33 | | | (19) op(e2, e0) = e0
% 168.81/25.33 | | |
% 168.81/25.33 | | | BETA: splitting (9) gives:
% 168.81/25.33 | | |
% 168.81/25.33 | | | Case 1:
% 168.81/25.33 | | | |
% 168.81/25.33 | | | | (20) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2)
% 168.81/25.33 | | | | = e3)
% 168.81/25.33 | | | |
% 168.81/25.33 | | | | BETA: splitting (20) gives:
% 168.81/25.33 | | | |
% 168.81/25.33 | | | | Case 1:
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | (21) all_58_2 = e3 & op(e2, e3) = e3
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | ALPHA: (21) implies:
% 168.81/25.33 | | | | | (22) all_58_2 = e3
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | REF_CLOSE: (1), (10), (22) are inconsistent by sub-proof #938.
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | Case 2:
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | (23) all_58_3 = e3 & op(e2, e2) = e3
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | ALPHA: (23) implies:
% 168.81/25.33 | | | | | (24) all_58_3 = e3
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | REF_CLOSE: (1), (3), (24) are inconsistent by sub-proof #328.
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | End of split
% 168.81/25.33 | | | |
% 168.81/25.33 | | | Case 2:
% 168.81/25.33 | | | |
% 168.81/25.33 | | | | (25) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0)
% 168.81/25.33 | | | | = e3)
% 168.81/25.33 | | | |
% 168.81/25.33 | | | | BETA: splitting (25) gives:
% 168.81/25.33 | | | |
% 168.81/25.33 | | | | Case 1:
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | (26) all_58_5 = e3 & op(e2, e1) = e3
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | REF_CLOSE: (6), (8), (11), (26) are inconsistent by sub-proof #150.
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | Case 2:
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | (27) all_58_10 = e3 & op(e2, e0) = e3
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | ALPHA: (27) implies:
% 168.81/25.33 | | | | | (28) op(e2, e0) = e3
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | | REF_CLOSE: (4), (6), (19), (28) are inconsistent by sub-proof #123.
% 168.81/25.33 | | | | |
% 168.81/25.33 | | | | End of split
% 168.81/25.33 | | | |
% 168.81/25.33 | | | End of split
% 168.81/25.33 | | |
% 168.81/25.33 | | End of split
% 168.81/25.33 | |
% 168.81/25.33 | End of split
% 168.81/25.33 |
% 168.81/25.33 End of proof
% 168.81/25.33
% 168.81/25.33 Sub-proof #107 shows that the following formulas are inconsistent:
% 168.81/25.33 ----------------------------------------------------------------
% 168.81/25.33 (1) op(e0, e1) = e3
% 168.81/25.33 (2) op(e0, e0) = e2
% 168.81/25.33 (3) ~ (e3 = e1)
% 168.81/25.33 (4) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 168.81/25.33 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.33 (6) ~ (e2 = e1)
% 168.81/25.33
% 168.81/25.33 Begin of proof
% 168.81/25.33 |
% 168.81/25.33 | BETA: splitting (4) gives:
% 168.81/25.33 |
% 168.81/25.33 | Case 1:
% 168.81/25.33 | |
% 168.81/25.33 | | (7) all_58_14 = e1 & op(e0, e1) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | ALPHA: (7) implies:
% 168.81/25.33 | | (8) op(e0, e1) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #133.
% 168.81/25.33 | |
% 168.81/25.33 | Case 2:
% 168.81/25.33 | |
% 168.81/25.33 | | (9) all_58_15 = e1 & op(e0, e0) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | ALPHA: (9) implies:
% 168.81/25.33 | | (10) op(e0, e0) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #640.
% 168.81/25.33 | |
% 168.81/25.33 | End of split
% 168.81/25.33 |
% 168.81/25.33 End of proof
% 168.81/25.33
% 168.81/25.33 Sub-proof #108 shows that the following formulas are inconsistent:
% 168.81/25.33 ----------------------------------------------------------------
% 168.81/25.33 (1) all_58_15 = e2
% 168.81/25.33 (2) ~ (e3 = e1)
% 168.81/25.33 (3) op(e0, e1) = e1
% 168.81/25.33 (4) all_58_13 = e0
% 168.81/25.33 (5) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 168.81/25.33 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 168.81/25.33 (6) ~ (e3 = e0)
% 168.81/25.33 (7) all_58_12 = e0
% 168.81/25.33 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.33 (9) ~ (e3 = e2)
% 168.81/25.33
% 168.81/25.33 Begin of proof
% 168.81/25.33 |
% 168.81/25.33 | BETA: splitting (5) gives:
% 168.81/25.33 |
% 168.81/25.33 | Case 1:
% 168.81/25.33 | |
% 168.81/25.33 | | (10) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 168.81/25.33 | | e3)
% 168.81/25.33 | |
% 168.81/25.33 | | BETA: splitting (10) gives:
% 168.81/25.33 | |
% 168.81/25.33 | | Case 1:
% 168.81/25.33 | | |
% 168.81/25.33 | | | (11) all_58_12 = e3 & op(e0, e3) = e3
% 168.81/25.33 | | |
% 168.81/25.33 | | | REF_CLOSE: (6), (7), (11) are inconsistent by sub-proof #110.
% 168.81/25.33 | | |
% 168.81/25.33 | | Case 2:
% 168.81/25.33 | | |
% 168.81/25.33 | | | (12) all_58_13 = e3 & op(e0, e2) = e3
% 168.81/25.33 | | |
% 168.81/25.33 | | | ALPHA: (12) implies:
% 168.81/25.33 | | | (13) all_58_13 = e3
% 168.81/25.33 | | |
% 168.81/25.33 | | | REF_CLOSE: (4), (6), (13) are inconsistent by sub-proof #708.
% 168.81/25.33 | | |
% 168.81/25.33 | | End of split
% 168.81/25.33 | |
% 168.81/25.33 | Case 2:
% 168.81/25.33 | |
% 168.81/25.33 | | (14) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 168.81/25.33 | | e3)
% 168.81/25.33 | |
% 168.81/25.33 | | BETA: splitting (14) gives:
% 168.81/25.33 | |
% 168.81/25.33 | | Case 1:
% 168.81/25.33 | | |
% 168.81/25.33 | | | (15) all_58_14 = e3 & op(e0, e1) = e3
% 168.81/25.33 | | |
% 168.81/25.33 | | | ALPHA: (15) implies:
% 168.81/25.33 | | | (16) op(e0, e1) = e3
% 168.81/25.33 | | |
% 168.81/25.33 | | | REF_CLOSE: (2), (3), (8), (16) are inconsistent by sub-proof #133.
% 168.81/25.33 | | |
% 168.81/25.33 | | Case 2:
% 168.81/25.33 | | |
% 168.81/25.33 | | | (17) all_58_15 = e3 & op(e0, e0) = e3
% 168.81/25.33 | | |
% 168.81/25.33 | | | ALPHA: (17) implies:
% 168.81/25.33 | | | (18) all_58_15 = e3
% 168.81/25.33 | | |
% 168.81/25.33 | | | REF_CLOSE: (1), (9), (18) are inconsistent by sub-proof #856.
% 168.81/25.33 | | |
% 168.81/25.33 | | End of split
% 168.81/25.33 | |
% 168.81/25.33 | End of split
% 168.81/25.33 |
% 168.81/25.33 End of proof
% 168.81/25.33
% 168.81/25.33 Sub-proof #109 shows that the following formulas are inconsistent:
% 168.81/25.33 ----------------------------------------------------------------
% 168.81/25.33 (1) ~ (e1 = e0)
% 168.81/25.33 (2) all_58_3 = e1
% 168.81/25.33 (3) op(e3, e2) = e2
% 168.81/25.33 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.33 (5) ~ (e2 = e0)
% 168.81/25.33 (6) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 168.81/25.33
% 168.81/25.33 Begin of proof
% 168.81/25.33 |
% 168.81/25.33 | BETA: splitting (6) gives:
% 168.81/25.33 |
% 168.81/25.33 | Case 1:
% 168.81/25.33 | |
% 168.81/25.33 | | (7) all_58_1 = e0 & op(e3, e2) = e0
% 168.81/25.33 | |
% 168.81/25.33 | | ALPHA: (7) implies:
% 168.81/25.33 | | (8) op(e3, e2) = e0
% 168.81/25.33 | |
% 168.81/25.33 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #953.
% 168.81/25.33 | |
% 168.81/25.33 | Case 2:
% 168.81/25.33 | |
% 168.81/25.33 | | (9) all_58_3 = e0 & op(e2, e2) = e0
% 168.81/25.33 | |
% 168.81/25.33 | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #927.
% 168.81/25.33 | |
% 168.81/25.33 | End of split
% 168.81/25.33 |
% 168.81/25.33 End of proof
% 168.81/25.33
% 168.81/25.33 Sub-proof #110 shows that the following formulas are inconsistent:
% 168.81/25.33 ----------------------------------------------------------------
% 168.81/25.33 (1) all_58_12 = e3 & op(e0, e3) = e3
% 168.81/25.33 (2) all_58_12 = e0
% 168.81/25.33 (3) ~ (e3 = e0)
% 168.81/25.33
% 168.81/25.33 Begin of proof
% 168.81/25.33 |
% 168.81/25.33 | ALPHA: (1) implies:
% 168.81/25.33 | (4) all_58_12 = e3
% 168.81/25.33 |
% 168.81/25.33 | COMBINE_EQS: (2), (4) imply:
% 168.81/25.33 | (5) e3 = e0
% 168.81/25.33 |
% 168.81/25.33 | REDUCE: (3), (5) imply:
% 168.81/25.33 | (6) $false
% 168.81/25.33 |
% 168.81/25.33 | CLOSE: (6) is inconsistent.
% 168.81/25.33 |
% 168.81/25.33 End of proof
% 168.81/25.33
% 168.81/25.33 Sub-proof #111 shows that the following formulas are inconsistent:
% 168.81/25.33 ----------------------------------------------------------------
% 168.81/25.33 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 168.81/25.33 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 168.81/25.33 (2) all_58_0 = e1
% 168.81/25.33 (3) ~ (e3 = e1)
% 168.81/25.33 (4) op(e3, e3) = e1
% 168.81/25.33 (5) ~ (e1 = e0)
% 168.81/25.33 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 168.81/25.33 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 168.81/25.33 (7) op(e0, e2) = e0
% 168.81/25.33 (8) all_58_6 = e2
% 168.81/25.33 (9) ~ (e3 = e0)
% 168.81/25.33 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 168.81/25.33 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.81/25.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.81/25.33 (12) ~ (e2 = e0)
% 168.81/25.33 (13) op(e0, e2) = all_52_7
% 168.81/25.33 (14) ~ (e3 = e2)
% 168.81/25.33
% 168.81/25.33 Begin of proof
% 168.81/25.33 |
% 168.81/25.33 | BETA: splitting (10) gives:
% 168.81/25.33 |
% 168.81/25.33 | Case 1:
% 168.81/25.33 | |
% 168.81/25.33 | | (15) all_58_12 = e1 & op(e0, e3) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | ALPHA: (15) implies:
% 168.81/25.33 | | (16) op(e0, e3) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (14), (16)
% 168.81/25.33 | | are inconsistent by sub-proof #124.
% 168.81/25.33 | |
% 168.81/25.33 | Case 2:
% 168.81/25.33 | |
% 168.81/25.33 | | (17) all_58_13 = e1 & op(e0, e2) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | ALPHA: (17) implies:
% 168.81/25.33 | | (18) op(e0, e2) = e1
% 168.81/25.33 | |
% 168.81/25.33 | | REF_CLOSE: (5), (7), (11), (13), (18) are inconsistent by sub-proof #889.
% 168.81/25.33 | |
% 168.81/25.33 | End of split
% 168.81/25.33 |
% 168.81/25.33 End of proof
% 168.81/25.33
% 168.81/25.33 Sub-proof #112 shows that the following formulas are inconsistent:
% 168.81/25.33 ----------------------------------------------------------------
% 168.81/25.33 (1) all_56_2 = e1
% 168.81/25.33 (2) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 =
% 168.81/25.33 e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4)))
% 168.81/25.33 & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.81/25.33 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.81/25.33 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.81/25.33 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 168.81/25.33 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.81/25.33 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.81/25.33 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.81/25.33 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.81/25.33 (3) all_56_14 = e3
% 168.81/25.33 (4) all_56_12 = e1
% 168.81/25.33 (5) all_56_5 = e2
% 168.81/25.33
% 168.81/25.33 Begin of proof
% 168.81/25.33 |
% 168.81/25.33 | BETA: splitting (2) gives:
% 168.81/25.33 |
% 168.81/25.33 | Case 1:
% 168.81/25.33 | |
% 168.81/25.33 | | (6) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.99/25.33 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 168.99/25.33 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.99/25.33 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | (
% 168.99/25.33 | | ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 168.99/25.33 | |
% 168.99/25.33 | | ALPHA: (6) implies:
% 168.99/25.33 | | (7) ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.33 | | $i(all_56_5))
% 168.99/25.33 | |
% 168.99/25.33 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #148.
% 168.99/25.33 | |
% 168.99/25.33 | Case 2:
% 168.99/25.33 | |
% 168.99/25.33 | | (8) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.99/25.33 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 168.99/25.33 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.99/25.33 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 168.99/25.33 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 168.99/25.33 | |
% 168.99/25.33 | | ALPHA: (8) implies:
% 168.99/25.33 | | (9) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.33 | | $i(all_56_2))
% 168.99/25.33 | |
% 168.99/25.33 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #485.
% 168.99/25.33 | |
% 168.99/25.33 | End of split
% 168.99/25.33 |
% 168.99/25.33 End of proof
% 168.99/25.33
% 168.99/25.33 Sub-proof #113 shows that the following formulas are inconsistent:
% 168.99/25.33 ----------------------------------------------------------------
% 168.99/25.33 (1) ~ (all_52_1 = e3)
% 168.99/25.33 (2) all_56_2 = e1
% 168.99/25.33 (3) all_56_14 = e3
% 168.99/25.33 (4) op(e2, e3) = all_52_1
% 168.99/25.33 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.99/25.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.99/25.33 (6) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 168.99/25.33 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 168.99/25.33 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.33 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.99/25.33 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.99/25.33 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 168.99/25.33 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.33 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.33 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.33 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.99/25.33
% 168.99/25.33 Begin of proof
% 168.99/25.33 |
% 168.99/25.33 | BETA: splitting (6) gives:
% 168.99/25.33 |
% 168.99/25.33 | Case 1:
% 168.99/25.33 | |
% 168.99/25.33 | | (7) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 168.99/25.33 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 168.99/25.33 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 168.99/25.33 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 168.99/25.33 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 168.99/25.33 | |
% 168.99/25.33 | | ALPHA: (7) implies:
% 168.99/25.33 | | (8) op(e2, e3) = e3
% 168.99/25.33 | |
% 168.99/25.33 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #989.
% 168.99/25.33 | |
% 168.99/25.33 | Case 2:
% 168.99/25.33 | |
% 168.99/25.33 | | (9) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.99/25.33 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 168.99/25.33 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.99/25.33 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 168.99/25.33 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 168.99/25.33 | |
% 168.99/25.33 | | ALPHA: (9) implies:
% 168.99/25.33 | | (10) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.33 | | $i(all_56_2))
% 168.99/25.33 | |
% 168.99/25.33 | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #485.
% 168.99/25.33 | |
% 168.99/25.33 | End of split
% 168.99/25.33 |
% 168.99/25.33 End of proof
% 168.99/25.33
% 168.99/25.33 Sub-proof #114 shows that the following formulas are inconsistent:
% 168.99/25.33 ----------------------------------------------------------------
% 168.99/25.33 (1) all_58_13 = e1 & op(e0, e2) = e1
% 168.99/25.33 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.99/25.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.99/25.33 (3) op(e0, e2) = all_52_7
% 168.99/25.33 (4) ~ (all_52_7 = e1)
% 168.99/25.34
% 168.99/25.34 Begin of proof
% 168.99/25.34 |
% 168.99/25.34 | ALPHA: (1) implies:
% 168.99/25.34 | (5) op(e0, e2) = e1
% 168.99/25.34 |
% 168.99/25.34 | GROUND_INST: instantiating (2) with all_52_7, e1, e2, e0, simplifying with
% 168.99/25.34 | (3), (5) gives:
% 168.99/25.34 | (6) all_52_7 = e1
% 168.99/25.34 |
% 168.99/25.34 | REDUCE: (4), (6) imply:
% 168.99/25.34 | (7) $false
% 168.99/25.34 |
% 168.99/25.34 | CLOSE: (7) is inconsistent.
% 168.99/25.34 |
% 168.99/25.34 End of proof
% 168.99/25.34
% 168.99/25.34 Sub-proof #115 shows that the following formulas are inconsistent:
% 168.99/25.34 ----------------------------------------------------------------
% 168.99/25.34 (1) all_58_11 = e3 & op(e1, e0) = e3
% 168.99/25.34 (2) all_58_11 = e1
% 168.99/25.34 (3) ~ (e3 = e1)
% 168.99/25.34
% 168.99/25.34 Begin of proof
% 168.99/25.34 |
% 168.99/25.34 | ALPHA: (1) implies:
% 168.99/25.34 | (4) all_58_11 = e3
% 168.99/25.34 |
% 168.99/25.34 | COMBINE_EQS: (2), (4) imply:
% 168.99/25.34 | (5) e3 = e1
% 168.99/25.34 |
% 168.99/25.34 | REDUCE: (3), (5) imply:
% 168.99/25.34 | (6) $false
% 168.99/25.34 |
% 168.99/25.34 | CLOSE: (6) is inconsistent.
% 168.99/25.34 |
% 168.99/25.34 End of proof
% 168.99/25.34
% 168.99/25.34 Sub-proof #116 shows that the following formulas are inconsistent:
% 168.99/25.34 ----------------------------------------------------------------
% 168.99/25.34 (1) ~ (e3 = e1)
% 168.99/25.34 (2) ~ (e1 = e0)
% 168.99/25.34 (3) all_58_10 = e3
% 168.99/25.34 (4) all_58_3 = e1
% 168.99/25.34 (5) ~ (e3 = e0)
% 168.99/25.34 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 168.99/25.34 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 168.99/25.34 (7) ~ (e2 = e0)
% 168.99/25.34 (8) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 168.99/25.34 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 168.99/25.34 (9) ~ (e2 = e1)
% 168.99/25.34 (10) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 168.99/25.34 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 168.99/25.34 (11) all_58_2 = e0
% 168.99/25.34 (12) e3 = e1
% 168.99/25.34 (13) ~ (e3 = e2)
% 168.99/25.34
% 168.99/25.34 Begin of proof
% 168.99/25.34 |
% 168.99/25.34 | SIMP: (12) implies:
% 168.99/25.34 | (14) e3 = e1
% 168.99/25.34 |
% 168.99/25.34 | COMBINE_EQS: (3), (14) imply:
% 168.99/25.34 | (15) all_58_10 = e1
% 168.99/25.34 |
% 168.99/25.34 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (13), (15) are
% 168.99/25.34 | inconsistent by sub-proof #128.
% 168.99/25.34 |
% 168.99/25.34 End of proof
% 168.99/25.34
% 168.99/25.34 Sub-proof #117 shows that the following formulas are inconsistent:
% 168.99/25.34 ----------------------------------------------------------------
% 168.99/25.34 (1) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 168.99/25.34 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 168.99/25.34 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.34 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.99/25.34 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.99/25.34 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 168.99/25.34 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.34 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.34 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.34 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 168.99/25.34 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 168.99/25.34 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.34 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.34 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.34 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.99/25.34 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 168.99/25.34 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.34 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.34 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.34 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.99/25.34 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 168.99/25.34 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.34 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.34 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.34 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 168.99/25.34 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 168.99/25.34 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.34 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.34 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.99/25.34 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.99/25.34 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 168.99/25.34 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.34 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.34 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.34 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 168.99/25.34 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 168.99/25.34 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.34 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.34 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.99/25.34 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.99/25.34 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 168.99/25.34 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.34 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.34 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.34 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 168.99/25.34 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.99/25.34 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.99/25.34 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 168.99/25.34 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.99/25.34 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 168.99/25.34 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.99/25.34 (2) ~ (all_52_14 = all_4_2)
% 168.99/25.34 (3) all_58_9 = e2
% 168.99/25.34 (4) ~ (all_56_14 = e0) | (all_56_13 = e1 & op(e1, e0) = e1)
% 168.99/25.34 (5) ~ (all_6_2 = e3)
% 168.99/25.34 (6) ~ (all_52_12 = e1)
% 168.99/25.34 (7) ~ (all_52_1 = all_52_13)
% 168.99/25.34 (8) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 168.99/25.34 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 168.99/25.34 (9) ~ (e3 = e1)
% 168.99/25.34 (10) all_56_14 = all_6_2
% 168.99/25.34 (11) op(e3, e3) = e1
% 168.99/25.34 (12) op(e3, e0) = all_52_12
% 168.99/25.34 (13) all_56_4 = e3
% 168.99/25.34 (14) op(e3, e1) = all_52_8
% 168.99/25.34 (15) ~ (e1 = e0)
% 168.99/25.34 (16) all_56_10 = e1
% 168.99/25.34 (17) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 168.99/25.34 (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 168.99/25.34 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 168.99/25.34 (19) op(e2, e3) = all_52_1
% 168.99/25.34 (20) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 168.99/25.34 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 168.99/25.34 (21) ~ (all_52_12 = all_4_2)
% 168.99/25.34 (22) op(e3, e0) = e2
% 168.99/25.34 (23) ~ (all_52_14 = all_6_2)
% 168.99/25.34 (24) ~ (all_6_2 = e2)
% 168.99/25.34 (25) op(e1, e1) = all_6_2
% 168.99/25.34 (26) all_56_15 = all_4_2
% 168.99/25.34 (27) ~ (e3 = e0)
% 168.99/25.34 (28) ~ (all_52_8 = e1)
% 168.99/25.34 (29) ~ (all_52_13 = all_52_14)
% 168.99/25.34 (30) all_56_12 = e1
% 168.99/25.34 (31) ~ (all_52_8 = e2)
% 168.99/25.34 (32) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.99/25.34 (33) all_58_14 = e3
% 168.99/25.34 (34) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 168.99/25.34 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 168.99/25.34 (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 168.99/25.34 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 168.99/25.34 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.99/25.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.99/25.34 (37) ~ (e2 = e0)
% 168.99/25.34 (38) op(e1, e0) = all_52_14
% 168.99/25.34 (39) op(e2, e1) = e2
% 168.99/25.34 (40) ~ (all_52_13 = all_4_2)
% 168.99/25.34 (41) ~ (all_52_12 = all_52_13)
% 168.99/25.34 (42) all_56_5 = e2
% 168.99/25.34 (43) ~ (e2 = e1)
% 168.99/25.34 (44) all_58_9 = e3 & op(e3, e0) = e3
% 168.99/25.34 (45) op(e3, e2) = all_52_4
% 168.99/25.34 (46) all_54_7 = all_52_13
% 168.99/25.34 (47) ~ (all_52_4 = e1)
% 168.99/25.34 (48) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 168.99/25.34 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 168.99/25.34 (49) op(e2, e0) = all_52_13
% 168.99/25.34 (50) op(e1, e0) = e1
% 168.99/25.34 (51) ~ (e3 = e2)
% 168.99/25.34
% 168.99/25.34 Begin of proof
% 168.99/25.34 |
% 168.99/25.34 | ALPHA: (44) implies:
% 168.99/25.34 | (52) all_58_9 = e3
% 168.99/25.34 |
% 168.99/25.34 | COMBINE_EQS: (3), (52) imply:
% 168.99/25.34 | (53) e3 = e2
% 168.99/25.34 |
% 168.99/25.34 | COMBINE_EQS: (33), (53) imply:
% 168.99/25.34 | (54) all_58_14 = e2
% 168.99/25.34 |
% 168.99/25.34 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 168.99/25.34 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 168.99/25.34 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (34), (35),
% 168.99/25.34 | (36), (37), (38), (39), (40), (41), (42), (43), (45), (46), (47),
% 168.99/25.34 | (48), (49), (50), (51), (54) are inconsistent by sub-proof #118.
% 168.99/25.34 |
% 168.99/25.34 End of proof
% 168.99/25.34
% 168.99/25.34 Sub-proof #118 shows that the following formulas are inconsistent:
% 168.99/25.34 ----------------------------------------------------------------
% 168.99/25.34 (1) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 168.99/25.34 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 168.99/25.34 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.34 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.99/25.34 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.99/25.34 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 168.99/25.34 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.34 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.34 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.34 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 168.99/25.34 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 168.99/25.34 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.34 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.34 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.34 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.99/25.34 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 168.99/25.34 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.34 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.34 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.34 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.99/25.34 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 168.99/25.34 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.34 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.34 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.34 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 168.99/25.34 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 168.99/25.34 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.34 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.34 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.99/25.34 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.99/25.34 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 168.99/25.34 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.34 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.34 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.34 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 168.99/25.34 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 168.99/25.34 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.34 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.34 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.99/25.34 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.99/25.34 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 168.99/25.34 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.34 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.34 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.34 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 168.99/25.34 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.99/25.34 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.99/25.34 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 168.99/25.34 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.99/25.34 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 168.99/25.34 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.99/25.34 (2) all_58_14 = e2
% 168.99/25.34 (3) ~ (all_52_14 = all_4_2)
% 168.99/25.34 (4) all_58_9 = e2
% 168.99/25.34 (5) ~ (all_56_14 = e0) | (all_56_13 = e1 & op(e1, e0) = e1)
% 168.99/25.34 (6) ~ (all_6_2 = e3)
% 168.99/25.34 (7) ~ (all_52_12 = e1)
% 168.99/25.34 (8) ~ (all_52_1 = all_52_13)
% 168.99/25.34 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 168.99/25.34 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 168.99/25.34 (10) ~ (e3 = e1)
% 168.99/25.34 (11) all_56_14 = all_6_2
% 168.99/25.34 (12) op(e3, e3) = e1
% 168.99/25.34 (13) op(e3, e0) = all_52_12
% 168.99/25.34 (14) all_56_4 = e3
% 168.99/25.34 (15) op(e3, e1) = all_52_8
% 168.99/25.34 (16) ~ (e1 = e0)
% 168.99/25.34 (17) all_56_10 = e1
% 168.99/25.34 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 168.99/25.34 (19) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 168.99/25.34 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 168.99/25.34 (20) op(e2, e3) = all_52_1
% 168.99/25.34 (21) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 168.99/25.34 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 168.99/25.34 (22) ~ (all_52_12 = all_4_2)
% 168.99/25.34 (23) op(e3, e0) = e2
% 168.99/25.34 (24) ~ (all_52_14 = all_6_2)
% 168.99/25.34 (25) ~ (all_6_2 = e2)
% 168.99/25.34 (26) op(e1, e1) = all_6_2
% 168.99/25.34 (27) all_56_15 = all_4_2
% 168.99/25.34 (28) ~ (e3 = e0)
% 168.99/25.34 (29) ~ (all_52_8 = e1)
% 168.99/25.34 (30) ~ (all_52_13 = all_52_14)
% 168.99/25.34 (31) all_56_12 = e1
% 168.99/25.34 (32) ~ (all_52_8 = e2)
% 168.99/25.34 (33) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.99/25.34 (34) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 168.99/25.34 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 168.99/25.34 (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 168.99/25.34 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 168.99/25.34 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.99/25.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.99/25.34 (37) ~ (e2 = e0)
% 168.99/25.34 (38) op(e1, e0) = all_52_14
% 168.99/25.34 (39) op(e2, e1) = e2
% 168.99/25.34 (40) ~ (all_52_13 = all_4_2)
% 168.99/25.34 (41) ~ (all_52_12 = all_52_13)
% 168.99/25.34 (42) all_56_5 = e2
% 168.99/25.34 (43) ~ (e2 = e1)
% 168.99/25.34 (44) op(e3, e2) = all_52_4
% 168.99/25.34 (45) all_54_7 = all_52_13
% 168.99/25.34 (46) ~ (all_52_4 = e1)
% 168.99/25.34 (47) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 168.99/25.34 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 168.99/25.34 (48) op(e2, e0) = all_52_13
% 168.99/25.34 (49) op(e1, e0) = e1
% 168.99/25.34 (50) ~ (e3 = e2)
% 168.99/25.34
% 168.99/25.34 Begin of proof
% 168.99/25.34 |
% 168.99/25.34 | BETA: splitting (19) gives:
% 168.99/25.34 |
% 168.99/25.34 | Case 1:
% 168.99/25.34 | |
% 168.99/25.34 | | (51) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 168.99/25.34 | | e3)
% 168.99/25.35 | |
% 168.99/25.35 | | BETA: splitting (51) gives:
% 168.99/25.35 | |
% 168.99/25.35 | | Case 1:
% 168.99/25.35 | | |
% 168.99/25.35 | | | (52) all_58_4 = e3 & op(e3, e1) = e3
% 168.99/25.35 | | |
% 168.99/25.35 | | | ALPHA: (52) implies:
% 168.99/25.35 | | | (53) all_58_4 = e3
% 168.99/25.35 | | |
% 168.99/25.35 | | | BETA: splitting (34) gives:
% 168.99/25.35 | | |
% 168.99/25.35 | | | Case 1:
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | (54) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 168.99/25.35 | | | | = e1)
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | BETA: splitting (54) gives:
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | Case 1:
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | (55) all_58_0 = e1 & op(e3, e3) = e1
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | ALPHA: (55) implies:
% 168.99/25.35 | | | | | (56) all_58_0 = e1
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | BETA: splitting (21) gives:
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | Case 1:
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | (57) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2,
% 168.99/25.35 | | | | | | e1) = e0)
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | BETA: splitting (57) gives:
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | Case 1:
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | (58) all_58_4 = e0 & op(e3, e1) = e0
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | ALPHA: (58) implies:
% 168.99/25.35 | | | | | | | (59) all_58_4 = e0
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | REF_CLOSE: (28), (53), (59) are inconsistent by sub-proof #894.
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | Case 2:
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | (60) all_58_5 = e0 & op(e2, e1) = e0
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | REF_CLOSE: (36), (37), (39), (60) are inconsistent by sub-proof
% 168.99/25.35 | | | | | | | #151.
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | End of split
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | Case 2:
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | (61) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0,
% 168.99/25.35 | | | | | | e1) = e0)
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | BETA: splitting (61) gives:
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | Case 1:
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | (62) all_58_8 = e0 & op(e1, e1) = e0
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | ALPHA: (62) implies:
% 168.99/25.35 | | | | | | | (63) op(e1, e1) = e0
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 168.99/25.35 | | | | | | | (12), (13), (14), (15), (16), (17), (18), (20), (22),
% 168.99/25.35 | | | | | | | (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 168.99/25.35 | | | | | | | (32), (33), (34), (35), (36), (37), (38), (40), (41),
% 168.99/25.35 | | | | | | | (42), (43), (44), (45), (47), (48), (49), (50), (53),
% 168.99/25.35 | | | | | | | (56), (63) are inconsistent by sub-proof #119.
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | Case 2:
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | (64) all_58_14 = e0 & op(e0, e1) = e0
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | REF_CLOSE: (2), (37), (64) are inconsistent by sub-proof #858.
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | End of split
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | End of split
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | Case 2:
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | (65) all_58_1 = e1 & op(e3, e2) = e1
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REF_CLOSE: (36), (44), (46), (65) are inconsistent by sub-proof #863.
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | End of split
% 168.99/25.35 | | | |
% 168.99/25.35 | | | Case 2:
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | (66) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 168.99/25.35 | | | | = e1)
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | BETA: splitting (66) gives:
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | Case 1:
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | (67) all_58_4 = e1 & op(e3, e1) = e1
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REF_CLOSE: (10), (53), (67) are inconsistent by sub-proof #702.
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | Case 2:
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | (68) all_58_9 = e1 & op(e3, e0) = e1
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | ALPHA: (68) implies:
% 168.99/25.35 | | | | | (69) all_58_9 = e1
% 168.99/25.35 | | | | | (70) op(e3, e0) = e1
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REF_CLOSE: (2), (6), (9), (10), (12), (15), (16), (19), (26), (28),
% 168.99/25.35 | | | | | (35), (36), (37), (39), (43), (47), (50), (69), (70) are
% 168.99/25.35 | | | | | inconsistent by sub-proof #135.
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | End of split
% 168.99/25.35 | | | |
% 168.99/25.35 | | | End of split
% 168.99/25.35 | | |
% 168.99/25.35 | | Case 2:
% 168.99/25.35 | | |
% 168.99/25.35 | | | (71) all_58_5 = e3 & op(e2, e1) = e3
% 168.99/25.35 | | |
% 168.99/25.35 | | | REF_CLOSE: (36), (39), (50), (71) are inconsistent by sub-proof #150.
% 168.99/25.35 | | |
% 168.99/25.35 | | End of split
% 168.99/25.35 | |
% 168.99/25.35 | Case 2:
% 168.99/25.35 | |
% 168.99/25.35 | | (72) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 168.99/25.35 | | e3)
% 168.99/25.35 | |
% 168.99/25.35 | | BETA: splitting (72) gives:
% 168.99/25.35 | |
% 168.99/25.35 | | Case 1:
% 168.99/25.35 | | |
% 168.99/25.35 | | | (73) all_58_8 = e3 & op(e1, e1) = e3
% 168.99/25.35 | | |
% 168.99/25.35 | | | REF_CLOSE: (6), (26), (36), (73) are inconsistent by sub-proof #961.
% 168.99/25.35 | | |
% 168.99/25.35 | | Case 2:
% 168.99/25.35 | | |
% 168.99/25.35 | | | (74) all_58_14 = e3 & op(e0, e1) = e3
% 168.99/25.35 | | |
% 168.99/25.35 | | | REF_CLOSE: (2), (50), (74) are inconsistent by sub-proof #809.
% 168.99/25.35 | | |
% 168.99/25.35 | | End of split
% 168.99/25.35 | |
% 168.99/25.35 | End of split
% 168.99/25.35 |
% 168.99/25.35 End of proof
% 168.99/25.35
% 168.99/25.35 Sub-proof #119 shows that the following formulas are inconsistent:
% 168.99/25.35 ----------------------------------------------------------------
% 168.99/25.35 (1) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 168.99/25.35 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 168.99/25.35 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.35 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.99/25.35 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.99/25.35 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 168.99/25.35 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.35 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.35 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.35 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 168.99/25.35 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 168.99/25.35 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.35 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.35 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.35 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.99/25.35 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 168.99/25.35 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.35 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.35 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.35 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.99/25.35 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 168.99/25.35 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.35 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.35 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.35 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 168.99/25.35 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 168.99/25.35 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.35 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.35 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.99/25.35 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.99/25.35 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 168.99/25.35 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.35 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.35 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.35 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 168.99/25.35 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 168.99/25.35 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.35 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.35 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 168.99/25.35 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.99/25.35 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 168.99/25.35 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.35 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.35 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.35 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 168.99/25.35 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.99/25.35 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.99/25.35 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 168.99/25.35 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.99/25.35 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 168.99/25.35 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.99/25.35 (2) ~ (all_52_14 = all_4_2)
% 168.99/25.35 (3) all_58_9 = e2
% 168.99/25.35 (4) all_58_0 = e1
% 168.99/25.35 (5) ~ (all_56_14 = e0) | (all_56_13 = e1 & op(e1, e0) = e1)
% 168.99/25.35 (6) ~ (all_6_2 = e3)
% 168.99/25.35 (7) ~ (all_52_12 = e1)
% 168.99/25.35 (8) ~ (all_52_1 = all_52_13)
% 168.99/25.35 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 168.99/25.35 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 168.99/25.35 (10) ~ (e3 = e1)
% 168.99/25.35 (11) all_56_14 = all_6_2
% 168.99/25.35 (12) op(e3, e3) = e1
% 168.99/25.35 (13) op(e3, e0) = all_52_12
% 168.99/25.35 (14) all_56_4 = e3
% 168.99/25.35 (15) op(e3, e1) = all_52_8
% 168.99/25.35 (16) ~ (e1 = e0)
% 168.99/25.35 (17) all_56_10 = e1
% 168.99/25.35 (18) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 168.99/25.35 (19) op(e2, e3) = all_52_1
% 168.99/25.35 (20) ~ (all_52_12 = all_4_2)
% 168.99/25.35 (21) op(e3, e0) = e2
% 168.99/25.35 (22) ~ (all_52_14 = all_6_2)
% 168.99/25.35 (23) ~ (all_6_2 = e2)
% 168.99/25.35 (24) op(e1, e1) = all_6_2
% 168.99/25.35 (25) all_56_15 = all_4_2
% 168.99/25.35 (26) ~ (e3 = e0)
% 168.99/25.35 (27) ~ (all_52_8 = e1)
% 168.99/25.35 (28) ~ (all_52_13 = all_52_14)
% 168.99/25.35 (29) all_56_12 = e1
% 168.99/25.35 (30) ~ (all_52_8 = e2)
% 168.99/25.35 (31) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.99/25.35 (32) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 168.99/25.35 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 168.99/25.35 (33) all_58_4 = e3
% 168.99/25.35 (34) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 168.99/25.35 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 168.99/25.35 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 168.99/25.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 168.99/25.35 (36) ~ (e2 = e0)
% 168.99/25.35 (37) op(e1, e0) = all_52_14
% 168.99/25.35 (38) ~ (all_52_13 = all_4_2)
% 168.99/25.35 (39) ~ (all_52_12 = all_52_13)
% 168.99/25.35 (40) all_56_5 = e2
% 168.99/25.35 (41) op(e1, e1) = e0
% 168.99/25.35 (42) ~ (e2 = e1)
% 168.99/25.35 (43) op(e3, e2) = all_52_4
% 168.99/25.35 (44) all_54_7 = all_52_13
% 168.99/25.35 (45) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 168.99/25.35 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 168.99/25.35 (46) op(e2, e0) = all_52_13
% 168.99/25.35 (47) op(e1, e0) = e1
% 168.99/25.35 (48) ~ (e3 = e2)
% 168.99/25.35
% 168.99/25.35 Begin of proof
% 168.99/25.35 |
% 168.99/25.35 | BETA: splitting (9) gives:
% 168.99/25.35 |
% 168.99/25.35 | Case 1:
% 168.99/25.35 | |
% 168.99/25.35 | | (49) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 168.99/25.35 | | e0)
% 168.99/25.35 | |
% 168.99/25.35 | | BETA: splitting (49) gives:
% 168.99/25.35 | |
% 168.99/25.35 | | Case 1:
% 168.99/25.35 | | |
% 168.99/25.35 | | | (50) all_58_0 = e0 & op(e3, e3) = e0
% 168.99/25.35 | | |
% 168.99/25.35 | | | ALPHA: (50) implies:
% 168.99/25.35 | | | (51) op(e3, e3) = e0
% 168.99/25.35 | | |
% 168.99/25.35 | | | REF_CLOSE: (12), (16), (35), (51) are inconsistent by sub-proof #907.
% 168.99/25.35 | | |
% 168.99/25.35 | | Case 2:
% 168.99/25.35 | | |
% 168.99/25.35 | | | (52) all_58_1 = e0 & op(e3, e2) = e0
% 168.99/25.35 | | |
% 168.99/25.35 | | | ALPHA: (52) implies:
% 168.99/25.35 | | | (53) all_58_1 = e0
% 168.99/25.35 | | | (54) op(e3, e2) = e0
% 168.99/25.35 | | |
% 168.99/25.35 | | | BETA: splitting (34) gives:
% 168.99/25.35 | | |
% 168.99/25.35 | | | Case 1:
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | (55) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 168.99/25.35 | | | | = e3)
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | BETA: splitting (55) gives:
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | Case 1:
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | (56) all_58_0 = e3 & op(e3, e3) = e3
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | ALPHA: (56) implies:
% 168.99/25.35 | | | | | (57) all_58_0 = e3
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | COMBINE_EQS: (4), (57) imply:
% 168.99/25.35 | | | | | (58) e3 = e1
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | SIMP: (58) implies:
% 168.99/25.35 | | | | | (59) e3 = e1
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | COMBINE_EQS: (33), (59) imply:
% 168.99/25.35 | | | | | (60) all_58_4 = e1
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REF_CLOSE: (3), (4), (9), (10), (12), (16), (26), (34), (35), (36),
% 168.99/25.35 | | | | | (48), (60) are inconsistent by sub-proof #788.
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | Case 2:
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | (61) all_58_1 = e3 & op(e3, e2) = e3
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REF_CLOSE: (26), (53), (61) are inconsistent by sub-proof #803.
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | End of split
% 168.99/25.35 | | | |
% 168.99/25.35 | | | Case 2:
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | (62) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 168.99/25.35 | | | | = e3)
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | BETA: splitting (62) gives:
% 168.99/25.35 | | | |
% 168.99/25.35 | | | | Case 1:
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | (63) all_58_4 = e3 & op(e3, e1) = e3
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | ALPHA: (63) implies:
% 168.99/25.35 | | | | | (64) op(e3, e1) = e3
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | GROUND_INST: instantiating (35) with all_52_14, e1, e0, e1,
% 168.99/25.35 | | | | | simplifying with (37), (47) gives:
% 168.99/25.35 | | | | | (65) all_52_14 = e1
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | GROUND_INST: instantiating (35) with all_6_2, e0, e1, e1, simplifying
% 168.99/25.35 | | | | | with (24), (41) gives:
% 168.99/25.35 | | | | | (66) all_6_2 = e0
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | GROUND_INST: instantiating (35) with all_52_12, e2, e0, e3,
% 168.99/25.35 | | | | | simplifying with (13), (21) gives:
% 168.99/25.35 | | | | | (67) all_52_12 = e2
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | GROUND_INST: instantiating (35) with all_52_8, e3, e1, e3, simplifying
% 168.99/25.35 | | | | | with (15), (64) gives:
% 168.99/25.35 | | | | | (68) all_52_8 = e3
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | GROUND_INST: instantiating (35) with all_52_4, e0, e2, e3, simplifying
% 168.99/25.35 | | | | | with (43), (54) gives:
% 168.99/25.35 | | | | | (69) all_52_4 = e0
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | COMBINE_EQS: (11), (66) imply:
% 168.99/25.35 | | | | | (70) all_56_14 = e0
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REDUCE: (39), (67) imply:
% 168.99/25.35 | | | | | (71) ~ (all_52_13 = e2)
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | SIMP: (71) implies:
% 168.99/25.35 | | | | | (72) ~ (all_52_13 = e2)
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REDUCE: (20), (67) imply:
% 168.99/25.35 | | | | | (73) ~ (all_4_2 = e2)
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | SIMP: (73) implies:
% 168.99/25.35 | | | | | (74) ~ (all_4_2 = e2)
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REDUCE: (28), (65) imply:
% 168.99/25.35 | | | | | (75) ~ (all_52_13 = e1)
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REDUCE: (2), (65) imply:
% 168.99/25.35 | | | | | (76) ~ (all_4_2 = e1)
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | SIMP: (76) implies:
% 168.99/25.35 | | | | | (77) ~ (all_4_2 = e1)
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REDUCE: (6), (66) imply:
% 168.99/25.35 | | | | | (78) ~ (e3 = e0)
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | REDUCE: (23), (66) imply:
% 168.99/25.35 | | | | | (79) ~ (e2 = e0)
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | BETA: splitting (5) gives:
% 168.99/25.35 | | | | |
% 168.99/25.35 | | | | | Case 1:
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | (80) ~ (all_56_14 = e0)
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | REDUCE: (70), (80) imply:
% 168.99/25.35 | | | | | | (81) $false
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | CLOSE: (81) is inconsistent.
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | Case 2:
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | (82) all_56_13 = e1 & op(e1, e0) = e1
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | ALPHA: (82) implies:
% 168.99/25.35 | | | | | | (83) all_56_13 = e1
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | BETA: splitting (31) gives:
% 168.99/25.35 | | | | | |
% 168.99/25.35 | | | | | | Case 1:
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | (84) all_56_10 = e3
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | COMBINE_EQS: (17), (84) imply:
% 168.99/25.35 | | | | | | | (85) e3 = e1
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | COMBINE_EQS: (33), (85) imply:
% 168.99/25.35 | | | | | | | (86) all_58_4 = e1
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | REF_CLOSE: (3), (4), (9), (10), (12), (16), (26), (34), (35),
% 168.99/25.35 | | | | | | | (36), (48), (86) are inconsistent by sub-proof #788.
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | Case 2:
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | (87) ~ (all_56_10 = e3)
% 168.99/25.35 | | | | | | | (88) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | REDUCE: (17), (87) imply:
% 168.99/25.35 | | | | | | | (89) ~ (e3 = e1)
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | BETA: splitting (88) gives:
% 168.99/25.35 | | | | | | |
% 168.99/25.35 | | | | | | | Case 1:
% 168.99/25.35 | | | | | | | |
% 168.99/25.35 | | | | | | | | (90) all_56_12 = e2
% 168.99/25.35 | | | | | | | |
% 168.99/25.35 | | | | | | | | COMBINE_EQS: (29), (90) imply:
% 168.99/25.35 | | | | | | | | (91) e2 = e1
% 168.99/25.35 | | | | | | | |
% 168.99/25.35 | | | | | | | | COMBINE_EQS: (3), (91) imply:
% 168.99/25.35 | | | | | | | | (92) all_58_9 = e1
% 168.99/25.35 | | | | | | | |
% 168.99/25.35 | | | | | | | | REF_CLOSE: (10), (12), (15), (26), (34), (35), (36), (42), (45),
% 168.99/25.35 | | | | | | | | (48), (53), (54), (64), (92) are inconsistent by
% 168.99/25.35 | | | | | | | | sub-proof #137.
% 168.99/25.35 | | | | | | | |
% 168.99/25.35 | | | | | | | Case 2:
% 168.99/25.35 | | | | | | | |
% 168.99/25.35 | | | | | | | | (93) ~ (all_56_12 = e2)
% 168.99/25.35 | | | | | | | | (94) all_56_14 = e1 | all_56_15 = e0
% 168.99/25.35 | | | | | | | |
% 168.99/25.35 | | | | | | | | REDUCE: (29), (93) imply:
% 168.99/25.35 | | | | | | | | (95) ~ (e2 = e1)
% 168.99/25.35 | | | | | | | |
% 168.99/25.35 | | | | | | | | BETA: splitting (94) gives:
% 168.99/25.35 | | | | | | | |
% 168.99/25.35 | | | | | | | | Case 1:
% 168.99/25.35 | | | | | | | | |
% 168.99/25.35 | | | | | | | | | (96) all_56_14 = e1
% 168.99/25.35 | | | | | | | | |
% 168.99/25.35 | | | | | | | | | COMBINE_EQS: (70), (96) imply:
% 168.99/25.35 | | | | | | | | | (97) e1 = e0
% 168.99/25.35 | | | | | | | | |
% 168.99/25.35 | | | | | | | | | REDUCE: (16), (97) imply:
% 168.99/25.35 | | | | | | | | | (98) $false
% 168.99/25.35 | | | | | | | | |
% 168.99/25.35 | | | | | | | | | CLOSE: (98) is inconsistent.
% 168.99/25.35 | | | | | | | | |
% 168.99/25.35 | | | | | | | | Case 2:
% 168.99/25.35 | | | | | | | | |
% 168.99/25.36 | | | | | | | | | (99) all_56_15 = e0
% 168.99/25.36 | | | | | | | | |
% 168.99/25.36 | | | | | | | | | COMBINE_EQS: (25), (99) imply:
% 168.99/25.36 | | | | | | | | | (100) all_4_2 = e0
% 168.99/25.36 | | | | | | | | |
% 168.99/25.36 | | | | | | | | | REDUCE: (38), (100) imply:
% 168.99/25.36 | | | | | | | | | (101) ~ (all_52_13 = e0)
% 168.99/25.36 | | | | | | | | |
% 168.99/25.36 | | | | | | | | | REDUCE: (77), (100) imply:
% 168.99/25.36 | | | | | | | | | (102) ~ (e1 = e0)
% 168.99/25.36 | | | | | | | | |
% 168.99/25.36 | | | | | | | | | BETA: splitting (1) gives:
% 168.99/25.36 | | | | | | | | |
% 168.99/25.36 | | | | | | | | | Case 1:
% 168.99/25.36 | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | (103) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 168.99/25.36 | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.99/25.36 | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))) |
% 168.99/25.36 | | | | | | | | | | (all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 168.99/25.36 | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.99/25.36 | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))) |
% 168.99/25.36 | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 168.99/25.36 | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.99/25.36 | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.99/25.36 | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) |
% 168.99/25.36 | | | | | | | | | | (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 168.99/25.36 | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.99/25.36 | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.99/25.36 | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) |
% 168.99/25.36 | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 168.99/25.36 | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.99/25.36 | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | e3) = all_56_6 & $i(all_56_6))))
% 168.99/25.36 | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | BETA: splitting (103) gives:
% 168.99/25.36 | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | Case 1:
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | (104) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 168.99/25.36 | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.99/25.36 | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 168.99/25.36 | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.99/25.36 | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.99/25.36 | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.36 | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | BETA: splitting (104) gives:
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | Case 1:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | (105) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 168.99/25.36 | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.99/25.36 | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | ALPHA: (105) implies:
% 168.99/25.36 | | | | | | | | | | | | (106) op(e2, e3) = e3
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | BETA: splitting (18) gives:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | Case 1:
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | (107) all_54_7 = e3
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | COMBINE_EQS: (44), (107) imply:
% 168.99/25.36 | | | | | | | | | | | | | (108) all_52_13 = e3
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | SIMP: (108) implies:
% 168.99/25.36 | | | | | | | | | | | | | (109) all_52_13 = e3
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | REDUCE: (8), (109) imply:
% 168.99/25.36 | | | | | | | | | | | | | (110) ~ (all_52_1 = e3)
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | REF_CLOSE: (19), (35), (106), (110) are inconsistent by
% 168.99/25.36 | | | | | | | | | | | | | sub-proof #989.
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | Case 2:
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | (111) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | REF_CLOSE: (44), (72), (75), (101), (111) are inconsistent by
% 168.99/25.36 | | | | | | | | | | | | | sub-proof #615.
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | End of split
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | Case 2:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | (112) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 168.99/25.36 | | | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.99/25.36 | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | ALPHA: (112) implies:
% 168.99/25.36 | | | | | | | | | | | | (113) op(e3, e2) = e2
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | REF_CLOSE: (35), (36), (54), (113) are inconsistent by
% 168.99/25.36 | | | | | | | | | | | | sub-proof #953.
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | End of split
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | Case 2:
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | (114) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 168.99/25.36 | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.99/25.36 | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 168.99/25.36 | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.99/25.36 | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.99/25.36 | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.36 | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 168.99/25.36 | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 168.99/25.36 | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 168.99/25.36 | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_6))))
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | BETA: splitting (114) gives:
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | Case 1:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | (115) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 168.99/25.36 | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.99/25.36 | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.99/25.36 | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | ALPHA: (115) implies:
% 168.99/25.36 | | | | | | | | | | | | (116) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 168.99/25.36 | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | REF_CLOSE: (14), (17), (116) are inconsistent by sub-proof
% 168.99/25.36 | | | | | | | | | | | | #795.
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | Case 2:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | (117) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 168.99/25.36 | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.99/25.36 | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.99/25.36 | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.36 | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.99/25.36 | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.99/25.36 | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.99/25.36 | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.36 | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | BETA: splitting (117) gives:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | Case 1:
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | (118) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 168.99/25.36 | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.99/25.36 | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.99/25.36 | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | ALPHA: (118) implies:
% 168.99/25.36 | | | | | | | | | | | | | (119) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 168.99/25.36 | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | REF_CLOSE: (14), (17), (119) are inconsistent by sub-proof
% 168.99/25.36 | | | | | | | | | | | | | #795.
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | Case 2:
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | (120) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 168.99/25.36 | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.99/25.36 | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | ALPHA: (120) implies:
% 168.99/25.36 | | | | | | | | | | | | | (121) all_56_4 = e1
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | COMBINE_EQS: (14), (121) imply:
% 168.99/25.36 | | | | | | | | | | | | | (122) e3 = e1
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | COMBINE_EQS: (33), (122) imply:
% 168.99/25.36 | | | | | | | | | | | | | (123) all_58_4 = e1
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | REF_CLOSE: (3), (4), (9), (10), (12), (16), (26), (34), (35),
% 168.99/25.36 | | | | | | | | | | | | | (36), (48), (123) are inconsistent by sub-proof
% 168.99/25.36 | | | | | | | | | | | | | #788.
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | End of split
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | End of split
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | End of split
% 168.99/25.36 | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | Case 2:
% 168.99/25.36 | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | (124) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 168.99/25.36 | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.99/25.36 | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))) |
% 168.99/25.36 | | | | | | | | | | (all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 168.99/25.36 | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.99/25.36 | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))) |
% 168.99/25.36 | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.99/25.36 | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 168.99/25.36 | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & (
% 168.99/25.36 | | | | | | | | | | ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 168.99/25.36 | | | | | | | | | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))) |
% 168.99/25.36 | | | | | | | | | | (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 168.99/25.36 | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 168.99/25.36 | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & (
% 168.99/25.36 | | | | | | | | | | ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.99/25.36 | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) | ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.99/25.36 | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.99/25.36 | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.99/25.36 | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.99/25.36 | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 168.99/25.36 | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.99/25.36 | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.99/25.36 | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | BETA: splitting (124) gives:
% 168.99/25.36 | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | Case 1:
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | (125) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 168.99/25.36 | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.99/25.36 | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 168.99/25.36 | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.99/25.36 | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 168.99/25.36 | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 168.99/25.36 | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | BETA: splitting (125) gives:
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | Case 1:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | (126) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 168.99/25.36 | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 168.99/25.36 | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | ALPHA: (126) implies:
% 168.99/25.36 | | | | | | | | | | | | (127) all_56_5 = e1
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | COMBINE_EQS: (40), (127) imply:
% 168.99/25.36 | | | | | | | | | | | | (128) e2 = e1
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | COMBINE_EQS: (3), (128) imply:
% 168.99/25.36 | | | | | | | | | | | | (129) all_58_9 = e1
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | REF_CLOSE: (10), (12), (15), (26), (34), (35), (36), (42),
% 168.99/25.36 | | | | | | | | | | | | (45), (48), (53), (54), (64), (129) are
% 168.99/25.36 | | | | | | | | | | | | inconsistent by sub-proof #137.
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | Case 2:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | (130) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 168.99/25.36 | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 168.99/25.36 | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | ALPHA: (130) implies:
% 168.99/25.36 | | | | | | | | | | | | (131) op(e3, e0) = e0
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | REF_CLOSE: (21), (35), (36), (131) are inconsistent by
% 168.99/25.36 | | | | | | | | | | | | sub-proof #699.
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | End of split
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | Case 2:
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | (132) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.99/25.36 | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 168.99/25.36 | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 168.99/25.36 | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 168.99/25.36 | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 168.99/25.36 | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 168.99/25.36 | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 168.99/25.36 | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.99/25.36 | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.99/25.36 | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 168.99/25.36 | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 168.99/25.36 | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | BETA: splitting (132) gives:
% 168.99/25.36 | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | Case 1:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | (133) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 168.99/25.36 | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 168.99/25.36 | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 168.99/25.36 | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | ALPHA: (133) implies:
% 168.99/25.36 | | | | | | | | | | | | (134) op(e2, e0) = e0
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | REF_CLOSE: (18), (35), (44), (46), (72), (75), (101), (134)
% 168.99/25.36 | | | | | | | | | | | | are inconsistent by sub-proof #122.
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | Case 2:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | (135) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 168.99/25.36 | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 168.99/25.36 | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 168.99/25.36 | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 168.99/25.36 | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 168.99/25.36 | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 168.99/25.36 | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 168.99/25.36 | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 168.99/25.36 | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 168.99/25.36 | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 168.99/25.36 | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 168.99/25.36 | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 168.99/25.36 | | | | | | | | | | | | op(e0, e1) = e1)))
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | BETA: splitting (135) gives:
% 168.99/25.36 | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | Case 1:
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | (136) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 168.99/25.36 | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 168.99/25.36 | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 168.99/25.36 | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 168.99/25.36 | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 168.99/25.36 | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | ALPHA: (136) implies:
% 168.99/25.36 | | | | | | | | | | | | | (137) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 168.99/25.36 | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | | REF_CLOSE: (14), (17), (137) are inconsistent by sub-proof
% 168.99/25.36 | | | | | | | | | | | | | #795.
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.36 | | | | | | | | | | | | Case 2:
% 168.99/25.36 | | | | | | | | | | | | |
% 168.99/25.37 | | | | | | | | | | | | | (138) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 168.99/25.37 | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 168.99/25.37 | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 168.99/25.37 | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 168.99/25.37 | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 168.99/25.37 | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 168.99/25.37 | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 168.99/25.37 | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 168.99/25.37 | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 168.99/25.37 | | | | | | | | | | | | |
% 168.99/25.37 | | | | | | | | | | | | | ALPHA: (138) implies:
% 168.99/25.37 | | | | | | | | | | | | | (139) ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 168.99/25.37 | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))
% 168.99/25.37 | | | | | | | | | | | | |
% 168.99/25.37 | | | | | | | | | | | | | REF_CLOSE: (70), (83), (139) are inconsistent by sub-proof
% 168.99/25.37 | | | | | | | | | | | | | #616.
% 168.99/25.37 | | | | | | | | | | | | |
% 168.99/25.37 | | | | | | | | | | | | End of split
% 168.99/25.37 | | | | | | | | | | | |
% 168.99/25.37 | | | | | | | | | | | End of split
% 168.99/25.37 | | | | | | | | | | |
% 168.99/25.37 | | | | | | | | | | End of split
% 168.99/25.37 | | | | | | | | | |
% 168.99/25.37 | | | | | | | | | End of split
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | End of split
% 168.99/25.37 | | | | | | | |
% 168.99/25.37 | | | | | | | End of split
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | End of split
% 168.99/25.37 | | | | | |
% 168.99/25.37 | | | | | End of split
% 168.99/25.37 | | | | |
% 168.99/25.37 | | | | Case 2:
% 168.99/25.37 | | | | |
% 168.99/25.37 | | | | | (140) all_58_9 = e3 & op(e3, e0) = e3
% 168.99/25.37 | | | | |
% 168.99/25.37 | | | | | ALPHA: (140) implies:
% 168.99/25.37 | | | | | (141) all_58_9 = e3
% 168.99/25.37 | | | | |
% 168.99/25.37 | | | | | COMBINE_EQS: (3), (141) imply:
% 168.99/25.37 | | | | | (142) e3 = e2
% 168.99/25.37 | | | | |
% 168.99/25.37 | | | | | COMBINE_EQS: (33), (142) imply:
% 168.99/25.37 | | | | | (143) all_58_4 = e2
% 168.99/25.37 | | | | |
% 168.99/25.37 | | | | | BETA: splitting (9) gives:
% 168.99/25.37 | | | | |
% 168.99/25.37 | | | | | Case 1:
% 168.99/25.37 | | | | | |
% 168.99/25.37 | | | | | |
% 168.99/25.37 | | | | | | BETA: splitting (49) gives:
% 168.99/25.37 | | | | | |
% 168.99/25.37 | | | | | | Case 1:
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | | (144) all_58_0 = e0 & op(e3, e3) = e0
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | | ALPHA: (144) implies:
% 168.99/25.37 | | | | | | | (145) op(e3, e3) = e0
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | | REF_CLOSE: (3), (9), (10), (16), (26), (32), (34), (35), (36),
% 168.99/25.37 | | | | | | | (42), (48), (143), (145) are inconsistent by sub-proof
% 168.99/25.37 | | | | | | | #120.
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | Case 2:
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | | BETA: splitting (34) gives:
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | | Case 1:
% 168.99/25.37 | | | | | | | |
% 168.99/25.37 | | | | | | | | (146) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 168.99/25.37 | | | | | | | | op(e3, e2) = e3)
% 168.99/25.37 | | | | | | | |
% 168.99/25.37 | | | | | | | | BETA: splitting (146) gives:
% 168.99/25.37 | | | | | | | |
% 168.99/25.37 | | | | | | | | Case 1:
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | | (147) all_58_0 = e3 & op(e3, e3) = e3
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | | ALPHA: (147) implies:
% 168.99/25.37 | | | | | | | | | (148) all_58_0 = e3
% 168.99/25.37 | | | | | | | | | (149) op(e3, e3) = e3
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | | REF_CLOSE: (3), (9), (10), (16), (26), (32), (35), (36), (42),
% 168.99/25.37 | | | | | | | | | (143), (148), (149) are inconsistent by sub-proof
% 168.99/25.37 | | | | | | | | | #941.
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | Case 2:
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | | (150) all_58_1 = e3 & op(e3, e2) = e3
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | | REF_CLOSE: (26), (53), (150) are inconsistent by sub-proof
% 168.99/25.37 | | | | | | | | | #803.
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | End of split
% 168.99/25.37 | | | | | | | |
% 168.99/25.37 | | | | | | | Case 2:
% 168.99/25.37 | | | | | | | |
% 168.99/25.37 | | | | | | | |
% 168.99/25.37 | | | | | | | | BETA: splitting (62) gives:
% 168.99/25.37 | | | | | | | |
% 168.99/25.37 | | | | | | | | Case 1:
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | | (151) all_58_4 = e3 & op(e3, e1) = e3
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | | REF_CLOSE: (48), (143), (151) are inconsistent by sub-proof
% 168.99/25.37 | | | | | | | | | #952.
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | Case 2:
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | | REF_CLOSE: (3), (48), (140) are inconsistent by sub-proof
% 168.99/25.37 | | | | | | | | | #940.
% 168.99/25.37 | | | | | | | | |
% 168.99/25.37 | | | | | | | | End of split
% 168.99/25.37 | | | | | | | |
% 168.99/25.37 | | | | | | | End of split
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | End of split
% 168.99/25.37 | | | | | |
% 168.99/25.37 | | | | | Case 2:
% 168.99/25.37 | | | | | |
% 168.99/25.37 | | | | | | (152) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 168.99/25.37 | | | | | | e0) = e0)
% 168.99/25.37 | | | | | |
% 168.99/25.37 | | | | | | BETA: splitting (152) gives:
% 168.99/25.37 | | | | | |
% 168.99/25.37 | | | | | | Case 1:
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | | (153) all_58_4 = e0 & op(e3, e1) = e0
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | | REF_CLOSE: (36), (143), (153) are inconsistent by sub-proof #902.
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | Case 2:
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | | (154) all_58_9 = e0 & op(e3, e0) = e0
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | | ALPHA: (154) implies:
% 168.99/25.37 | | | | | | | (155) op(e3, e0) = e0
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | | REF_CLOSE: (21), (35), (36), (155) are inconsistent by sub-proof
% 168.99/25.37 | | | | | | | #699.
% 168.99/25.37 | | | | | | |
% 168.99/25.37 | | | | | | End of split
% 168.99/25.37 | | | | | |
% 168.99/25.37 | | | | | End of split
% 168.99/25.37 | | | | |
% 168.99/25.37 | | | | End of split
% 168.99/25.37 | | | |
% 168.99/25.37 | | | End of split
% 168.99/25.37 | | |
% 168.99/25.37 | | End of split
% 168.99/25.37 | |
% 168.99/25.37 | Case 2:
% 168.99/25.37 | |
% 168.99/25.37 | | (156) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 168.99/25.37 | | e0)
% 168.99/25.37 | |
% 169.04/25.37 | | BETA: splitting (156) gives:
% 169.04/25.37 | |
% 169.04/25.37 | | Case 1:
% 169.04/25.37 | | |
% 169.04/25.37 | | | (157) all_58_4 = e0 & op(e3, e1) = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | ALPHA: (157) implies:
% 169.04/25.37 | | | (158) all_58_4 = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | REF_CLOSE: (26), (33), (158) are inconsistent by sub-proof #894.
% 169.04/25.37 | | |
% 169.04/25.37 | | Case 2:
% 169.04/25.37 | | |
% 169.04/25.37 | | | (159) all_58_9 = e0 & op(e3, e0) = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | ALPHA: (159) implies:
% 169.04/25.37 | | | (160) op(e3, e0) = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | REF_CLOSE: (21), (35), (36), (160) are inconsistent by sub-proof #699.
% 169.04/25.37 | | |
% 169.04/25.37 | | End of split
% 169.04/25.37 | |
% 169.04/25.37 | End of split
% 169.04/25.37 |
% 169.04/25.37 End of proof
% 169.04/25.37
% 169.04/25.37 Sub-proof #120 shows that the following formulas are inconsistent:
% 169.04/25.37 ----------------------------------------------------------------
% 169.04/25.37 (1) all_58_9 = e2
% 169.04/25.37 (2) op(e3, e3) = e0
% 169.04/25.37 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.04/25.37 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.37 (4) ~ (e3 = e1)
% 169.04/25.37 (5) ~ (e1 = e0)
% 169.04/25.37 (6) ~ (e3 = e0)
% 169.04/25.37 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.04/25.37 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.04/25.37 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.04/25.37 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.04/25.37 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.37 (10) ~ (e2 = e0)
% 169.04/25.37 (11) ~ (e2 = e1)
% 169.04/25.37 (12) all_58_4 = e2
% 169.04/25.37 (13) ~ (e3 = e2)
% 169.04/25.37
% 169.04/25.37 Begin of proof
% 169.04/25.37 |
% 169.04/25.37 | BETA: splitting (7) gives:
% 169.04/25.37 |
% 169.04/25.37 | Case 1:
% 169.04/25.37 | |
% 169.04/25.37 | | (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 169.04/25.37 | | e1)
% 169.04/25.37 | |
% 169.04/25.37 | | BETA: splitting (14) gives:
% 169.04/25.37 | |
% 169.04/25.37 | | Case 1:
% 169.04/25.37 | | |
% 169.04/25.37 | | | (15) all_58_0 = e1 & op(e3, e3) = e1
% 169.04/25.37 | | |
% 169.04/25.37 | | | ALPHA: (15) implies:
% 169.04/25.37 | | | (16) op(e3, e3) = e1
% 169.04/25.37 | | |
% 169.04/25.37 | | | REF_CLOSE: (2), (5), (9), (16) are inconsistent by sub-proof #907.
% 169.04/25.37 | | |
% 169.04/25.37 | | Case 2:
% 169.04/25.37 | | |
% 169.04/25.37 | | | (17) all_58_1 = e1 & op(e3, e2) = e1
% 169.04/25.37 | | |
% 169.04/25.37 | | | ALPHA: (17) implies:
% 169.04/25.37 | | | (18) all_58_1 = e1
% 169.04/25.37 | | |
% 169.04/25.37 | | | BETA: splitting (8) gives:
% 169.04/25.37 | | |
% 169.04/25.37 | | | Case 1:
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 169.04/25.37 | | | | = e3)
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | BETA: splitting (19) gives:
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | Case 1:
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | (20) all_58_0 = e3 & op(e3, e3) = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | ALPHA: (20) implies:
% 169.04/25.37 | | | | | (21) all_58_0 = e3
% 169.04/25.37 | | | | | (22) op(e3, e3) = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (21),
% 169.04/25.37 | | | | | (22) are inconsistent by sub-proof #941.
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | Case 2:
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | (23) all_58_1 = e3 & op(e3, e2) = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | REF_CLOSE: (4), (18), (23) are inconsistent by sub-proof #121.
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | End of split
% 169.04/25.37 | | | |
% 169.04/25.37 | | | Case 2:
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | (24) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 169.04/25.37 | | | | = e3)
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | BETA: splitting (24) gives:
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | Case 1:
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | (25) all_58_4 = e3 & op(e3, e1) = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | REF_CLOSE: (12), (13), (25) are inconsistent by sub-proof #952.
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | Case 2:
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | (26) all_58_9 = e3 & op(e3, e0) = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | REF_CLOSE: (1), (13), (26) are inconsistent by sub-proof #940.
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | End of split
% 169.04/25.37 | | | |
% 169.04/25.37 | | | End of split
% 169.04/25.37 | | |
% 169.04/25.37 | | End of split
% 169.04/25.37 | |
% 169.04/25.37 | Case 2:
% 169.04/25.37 | |
% 169.04/25.37 | | (27) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 169.04/25.37 | | e1)
% 169.04/25.37 | |
% 169.04/25.37 | | BETA: splitting (27) gives:
% 169.04/25.37 | |
% 169.04/25.37 | | Case 1:
% 169.04/25.37 | | |
% 169.04/25.37 | | | (28) all_58_4 = e1 & op(e3, e1) = e1
% 169.04/25.37 | | |
% 169.04/25.37 | | | REF_CLOSE: (11), (12), (28) are inconsistent by sub-proof #510.
% 169.04/25.37 | | |
% 169.04/25.37 | | Case 2:
% 169.04/25.37 | | |
% 169.04/25.37 | | | (29) all_58_9 = e1 & op(e3, e0) = e1
% 169.04/25.37 | | |
% 169.04/25.37 | | | ALPHA: (29) implies:
% 169.04/25.37 | | | (30) all_58_9 = e1
% 169.04/25.37 | | |
% 169.04/25.37 | | | REF_CLOSE: (1), (11), (30) are inconsistent by sub-proof #942.
% 169.04/25.37 | | |
% 169.04/25.37 | | End of split
% 169.04/25.37 | |
% 169.04/25.37 | End of split
% 169.04/25.37 |
% 169.04/25.37 End of proof
% 169.04/25.37
% 169.04/25.37 Sub-proof #121 shows that the following formulas are inconsistent:
% 169.04/25.37 ----------------------------------------------------------------
% 169.04/25.37 (1) all_58_1 = e3 & op(e3, e2) = e3
% 169.04/25.37 (2) all_58_1 = e1
% 169.04/25.37 (3) ~ (e3 = e1)
% 169.04/25.37
% 169.04/25.37 Begin of proof
% 169.04/25.37 |
% 169.04/25.37 | ALPHA: (1) implies:
% 169.04/25.37 | (4) all_58_1 = e3
% 169.04/25.37 |
% 169.04/25.37 | COMBINE_EQS: (2), (4) imply:
% 169.04/25.37 | (5) e3 = e1
% 169.04/25.37 |
% 169.04/25.37 | SIMP: (5) implies:
% 169.04/25.37 | (6) e3 = e1
% 169.04/25.37 |
% 169.04/25.37 | REDUCE: (3), (6) imply:
% 169.04/25.37 | (7) $false
% 169.04/25.37 |
% 169.04/25.37 | CLOSE: (7) is inconsistent.
% 169.04/25.37 |
% 169.04/25.37 End of proof
% 169.04/25.37
% 169.04/25.37 Sub-proof #122 shows that the following formulas are inconsistent:
% 169.04/25.37 ----------------------------------------------------------------
% 169.04/25.37 (1) ~ (all_52_13 = e0)
% 169.04/25.37 (2) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 169.04/25.37 (3) ~ (all_52_13 = e1)
% 169.04/25.37 (4) op(e2, e0) = e0
% 169.04/25.37 (5) ~ (all_52_13 = e2)
% 169.04/25.37 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.37 (7) all_54_7 = all_52_13
% 169.04/25.37 (8) op(e2, e0) = all_52_13
% 169.04/25.37
% 169.04/25.37 Begin of proof
% 169.04/25.37 |
% 169.04/25.37 | BETA: splitting (2) gives:
% 169.04/25.37 |
% 169.04/25.37 | Case 1:
% 169.04/25.37 | |
% 169.04/25.37 | | (9) all_54_7 = e3
% 169.04/25.37 | |
% 169.04/25.37 | | COMBINE_EQS: (7), (9) imply:
% 169.04/25.37 | | (10) all_52_13 = e3
% 169.04/25.37 | |
% 169.04/25.37 | | SIMP: (10) implies:
% 169.04/25.37 | | (11) all_52_13 = e3
% 169.04/25.37 | |
% 169.04/25.37 | | REDUCE: (1), (11) imply:
% 169.04/25.37 | | (12) ~ (e3 = e0)
% 169.04/25.37 | |
% 169.04/25.37 | | REDUCE: (8), (11) imply:
% 169.04/25.37 | | (13) op(e2, e0) = e3
% 169.04/25.37 | |
% 169.04/25.37 | | REF_CLOSE: (4), (6), (12), (13) are inconsistent by sub-proof #123.
% 169.04/25.37 | |
% 169.04/25.37 | Case 2:
% 169.04/25.37 | |
% 169.04/25.37 | | (14) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 169.04/25.37 | |
% 169.04/25.37 | | REF_CLOSE: (1), (3), (5), (7), (14) are inconsistent by sub-proof #615.
% 169.04/25.37 | |
% 169.04/25.37 | End of split
% 169.04/25.37 |
% 169.04/25.37 End of proof
% 169.04/25.37
% 169.04/25.37 Sub-proof #123 shows that the following formulas are inconsistent:
% 169.04/25.37 ----------------------------------------------------------------
% 169.04/25.37 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.37 (2) op(e2, e0) = e3
% 169.04/25.37 (3) op(e2, e0) = e0
% 169.04/25.37 (4) ~ (e3 = e0)
% 169.04/25.37
% 169.04/25.37 Begin of proof
% 169.04/25.37 |
% 169.04/25.37 | GROUND_INST: instantiating (1) with e0, e3, e0, e2, simplifying with (2), (3)
% 169.04/25.37 | gives:
% 169.04/25.37 | (5) e3 = e0
% 169.04/25.37 |
% 169.04/25.37 | REDUCE: (4), (5) imply:
% 169.04/25.37 | (6) $false
% 169.04/25.37 |
% 169.04/25.37 | CLOSE: (6) is inconsistent.
% 169.04/25.37 |
% 169.04/25.37 End of proof
% 169.04/25.37
% 169.04/25.37 Sub-proof #124 shows that the following formulas are inconsistent:
% 169.04/25.37 ----------------------------------------------------------------
% 169.04/25.37 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.04/25.37 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.04/25.37 (2) all_58_0 = e1
% 169.04/25.37 (3) ~ (e3 = e1)
% 169.04/25.37 (4) op(e3, e3) = e1
% 169.04/25.37 (5) ~ (e1 = e0)
% 169.04/25.37 (6) op(e0, e3) = e1
% 169.04/25.37 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.04/25.37 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.04/25.37 (8) all_58_6 = e2
% 169.04/25.37 (9) ~ (e3 = e0)
% 169.04/25.37 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.37 (11) ~ (e2 = e0)
% 169.04/25.37 (12) ~ (e3 = e2)
% 169.04/25.37
% 169.04/25.37 Begin of proof
% 169.04/25.37 |
% 169.04/25.37 | BETA: splitting (1) gives:
% 169.04/25.37 |
% 169.04/25.37 | Case 1:
% 169.04/25.37 | |
% 169.04/25.37 | | (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.04/25.37 | | e0)
% 169.04/25.37 | |
% 169.04/25.37 | | BETA: splitting (13) gives:
% 169.04/25.37 | |
% 169.04/25.37 | | Case 1:
% 169.04/25.37 | | |
% 169.04/25.37 | | | (14) all_58_0 = e0 & op(e3, e3) = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | ALPHA: (14) implies:
% 169.04/25.37 | | | (15) op(e3, e3) = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | REF_CLOSE: (4), (5), (10), (15) are inconsistent by sub-proof #907.
% 169.04/25.37 | | |
% 169.04/25.37 | | Case 2:
% 169.04/25.37 | | |
% 169.04/25.37 | | | (16) all_58_2 = e0 & op(e2, e3) = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | ALPHA: (16) implies:
% 169.04/25.37 | | | (17) all_58_2 = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | BETA: splitting (7) gives:
% 169.04/25.37 | | |
% 169.04/25.37 | | | Case 1:
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 169.04/25.37 | | | | = e3)
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | BETA: splitting (18) gives:
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | Case 1:
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | (19) all_58_0 = e3 & op(e3, e3) = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | REF_CLOSE: (2), (3), (19) are inconsistent by sub-proof #905.
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | Case 2:
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | (20) all_58_2 = e3 & op(e2, e3) = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | ALPHA: (20) implies:
% 169.04/25.37 | | | | | (21) all_58_2 = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | REF_CLOSE: (9), (17), (21) are inconsistent by sub-proof #913.
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | End of split
% 169.04/25.37 | | | |
% 169.04/25.37 | | | Case 2:
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | (22) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 169.04/25.37 | | | | = e3)
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | BETA: splitting (22) gives:
% 169.04/25.37 | | | |
% 169.04/25.37 | | | | Case 1:
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | (23) all_58_6 = e3 & op(e1, e3) = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | ALPHA: (23) implies:
% 169.04/25.37 | | | | | (24) all_58_6 = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | COMBINE_EQS: (8), (24) imply:
% 169.04/25.37 | | | | | (25) e3 = e2
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | REDUCE: (12), (25) imply:
% 169.04/25.37 | | | | | (26) $false
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | CLOSE: (26) is inconsistent.
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | Case 2:
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | (27) all_58_12 = e3 & op(e0, e3) = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | ALPHA: (27) implies:
% 169.04/25.37 | | | | | (28) op(e0, e3) = e3
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | | REF_CLOSE: (3), (6), (10), (28) are inconsistent by sub-proof #125.
% 169.04/25.37 | | | | |
% 169.04/25.37 | | | | End of split
% 169.04/25.37 | | | |
% 169.04/25.37 | | | End of split
% 169.04/25.37 | | |
% 169.04/25.37 | | End of split
% 169.04/25.37 | |
% 169.04/25.37 | Case 2:
% 169.04/25.37 | |
% 169.04/25.37 | | (29) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.04/25.37 | | e0)
% 169.04/25.37 | |
% 169.04/25.37 | | BETA: splitting (29) gives:
% 169.04/25.37 | |
% 169.04/25.37 | | Case 1:
% 169.04/25.37 | | |
% 169.04/25.37 | | | (30) all_58_6 = e0 & op(e1, e3) = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | REF_CLOSE: (8), (11), (30) are inconsistent by sub-proof #769.
% 169.04/25.37 | | |
% 169.04/25.37 | | Case 2:
% 169.04/25.37 | | |
% 169.04/25.37 | | | (31) all_58_12 = e0 & op(e0, e3) = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | ALPHA: (31) implies:
% 169.04/25.37 | | | (32) op(e0, e3) = e0
% 169.04/25.37 | | |
% 169.04/25.37 | | | REF_CLOSE: (5), (6), (10), (32) are inconsistent by sub-proof #531.
% 169.04/25.37 | | |
% 169.04/25.37 | | End of split
% 169.04/25.37 | |
% 169.04/25.37 | End of split
% 169.04/25.37 |
% 169.04/25.37 End of proof
% 169.04/25.37
% 169.04/25.37 Sub-proof #125 shows that the following formulas are inconsistent:
% 169.04/25.37 ----------------------------------------------------------------
% 169.04/25.37 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.37 (2) op(e0, e3) = e3
% 169.04/25.37 (3) op(e0, e3) = e1
% 169.04/25.37 (4) ~ (e3 = e1)
% 169.04/25.37
% 169.04/25.37 Begin of proof
% 169.04/25.37 |
% 169.04/25.37 | GROUND_INST: instantiating (1) with e1, e3, e3, e0, simplifying with (2), (3)
% 169.04/25.37 | gives:
% 169.04/25.37 | (5) e3 = e1
% 169.04/25.37 |
% 169.04/25.37 | REDUCE: (4), (5) imply:
% 169.04/25.37 | (6) $false
% 169.04/25.37 |
% 169.04/25.37 | CLOSE: (6) is inconsistent.
% 169.04/25.37 |
% 169.04/25.37 End of proof
% 169.04/25.37
% 169.04/25.37 Sub-proof #126 shows that the following formulas are inconsistent:
% 169.04/25.37 ----------------------------------------------------------------
% 169.04/25.37 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.04/25.37 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.04/25.37 (2) all_58_12 = e1
% 169.04/25.37 (3) ~ (all_4_2 = e2)
% 169.04/25.37 (4) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.37 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.04/25.37 (5) all_58_9 = e2
% 169.04/25.37 (6) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 169.04/25.37 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 169.04/25.37 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.04/25.37 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.04/25.37 (8) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.04/25.37 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.04/25.37 (9) ~ (all_6_2 = e3)
% 169.04/25.37 (10) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.04/25.37 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.37 (11) ~ (e3 = e1)
% 169.04/25.37 (12) op(e3, e3) = e1
% 169.04/25.37 (13) op(e3, e1) = all_52_8
% 169.04/25.37 (14) ~ (e1 = e0)
% 169.04/25.37 (15) all_56_10 = e1
% 169.04/25.37 (16) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.04/25.37 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.04/25.37 (17) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.04/25.37 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.04/25.37 (18) op(e2, e3) = all_52_1
% 169.04/25.37 (19) all_58_3 = e1
% 169.04/25.37 (20) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.04/25.37 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.04/25.38 (21) ~ (all_6_2 = e2)
% 169.04/25.38 (22) op(e1, e1) = all_6_2
% 169.04/25.38 (23) ~ (e3 = e0)
% 169.04/25.38 (24) all_58_12 = e2 & op(e0, e3) = e2
% 169.04/25.38 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.38 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.04/25.38 (26) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.04/25.38 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.04/25.38 (27) op(e0, e0) = all_4_2
% 169.04/25.38 (28) ~ (all_52_13 = e2)
% 169.04/25.38 (29) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.38 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.04/25.38 (30) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.04/25.38 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.04/25.38 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.38 (32) ~ (e2 = e0)
% 169.04/25.38 (33) op(e2, e1) = e2
% 169.04/25.38 (34) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.04/25.38 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.04/25.38 (35) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.04/25.38 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.04/25.38 (36) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 169.04/25.38 (37) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.38 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.04/25.38 (38) ~ (e2 = e1)
% 169.04/25.38 (39) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.04/25.38 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.04/25.38 (40) op(e2, e0) = all_52_13
% 169.04/25.38 (41) ~ (e3 = e2)
% 169.04/25.38
% 169.04/25.38 Begin of proof
% 169.04/25.38 |
% 169.04/25.38 | ALPHA: (24) implies:
% 169.04/25.38 | (42) all_58_12 = e2
% 169.04/25.38 |
% 169.04/25.38 | COMBINE_EQS: (2), (42) imply:
% 169.04/25.38 | (43) e2 = e1
% 169.04/25.38 |
% 169.04/25.38 | COMBINE_EQS: (5), (43) imply:
% 169.04/25.38 | (44) all_58_9 = e1
% 169.04/25.38 |
% 169.04/25.38 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.04/25.38 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 169.04/25.38 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 169.04/25.38 | (37), (38), (39), (40), (41), (44) are inconsistent by sub-proof
% 169.04/25.38 | #139.
% 169.04/25.38 |
% 169.04/25.38 End of proof
% 169.04/25.38
% 169.04/25.38 Sub-proof #127 shows that the following formulas are inconsistent:
% 169.04/25.38 ----------------------------------------------------------------
% 169.04/25.38 (1) ~ (e3 = e1)
% 169.04/25.38 (2) ~ (e1 = e0)
% 169.04/25.38 (3) all_58_3 = e1
% 169.04/25.38 (4) ~ (e3 = e0)
% 169.04/25.38 (5) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.38 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.04/25.38 (6) op(e2, e0) = e1
% 169.04/25.38 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.38 (8) ~ (e2 = e0)
% 169.04/25.38 (9) op(e2, e1) = e2
% 169.04/25.38 (10) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.38 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.04/25.38 (11) ~ (e2 = e1)
% 169.04/25.38 (12) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.04/25.38 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 169.04/25.38 (13) all_58_10 = e1
% 169.04/25.38 (14) ~ (e3 = e2)
% 169.04/25.38
% 169.04/25.38 Begin of proof
% 169.04/25.38 |
% 169.04/25.38 | BETA: splitting (5) gives:
% 169.04/25.38 |
% 169.04/25.38 | Case 1:
% 169.04/25.38 | |
% 169.04/25.38 | | (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 169.04/25.38 | | e0)
% 169.04/25.38 | |
% 169.04/25.38 | | BETA: splitting (15) gives:
% 169.04/25.38 | |
% 169.04/25.38 | | Case 1:
% 169.04/25.38 | | |
% 169.04/25.38 | | | (16) all_58_2 = e0 & op(e2, e3) = e0
% 169.04/25.38 | | |
% 169.04/25.38 | | | ALPHA: (16) implies:
% 169.04/25.38 | | | (17) all_58_2 = e0
% 169.04/25.38 | | |
% 169.04/25.38 | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (11), (12), (13), (14),
% 169.04/25.38 | | | (17) are inconsistent by sub-proof #128.
% 169.04/25.38 | | |
% 169.04/25.38 | | Case 2:
% 169.04/25.38 | | |
% 169.04/25.38 | | | (18) all_58_3 = e0 & op(e2, e2) = e0
% 169.04/25.38 | | |
% 169.04/25.38 | | | ALPHA: (18) implies:
% 169.04/25.38 | | | (19) all_58_3 = e0
% 169.04/25.38 | | |
% 169.04/25.38 | | | REF_CLOSE: (2), (3), (19) are inconsistent by sub-proof #523.
% 169.04/25.38 | | |
% 169.04/25.38 | | End of split
% 169.04/25.38 | |
% 169.04/25.38 | Case 2:
% 169.04/25.38 | |
% 169.04/25.38 | | (20) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 169.04/25.38 | | e0)
% 169.04/25.38 | |
% 169.04/25.38 | | BETA: splitting (20) gives:
% 169.04/25.38 | |
% 169.04/25.38 | | Case 1:
% 169.04/25.38 | | |
% 169.04/25.38 | | | (21) all_58_5 = e0 & op(e2, e1) = e0
% 169.04/25.38 | | |
% 169.04/25.38 | | | REF_CLOSE: (7), (8), (9), (21) are inconsistent by sub-proof #151.
% 169.04/25.38 | | |
% 169.04/25.38 | | Case 2:
% 169.04/25.38 | | |
% 169.04/25.38 | | | (22) all_58_10 = e0 & op(e2, e0) = e0
% 169.04/25.38 | | |
% 169.04/25.38 | | | ALPHA: (22) implies:
% 169.04/25.38 | | | (23) op(e2, e0) = e0
% 169.04/25.38 | | |
% 169.04/25.38 | | | REF_CLOSE: (2), (6), (7), (23) are inconsistent by sub-proof #849.
% 169.04/25.38 | | |
% 169.04/25.38 | | End of split
% 169.04/25.38 | |
% 169.04/25.38 | End of split
% 169.04/25.38 |
% 169.04/25.38 End of proof
% 169.04/25.38
% 169.04/25.38 Sub-proof #128 shows that the following formulas are inconsistent:
% 169.04/25.38 ----------------------------------------------------------------
% 169.04/25.38 (1) ~ (e3 = e1)
% 169.04/25.38 (2) ~ (e1 = e0)
% 169.04/25.38 (3) all_58_3 = e1
% 169.04/25.38 (4) ~ (e3 = e0)
% 169.04/25.38 (5) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.38 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.04/25.38 (6) ~ (e2 = e0)
% 169.04/25.38 (7) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.38 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.04/25.38 (8) ~ (e2 = e1)
% 169.04/25.38 (9) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.04/25.38 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 169.04/25.38 (10) all_58_10 = e1
% 169.04/25.38 (11) all_58_2 = e0
% 169.04/25.38 (12) ~ (e3 = e2)
% 169.04/25.38
% 169.04/25.38 Begin of proof
% 169.04/25.38 |
% 169.04/25.38 | BETA: splitting (7) gives:
% 169.04/25.38 |
% 169.04/25.38 | Case 1:
% 169.04/25.38 | |
% 169.04/25.38 | | (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 169.04/25.38 | | e3)
% 169.04/25.38 | |
% 169.04/25.38 | | BETA: splitting (13) gives:
% 169.04/25.38 | |
% 169.04/25.38 | | Case 1:
% 169.04/25.38 | | |
% 169.04/25.38 | | | (14) all_58_2 = e3 & op(e2, e3) = e3
% 169.04/25.38 | | |
% 169.04/25.38 | | | REF_CLOSE: (4), (11), (14) are inconsistent by sub-proof #744.
% 169.04/25.38 | | |
% 169.04/25.38 | | Case 2:
% 169.04/25.38 | | |
% 169.04/25.38 | | | (15) all_58_3 = e3 & op(e2, e2) = e3
% 169.04/25.38 | | |
% 169.04/25.38 | | | ALPHA: (15) implies:
% 169.04/25.38 | | | (16) all_58_3 = e3
% 169.04/25.38 | | |
% 169.04/25.38 | | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #328.
% 169.04/25.38 | | |
% 169.04/25.38 | | End of split
% 169.04/25.38 | |
% 169.04/25.38 | Case 2:
% 169.04/25.38 | |
% 169.04/25.38 | | (17) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 169.04/25.38 | | e3)
% 169.04/25.38 | |
% 169.04/25.38 | | BETA: splitting (17) gives:
% 169.04/25.38 | |
% 169.04/25.38 | | Case 1:
% 169.04/25.38 | | |
% 169.04/25.38 | | | (18) all_58_5 = e3 & op(e2, e1) = e3
% 169.04/25.38 | | |
% 169.04/25.38 | | | ALPHA: (18) implies:
% 169.04/25.38 | | | (19) all_58_5 = e3
% 169.04/25.38 | | |
% 169.04/25.38 | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (12), (19) are
% 169.04/25.38 | | | inconsistent by sub-proof #921.
% 169.04/25.38 | | |
% 169.04/25.38 | | Case 2:
% 169.04/25.38 | | |
% 169.04/25.38 | | | (20) all_58_10 = e3 & op(e2, e0) = e3
% 169.04/25.38 | | |
% 169.04/25.38 | | | REF_CLOSE: (1), (10), (20) are inconsistent by sub-proof #813.
% 169.04/25.38 | | |
% 169.04/25.38 | | End of split
% 169.04/25.38 | |
% 169.04/25.38 | End of split
% 169.04/25.38 |
% 169.04/25.38 End of proof
% 169.04/25.38
% 169.04/25.38 Sub-proof #129 shows that the following formulas are inconsistent:
% 169.04/25.38 ----------------------------------------------------------------
% 169.04/25.38 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.04/25.38 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.04/25.38 (2) ~ (all_4_2 = e2)
% 169.04/25.38 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.04/25.38 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.04/25.38 (4) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.38 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.04/25.38 (5) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 169.04/25.38 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 169.04/25.38 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.04/25.38 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.04/25.38 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.04/25.38 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.04/25.38 (8) ~ (all_6_2 = e3)
% 169.04/25.38 (9) ~ (all_4_2 = e1)
% 169.04/25.38 (10) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.04/25.38 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.38 (11) ~ (e3 = e1)
% 169.04/25.38 (12) op(e3, e3) = e1
% 169.04/25.38 (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.04/25.38 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.04/25.38 e1)
% 169.04/25.38 (14) op(e1, e3) = all_52_2
% 169.04/25.38 (15) op(e3, e1) = all_52_8
% 169.04/25.38 (16) ~ (e1 = e0)
% 169.04/25.38 (17) all_56_10 = e1
% 169.04/25.38 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.04/25.38 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.04/25.38 (19) ~ (all_56_12 = e0) | (all_56_11 = e2 & op(e2, e0) = e2)
% 169.04/25.38 (20) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.04/25.38 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.04/25.38 (21) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.04/25.38 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.04/25.38 (22) op(e2, e3) = all_52_1
% 169.04/25.38 (23) all_58_3 = e1
% 169.04/25.38 (24) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.04/25.38 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.04/25.38 (25) op(e3, e1) = e3
% 169.04/25.38 (26) ~ (all_6_2 = e2)
% 169.04/25.38 (27) op(e1, e1) = all_6_2
% 169.04/25.38 (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.04/25.38 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.04/25.38 (29) ~ (e3 = e0)
% 169.04/25.38 (30) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.38 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.04/25.38 (31) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.04/25.38 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.04/25.38 (32) all_56_12 = e1
% 169.04/25.38 (33) op(e0, e0) = all_4_2
% 169.04/25.38 (34) op(e3, e0) = e1
% 169.04/25.38 (35) ~ (all_52_13 = e2)
% 169.04/25.38 (36) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.38 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.04/25.38 (37) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.04/25.38 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.04/25.38 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.38 (39) ~ (e2 = e0)
% 169.04/25.38 (40) op(e2, e1) = e2
% 169.04/25.38 (41) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.04/25.38 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.04/25.38 (42) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.04/25.38 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.04/25.38 (43) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 169.04/25.38 (44) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.38 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.04/25.38 (45) ~ (e2 = e1)
% 169.04/25.38 (46) all_58_9 = e1
% 169.04/25.38 (47) op(e0, e2) = all_52_7
% 169.04/25.38 (48) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.04/25.38 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.04/25.38 (49) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.04/25.38 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.04/25.38 (50) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.38 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.04/25.38 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.04/25.38 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.04/25.38 (51) op(e2, e0) = all_52_13
% 169.04/25.38 (52) ~ (e3 = e2)
% 169.04/25.38
% 169.04/25.38 Begin of proof
% 169.04/25.38 |
% 169.04/25.38 | BETA: splitting (13) gives:
% 169.04/25.38 |
% 169.04/25.38 | Case 1:
% 169.04/25.38 | |
% 169.04/25.38 | | (53) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.04/25.38 | | e1)
% 169.04/25.38 | |
% 169.04/25.38 | | BETA: splitting (53) gives:
% 169.04/25.38 | |
% 169.04/25.38 | | Case 1:
% 169.04/25.38 | | |
% 169.04/25.38 | | | (54) all_58_12 = e1 & op(e0, e3) = e1
% 169.04/25.38 | | |
% 169.04/25.38 | | | ALPHA: (54) implies:
% 169.04/25.38 | | | (55) all_58_12 = e1
% 169.04/25.38 | | |
% 169.04/25.38 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (12), (15),
% 169.04/25.38 | | | (16), (17), (20), (21), (22), (23), (24), (26), (27), (29),
% 169.04/25.38 | | | (30), (31), (33), (35), (36), (37), (38), (39), (40), (41),
% 169.04/25.38 | | | (42), (43), (44), (45), (46), (49), (51), (52), (55) are
% 169.04/25.38 | | | inconsistent by sub-proof #139.
% 169.04/25.38 | | |
% 169.04/25.38 | | Case 2:
% 169.04/25.38 | | |
% 169.04/25.38 | | | (56) all_58_13 = e1 & op(e0, e2) = e1
% 169.04/25.38 | | |
% 169.04/25.38 | | | ALPHA: (56) implies:
% 169.04/25.38 | | | (57) all_58_13 = e1
% 169.04/25.38 | | | (58) op(e0, e2) = e1
% 169.04/25.38 | | |
% 169.04/25.38 | | | BETA: splitting (21) gives:
% 169.04/25.38 | | |
% 169.04/25.38 | | | Case 1:
% 169.04/25.38 | | | |
% 169.04/25.38 | | | | (59) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 169.04/25.38 | | | | = e2)
% 169.04/25.38 | | | |
% 169.04/25.38 | | | | REF_CLOSE: (35), (38), (45), (46), (51), (59) are inconsistent by
% 169.04/25.38 | | | | sub-proof #142.
% 169.04/25.38 | | | |
% 169.04/25.38 | | | Case 2:
% 169.04/25.38 | | | |
% 169.04/25.38 | | | | (60) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 169.04/25.38 | | | | e0) = e2)
% 169.04/25.38 | | | |
% 169.04/25.38 | | | | BETA: splitting (60) gives:
% 169.04/25.38 | | | |
% 169.04/25.38 | | | | Case 1:
% 169.04/25.38 | | | | |
% 169.04/25.38 | | | | | (61) all_58_11 = e2 & op(e1, e0) = e2
% 169.04/25.38 | | | | |
% 169.04/25.38 | | | | | ALPHA: (61) implies:
% 169.04/25.38 | | | | | (62) all_58_11 = e2
% 169.04/25.38 | | | | |
% 169.04/25.38 | | | | | BETA: splitting (1) gives:
% 169.04/25.38 | | | | |
% 169.04/25.38 | | | | | Case 1:
% 169.04/25.38 | | | | | |
% 169.04/25.38 | | | | | | (63) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 169.04/25.38 | | | | | | op(e0, e2) = e2)
% 169.04/25.38 | | | | | |
% 169.04/25.38 | | | | | | BETA: splitting (63) gives:
% 169.04/25.38 | | | | | |
% 169.04/25.38 | | | | | | Case 1:
% 169.04/25.38 | | | | | | |
% 169.04/25.38 | | | | | | | (64) all_58_12 = e2 & op(e0, e3) = e2
% 169.04/25.38 | | | | | | |
% 169.04/25.38 | | | | | | | ALPHA: (64) implies:
% 169.04/25.38 | | | | | | | (65) all_58_12 = e2
% 169.04/25.38 | | | | | | |
% 169.04/25.38 | | | | | | | BETA: splitting (49) gives:
% 169.04/25.38 | | | | | | |
% 169.04/25.38 | | | | | | | Case 1:
% 169.04/25.38 | | | | | | | |
% 169.04/25.38 | | | | | | | | (66) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 169.04/25.38 | | | | | | | | op(e3, e2) = e2)
% 169.04/25.38 | | | | | | | |
% 169.04/25.38 | | | | | | | | BETA: splitting (66) gives:
% 169.04/25.38 | | | | | | | |
% 169.04/25.38 | | | | | | | | Case 1:
% 169.04/25.38 | | | | | | | | |
% 169.04/25.38 | | | | | | | | | (67) all_58_0 = e2 & op(e3, e3) = e2
% 169.04/25.38 | | | | | | | | |
% 169.04/25.38 | | | | | | | | | ALPHA: (67) implies:
% 169.04/25.38 | | | | | | | | | (68) all_58_0 = e2
% 169.04/25.38 | | | | | | | | | (69) op(e3, e3) = e2
% 169.04/25.38 | | | | | | | | |
% 169.04/25.38 | | | | | | | | | REF_CLOSE: (3), (11), (14), (16), (18), (28), (29), (38),
% 169.04/25.38 | | | | | | | | | (39), (45), (52), (65), (68), (69) are inconsistent
% 169.04/25.38 | | | | | | | | | by sub-proof #138.
% 169.04/25.38 | | | | | | | | |
% 169.04/25.38 | | | | | | | | Case 2:
% 169.04/25.38 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | (70) all_58_1 = e2 & op(e3, e2) = e2
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | ALPHA: (70) implies:
% 169.04/25.39 | | | | | | | | | (71) all_58_1 = e2
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | BETA: splitting (20) gives:
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | Case 1:
% 169.04/25.39 | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | (72) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 169.04/25.39 | | | | | | | | | | op(e2, e1) = e3)
% 169.04/25.39 | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | REF_CLOSE: (10), (11), (12), (15), (16), (29), (34), (37),
% 169.04/25.39 | | | | | | | | | | (38), (39), (40), (45), (46), (49), (52), (72) are
% 169.04/25.39 | | | | | | | | | | inconsistent by sub-proof #136.
% 169.04/25.39 | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | Case 2:
% 169.04/25.39 | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | (73) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3
% 169.04/25.39 | | | | | | | | | | & op(e0, e1) = e3)
% 169.04/25.39 | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | BETA: splitting (73) gives:
% 169.04/25.39 | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | Case 1:
% 169.04/25.39 | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | (74) all_58_8 = e3 & op(e1, e1) = e3
% 169.04/25.39 | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | REF_CLOSE: (8), (27), (38), (74) are inconsistent by
% 169.04/25.39 | | | | | | | | | | | sub-proof #961.
% 169.04/25.39 | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | Case 2:
% 169.04/25.39 | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | (75) all_58_14 = e3 & op(e0, e1) = e3
% 169.04/25.39 | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | ALPHA: (75) implies:
% 169.04/25.39 | | | | | | | | | | | (76) all_58_14 = e3
% 169.04/25.39 | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | BETA: splitting (4) gives:
% 169.04/25.39 | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | Case 1:
% 169.04/25.39 | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | (77) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 169.04/25.39 | | | | | | | | | | | | & op(e2, e2) = e3)
% 169.04/25.39 | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | BETA: splitting (77) gives:
% 169.04/25.39 | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | Case 1:
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | (78) all_58_1 = e3 & op(e3, e2) = e3
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | ALPHA: (78) implies:
% 169.04/25.39 | | | | | | | | | | | | | (79) all_58_1 = e3
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | COMBINE_EQS: (71), (79) imply:
% 169.04/25.39 | | | | | | | | | | | | | (80) e3 = e2
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | SIMP: (80) implies:
% 169.04/25.39 | | | | | | | | | | | | | (81) e3 = e2
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | COMBINE_EQS: (76), (81) imply:
% 169.04/25.39 | | | | | | | | | | | | | (82) all_58_14 = e2
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | REF_CLOSE: (8), (10), (11), (12), (15), (16), (20), (27),
% 169.04/25.39 | | | | | | | | | | | | | (29), (34), (37), (38), (39), (40), (45), (46),
% 169.04/25.39 | | | | | | | | | | | | | (49), (52), (82) are inconsistent by sub-proof
% 169.04/25.39 | | | | | | | | | | | | | #135.
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | Case 2:
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | (83) all_58_3 = e3 & op(e2, e2) = e3
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | ALPHA: (83) implies:
% 169.04/25.39 | | | | | | | | | | | | | (84) all_58_3 = e3
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | REF_CLOSE: (11), (23), (84) are inconsistent by sub-proof
% 169.04/25.39 | | | | | | | | | | | | | #328.
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | End of split
% 169.04/25.39 | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | Case 2:
% 169.04/25.39 | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | (85) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 169.04/25.39 | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 169.04/25.39 | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | BETA: splitting (85) gives:
% 169.04/25.39 | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | Case 1:
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | (86) all_58_7 = e3 & op(e1, e2) = e3
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | ALPHA: (86) implies:
% 169.04/25.39 | | | | | | | | | | | | | (87) all_58_7 = e3
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | BETA: splitting (36) gives:
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | Case 1:
% 169.04/25.39 | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | (88) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 169.04/25.39 | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 169.04/25.39 | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 169.04/25.39 | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | Case 1:
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | (89) all_58_1 = e0 & op(e3, e2) = e0
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 169.04/25.39 | | | | | | | | | | | | | | | (90) all_58_1 = e0
% 169.04/25.39 | | | | | | | | | | | | | | | (91) op(e3, e2) = e0
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (15), (25), (29), (37), (38), (39),
% 169.04/25.39 | | | | | | | | | | | | | | | (45), (46), (49), (52), (90), (91) are
% 169.04/25.39 | | | | | | | | | | | | | | | inconsistent by sub-proof #137.
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | Case 2:
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | (92) all_58_3 = e0 & op(e2, e2) = e0
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 169.04/25.39 | | | | | | | | | | | | | | | (93) all_58_3 = e0
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | COMBINE_EQS: (23), (93) imply:
% 169.04/25.39 | | | | | | | | | | | | | | | (94) e1 = e0
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | COMBINE_EQS: (32), (94) imply:
% 169.04/25.39 | | | | | | | | | | | | | | | (95) all_56_12 = e0
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (19), (29), (38), (39), (46), (48),
% 169.04/25.39 | | | | | | | | | | | | | | | (50), (51), (52), (62), (95) are inconsistent by
% 169.04/25.39 | | | | | | | | | | | | | | | sub-proof #134.
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | End of split
% 169.04/25.39 | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | Case 2:
% 169.04/25.39 | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | (96) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 169.04/25.39 | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 169.04/25.39 | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 169.04/25.39 | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | Case 1:
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | (97) all_58_7 = e0 & op(e1, e2) = e0
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 169.04/25.39 | | | | | | | | | | | | | | | (98) all_58_7 = e0
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | REF_CLOSE: (29), (87), (98) are inconsistent by sub-proof
% 169.04/25.39 | | | | | | | | | | | | | | | #748.
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | Case 2:
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | (99) all_58_13 = e0 & op(e0, e2) = e0
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 169.04/25.39 | | | | | | | | | | | | | | | (100) op(e0, e2) = e0
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | | REF_CLOSE: (16), (38), (47), (58), (100) are inconsistent by
% 169.04/25.39 | | | | | | | | | | | | | | | sub-proof #889.
% 169.04/25.39 | | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | | End of split
% 169.04/25.39 | | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | End of split
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | Case 2:
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | (101) all_58_13 = e3 & op(e0, e2) = e3
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | ALPHA: (101) implies:
% 169.04/25.39 | | | | | | | | | | | | | (102) all_58_13 = e3
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | | REF_CLOSE: (11), (57), (102) are inconsistent by sub-proof
% 169.04/25.39 | | | | | | | | | | | | | #194.
% 169.04/25.39 | | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | | End of split
% 169.04/25.39 | | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | | End of split
% 169.04/25.39 | | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | | End of split
% 169.04/25.39 | | | | | | | | | |
% 169.04/25.39 | | | | | | | | | End of split
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | End of split
% 169.04/25.39 | | | | | | | |
% 169.04/25.39 | | | | | | | Case 2:
% 169.04/25.39 | | | | | | | |
% 169.04/25.39 | | | | | | | | (103) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 &
% 169.04/25.39 | | | | | | | | op(e3, e0) = e2)
% 169.04/25.39 | | | | | | | |
% 169.04/25.39 | | | | | | | | BETA: splitting (103) gives:
% 169.04/25.39 | | | | | | | |
% 169.04/25.39 | | | | | | | | Case 1:
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | (104) all_58_4 = e2 & op(e3, e1) = e2
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | ALPHA: (104) implies:
% 169.04/25.39 | | | | | | | | | (105) all_58_4 = e2
% 169.04/25.39 | | | | | | | | | (106) op(e3, e1) = e2
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | REF_CLOSE: (10), (11), (12), (15), (16), (17), (29), (37),
% 169.04/25.39 | | | | | | | | | (38), (39), (43), (45), (46), (52), (105), (106)
% 169.04/25.39 | | | | | | | | | are inconsistent by sub-proof #801.
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | Case 2:
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | (107) all_58_9 = e2 & op(e3, e0) = e2
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | ALPHA: (107) implies:
% 169.04/25.39 | | | | | | | | | (108) all_58_9 = e2
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | COMBINE_EQS: (46), (108) imply:
% 169.04/25.39 | | | | | | | | | (109) e2 = e1
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | SIMP: (109) implies:
% 169.04/25.39 | | | | | | | | | (110) e2 = e1
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | COMBINE_EQS: (65), (110) imply:
% 169.04/25.39 | | | | | | | | | (111) all_58_12 = e1
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11),
% 169.04/25.39 | | | | | | | | | (12), (15), (16), (17), (20), (22), (23), (24),
% 169.04/25.39 | | | | | | | | | (26), (27), (29), (30), (31), (33), (36), (37),
% 169.04/25.39 | | | | | | | | | (38), (39), (40), (41), (42), (43), (44), (45),
% 169.04/25.39 | | | | | | | | | (46), (49), (52), (62), (111) are inconsistent by
% 169.04/25.39 | | | | | | | | | sub-proof #140.
% 169.04/25.39 | | | | | | | | |
% 169.04/25.39 | | | | | | | | End of split
% 169.04/25.39 | | | | | | | |
% 169.04/25.39 | | | | | | | End of split
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | Case 2:
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | | (112) all_58_13 = e2 & op(e0, e2) = e2
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | | ALPHA: (112) implies:
% 169.04/25.39 | | | | | | | (113) op(e0, e2) = e2
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | | REF_CLOSE: (38), (45), (58), (113) are inconsistent by sub-proof
% 169.04/25.39 | | | | | | | #968.
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | End of split
% 169.04/25.39 | | | | | |
% 169.04/25.39 | | | | | Case 2:
% 169.04/25.39 | | | | | |
% 169.04/25.39 | | | | | | (114) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 169.04/25.39 | | | | | | op(e0, e0) = e2)
% 169.04/25.39 | | | | | |
% 169.04/25.39 | | | | | | BETA: splitting (114) gives:
% 169.04/25.39 | | | | | |
% 169.04/25.39 | | | | | | Case 1:
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | | (115) all_58_14 = e2 & op(e0, e1) = e2
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | | ALPHA: (115) implies:
% 169.04/25.39 | | | | | | | (116) all_58_14 = e2
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | | REF_CLOSE: (8), (10), (11), (12), (15), (16), (20), (27), (29),
% 169.04/25.39 | | | | | | | (34), (37), (38), (39), (40), (45), (46), (49), (52),
% 169.04/25.39 | | | | | | | (116) are inconsistent by sub-proof #135.
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | Case 2:
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | | (117) all_58_15 = e2 & op(e0, e0) = e2
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | | REF_CLOSE: (2), (33), (38), (117) are inconsistent by sub-proof
% 169.04/25.39 | | | | | | | #854.
% 169.04/25.39 | | | | | | |
% 169.04/25.39 | | | | | | End of split
% 169.04/25.39 | | | | | |
% 169.04/25.39 | | | | | End of split
% 169.04/25.39 | | | | |
% 169.04/25.39 | | | | Case 2:
% 169.04/25.39 | | | | |
% 169.04/25.39 | | | | | (118) all_58_15 = e2 & op(e0, e0) = e2
% 169.04/25.39 | | | | |
% 169.04/25.39 | | | | | REF_CLOSE: (2), (33), (38), (118) are inconsistent by sub-proof #854.
% 169.04/25.39 | | | | |
% 169.04/25.39 | | | | End of split
% 169.04/25.39 | | | |
% 169.04/25.39 | | | End of split
% 169.04/25.39 | | |
% 169.04/25.39 | | End of split
% 169.04/25.39 | |
% 169.04/25.39 | Case 2:
% 169.04/25.39 | |
% 169.04/25.39 | | (119) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.04/25.39 | | e1)
% 169.04/25.39 | |
% 169.04/25.39 | | BETA: splitting (119) gives:
% 169.04/25.39 | |
% 169.04/25.39 | | Case 1:
% 169.04/25.39 | | |
% 169.04/25.39 | | | (120) all_58_14 = e1 & op(e0, e1) = e1
% 169.04/25.39 | | |
% 169.04/25.39 | | | REF_CLOSE: (8), (10), (11), (12), (15), (16), (20), (27), (29), (34),
% 169.04/25.39 | | | (37), (38), (39), (40), (45), (46), (49), (52), (120) are
% 169.04/25.39 | | | inconsistent by sub-proof #131.
% 169.04/25.39 | | |
% 169.04/25.39 | | Case 2:
% 169.04/25.39 | | |
% 169.04/25.39 | | | (121) all_58_15 = e1 & op(e0, e0) = e1
% 169.04/25.39 | | |
% 169.04/25.39 | | | REF_CLOSE: (9), (33), (38), (121) are inconsistent by sub-proof #130.
% 169.04/25.39 | | |
% 169.04/25.39 | | End of split
% 169.04/25.39 | |
% 169.04/25.39 | End of split
% 169.04/25.39 |
% 169.04/25.39 End of proof
% 169.04/25.39
% 169.04/25.39 Sub-proof #130 shows that the following formulas are inconsistent:
% 169.04/25.39 ----------------------------------------------------------------
% 169.04/25.39 (1) all_58_15 = e1 & op(e0, e0) = e1
% 169.04/25.39 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.39 (3) op(e0, e0) = all_4_2
% 169.04/25.39 (4) ~ (all_4_2 = e1)
% 169.04/25.39
% 169.04/25.39 Begin of proof
% 169.04/25.39 |
% 169.04/25.39 | ALPHA: (1) implies:
% 169.04/25.39 | (5) op(e0, e0) = e1
% 169.04/25.39 |
% 169.04/25.39 | GROUND_INST: instantiating (2) with all_4_2, e1, e0, e0, simplifying with (3),
% 169.04/25.39 | (5) gives:
% 169.04/25.39 | (6) all_4_2 = e1
% 169.04/25.39 |
% 169.04/25.39 | REDUCE: (4), (6) imply:
% 169.04/25.39 | (7) $false
% 169.04/25.39 |
% 169.04/25.39 | CLOSE: (7) is inconsistent.
% 169.04/25.39 |
% 169.04/25.39 End of proof
% 169.04/25.39
% 169.04/25.39 Sub-proof #131 shows that the following formulas are inconsistent:
% 169.04/25.39 ----------------------------------------------------------------
% 169.04/25.39 (1) all_58_14 = e1 & op(e0, e1) = e1
% 169.04/25.39 (2) ~ (all_6_2 = e3)
% 169.04/25.39 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.04/25.39 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.39 (4) ~ (e3 = e1)
% 169.04/25.39 (5) op(e3, e3) = e1
% 169.04/25.39 (6) op(e3, e1) = all_52_8
% 169.04/25.39 (7) ~ (e1 = e0)
% 169.04/25.39 (8) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.04/25.39 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.04/25.39 (9) op(e1, e1) = all_6_2
% 169.04/25.39 (10) ~ (e3 = e0)
% 169.04/25.39 (11) op(e3, e0) = e1
% 169.04/25.39 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.04/25.39 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.04/25.39 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.39 (14) ~ (e2 = e0)
% 169.04/25.39 (15) op(e2, e1) = e2
% 169.04/25.39 (16) ~ (e2 = e1)
% 169.04/25.39 (17) all_58_9 = e1
% 169.04/25.39 (18) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.04/25.39 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.04/25.39 (19) ~ (e3 = e2)
% 169.04/25.39
% 169.04/25.39 Begin of proof
% 169.04/25.39 |
% 169.04/25.39 | ALPHA: (1) implies:
% 169.04/25.39 | (20) op(e0, e1) = e1
% 169.04/25.39 |
% 169.04/25.39 | BETA: splitting (8) gives:
% 169.04/25.39 |
% 169.04/25.39 | Case 1:
% 169.04/25.39 | |
% 169.04/25.39 | | (21) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 169.04/25.39 | | e3)
% 169.04/25.39 | |
% 169.04/25.39 | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (11), (12), (13), (14), (15),
% 169.04/25.39 | | (16), (17), (18), (19), (21) are inconsistent by sub-proof #136.
% 169.04/25.39 | |
% 169.04/25.39 | Case 2:
% 169.04/25.39 | |
% 169.04/25.39 | | (22) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 169.04/25.39 | | e3)
% 169.04/25.39 | |
% 169.04/25.39 | | REF_CLOSE: (2), (4), (9), (13), (20), (22) are inconsistent by sub-proof
% 169.04/25.39 | | #132.
% 169.04/25.39 | |
% 169.04/25.39 | End of split
% 169.04/25.39 |
% 169.04/25.39 End of proof
% 169.04/25.39
% 169.04/25.39 Sub-proof #132 shows that the following formulas are inconsistent:
% 169.04/25.39 ----------------------------------------------------------------
% 169.04/25.39 (1) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.04/25.39 (2) ~ (all_6_2 = e3)
% 169.04/25.39 (3) ~ (e3 = e1)
% 169.04/25.39 (4) op(e0, e1) = e1
% 169.04/25.39 (5) op(e1, e1) = all_6_2
% 169.04/25.39 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.39
% 169.04/25.39 Begin of proof
% 169.04/25.39 |
% 169.04/25.39 | BETA: splitting (1) gives:
% 169.04/25.39 |
% 169.04/25.39 | Case 1:
% 169.04/25.39 | |
% 169.04/25.39 | | (7) all_58_8 = e3 & op(e1, e1) = e3
% 169.04/25.39 | |
% 169.04/25.39 | | REF_CLOSE: (2), (5), (6), (7) are inconsistent by sub-proof #961.
% 169.04/25.39 | |
% 169.04/25.39 | Case 2:
% 169.04/25.39 | |
% 169.04/25.39 | | (8) all_58_14 = e3 & op(e0, e1) = e3
% 169.04/25.39 | |
% 169.04/25.39 | | ALPHA: (8) implies:
% 169.04/25.39 | | (9) op(e0, e1) = e3
% 169.04/25.39 | |
% 169.04/25.39 | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #133.
% 169.04/25.39 | |
% 169.04/25.39 | End of split
% 169.04/25.39 |
% 169.04/25.39 End of proof
% 169.04/25.39
% 169.04/25.39 Sub-proof #133 shows that the following formulas are inconsistent:
% 169.04/25.39 ----------------------------------------------------------------
% 169.04/25.39 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.39 (2) op(e0, e1) = e3
% 169.04/25.39 (3) op(e0, e1) = e1
% 169.04/25.39 (4) ~ (e3 = e1)
% 169.04/25.39
% 169.04/25.39 Begin of proof
% 169.04/25.39 |
% 169.04/25.39 | GROUND_INST: instantiating (1) with e1, e3, e1, e0, simplifying with (2), (3)
% 169.04/25.39 | gives:
% 169.04/25.39 | (5) e3 = e1
% 169.04/25.39 |
% 169.04/25.39 | REDUCE: (4), (5) imply:
% 169.04/25.39 | (6) $false
% 169.04/25.39 |
% 169.04/25.39 | CLOSE: (6) is inconsistent.
% 169.04/25.39 |
% 169.04/25.39 End of proof
% 169.04/25.39
% 169.04/25.39 Sub-proof #134 shows that the following formulas are inconsistent:
% 169.04/25.39 ----------------------------------------------------------------
% 169.04/25.39 (1) ~ (e3 = e1)
% 169.04/25.39 (2) all_56_12 = e0
% 169.04/25.39 (3) ~ (e1 = e0)
% 169.04/25.39 (4) ~ (all_56_12 = e0) | (all_56_11 = e2 & op(e2, e0) = e2)
% 169.04/25.39 (5) all_58_11 = e2
% 169.04/25.39 (6) ~ (e3 = e0)
% 169.04/25.39 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.39 (8) ~ (e2 = e0)
% 169.04/25.39 (9) all_58_9 = e1
% 169.04/25.39 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.04/25.39 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.04/25.39 (11) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.39 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.04/25.39 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.04/25.39 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.04/25.39 (12) op(e2, e0) = all_52_13
% 169.04/25.39 (13) ~ (e3 = e2)
% 169.04/25.39
% 169.04/25.39 Begin of proof
% 169.04/25.39 |
% 169.04/25.39 | BETA: splitting (4) gives:
% 169.04/25.39 |
% 169.04/25.39 | Case 1:
% 169.04/25.39 | |
% 169.04/25.39 | | (14) ~ (all_56_12 = e0)
% 169.04/25.39 | |
% 169.04/25.39 | | REDUCE: (2), (14) imply:
% 169.04/25.39 | | (15) $false
% 169.04/25.39 | |
% 169.04/25.39 | | CLOSE: (15) is inconsistent.
% 169.04/25.39 | |
% 169.04/25.39 | Case 2:
% 169.04/25.39 | |
% 169.04/25.39 | | (16) all_56_11 = e2 & op(e2, e0) = e2
% 169.04/25.39 | |
% 169.04/25.39 | | ALPHA: (16) implies:
% 169.04/25.39 | | (17) op(e2, e0) = e2
% 169.04/25.39 | |
% 169.04/25.39 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (17)
% 169.04/25.39 | | are inconsistent by sub-proof #527.
% 169.04/25.39 | |
% 169.04/25.39 | End of split
% 169.04/25.39 |
% 169.04/25.39 End of proof
% 169.04/25.39
% 169.04/25.39 Sub-proof #135 shows that the following formulas are inconsistent:
% 169.04/25.39 ----------------------------------------------------------------
% 169.04/25.39 (1) all_58_14 = e2
% 169.04/25.39 (2) ~ (all_6_2 = e3)
% 169.04/25.39 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.04/25.39 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.39 (4) ~ (e3 = e1)
% 169.04/25.39 (5) op(e3, e3) = e1
% 169.04/25.39 (6) op(e3, e1) = all_52_8
% 169.04/25.39 (7) ~ (e1 = e0)
% 169.04/25.39 (8) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.04/25.39 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.04/25.39 (9) op(e1, e1) = all_6_2
% 169.04/25.39 (10) ~ (e3 = e0)
% 169.04/25.40 (11) op(e3, e0) = e1
% 169.04/25.40 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.04/25.40 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.04/25.40 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.40 (14) ~ (e2 = e0)
% 169.04/25.40 (15) op(e2, e1) = e2
% 169.04/25.40 (16) ~ (e2 = e1)
% 169.04/25.40 (17) all_58_9 = e1
% 169.04/25.40 (18) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.04/25.40 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.04/25.40 (19) ~ (e3 = e2)
% 169.04/25.40
% 169.04/25.40 Begin of proof
% 169.04/25.40 |
% 169.04/25.40 | BETA: splitting (8) gives:
% 169.04/25.40 |
% 169.04/25.40 | Case 1:
% 169.04/25.40 | |
% 169.04/25.40 | | (20) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 169.04/25.40 | | e3)
% 169.04/25.40 | |
% 169.04/25.40 | | REF_CLOSE: (3), (4), (5), (6), (7), (10), (11), (12), (13), (14), (15),
% 169.04/25.40 | | (16), (17), (18), (19), (20) are inconsistent by sub-proof #136.
% 169.04/25.40 | |
% 169.04/25.40 | Case 2:
% 169.04/25.40 | |
% 169.04/25.40 | | (21) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 169.04/25.40 | | e3)
% 169.04/25.40 | |
% 169.04/25.40 | | BETA: splitting (21) gives:
% 169.04/25.40 | |
% 169.04/25.40 | | Case 1:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (22) all_58_8 = e3 & op(e1, e1) = e3
% 169.04/25.40 | | |
% 169.04/25.40 | | | REF_CLOSE: (2), (9), (13), (22) are inconsistent by sub-proof #961.
% 169.04/25.40 | | |
% 169.04/25.40 | | Case 2:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (23) all_58_14 = e3 & op(e0, e1) = e3
% 169.04/25.40 | | |
% 169.04/25.40 | | | REF_CLOSE: (1), (19), (23) are inconsistent by sub-proof #809.
% 169.04/25.40 | | |
% 169.04/25.40 | | End of split
% 169.04/25.40 | |
% 169.04/25.40 | End of split
% 169.04/25.40 |
% 169.04/25.40 End of proof
% 169.04/25.40
% 169.04/25.40 Sub-proof #136 shows that the following formulas are inconsistent:
% 169.04/25.40 ----------------------------------------------------------------
% 169.04/25.40 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.04/25.40 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.40 (2) ~ (e3 = e1)
% 169.04/25.40 (3) op(e3, e3) = e1
% 169.04/25.40 (4) op(e3, e1) = all_52_8
% 169.04/25.40 (5) ~ (e1 = e0)
% 169.04/25.40 (6) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 169.04/25.40 (7) ~ (e3 = e0)
% 169.04/25.40 (8) op(e3, e0) = e1
% 169.04/25.40 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.04/25.40 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.04/25.40 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.40 (11) ~ (e2 = e0)
% 169.04/25.40 (12) op(e2, e1) = e2
% 169.04/25.40 (13) ~ (e2 = e1)
% 169.04/25.40 (14) all_58_9 = e1
% 169.04/25.40 (15) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.04/25.40 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.04/25.40 (16) ~ (e3 = e2)
% 169.04/25.40
% 169.04/25.40 Begin of proof
% 169.04/25.40 |
% 169.04/25.40 | BETA: splitting (6) gives:
% 169.04/25.40 |
% 169.04/25.40 | Case 1:
% 169.04/25.40 | |
% 169.04/25.40 | | (17) all_58_4 = e3 & op(e3, e1) = e3
% 169.04/25.40 | |
% 169.04/25.40 | | ALPHA: (17) implies:
% 169.04/25.40 | | (18) all_58_4 = e3
% 169.04/25.40 | | (19) op(e3, e1) = e3
% 169.04/25.40 | |
% 169.04/25.40 | | BETA: splitting (1) gives:
% 169.04/25.40 | |
% 169.04/25.40 | | Case 1:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (20) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 169.04/25.40 | | | e0)
% 169.04/25.40 | | |
% 169.04/25.40 | | | BETA: splitting (20) gives:
% 169.04/25.40 | | |
% 169.04/25.40 | | | Case 1:
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | (21) all_58_0 = e0 & op(e3, e3) = e0
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | ALPHA: (21) implies:
% 169.04/25.40 | | | | (22) op(e3, e3) = e0
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | REF_CLOSE: (3), (5), (10), (22) are inconsistent by sub-proof #907.
% 169.04/25.40 | | | |
% 169.04/25.40 | | | Case 2:
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | (23) all_58_1 = e0 & op(e3, e2) = e0
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | ALPHA: (23) implies:
% 169.04/25.40 | | | | (24) all_58_1 = e0
% 169.04/25.40 | | | | (25) op(e3, e2) = e0
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | REF_CLOSE: (2), (3), (4), (7), (9), (10), (11), (13), (14), (15), (16),
% 169.04/25.40 | | | | (19), (24), (25) are inconsistent by sub-proof #137.
% 169.04/25.40 | | | |
% 169.04/25.40 | | | End of split
% 169.04/25.40 | | |
% 169.04/25.40 | | Case 2:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (26) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 169.04/25.40 | | | e0)
% 169.04/25.40 | | |
% 169.04/25.40 | | | BETA: splitting (26) gives:
% 169.04/25.40 | | |
% 169.04/25.40 | | | Case 1:
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | (27) all_58_4 = e0 & op(e3, e1) = e0
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | ALPHA: (27) implies:
% 169.04/25.40 | | | | (28) all_58_4 = e0
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | REF_CLOSE: (7), (18), (28) are inconsistent by sub-proof #894.
% 169.04/25.40 | | | |
% 169.04/25.40 | | | Case 2:
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | (29) all_58_9 = e0 & op(e3, e0) = e0
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | ALPHA: (29) implies:
% 169.04/25.40 | | | | (30) op(e3, e0) = e0
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | REF_CLOSE: (5), (8), (10), (30) are inconsistent by sub-proof #553.
% 169.04/25.40 | | | |
% 169.04/25.40 | | | End of split
% 169.04/25.40 | | |
% 169.04/25.40 | | End of split
% 169.04/25.40 | |
% 169.04/25.40 | Case 2:
% 169.04/25.40 | |
% 169.04/25.40 | | (31) all_58_5 = e3 & op(e2, e1) = e3
% 169.04/25.40 | |
% 169.04/25.40 | | REF_CLOSE: (10), (12), (16), (31) are inconsistent by sub-proof #150.
% 169.04/25.40 | |
% 169.04/25.40 | End of split
% 169.04/25.40 |
% 169.04/25.40 End of proof
% 169.04/25.40
% 169.04/25.40 Sub-proof #137 shows that the following formulas are inconsistent:
% 169.04/25.40 ----------------------------------------------------------------
% 169.04/25.40 (1) ~ (e3 = e1)
% 169.04/25.40 (2) op(e3, e3) = e1
% 169.04/25.40 (3) op(e3, e1) = all_52_8
% 169.04/25.40 (4) op(e3, e1) = e3
% 169.04/25.40 (5) ~ (e3 = e0)
% 169.04/25.40 (6) op(e3, e2) = e0
% 169.04/25.40 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.04/25.40 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.04/25.40 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.40 (9) ~ (e2 = e0)
% 169.04/25.40 (10) ~ (e2 = e1)
% 169.04/25.40 (11) all_58_9 = e1
% 169.04/25.40 (12) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.04/25.40 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.04/25.40 (13) all_58_1 = e0
% 169.04/25.40 (14) ~ (e3 = e2)
% 169.04/25.40
% 169.04/25.40 Begin of proof
% 169.04/25.40 |
% 169.04/25.40 | BETA: splitting (12) gives:
% 169.04/25.40 |
% 169.04/25.40 | Case 1:
% 169.04/25.40 | |
% 169.04/25.40 | | (15) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 169.04/25.40 | | e2)
% 169.04/25.40 | |
% 169.04/25.40 | | BETA: splitting (15) gives:
% 169.04/25.40 | |
% 169.04/25.40 | | Case 1:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (16) all_58_0 = e2 & op(e3, e3) = e2
% 169.04/25.40 | | |
% 169.04/25.40 | | | ALPHA: (16) implies:
% 169.04/25.40 | | | (17) op(e3, e3) = e2
% 169.04/25.40 | | |
% 169.04/25.40 | | | REF_CLOSE: (2), (8), (10), (17) are inconsistent by sub-proof #957.
% 169.04/25.40 | | |
% 169.04/25.40 | | Case 2:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (18) all_58_1 = e2 & op(e3, e2) = e2
% 169.04/25.40 | | |
% 169.04/25.40 | | | ALPHA: (18) implies:
% 169.04/25.40 | | | (19) op(e3, e2) = e2
% 169.04/25.40 | | |
% 169.04/25.40 | | | REF_CLOSE: (6), (8), (9), (19) are inconsistent by sub-proof #953.
% 169.04/25.40 | | |
% 169.04/25.40 | | End of split
% 169.04/25.40 | |
% 169.04/25.40 | Case 2:
% 169.04/25.40 | |
% 169.04/25.40 | | (20) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 169.04/25.40 | | e2)
% 169.04/25.40 | |
% 169.04/25.40 | | BETA: splitting (20) gives:
% 169.04/25.40 | |
% 169.04/25.40 | | Case 1:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (21) all_58_4 = e2 & op(e3, e1) = e2
% 169.04/25.40 | | |
% 169.04/25.40 | | | ALPHA: (21) implies:
% 169.04/25.40 | | | (22) all_58_4 = e2
% 169.04/25.40 | | | (23) op(e3, e1) = e2
% 169.04/25.40 | | |
% 169.04/25.40 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (13), (14),
% 169.04/25.40 | | | (22), (23) are inconsistent by sub-proof #802.
% 169.04/25.40 | | |
% 169.04/25.40 | | Case 2:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (24) all_58_9 = e2 & op(e3, e0) = e2
% 169.04/25.40 | | |
% 169.04/25.40 | | | ALPHA: (24) implies:
% 169.04/25.40 | | | (25) all_58_9 = e2
% 169.04/25.40 | | |
% 169.04/25.40 | | | REF_CLOSE: (10), (11), (25) are inconsistent by sub-proof #942.
% 169.04/25.40 | | |
% 169.04/25.40 | | End of split
% 169.04/25.40 | |
% 169.04/25.40 | End of split
% 169.04/25.40 |
% 169.04/25.40 End of proof
% 169.04/25.40
% 169.04/25.40 Sub-proof #138 shows that the following formulas are inconsistent:
% 169.04/25.40 ----------------------------------------------------------------
% 169.04/25.40 (1) all_58_12 = e2
% 169.04/25.40 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.04/25.40 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.04/25.40 (3) ~ (e3 = e1)
% 169.04/25.40 (4) op(e1, e3) = all_52_2
% 169.04/25.40 (5) ~ (e1 = e0)
% 169.04/25.40 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.04/25.40 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.04/25.40 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.04/25.40 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.04/25.40 (8) ~ (e3 = e0)
% 169.04/25.40 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.40 (10) ~ (e2 = e0)
% 169.04/25.40 (11) all_58_0 = e2
% 169.04/25.40 (12) op(e3, e3) = e2
% 169.04/25.40 (13) ~ (e2 = e1)
% 169.04/25.40 (14) ~ (e3 = e2)
% 169.04/25.40
% 169.04/25.40 Begin of proof
% 169.04/25.40 |
% 169.04/25.40 | BETA: splitting (7) gives:
% 169.04/25.40 |
% 169.04/25.40 | Case 1:
% 169.04/25.40 | |
% 169.04/25.40 | | (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 169.04/25.40 | | e1)
% 169.04/25.40 | |
% 169.04/25.40 | | BETA: splitting (15) gives:
% 169.04/25.40 | |
% 169.04/25.40 | | Case 1:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (16) all_58_0 = e1 & op(e3, e3) = e1
% 169.04/25.40 | | |
% 169.04/25.40 | | | ALPHA: (16) implies:
% 169.04/25.40 | | | (17) op(e3, e3) = e1
% 169.04/25.40 | | |
% 169.04/25.40 | | | REF_CLOSE: (9), (12), (13), (17) are inconsistent by sub-proof #957.
% 169.04/25.40 | | |
% 169.04/25.40 | | Case 2:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (18) all_58_2 = e1 & op(e2, e3) = e1
% 169.04/25.40 | | |
% 169.04/25.40 | | | ALPHA: (18) implies:
% 169.04/25.40 | | | (19) all_58_2 = e1
% 169.04/25.40 | | |
% 169.04/25.40 | | | BETA: splitting (6) gives:
% 169.04/25.40 | | |
% 169.04/25.40 | | | Case 1:
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 169.04/25.40 | | | | = e3)
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | BETA: splitting (20) gives:
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | Case 1:
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | (21) all_58_0 = e3 & op(e3, e3) = e3
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | ALPHA: (21) implies:
% 169.04/25.40 | | | | | (22) op(e3, e3) = e3
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | REF_CLOSE: (9), (12), (14), (22) are inconsistent by sub-proof #838.
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | Case 2:
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | (23) all_58_2 = e3 & op(e2, e3) = e3
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | REF_CLOSE: (3), (19), (23) are inconsistent by sub-proof #679.
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | End of split
% 169.04/25.40 | | | |
% 169.04/25.40 | | | Case 2:
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | (24) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 169.04/25.40 | | | | = e3)
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | BETA: splitting (24) gives:
% 169.04/25.40 | | | |
% 169.04/25.40 | | | | Case 1:
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | (25) all_58_6 = e3 & op(e1, e3) = e3
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | ALPHA: (25) implies:
% 169.04/25.40 | | | | | (26) all_58_6 = e3
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | REF_CLOSE: (1), (2), (5), (8), (10), (11), (19), (26) are inconsistent
% 169.04/25.40 | | | | | by sub-proof #488.
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | Case 2:
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | (27) all_58_12 = e3 & op(e0, e3) = e3
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | ALPHA: (27) implies:
% 169.04/25.40 | | | | | (28) all_58_12 = e3
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | | REF_CLOSE: (1), (14), (28) are inconsistent by sub-proof #635.
% 169.04/25.40 | | | | |
% 169.04/25.40 | | | | End of split
% 169.04/25.40 | | | |
% 169.04/25.40 | | | End of split
% 169.04/25.40 | | |
% 169.04/25.40 | | End of split
% 169.04/25.40 | |
% 169.04/25.40 | Case 2:
% 169.04/25.40 | |
% 169.04/25.40 | | (29) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 169.04/25.40 | | e1)
% 169.04/25.40 | |
% 169.04/25.40 | | BETA: splitting (29) gives:
% 169.04/25.40 | |
% 169.04/25.40 | | Case 1:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (30) all_58_6 = e1 & op(e1, e3) = e1
% 169.04/25.40 | | |
% 169.04/25.40 | | | ALPHA: (30) implies:
% 169.04/25.40 | | | (31) op(e1, e3) = e1
% 169.04/25.40 | | |
% 169.04/25.40 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.04/25.40 | | | (13), (14), (31) are inconsistent by sub-proof #486.
% 169.04/25.40 | | |
% 169.04/25.40 | | Case 2:
% 169.04/25.40 | | |
% 169.04/25.40 | | | (32) all_58_12 = e1 & op(e0, e3) = e1
% 169.04/25.40 | | |
% 169.04/25.40 | | | REF_CLOSE: (1), (13), (32) are inconsistent by sub-proof #891.
% 169.04/25.40 | | |
% 169.04/25.40 | | End of split
% 169.04/25.40 | |
% 169.04/25.40 | End of split
% 169.04/25.40 |
% 169.04/25.40 End of proof
% 169.04/25.40
% 169.04/25.40 Sub-proof #139 shows that the following formulas are inconsistent:
% 169.04/25.40 ----------------------------------------------------------------
% 169.04/25.40 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.04/25.40 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.04/25.40 (2) all_58_12 = e1
% 169.04/25.40 (3) ~ (all_4_2 = e2)
% 169.04/25.40 (4) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.40 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.04/25.40 (5) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 169.04/25.40 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 169.04/25.40 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.04/25.40 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.04/25.40 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.04/25.40 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.04/25.40 (8) ~ (all_6_2 = e3)
% 169.04/25.40 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.04/25.40 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.40 (10) ~ (e3 = e1)
% 169.04/25.40 (11) op(e3, e3) = e1
% 169.04/25.40 (12) op(e3, e1) = all_52_8
% 169.04/25.40 (13) ~ (e1 = e0)
% 169.04/25.40 (14) all_56_10 = e1
% 169.04/25.40 (15) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.04/25.40 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.04/25.40 (16) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.04/25.40 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.04/25.40 (17) op(e2, e3) = all_52_1
% 169.04/25.40 (18) all_58_3 = e1
% 169.04/25.40 (19) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.04/25.40 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.04/25.40 (20) ~ (all_6_2 = e2)
% 169.04/25.40 (21) op(e1, e1) = all_6_2
% 169.04/25.40 (22) ~ (e3 = e0)
% 169.04/25.40 (23) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.40 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.04/25.40 (24) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.04/25.40 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.04/25.40 (25) op(e0, e0) = all_4_2
% 169.04/25.40 (26) ~ (all_52_13 = e2)
% 169.04/25.40 (27) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.40 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.04/25.40 (28) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.04/25.40 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.04/25.40 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.40 (30) ~ (e2 = e0)
% 169.04/25.40 (31) op(e2, e1) = e2
% 169.04/25.40 (32) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.04/25.40 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.04/25.40 (33) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.04/25.40 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.04/25.40 (34) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 169.04/25.40 (35) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.40 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.04/25.40 (36) ~ (e2 = e1)
% 169.04/25.40 (37) all_58_9 = e1
% 169.04/25.41 (38) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.04/25.41 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.04/25.41 (39) op(e2, e0) = all_52_13
% 169.04/25.41 (40) ~ (e3 = e2)
% 169.04/25.41
% 169.04/25.41 Begin of proof
% 169.04/25.41 |
% 169.04/25.41 | BETA: splitting (16) gives:
% 169.04/25.41 |
% 169.04/25.41 | Case 1:
% 169.04/25.41 | |
% 169.04/25.41 | | (41) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 169.04/25.41 | | e2)
% 169.04/25.41 | |
% 169.04/25.41 | | REF_CLOSE: (26), (29), (36), (37), (39), (41) are inconsistent by sub-proof
% 169.04/25.41 | | #142.
% 169.04/25.41 | |
% 169.04/25.41 | Case 2:
% 169.04/25.41 | |
% 169.04/25.41 | | (42) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.04/25.41 | | e2)
% 169.04/25.41 | |
% 169.04/25.41 | | BETA: splitting (42) gives:
% 169.04/25.41 | |
% 169.04/25.41 | | Case 1:
% 169.04/25.41 | | |
% 169.04/25.41 | | | (43) all_58_11 = e2 & op(e1, e0) = e2
% 169.04/25.41 | | |
% 169.04/25.41 | | | ALPHA: (43) implies:
% 169.04/25.41 | | | (44) all_58_11 = e2
% 169.04/25.41 | | |
% 169.04/25.41 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.04/25.41 | | | (13), (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 169.04/25.41 | | | (24), (25), (27), (28), (29), (30), (31), (32), (33), (34),
% 169.04/25.41 | | | (35), (36), (37), (38), (40), (44) are inconsistent by
% 169.04/25.41 | | | sub-proof #140.
% 169.04/25.41 | | |
% 169.04/25.41 | | Case 2:
% 169.04/25.41 | | |
% 169.04/25.41 | | | (45) all_58_15 = e2 & op(e0, e0) = e2
% 169.04/25.41 | | |
% 169.04/25.41 | | | REF_CLOSE: (3), (25), (29), (45) are inconsistent by sub-proof #854.
% 169.04/25.41 | | |
% 169.04/25.41 | | End of split
% 169.04/25.41 | |
% 169.04/25.41 | End of split
% 169.04/25.41 |
% 169.04/25.41 End of proof
% 169.04/25.41
% 169.04/25.41 Sub-proof #140 shows that the following formulas are inconsistent:
% 169.04/25.41 ----------------------------------------------------------------
% 169.04/25.41 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.04/25.41 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.04/25.41 (2) all_58_12 = e1
% 169.04/25.41 (3) ~ (all_4_2 = e2)
% 169.04/25.41 (4) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.41 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.04/25.41 (5) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 169.04/25.41 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 169.04/25.41 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.04/25.41 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.04/25.41 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.04/25.41 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.04/25.41 (8) ~ (all_6_2 = e3)
% 169.04/25.41 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.04/25.41 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.41 (10) ~ (e3 = e1)
% 169.04/25.41 (11) op(e3, e3) = e1
% 169.04/25.41 (12) op(e3, e1) = all_52_8
% 169.04/25.41 (13) ~ (e1 = e0)
% 169.04/25.41 (14) all_56_10 = e1
% 169.04/25.41 (15) all_58_11 = e2
% 169.04/25.41 (16) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.04/25.41 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.04/25.41 (17) op(e2, e3) = all_52_1
% 169.04/25.41 (18) all_58_3 = e1
% 169.04/25.41 (19) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.04/25.41 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.04/25.41 (20) ~ (all_6_2 = e2)
% 169.04/25.41 (21) op(e1, e1) = all_6_2
% 169.04/25.41 (22) ~ (e3 = e0)
% 169.04/25.41 (23) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.41 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.04/25.41 (24) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.04/25.41 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.04/25.41 (25) op(e0, e0) = all_4_2
% 169.04/25.41 (26) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.41 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.04/25.41 (27) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.04/25.41 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.04/25.41 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.41 (29) ~ (e2 = e0)
% 169.04/25.41 (30) op(e2, e1) = e2
% 169.04/25.41 (31) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.04/25.41 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.04/25.41 (32) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.04/25.41 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.04/25.41 (33) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 169.04/25.41 (34) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.41 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.04/25.41 (35) ~ (e2 = e1)
% 169.04/25.41 (36) all_58_9 = e1
% 169.04/25.41 (37) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.04/25.41 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.04/25.41 (38) ~ (e3 = e2)
% 169.04/25.41
% 169.04/25.41 Begin of proof
% 169.04/25.41 |
% 169.04/25.41 | BETA: splitting (1) gives:
% 169.04/25.41 |
% 169.04/25.41 | Case 1:
% 169.04/25.41 | |
% 169.04/25.41 | | (39) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 169.04/25.41 | | e2)
% 169.04/25.41 | |
% 169.04/25.41 | | BETA: splitting (39) gives:
% 169.04/25.41 | |
% 169.04/25.41 | | Case 1:
% 169.04/25.41 | | |
% 169.04/25.41 | | | (40) all_58_12 = e2 & op(e0, e3) = e2
% 169.04/25.41 | | |
% 169.04/25.41 | | | REF_CLOSE: (2), (35), (40) are inconsistent by sub-proof #814.
% 169.04/25.41 | | |
% 169.04/25.41 | | Case 2:
% 169.04/25.41 | | |
% 169.04/25.41 | | | (41) all_58_13 = e2 & op(e0, e2) = e2
% 169.04/25.41 | | |
% 169.04/25.41 | | | ALPHA: (41) implies:
% 169.04/25.41 | | | (42) all_58_13 = e2
% 169.04/25.41 | | |
% 169.04/25.41 | | | BETA: splitting (37) gives:
% 169.04/25.41 | | |
% 169.04/25.41 | | | Case 1:
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | (43) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 169.04/25.41 | | | | = e2)
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | BETA: splitting (43) gives:
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | Case 1:
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | (44) all_58_0 = e2 & op(e3, e3) = e2
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | ALPHA: (44) implies:
% 169.04/25.41 | | | | | (45) op(e3, e3) = e2
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | REF_CLOSE: (11), (28), (35), (45) are inconsistent by sub-proof #957.
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | Case 2:
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | (46) all_58_1 = e2 & op(e3, e2) = e2
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | ALPHA: (46) implies:
% 169.04/25.41 | | | | | (47) all_58_1 = e2
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | BETA: splitting (4) gives:
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | Case 1:
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | (48) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2,
% 169.04/25.41 | | | | | | e2) = e3)
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | BETA: splitting (48) gives:
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | Case 1:
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | (49) all_58_1 = e3 & op(e3, e2) = e3
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | REF_CLOSE: (38), (47), (49) are inconsistent by sub-proof #904.
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | Case 2:
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | (50) all_58_3 = e3 & op(e2, e2) = e3
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | ALPHA: (50) implies:
% 169.04/25.41 | | | | | | | (51) all_58_3 = e3
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | REF_CLOSE: (6), (10), (13), (22), (26), (29), (35), (42), (47),
% 169.04/25.41 | | | | | | | (51) are inconsistent by sub-proof #864.
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | End of split
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | Case 2:
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | (52) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0,
% 169.04/25.41 | | | | | | e2) = e3)
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | BETA: splitting (52) gives:
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | Case 1:
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | (53) all_58_7 = e3 & op(e1, e2) = e3
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | ALPHA: (53) implies:
% 169.04/25.41 | | | | | | | (54) all_58_7 = e3
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | BETA: splitting (5) gives:
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | Case 1:
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | (55) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 &
% 169.04/25.41 | | | | | | | | op(e2, e3) = e2)
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | REF_CLOSE: (10), (11), (13), (17), (18), (22), (23), (28), (29),
% 169.04/25.41 | | | | | | | | (30), (34), (35), (38), (55) are inconsistent by
% 169.04/25.41 | | | | | | | | sub-proof #141.
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | Case 2:
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | (56) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 169.04/25.41 | | | | | | | | op(e0, e3) = e2)
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | BETA: splitting (56) gives:
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | Case 1:
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | (57) all_58_6 = e2 & op(e1, e3) = e2
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | ALPHA: (57) implies:
% 169.04/25.41 | | | | | | | | | (58) all_58_6 = e2
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | REF_CLOSE: (7), (10), (13), (15), (20), (21), (22), (24),
% 169.04/25.41 | | | | | | | | | (28), (29), (31), (32), (35), (38), (54), (58) are
% 169.04/25.41 | | | | | | | | | inconsistent by sub-proof #816.
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | Case 2:
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | (59) all_58_12 = e2 & op(e0, e3) = e2
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | ALPHA: (59) implies:
% 169.04/25.41 | | | | | | | | | (60) all_58_12 = e2
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | REF_CLOSE: (2), (35), (60) are inconsistent by sub-proof #862.
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | End of split
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | End of split
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | Case 2:
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | (61) all_58_13 = e3 & op(e0, e2) = e3
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | ALPHA: (61) implies:
% 169.04/25.41 | | | | | | | (62) all_58_13 = e3
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | REF_CLOSE: (38), (42), (62) are inconsistent by sub-proof #192.
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | End of split
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | End of split
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | End of split
% 169.04/25.41 | | | |
% 169.04/25.41 | | | Case 2:
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | (63) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 169.04/25.41 | | | | = e2)
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | REF_CLOSE: (9), (10), (11), (12), (13), (14), (22), (27), (28), (29),
% 169.04/25.41 | | | | (33), (35), (36), (38), (63) are inconsistent by sub-proof
% 169.04/25.41 | | | | #800.
% 169.04/25.41 | | | |
% 169.04/25.41 | | | End of split
% 169.04/25.41 | | |
% 169.04/25.41 | | End of split
% 169.04/25.41 | |
% 169.04/25.41 | Case 2:
% 169.04/25.41 | |
% 169.04/25.41 | | (64) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.04/25.41 | | e2)
% 169.04/25.41 | |
% 169.04/25.41 | | BETA: splitting (64) gives:
% 169.04/25.41 | |
% 169.04/25.41 | | Case 1:
% 169.04/25.41 | | |
% 169.04/25.41 | | | (65) all_58_14 = e2 & op(e0, e1) = e2
% 169.04/25.41 | | |
% 169.04/25.41 | | | ALPHA: (65) implies:
% 169.04/25.41 | | | (66) all_58_14 = e2
% 169.04/25.41 | | |
% 169.04/25.41 | | | BETA: splitting (16) gives:
% 169.04/25.41 | | |
% 169.04/25.41 | | | Case 1:
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | (67) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1)
% 169.04/25.41 | | | | = e3)
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | BETA: splitting (67) gives:
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | Case 1:
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | (68) all_58_4 = e3 & op(e3, e1) = e3
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | ALPHA: (68) implies:
% 169.04/25.41 | | | | | (69) all_58_4 = e3
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | BETA: splitting (5) gives:
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | Case 1:
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | (70) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 169.04/25.41 | | | | | | e3) = e2)
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | REF_CLOSE: (10), (11), (13), (17), (18), (22), (23), (28), (29),
% 169.04/25.41 | | | | | | (30), (34), (35), (38), (70) are inconsistent by
% 169.04/25.41 | | | | | | sub-proof #141.
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | Case 2:
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | (71) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0,
% 169.04/25.41 | | | | | | e3) = e2)
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | BETA: splitting (71) gives:
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | | Case 1:
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | (72) all_58_6 = e2 & op(e1, e3) = e2
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | ALPHA: (72) implies:
% 169.04/25.41 | | | | | | | (73) all_58_6 = e2
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | BETA: splitting (19) gives:
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | Case 1:
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | (74) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 &
% 169.04/25.41 | | | | | | | | op(e2, e1) = e0)
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | BETA: splitting (74) gives:
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | Case 1:
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | (75) all_58_4 = e0 & op(e3, e1) = e0
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | REF_CLOSE: (22), (69), (75) are inconsistent by sub-proof
% 169.04/25.41 | | | | | | | | | #704.
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | Case 2:
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | (76) all_58_5 = e0 & op(e2, e1) = e0
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | REF_CLOSE: (28), (29), (30), (76) are inconsistent by
% 169.04/25.41 | | | | | | | | | sub-proof #151.
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | End of split
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | Case 2:
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | (77) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 &
% 169.04/25.41 | | | | | | | | op(e0, e1) = e0)
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | BETA: splitting (77) gives:
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | | Case 1:
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | (78) all_58_8 = e0 & op(e1, e1) = e0
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | ALPHA: (78) implies:
% 169.04/25.41 | | | | | | | | | (79) all_58_8 = e0
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | REF_CLOSE: (10), (13), (15), (22), (31), (32), (35), (38),
% 169.04/25.41 | | | | | | | | | (73), (79) are inconsistent by sub-proof #817.
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | Case 2:
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | (80) all_58_14 = e0 & op(e0, e1) = e0
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | ALPHA: (80) implies:
% 169.04/25.41 | | | | | | | | | (81) all_58_14 = e0
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | | REF_CLOSE: (29), (66), (81) are inconsistent by sub-proof
% 169.04/25.41 | | | | | | | | | #806.
% 169.04/25.41 | | | | | | | | |
% 169.04/25.41 | | | | | | | | End of split
% 169.04/25.41 | | | | | | | |
% 169.04/25.41 | | | | | | | End of split
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | Case 2:
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | (82) all_58_12 = e2 & op(e0, e3) = e2
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | ALPHA: (82) implies:
% 169.04/25.41 | | | | | | | (83) all_58_12 = e2
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | | REF_CLOSE: (2), (35), (83) are inconsistent by sub-proof #862.
% 169.04/25.41 | | | | | | |
% 169.04/25.41 | | | | | | End of split
% 169.04/25.41 | | | | | |
% 169.04/25.41 | | | | | End of split
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | Case 2:
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | (84) all_58_5 = e3 & op(e2, e1) = e3
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | REF_CLOSE: (28), (30), (38), (84) are inconsistent by sub-proof #150.
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | End of split
% 169.04/25.41 | | | |
% 169.04/25.41 | | | Case 2:
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | (85) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1)
% 169.04/25.41 | | | | = e3)
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | BETA: splitting (85) gives:
% 169.04/25.41 | | | |
% 169.04/25.41 | | | | Case 1:
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | (86) all_58_8 = e3 & op(e1, e1) = e3
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | REF_CLOSE: (8), (21), (28), (86) are inconsistent by sub-proof #961.
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | Case 2:
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | (87) all_58_14 = e3 & op(e0, e1) = e3
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | | REF_CLOSE: (38), (66), (87) are inconsistent by sub-proof #809.
% 169.04/25.41 | | | | |
% 169.04/25.41 | | | | End of split
% 169.04/25.41 | | | |
% 169.04/25.41 | | | End of split
% 169.04/25.41 | | |
% 169.04/25.41 | | Case 2:
% 169.04/25.41 | | |
% 169.04/25.41 | | | (88) all_58_15 = e2 & op(e0, e0) = e2
% 169.04/25.41 | | |
% 169.04/25.41 | | | REF_CLOSE: (3), (25), (28), (88) are inconsistent by sub-proof #854.
% 169.04/25.41 | | |
% 169.04/25.41 | | End of split
% 169.04/25.41 | |
% 169.04/25.41 | End of split
% 169.04/25.41 |
% 169.04/25.41 End of proof
% 169.04/25.41
% 169.04/25.41 Sub-proof #141 shows that the following formulas are inconsistent:
% 169.04/25.41 ----------------------------------------------------------------
% 169.04/25.41 (1) ~ (e3 = e1)
% 169.04/25.41 (2) op(e3, e3) = e1
% 169.04/25.41 (3) ~ (e1 = e0)
% 169.04/25.41 (4) op(e2, e3) = all_52_1
% 169.04/25.41 (5) all_58_3 = e1
% 169.04/25.41 (6) ~ (e3 = e0)
% 169.04/25.41 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.41 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.04/25.41 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.41 (9) ~ (e2 = e0)
% 169.04/25.41 (10) op(e2, e1) = e2
% 169.04/25.41 (11) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.41 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.04/25.41 (12) ~ (e2 = e1)
% 169.04/25.41 (13) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 169.04/25.41 (14) ~ (e3 = e2)
% 169.04/25.41
% 169.04/25.41 Begin of proof
% 169.04/25.41 |
% 169.04/25.41 | BETA: splitting (13) gives:
% 169.04/25.41 |
% 169.04/25.41 | Case 1:
% 169.04/25.41 | |
% 169.04/25.41 | | (15) all_58_0 = e2 & op(e3, e3) = e2
% 169.04/25.41 | |
% 169.04/25.41 | | ALPHA: (15) implies:
% 169.04/25.41 | | (16) op(e3, e3) = e2
% 169.04/25.41 | |
% 169.04/25.41 | | REF_CLOSE: (2), (8), (12), (16) are inconsistent by sub-proof #957.
% 169.04/25.41 | |
% 169.04/25.41 | Case 2:
% 169.04/25.41 | |
% 169.04/25.41 | | (17) all_58_2 = e2 & op(e2, e3) = e2
% 169.04/25.41 | |
% 169.04/25.41 | | ALPHA: (17) implies:
% 169.04/25.41 | | (18) op(e2, e3) = e2
% 169.04/25.41 | |
% 169.04/25.41 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), (18)
% 169.04/25.41 | | are inconsistent by sub-proof #149.
% 169.04/25.41 | |
% 169.04/25.41 | End of split
% 169.04/25.41 |
% 169.04/25.41 End of proof
% 169.04/25.41
% 169.04/25.41 Sub-proof #142 shows that the following formulas are inconsistent:
% 169.04/25.41 ----------------------------------------------------------------
% 169.04/25.41 (1) ~ (all_52_13 = e2)
% 169.04/25.41 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.41 (3) ~ (e2 = e1)
% 169.04/25.41 (4) all_58_9 = e1
% 169.04/25.41 (5) op(e2, e0) = all_52_13
% 169.04/25.41 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 169.04/25.41
% 169.04/25.41 Begin of proof
% 169.04/25.41 |
% 169.04/25.41 | BETA: splitting (6) gives:
% 169.04/25.41 |
% 169.04/25.41 | Case 1:
% 169.04/25.41 | |
% 169.04/25.41 | | (7) all_58_9 = e2 & op(e3, e0) = e2
% 169.04/25.41 | |
% 169.04/25.41 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #382.
% 169.04/25.41 | |
% 169.04/25.41 | Case 2:
% 169.04/25.41 | |
% 169.04/25.41 | | (8) all_58_10 = e2 & op(e2, e0) = e2
% 169.04/25.41 | |
% 169.04/25.41 | | ALPHA: (8) implies:
% 169.04/25.41 | | (9) op(e2, e0) = e2
% 169.04/25.41 | |
% 169.04/25.41 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #662.
% 169.04/25.41 | |
% 169.04/25.41 | End of split
% 169.04/25.41 |
% 169.04/25.41 End of proof
% 169.04/25.41
% 169.04/25.41 Sub-proof #143 shows that the following formulas are inconsistent:
% 169.04/25.41 ----------------------------------------------------------------
% 169.04/25.41 (1) ~ (all_4_2 = e2)
% 169.04/25.41 (2) ~ (all_4_2 = e1)
% 169.04/25.42 (3) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3,
% 169.04/25.42 e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.04/25.42 (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~
% 169.04/25.42 (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.04/25.42 $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 169.04/25.42 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) = e1))
% 169.04/25.42 (4) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 169.04/25.42 (5) all_54_15 = all_4_2
% 169.04/25.42 (6) all_56_15 = all_4_2
% 169.04/25.42 (7) ~ (all_4_2 = e3)
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | ALPHA: (3) implies:
% 169.04/25.42 | (8) ~ (all_56_15 = e0)
% 169.04/25.42 |
% 169.04/25.42 | REDUCE: (6), (8) imply:
% 169.04/25.42 | (9) ~ (all_4_2 = e0)
% 169.04/25.42 |
% 169.04/25.42 | BETA: splitting (4) gives:
% 169.04/25.42 |
% 169.04/25.42 | Case 1:
% 169.04/25.42 | |
% 169.04/25.42 | | (10) all_54_15 = e3
% 169.04/25.42 | |
% 169.04/25.42 | | REF_CLOSE: (5), (7), (10) are inconsistent by sub-proof #992.
% 169.04/25.42 | |
% 169.04/25.42 | Case 2:
% 169.04/25.42 | |
% 169.04/25.42 | | (11) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 169.04/25.42 | |
% 169.04/25.42 | | REF_CLOSE: (1), (2), (5), (9), (11) are inconsistent by sub-proof #697.
% 169.04/25.42 | |
% 169.04/25.42 | End of split
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #144 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) op(e2, e0) = e3
% 169.04/25.42 (2) op(e3, e0) = all_52_12
% 169.04/25.42 (3) ~ (all_52_12 = e3)
% 169.04/25.42 (4) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 =
% 169.04/25.42 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) &
% 169.04/25.42 ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.04/25.42 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.04/25.42 e2) = all_56_7 & $i(all_56_7)))
% 169.04/25.42 (5) all_54_1 = all_52_4
% 169.04/25.42 (6) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 169.04/25.42 (7) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 169.04/25.42 (8) ~ (all_52_4 = e3)
% 169.04/25.42 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.42 (10) all_56_10 = e3
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | ALPHA: (4) implies:
% 169.04/25.42 | (11) op(e2, e0) = e0
% 169.04/25.42 |
% 169.04/25.42 | BETA: splitting (6) gives:
% 169.04/25.42 |
% 169.04/25.42 | Case 1:
% 169.04/25.42 | |
% 169.04/25.42 | | (12) all_54_1 = e3
% 169.04/25.42 | |
% 169.04/25.42 | | COMBINE_EQS: (5), (12) imply:
% 169.04/25.42 | | (13) all_52_4 = e3
% 169.04/25.42 | |
% 169.04/25.42 | | REDUCE: (8), (13) imply:
% 169.04/25.42 | | (14) $false
% 169.04/25.42 | |
% 169.04/25.42 | | CLOSE: (14) is inconsistent.
% 169.04/25.42 | |
% 169.04/25.42 | Case 2:
% 169.04/25.42 | |
% 169.04/25.42 | |
% 169.04/25.42 | | GROUND_INST: instantiating (9) with e0, e3, e0, e2, simplifying with (1),
% 169.04/25.42 | | (11) gives:
% 169.04/25.42 | | (15) e3 = e0
% 169.04/25.42 | |
% 169.04/25.42 | | COMBINE_EQS: (10), (15) imply:
% 169.04/25.42 | | (16) all_56_10 = e0
% 169.04/25.42 | |
% 169.04/25.42 | | REF_CLOSE: (2), (3), (7), (9), (16) are inconsistent by sub-proof #145.
% 169.04/25.42 | |
% 169.04/25.42 | End of split
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #145 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) op(e3, e0) = all_52_12
% 169.04/25.42 (2) ~ (all_52_12 = e3)
% 169.04/25.42 (3) all_56_10 = e0
% 169.04/25.42 (4) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 169.04/25.42 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | BETA: splitting (4) gives:
% 169.04/25.42 |
% 169.04/25.42 | Case 1:
% 169.04/25.42 | |
% 169.04/25.42 | | (6) ~ (all_56_10 = e0)
% 169.04/25.42 | |
% 169.04/25.42 | | REDUCE: (3), (6) imply:
% 169.04/25.42 | | (7) $false
% 169.04/25.42 | |
% 169.04/25.42 | | CLOSE: (7) is inconsistent.
% 169.04/25.42 | |
% 169.04/25.42 | Case 2:
% 169.04/25.42 | |
% 169.04/25.42 | | (8) all_56_9 = e3 & op(e3, e0) = e3
% 169.04/25.42 | |
% 169.04/25.42 | | ALPHA: (8) implies:
% 169.04/25.42 | | (9) op(e3, e0) = e3
% 169.04/25.42 | |
% 169.04/25.42 | | GROUND_INST: instantiating (5) with all_52_12, e3, e0, e3, simplifying with
% 169.04/25.42 | | (1), (9) gives:
% 169.04/25.42 | | (10) all_52_12 = e3
% 169.04/25.42 | |
% 169.04/25.42 | | REDUCE: (2), (10) imply:
% 169.04/25.42 | | (11) $false
% 169.04/25.42 | |
% 169.04/25.42 | | CLOSE: (11) is inconsistent.
% 169.04/25.42 | |
% 169.04/25.42 | End of split
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #146 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 =
% 169.04/25.42 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) &
% 169.04/25.42 ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.04/25.42 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.04/25.42 e2) = all_56_7 & $i(all_56_7)))
% 169.04/25.42 (2) all_56_5 = e2
% 169.04/25.42 (3) ~ (e2 = e1)
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | ALPHA: (1) implies:
% 169.04/25.42 | (4) all_56_5 = e1
% 169.04/25.42 |
% 169.04/25.42 | COMBINE_EQS: (2), (4) imply:
% 169.04/25.42 | (5) e2 = e1
% 169.04/25.42 |
% 169.04/25.42 | SIMP: (5) implies:
% 169.04/25.42 | (6) e2 = e1
% 169.04/25.42 |
% 169.04/25.42 | REDUCE: (3), (6) imply:
% 169.04/25.42 | (7) $false
% 169.04/25.42 |
% 169.04/25.42 | CLOSE: (7) is inconsistent.
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #147 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 =
% 169.04/25.42 e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4)))
% 169.04/25.42 & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.04/25.42 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.04/25.42 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.04/25.42 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 169.04/25.42 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.04/25.42 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.04/25.42 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.04/25.42 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.04/25.42 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.04/25.42 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.04/25.42 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.04/25.42 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.04/25.42 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.04/25.42 (2) all_56_12 = e1
% 169.04/25.42 (3) all_56_5 = e2
% 169.04/25.42 (4) all_56_10 = e3
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | BETA: splitting (1) gives:
% 169.04/25.42 |
% 169.04/25.42 | Case 1:
% 169.04/25.42 | |
% 169.04/25.42 | | (5) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 169.04/25.42 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.04/25.42 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.04/25.42 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | (
% 169.04/25.42 | | ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 169.04/25.42 | |
% 169.04/25.42 | | ALPHA: (5) implies:
% 169.04/25.42 | | (6) ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.04/25.42 | | $i(all_56_5))
% 169.04/25.42 | |
% 169.04/25.42 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #148.
% 169.04/25.42 | |
% 169.04/25.42 | Case 2:
% 169.04/25.42 | |
% 169.04/25.42 | | (7) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.04/25.42 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.04/25.42 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.04/25.42 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) |
% 169.04/25.42 | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 169.04/25.42 | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 169.04/25.42 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.04/25.42 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.04/25.42 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) |
% 169.04/25.42 | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.04/25.42 | |
% 169.04/25.42 | | BETA: splitting (7) gives:
% 169.04/25.42 | |
% 169.04/25.42 | | Case 1:
% 169.04/25.42 | | |
% 169.04/25.42 | | | (8) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.04/25.42 | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.04/25.42 | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.04/25.42 | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) |
% 169.04/25.42 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 169.04/25.42 | | |
% 169.04/25.42 | | | ALPHA: (8) implies:
% 169.04/25.42 | | | (9) ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.04/25.42 | | | $i(all_56_5))
% 169.04/25.42 | | |
% 169.04/25.42 | | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #148.
% 169.04/25.42 | | |
% 169.04/25.42 | | Case 2:
% 169.04/25.42 | | |
% 169.04/25.42 | | | (10) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 169.04/25.42 | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.04/25.42 | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.04/25.42 | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 169.04/25.42 | | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 169.04/25.42 | | |
% 169.04/25.42 | | | ALPHA: (10) implies:
% 169.04/25.42 | | | (11) ~ (all_56_10 = e3)
% 169.04/25.42 | | |
% 169.04/25.42 | | | REDUCE: (4), (11) imply:
% 169.04/25.42 | | | (12) $false
% 169.04/25.42 | | |
% 169.04/25.42 | | | CLOSE: (12) is inconsistent.
% 169.04/25.42 | | |
% 169.04/25.42 | | End of split
% 169.04/25.42 | |
% 169.04/25.42 | End of split
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #148 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.04/25.42 $i(all_56_5))
% 169.04/25.42 (2) all_56_12 = e1
% 169.04/25.42 (3) all_56_5 = e2
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | BETA: splitting (1) gives:
% 169.04/25.42 |
% 169.04/25.42 | Case 1:
% 169.04/25.42 | |
% 169.04/25.42 | | (4) ~ (all_56_12 = e1)
% 169.04/25.42 | |
% 169.04/25.42 | | REDUCE: (2), (4) imply:
% 169.04/25.42 | | (5) $false
% 169.04/25.42 | |
% 169.04/25.42 | | CLOSE: (5) is inconsistent.
% 169.04/25.42 | |
% 169.04/25.42 | Case 2:
% 169.04/25.42 | |
% 169.04/25.42 | | (6) ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 & $i(all_56_5)
% 169.04/25.42 | |
% 169.04/25.42 | | ALPHA: (6) implies:
% 169.04/25.42 | | (7) ~ (all_56_5 = e2)
% 169.04/25.42 | |
% 169.04/25.42 | | REDUCE: (3), (7) imply:
% 169.04/25.42 | | (8) $false
% 169.04/25.42 | |
% 169.04/25.42 | | CLOSE: (8) is inconsistent.
% 169.04/25.42 | |
% 169.04/25.42 | End of split
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #149 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) ~ (e3 = e1)
% 169.04/25.42 (2) ~ (e1 = e0)
% 169.04/25.42 (3) op(e2, e3) = all_52_1
% 169.04/25.42 (4) all_58_3 = e1
% 169.04/25.42 (5) op(e2, e3) = e2
% 169.04/25.42 (6) ~ (e3 = e0)
% 169.04/25.42 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.42 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.04/25.42 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.42 (9) ~ (e2 = e0)
% 169.04/25.42 (10) op(e2, e1) = e2
% 169.04/25.42 (11) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.42 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.04/25.42 (12) ~ (e3 = e2)
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | BETA: splitting (7) gives:
% 169.04/25.42 |
% 169.04/25.42 | Case 1:
% 169.04/25.42 | |
% 169.04/25.42 | | (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 169.04/25.42 | | e0)
% 169.04/25.42 | |
% 169.04/25.42 | | BETA: splitting (13) gives:
% 169.04/25.42 | |
% 169.04/25.42 | | Case 1:
% 169.04/25.42 | | |
% 169.04/25.42 | | | (14) all_58_2 = e0 & op(e2, e3) = e0
% 169.04/25.42 | | |
% 169.04/25.42 | | | REF_CLOSE: (3), (5), (8), (9), (14) are inconsistent by sub-proof #782.
% 169.04/25.42 | | |
% 169.04/25.42 | | Case 2:
% 169.04/25.42 | | |
% 169.04/25.42 | | | (15) all_58_3 = e0 & op(e2, e2) = e0
% 169.04/25.42 | | |
% 169.04/25.42 | | | REF_CLOSE: (2), (4), (15) are inconsistent by sub-proof #927.
% 169.04/25.42 | | |
% 169.04/25.42 | | End of split
% 169.04/25.42 | |
% 169.04/25.42 | Case 2:
% 169.04/25.42 | |
% 169.04/25.42 | | (16) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 169.04/25.42 | | e0)
% 169.04/25.42 | |
% 169.04/25.42 | | BETA: splitting (16) gives:
% 169.04/25.42 | |
% 169.04/25.42 | | Case 1:
% 169.04/25.42 | | |
% 169.04/25.42 | | | (17) all_58_5 = e0 & op(e2, e1) = e0
% 169.04/25.42 | | |
% 169.04/25.42 | | | REF_CLOSE: (8), (9), (10), (17) are inconsistent by sub-proof #151.
% 169.04/25.42 | | |
% 169.04/25.42 | | Case 2:
% 169.04/25.42 | | |
% 169.04/25.42 | | | (18) all_58_10 = e0 & op(e2, e0) = e0
% 169.04/25.42 | | |
% 169.04/25.42 | | | ALPHA: (18) implies:
% 169.04/25.42 | | | (19) all_58_10 = e0
% 169.04/25.42 | | |
% 169.04/25.42 | | | BETA: splitting (11) gives:
% 169.04/25.42 | | |
% 169.04/25.42 | | | Case 1:
% 169.04/25.42 | | | |
% 169.04/25.42 | | | | (20) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2)
% 169.04/25.42 | | | | = e3)
% 169.04/25.42 | | | |
% 169.04/25.42 | | | | BETA: splitting (20) gives:
% 169.04/25.42 | | | |
% 169.04/25.42 | | | | Case 1:
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | | (21) all_58_2 = e3 & op(e2, e3) = e3
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | | ALPHA: (21) implies:
% 169.04/25.42 | | | | | (22) op(e2, e3) = e3
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | | REF_CLOSE: (3), (5), (8), (12), (22) are inconsistent by sub-proof
% 169.04/25.42 | | | | | #462.
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | Case 2:
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | | (23) all_58_3 = e3 & op(e2, e2) = e3
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | | ALPHA: (23) implies:
% 169.04/25.42 | | | | | (24) all_58_3 = e3
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | | REF_CLOSE: (1), (4), (24) are inconsistent by sub-proof #328.
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | End of split
% 169.04/25.42 | | | |
% 169.04/25.42 | | | Case 2:
% 169.04/25.42 | | | |
% 169.04/25.42 | | | | (25) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0)
% 169.04/25.42 | | | | = e3)
% 169.04/25.42 | | | |
% 169.04/25.42 | | | | BETA: splitting (25) gives:
% 169.04/25.42 | | | |
% 169.04/25.42 | | | | Case 1:
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | | (26) all_58_5 = e3 & op(e2, e1) = e3
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | | REF_CLOSE: (8), (10), (12), (26) are inconsistent by sub-proof #150.
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | Case 2:
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | | (27) all_58_10 = e3 & op(e2, e0) = e3
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | | REF_CLOSE: (6), (19), (27) are inconsistent by sub-proof #542.
% 169.04/25.42 | | | | |
% 169.04/25.42 | | | | End of split
% 169.04/25.42 | | | |
% 169.04/25.42 | | | End of split
% 169.04/25.42 | | |
% 169.04/25.42 | | End of split
% 169.04/25.42 | |
% 169.04/25.42 | End of split
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #150 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) all_58_5 = e3 & op(e2, e1) = e3
% 169.04/25.42 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.42 (3) op(e2, e1) = e2
% 169.04/25.42 (4) ~ (e3 = e2)
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | ALPHA: (1) implies:
% 169.04/25.42 | (5) op(e2, e1) = e3
% 169.04/25.42 |
% 169.04/25.42 | GROUND_INST: instantiating (2) with e2, e3, e1, e2, simplifying with (3), (5)
% 169.04/25.42 | gives:
% 169.04/25.42 | (6) e3 = e2
% 169.04/25.42 |
% 169.04/25.42 | REDUCE: (4), (6) imply:
% 169.04/25.42 | (7) $false
% 169.04/25.42 |
% 169.04/25.42 | CLOSE: (7) is inconsistent.
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #151 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) all_58_5 = e0 & op(e2, e1) = e0
% 169.04/25.42 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.42 (3) op(e2, e1) = e2
% 169.04/25.42 (4) ~ (e2 = e0)
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | ALPHA: (1) implies:
% 169.04/25.42 | (5) op(e2, e1) = e0
% 169.04/25.42 |
% 169.04/25.42 | GROUND_INST: instantiating (2) with e2, e0, e1, e2, simplifying with (3), (5)
% 169.04/25.42 | gives:
% 169.04/25.42 | (6) e2 = e0
% 169.04/25.42 |
% 169.04/25.42 | REDUCE: (4), (6) imply:
% 169.04/25.42 | (7) $false
% 169.04/25.42 |
% 169.04/25.42 | CLOSE: (7) is inconsistent.
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #152 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) op(e3, e0) = all_52_12
% 169.04/25.42 (2) op(e3, e1) = all_52_8
% 169.04/25.42 (3) all_56_10 = e0
% 169.04/25.42 (4) ~ (e3 = e0)
% 169.04/25.42 (5) ~ (all_52_8 = e0)
% 169.04/25.42 (6) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 169.04/25.42 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.42 (8) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | BETA: splitting (8) gives:
% 169.04/25.42 |
% 169.04/25.42 | Case 1:
% 169.04/25.42 | |
% 169.04/25.42 | | (9) all_58_4 = e0 & op(e3, e1) = e0
% 169.04/25.42 | |
% 169.04/25.42 | | REF_CLOSE: (2), (5), (7), (9) are inconsistent by sub-proof #178.
% 169.04/25.42 | |
% 169.04/25.42 | Case 2:
% 169.04/25.42 | |
% 169.04/25.42 | | (10) all_58_9 = e0 & op(e3, e0) = e0
% 169.04/25.42 | |
% 169.04/25.42 | | ALPHA: (10) implies:
% 169.04/25.42 | | (11) op(e3, e0) = e0
% 169.04/25.42 | |
% 169.04/25.42 | | REF_CLOSE: (1), (3), (4), (6), (7), (11) are inconsistent by sub-proof #153.
% 169.04/25.42 | |
% 169.04/25.42 | End of split
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #153 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) op(e3, e0) = all_52_12
% 169.04/25.42 (2) op(e3, e0) = e0
% 169.04/25.42 (3) all_56_10 = e0
% 169.04/25.42 (4) ~ (e3 = e0)
% 169.04/25.42 (5) ~ (all_56_10 = e0) | (all_56_9 = e3 & op(e3, e0) = e3)
% 169.04/25.42 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.42
% 169.04/25.42 Begin of proof
% 169.04/25.42 |
% 169.04/25.42 | BETA: splitting (5) gives:
% 169.04/25.42 |
% 169.04/25.42 | Case 1:
% 169.04/25.42 | |
% 169.04/25.42 | | (7) ~ (all_56_10 = e0)
% 169.04/25.42 | |
% 169.04/25.42 | | REDUCE: (3), (7) imply:
% 169.04/25.42 | | (8) $false
% 169.04/25.42 | |
% 169.04/25.42 | | CLOSE: (8) is inconsistent.
% 169.04/25.42 | |
% 169.04/25.42 | Case 2:
% 169.04/25.42 | |
% 169.04/25.42 | | (9) all_56_9 = e3 & op(e3, e0) = e3
% 169.04/25.42 | |
% 169.04/25.42 | | ALPHA: (9) implies:
% 169.04/25.42 | | (10) op(e3, e0) = e3
% 169.04/25.42 | |
% 169.04/25.42 | | REF_CLOSE: (1), (2), (4), (6), (10) are inconsistent by sub-proof #154.
% 169.04/25.42 | |
% 169.04/25.42 | End of split
% 169.04/25.42 |
% 169.04/25.42 End of proof
% 169.04/25.42
% 169.04/25.42 Sub-proof #154 shows that the following formulas are inconsistent:
% 169.04/25.42 ----------------------------------------------------------------
% 169.04/25.42 (1) op(e3, e0) = e3
% 169.04/25.43 (2) op(e3, e0) = all_52_12
% 169.04/25.43 (3) op(e3, e0) = e0
% 169.04/25.43 (4) ~ (e3 = e0)
% 169.04/25.43 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.43
% 169.04/25.43 Begin of proof
% 169.04/25.43 |
% 169.04/25.43 | GROUND_INST: instantiating (5) with all_52_12, e0, e0, e3, simplifying with
% 169.04/25.43 | (2), (3) gives:
% 169.04/25.43 | (6) all_52_12 = e0
% 169.04/25.43 |
% 169.04/25.43 | GROUND_INST: instantiating (5) with all_52_12, e3, e0, e3, simplifying with
% 169.04/25.43 | (1), (2) gives:
% 169.04/25.43 | (7) all_52_12 = e3
% 169.04/25.43 |
% 169.04/25.43 | COMBINE_EQS: (6), (7) imply:
% 169.04/25.43 | (8) e3 = e0
% 169.04/25.43 |
% 169.04/25.43 | REDUCE: (4), (8) imply:
% 169.04/25.43 | (9) $false
% 169.04/25.43 |
% 169.04/25.43 | CLOSE: (9) is inconsistent.
% 169.04/25.43 |
% 169.04/25.43 End of proof
% 169.04/25.43
% 169.04/25.43 Sub-proof #155 shows that the following formulas are inconsistent:
% 169.04/25.43 ----------------------------------------------------------------
% 169.04/25.43 (1) all_58_1 = e0 & op(e3, e2) = e0
% 169.04/25.43 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.43 (3) op(e3, e2) = all_52_4
% 169.04/25.43 (4) ~ (all_52_4 = e0)
% 169.04/25.43
% 169.04/25.43 Begin of proof
% 169.04/25.43 |
% 169.04/25.43 | ALPHA: (1) implies:
% 169.04/25.43 | (5) op(e3, e2) = e0
% 169.04/25.43 |
% 169.04/25.43 | GROUND_INST: instantiating (2) with all_52_4, e0, e2, e3, simplifying with
% 169.04/25.43 | (3), (5) gives:
% 169.04/25.43 | (6) all_52_4 = e0
% 169.04/25.43 |
% 169.04/25.43 | REDUCE: (4), (6) imply:
% 169.04/25.43 | (7) $false
% 169.04/25.43 |
% 169.04/25.43 | CLOSE: (7) is inconsistent.
% 169.04/25.43 |
% 169.04/25.43 End of proof
% 169.04/25.43
% 169.04/25.43 Sub-proof #156 shows that the following formulas are inconsistent:
% 169.04/25.43 ----------------------------------------------------------------
% 169.04/25.43 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.04/25.43 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.04/25.43 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.04/25.43 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.04/25.43 (3) ~ (e3 = e1)
% 169.04/25.43 (4) ~ (e1 = e0)
% 169.04/25.43 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.04/25.43 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.04/25.43 (6) op(e2, e3) = all_52_1
% 169.04/25.43 (7) op(e2, e3) = e2
% 169.04/25.43 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.04/25.43 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.04/25.43 (9) ~ (e3 = e0)
% 169.04/25.43 (10) all_58_12 = e2 & op(e0, e3) = e2
% 169.04/25.43 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.04/25.43 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.04/25.43 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.04/25.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.04/25.43 (13) ~ (e2 = e0)
% 169.04/25.43 (14) all_58_3 = e3
% 169.04/25.43 (15) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.04/25.43 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.04/25.43 (16) ~ (e2 = e1)
% 169.04/25.43 (17) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.04/25.43 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 169.04/25.43 (18) ~ (e3 = e2)
% 169.04/25.43
% 169.04/25.43 Begin of proof
% 169.04/25.43 |
% 169.04/25.43 | ALPHA: (10) implies:
% 169.04/25.43 | (19) all_58_12 = e2
% 169.04/25.43 |
% 169.04/25.43 | BETA: splitting (17) gives:
% 169.04/25.43 |
% 169.04/25.43 | Case 1:
% 169.04/25.43 | |
% 169.04/25.43 | | (20) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 169.04/25.43 | | e2)
% 169.04/25.43 | |
% 169.04/25.43 | | BETA: splitting (20) gives:
% 169.04/25.43 | |
% 169.04/25.43 | | Case 1:
% 169.04/25.43 | | |
% 169.04/25.43 | | | (21) all_58_2 = e2 & op(e2, e3) = e2
% 169.04/25.43 | | |
% 169.04/25.43 | | | ALPHA: (21) implies:
% 169.04/25.43 | | | (22) all_58_2 = e2
% 169.04/25.43 | | |
% 169.04/25.43 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 169.04/25.43 | | | (14), (15), (16), (18), (19), (22) are inconsistent by
% 169.04/25.43 | | | sub-proof #433.
% 169.04/25.43 | | |
% 169.04/25.43 | | Case 2:
% 169.04/25.43 | | |
% 169.04/25.43 | | | (23) all_58_3 = e2 & op(e2, e2) = e2
% 169.04/25.43 | | |
% 169.04/25.43 | | | ALPHA: (23) implies:
% 169.04/25.43 | | | (24) all_58_3 = e2
% 169.04/25.43 | | |
% 169.04/25.43 | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11), (12), (13), (15), (16),
% 169.04/25.43 | | | (18), (24) are inconsistent by sub-proof #665.
% 169.04/25.43 | | |
% 169.04/25.43 | | End of split
% 169.04/25.43 | |
% 169.04/25.43 | Case 2:
% 169.04/25.43 | |
% 169.04/25.43 | | (25) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 169.04/25.43 | | e2)
% 169.04/25.43 | |
% 169.04/25.43 | | BETA: splitting (25) gives:
% 169.04/25.43 | |
% 169.04/25.43 | | Case 1:
% 169.04/25.43 | | |
% 169.04/25.43 | | | (26) all_58_5 = e2 & op(e2, e1) = e2
% 169.04/25.43 | | |
% 169.04/25.43 | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11), (12), (13), (14), (16),
% 169.04/25.43 | | | (26) are inconsistent by sub-proof #412.
% 169.04/25.43 | | |
% 169.04/25.43 | | Case 2:
% 169.04/25.43 | | |
% 169.04/25.43 | | | (27) all_58_10 = e2 & op(e2, e0) = e2
% 169.04/25.43 | | |
% 169.04/25.43 | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (11), (12), (13), (14), (16),
% 169.04/25.43 | | | (27) are inconsistent by sub-proof #447.
% 169.04/25.43 | | |
% 169.04/25.43 | | End of split
% 169.04/25.43 | |
% 169.04/25.43 | End of split
% 169.04/25.43 |
% 169.04/25.43 End of proof
% 169.04/25.43
% 169.04/25.43 Sub-proof #157 shows that the following formulas are inconsistent:
% 169.04/25.43 ----------------------------------------------------------------
% 169.04/25.43 (1) ~ (e3 = e1)
% 169.04/25.43 (2) ~ (e1 = e0)
% 169.04/25.43 (3) all_58_6 = e2
% 169.04/25.43 (4) ~ (e3 = e0)
% 169.04/25.43 (5) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.04/25.43 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.04/25.43 (6) all_58_11 = e3
% 169.04/25.43 (7) all_58_8 = e2
% 169.04/25.43 (8) ~ (e2 = e0)
% 169.04/25.43 (9) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.04/25.43 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.04/25.43 (10) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.04/25.43 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.04/25.43 (11) ~ (e2 = e1)
% 169.04/25.43 (12) ~ (e3 = e2)
% 169.04/25.43
% 169.04/25.43 Begin of proof
% 169.04/25.43 |
% 169.04/25.43 | BETA: splitting (9) gives:
% 169.04/25.43 |
% 169.04/25.43 | Case 1:
% 169.04/25.43 | |
% 169.04/25.43 | | (13) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 169.04/25.43 | | e1)
% 169.04/25.43 | |
% 169.04/25.43 | | BETA: splitting (13) gives:
% 169.04/25.43 | |
% 169.04/25.43 | | Case 1:
% 169.04/25.43 | | |
% 169.04/25.43 | | | (14) all_58_6 = e1 & op(e1, e3) = e1
% 169.04/25.43 | | |
% 169.04/25.43 | | | REF_CLOSE: (3), (11), (14) are inconsistent by sub-proof #774.
% 169.04/25.43 | | |
% 169.04/25.43 | | Case 2:
% 169.04/25.43 | | |
% 169.04/25.43 | | | (15) all_58_7 = e1 & op(e1, e2) = e1
% 169.04/25.43 | | |
% 169.04/25.43 | | | ALPHA: (15) implies:
% 169.04/25.43 | | | (16) all_58_7 = e1
% 169.04/25.43 | | |
% 169.04/25.43 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (12), (16) are
% 169.04/25.43 | | | inconsistent by sub-proof #158.
% 169.04/25.43 | | |
% 169.04/25.43 | | End of split
% 169.04/25.43 | |
% 169.04/25.43 | Case 2:
% 169.04/25.43 | |
% 169.04/25.43 | | (17) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 169.04/25.43 | | e1)
% 169.04/25.43 | |
% 169.04/25.43 | | BETA: splitting (17) gives:
% 169.04/25.43 | |
% 169.04/25.43 | | Case 1:
% 169.04/25.43 | | |
% 169.04/25.43 | | | (18) all_58_8 = e1 & op(e1, e1) = e1
% 169.04/25.43 | | |
% 169.04/25.43 | | | REF_CLOSE: (7), (11), (18) are inconsistent by sub-proof #397.
% 169.04/25.43 | | |
% 169.04/25.43 | | Case 2:
% 169.04/25.43 | | |
% 169.04/25.43 | | | (19) all_58_11 = e1 & op(e1, e0) = e1
% 169.04/25.43 | | |
% 169.04/25.43 | | | ALPHA: (19) implies:
% 169.04/25.43 | | | (20) all_58_11 = e1
% 169.04/25.43 | | |
% 169.04/25.43 | | | REF_CLOSE: (1), (6), (20) are inconsistent by sub-proof #755.
% 169.04/25.43 | | |
% 169.04/25.43 | | End of split
% 169.04/25.43 | |
% 169.04/25.43 | End of split
% 169.04/25.43 |
% 169.04/25.43 End of proof
% 169.04/25.43
% 169.04/25.43 Sub-proof #158 shows that the following formulas are inconsistent:
% 169.04/25.43 ----------------------------------------------------------------
% 169.04/25.43 (1) all_58_7 = e1
% 169.04/25.43 (2) ~ (e3 = e1)
% 169.04/25.43 (3) ~ (e1 = e0)
% 169.04/25.43 (4) all_58_6 = e2
% 169.04/25.43 (5) ~ (e3 = e0)
% 169.04/25.43 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.04/25.43 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.04/25.43 (7) all_58_8 = e2
% 169.04/25.43 (8) ~ (e2 = e0)
% 169.04/25.43 (9) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.04/25.43 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.04/25.43 (10) ~ (e3 = e2)
% 169.04/25.43
% 169.04/25.43 Begin of proof
% 169.04/25.43 |
% 169.04/25.43 | BETA: splitting (6) gives:
% 169.04/25.43 |
% 169.04/25.43 | Case 1:
% 169.04/25.43 | |
% 169.04/25.43 | | (11) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 169.04/25.43 | | e0)
% 169.04/25.43 | |
% 169.04/25.43 | | BETA: splitting (11) gives:
% 169.04/25.43 | |
% 169.04/25.43 | | Case 1:
% 169.04/25.43 | | |
% 169.04/25.43 | | | (12) all_58_6 = e0 & op(e1, e3) = e0
% 169.04/25.43 | | |
% 169.04/25.43 | | | REF_CLOSE: (4), (8), (12) are inconsistent by sub-proof #769.
% 169.04/25.43 | | |
% 169.04/25.43 | | Case 2:
% 169.04/25.43 | | |
% 169.04/25.43 | | | (13) all_58_7 = e0 & op(e1, e2) = e0
% 169.04/25.43 | | |
% 169.04/25.43 | | | REF_CLOSE: (1), (3), (13) are inconsistent by sub-proof #727.
% 169.04/25.43 | | |
% 169.04/25.43 | | End of split
% 169.04/25.43 | |
% 169.04/25.43 | Case 2:
% 169.04/25.43 | |
% 169.11/25.43 | | (14) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 169.11/25.43 | | e0)
% 169.11/25.43 | |
% 169.11/25.43 | | BETA: splitting (14) gives:
% 169.11/25.43 | |
% 169.11/25.43 | | Case 1:
% 169.11/25.43 | | |
% 169.11/25.43 | | | (15) all_58_8 = e0 & op(e1, e1) = e0
% 169.11/25.43 | | |
% 169.11/25.43 | | | REF_CLOSE: (7), (8), (15) are inconsistent by sub-proof #271.
% 169.11/25.43 | | |
% 169.11/25.43 | | Case 2:
% 169.11/25.43 | | |
% 169.11/25.43 | | | (16) all_58_11 = e0 & op(e1, e0) = e0
% 169.11/25.43 | | |
% 169.11/25.43 | | | ALPHA: (16) implies:
% 169.11/25.43 | | | (17) all_58_11 = e0
% 169.11/25.43 | | |
% 169.11/25.43 | | | BETA: splitting (9) gives:
% 169.11/25.43 | | |
% 169.11/25.43 | | | Case 1:
% 169.11/25.43 | | | |
% 169.11/25.43 | | | | (18) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 169.11/25.43 | | | | = e3)
% 169.11/25.43 | | | |
% 169.11/25.43 | | | | REF_CLOSE: (1), (2), (4), (10), (18) are inconsistent by sub-proof #820.
% 169.11/25.43 | | | |
% 169.11/25.43 | | | Case 2:
% 169.11/25.43 | | | |
% 169.11/25.43 | | | | (19) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0)
% 169.11/25.43 | | | | = e3)
% 169.11/25.43 | | | |
% 169.11/25.43 | | | | REF_CLOSE: (5), (7), (10), (17), (19) are inconsistent by sub-proof
% 169.11/25.43 | | | | #159.
% 169.11/25.43 | | | |
% 169.11/25.43 | | | End of split
% 169.11/25.43 | | |
% 169.11/25.43 | | End of split
% 169.11/25.43 | |
% 169.11/25.43 | End of split
% 169.11/25.43 |
% 169.11/25.43 End of proof
% 169.11/25.43
% 169.11/25.43 Sub-proof #159 shows that the following formulas are inconsistent:
% 169.11/25.43 ----------------------------------------------------------------
% 169.11/25.43 (1) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.11/25.43 (2) all_58_11 = e0
% 169.11/25.43 (3) ~ (e3 = e0)
% 169.11/25.43 (4) all_58_8 = e2
% 169.11/25.43 (5) ~ (e3 = e2)
% 169.11/25.43
% 169.11/25.43 Begin of proof
% 169.11/25.43 |
% 169.11/25.43 | BETA: splitting (1) gives:
% 169.11/25.43 |
% 169.11/25.43 | Case 1:
% 169.11/25.43 | |
% 169.11/25.43 | | (6) all_58_8 = e3 & op(e1, e1) = e3
% 169.11/25.43 | |
% 169.11/25.43 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #272.
% 169.11/25.43 | |
% 169.11/25.43 | Case 2:
% 169.11/25.43 | |
% 169.11/25.43 | | (7) all_58_11 = e3 & op(e1, e0) = e3
% 169.11/25.43 | |
% 169.11/25.43 | | ALPHA: (7) implies:
% 169.11/25.43 | | (8) all_58_11 = e3
% 169.11/25.43 | |
% 169.11/25.43 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #474.
% 169.11/25.43 | |
% 169.11/25.43 | End of split
% 169.11/25.43 |
% 169.11/25.43 End of proof
% 169.11/25.43
% 169.11/25.43 Sub-proof #160 shows that the following formulas are inconsistent:
% 169.11/25.43 ----------------------------------------------------------------
% 169.11/25.43 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.11/25.43 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.11/25.43 (2) all_58_15 = e2
% 169.11/25.43 (3) op(e0, e0) = e2
% 169.11/25.43 (4) ~ (e3 = e1)
% 169.11/25.43 (5) ~ (e1 = e0)
% 169.11/25.43 (6) ~ (e3 = e0)
% 169.11/25.43 (7) all_58_11 = e3
% 169.11/25.43 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.11/25.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.11/25.43 (9) ~ (e2 = e0)
% 169.11/25.43 (10) all_58_9 = e3
% 169.11/25.43 (11) ~ (e2 = e1)
% 169.11/25.43 (12) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.11/25.43 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.11/25.43 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.11/25.43 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.11/25.43
% 169.11/25.43 Begin of proof
% 169.11/25.43 |
% 169.11/25.43 | BETA: splitting (1) gives:
% 169.11/25.43 |
% 169.11/25.43 | Case 1:
% 169.11/25.43 | |
% 169.11/25.43 | | (13) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 169.11/25.43 | | e1)
% 169.11/25.43 | |
% 169.11/25.43 | | BETA: splitting (13) gives:
% 169.11/25.43 | |
% 169.11/25.43 | | Case 1:
% 169.11/25.43 | | |
% 169.11/25.43 | | | (14) all_58_9 = e1 & op(e3, e0) = e1
% 169.11/25.43 | | |
% 169.11/25.43 | | | REF_CLOSE: (4), (10), (14) are inconsistent by sub-proof #836.
% 169.11/25.43 | | |
% 169.11/25.43 | | Case 2:
% 169.11/25.43 | | |
% 169.11/25.43 | | | (15) all_58_10 = e1 & op(e2, e0) = e1
% 169.11/25.43 | | |
% 169.11/25.43 | | | ALPHA: (15) implies:
% 169.11/25.43 | | | (16) op(e2, e0) = e1
% 169.11/25.43 | | |
% 169.11/25.43 | | | BETA: splitting (12) gives:
% 169.11/25.43 | | |
% 169.11/25.43 | | | Case 1:
% 169.11/25.43 | | | |
% 169.11/25.43 | | | | (17) all_58_15 = e0 & op(e0, e0) = e0
% 169.11/25.43 | | | |
% 169.11/25.43 | | | | REF_CLOSE: (2), (9), (17) are inconsistent by sub-proof #874.
% 169.11/25.43 | | | |
% 169.11/25.43 | | | Case 2:
% 169.11/25.43 | | | |
% 169.11/25.43 | | | | (18) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 169.11/25.43 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 169.11/25.43 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 169.11/25.43 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.11/25.43 | | | |
% 169.11/25.43 | | | | ALPHA: (18) implies:
% 169.11/25.43 | | | | (19) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 169.11/25.43 | | | | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.11/25.43 | | | |
% 169.11/25.43 | | | | BETA: splitting (19) gives:
% 169.11/25.43 | | | |
% 169.11/25.43 | | | | Case 1:
% 169.11/25.43 | | | | |
% 169.11/25.43 | | | | | (20) all_58_9 = e0 & op(e3, e0) = e0
% 169.11/25.43 | | | | |
% 169.11/25.43 | | | | | ALPHA: (20) implies:
% 169.11/25.43 | | | | | (21) all_58_9 = e0
% 169.11/25.43 | | | | |
% 169.11/25.43 | | | | | REF_CLOSE: (6), (10), (21) are inconsistent by sub-proof #835.
% 169.11/25.43 | | | | |
% 169.11/25.43 | | | | Case 2:
% 169.11/25.43 | | | | |
% 169.11/25.43 | | | | | (22) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 169.11/25.43 | | | | | e0) = e0)
% 169.11/25.43 | | | | |
% 169.11/25.43 | | | | | REF_CLOSE: (5), (6), (7), (8), (16), (22) are inconsistent by
% 169.11/25.43 | | | | | sub-proof #723.
% 169.11/25.43 | | | | |
% 169.11/25.43 | | | | End of split
% 169.11/25.43 | | | |
% 169.11/25.43 | | | End of split
% 169.11/25.43 | | |
% 169.11/25.43 | | End of split
% 169.11/25.43 | |
% 169.11/25.43 | Case 2:
% 169.11/25.43 | |
% 169.11/25.43 | | (23) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.11/25.43 | | e1)
% 169.11/25.43 | |
% 169.11/25.43 | | BETA: splitting (23) gives:
% 169.11/25.43 | |
% 169.11/25.43 | | Case 1:
% 169.11/25.43 | | |
% 169.11/25.43 | | | (24) all_58_11 = e1 & op(e1, e0) = e1
% 169.11/25.43 | | |
% 169.11/25.43 | | | ALPHA: (24) implies:
% 169.11/25.43 | | | (25) all_58_11 = e1
% 169.11/25.43 | | |
% 169.11/25.43 | | | REF_CLOSE: (4), (7), (25) are inconsistent by sub-proof #755.
% 169.11/25.43 | | |
% 169.11/25.43 | | Case 2:
% 169.11/25.43 | | |
% 169.11/25.43 | | | (26) all_58_15 = e1 & op(e0, e0) = e1
% 169.11/25.43 | | |
% 169.11/25.43 | | | ALPHA: (26) implies:
% 169.11/25.43 | | | (27) op(e0, e0) = e1
% 169.11/25.43 | | |
% 169.11/25.43 | | | REF_CLOSE: (3), (8), (11), (27) are inconsistent by sub-proof #640.
% 169.11/25.43 | | |
% 169.11/25.43 | | End of split
% 169.11/25.43 | |
% 169.11/25.43 | End of split
% 169.11/25.43 |
% 169.11/25.43 End of proof
% 169.11/25.43
% 169.11/25.43 Sub-proof #161 shows that the following formulas are inconsistent:
% 169.11/25.43 ----------------------------------------------------------------
% 169.11/25.43 (1) all_58_15 = e3 & op(e0, e0) = e3
% 169.11/25.43 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.11/25.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.11/25.43 (3) op(e0, e0) = all_4_2
% 169.11/25.43 (4) ~ (all_4_2 = e3)
% 169.11/25.43
% 169.11/25.43 Begin of proof
% 169.11/25.43 |
% 169.11/25.43 | ALPHA: (1) implies:
% 169.11/25.43 | (5) op(e0, e0) = e3
% 169.11/25.43 |
% 169.11/25.43 | GROUND_INST: instantiating (2) with all_4_2, e3, e0, e0, simplifying with (3),
% 169.11/25.43 | (5) gives:
% 169.11/25.43 | (6) all_4_2 = e3
% 169.11/25.43 |
% 169.11/25.43 | REDUCE: (4), (6) imply:
% 169.11/25.43 | (7) $false
% 169.11/25.43 |
% 169.11/25.43 | CLOSE: (7) is inconsistent.
% 169.11/25.43 |
% 169.11/25.43 End of proof
% 169.11/25.43
% 169.11/25.43 Sub-proof #162 shows that the following formulas are inconsistent:
% 169.11/25.43 ----------------------------------------------------------------
% 169.11/25.43 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.11/25.43 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.11/25.43 (2) ~ (e3 = e1)
% 169.11/25.43 (3) ~ (e1 = e0)
% 169.11/25.43 (4) op(e2, e3) = all_52_1
% 169.11/25.43 (5) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.11/25.43 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.11/25.43 (6) ~ (all_6_2 = e2)
% 169.11/25.43 (7) op(e1, e1) = all_6_2
% 169.11/25.43 (8) op(e2, e3) = e2
% 169.11/25.43 (9) ~ (e3 = e0)
% 169.11/25.43 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.11/25.43 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.11/25.44 (11) all_58_14 = e3
% 169.11/25.44 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.11/25.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.11/25.44 (13) ~ (e2 = e0)
% 169.11/25.44 (14) all_58_8 = e3
% 169.11/25.44 (15) all_58_3 = e3
% 169.11/25.44 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.11/25.44 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.11/25.44 (17) ~ (e2 = e1)
% 169.11/25.44 (18) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.11/25.44 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.11/25.44 (19) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.11/25.44 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.11/25.44 (20) ~ (e3 = e2)
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | BETA: splitting (19) gives:
% 169.11/25.44 |
% 169.11/25.44 | Case 1:
% 169.11/25.44 | |
% 169.11/25.44 | | (21) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 169.11/25.44 | | e2)
% 169.11/25.44 | |
% 169.11/25.44 | | BETA: splitting (21) gives:
% 169.11/25.44 | |
% 169.11/25.44 | | Case 1:
% 169.11/25.44 | | |
% 169.11/25.44 | | | (22) all_58_4 = e2 & op(e3, e1) = e2
% 169.11/25.44 | | |
% 169.11/25.44 | | | ALPHA: (22) implies:
% 169.11/25.44 | | | (23) all_58_4 = e2
% 169.11/25.44 | | |
% 169.11/25.44 | | | REF_CLOSE: (2), (3), (5), (9), (11), (13), (14), (17), (18), (23) are
% 169.11/25.44 | | | inconsistent by sub-proof #422.
% 169.11/25.44 | | |
% 169.11/25.44 | | Case 2:
% 169.11/25.44 | | |
% 169.11/25.44 | | | (24) all_58_5 = e2 & op(e2, e1) = e2
% 169.11/25.44 | | |
% 169.11/25.44 | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (12), (13), (15), (17),
% 169.11/25.44 | | | (24) are inconsistent by sub-proof #412.
% 169.11/25.44 | | |
% 169.11/25.44 | | End of split
% 169.11/25.44 | |
% 169.11/25.44 | Case 2:
% 169.11/25.44 | |
% 169.11/25.44 | | (25) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 169.11/25.44 | | e2)
% 169.11/25.44 | |
% 169.11/25.44 | | BETA: splitting (25) gives:
% 169.11/25.44 | |
% 169.11/25.44 | | Case 1:
% 169.11/25.44 | | |
% 169.11/25.44 | | | (26) all_58_8 = e2 & op(e1, e1) = e2
% 169.11/25.44 | | |
% 169.11/25.44 | | | REF_CLOSE: (6), (7), (12), (26) are inconsistent by sub-proof #845.
% 169.11/25.44 | | |
% 169.11/25.44 | | Case 2:
% 169.11/25.44 | | |
% 169.11/25.44 | | | (27) all_58_14 = e2 & op(e0, e1) = e2
% 169.11/25.44 | | |
% 169.11/25.44 | | | ALPHA: (27) implies:
% 169.11/25.44 | | | (28) all_58_14 = e2
% 169.11/25.44 | | |
% 169.11/25.44 | | | COMBINE_EQS: (11), (28) imply:
% 169.11/25.44 | | | (29) e3 = e2
% 169.11/25.44 | | |
% 169.11/25.44 | | | COMBINE_EQS: (15), (29) imply:
% 169.11/25.44 | | | (30) all_58_3 = e2
% 169.11/25.44 | | |
% 169.11/25.44 | | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (12), (13), (16), (17),
% 169.11/25.44 | | | (20), (30) are inconsistent by sub-proof #665.
% 169.11/25.44 | | |
% 169.11/25.44 | | End of split
% 169.11/25.44 | |
% 169.11/25.44 | End of split
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #163 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) all_56_0 = e2
% 169.11/25.44 (2) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 =
% 169.11/25.44 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.11/25.44 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.11/25.44 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.11/25.44 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.11/25.44 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.11/25.44 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.44 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.11/25.44 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.11/25.44 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.11/25.44 (3) all_56_7 = e0
% 169.11/25.44 (4) all_56_12 = e3
% 169.11/25.44 (5) all_56_15 = e2
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | BETA: splitting (2) gives:
% 169.11/25.44 |
% 169.11/25.44 | Case 1:
% 169.11/25.44 | |
% 169.11/25.44 | | (6) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~
% 169.11/25.44 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 169.11/25.44 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 169.11/25.44 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 169.11/25.44 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 169.11/25.44 | |
% 169.11/25.44 | | ALPHA: (6) implies:
% 169.11/25.44 | | (7) ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.11/25.44 | | $i(all_56_7))
% 169.11/25.44 | |
% 169.11/25.44 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #164.
% 169.11/25.44 | |
% 169.11/25.44 | Case 2:
% 169.11/25.44 | |
% 169.11/25.44 | | (8) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.11/25.44 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.11/25.44 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.11/25.44 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 169.11/25.44 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 169.11/25.44 | |
% 169.11/25.44 | | ALPHA: (8) implies:
% 169.11/25.44 | | (9) ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.11/25.44 | | $i(all_56_0))
% 169.11/25.44 | |
% 169.11/25.44 | | REF_CLOSE: (1), (4), (9) are inconsistent by sub-proof #368.
% 169.11/25.44 | |
% 169.11/25.44 | End of split
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #164 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.11/25.44 $i(all_56_7))
% 169.11/25.44 (2) all_56_15 = e2
% 169.11/25.44 (3) all_56_7 = e0
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | BETA: splitting (1) gives:
% 169.11/25.44 |
% 169.11/25.44 | Case 1:
% 169.11/25.44 | |
% 169.11/25.44 | | (4) ~ (all_56_15 = e2)
% 169.11/25.44 | |
% 169.11/25.44 | | REDUCE: (2), (4) imply:
% 169.11/25.44 | | (5) $false
% 169.11/25.44 | |
% 169.11/25.44 | | CLOSE: (5) is inconsistent.
% 169.11/25.44 | |
% 169.11/25.44 | Case 2:
% 169.11/25.44 | |
% 169.11/25.44 | | (6) ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)
% 169.11/25.44 | |
% 169.11/25.44 | | ALPHA: (6) implies:
% 169.11/25.44 | | (7) ~ (all_56_7 = e0)
% 169.11/25.44 | |
% 169.11/25.44 | | REDUCE: (3), (7) imply:
% 169.11/25.44 | | (8) $false
% 169.11/25.44 | |
% 169.11/25.44 | | CLOSE: (8) is inconsistent.
% 169.11/25.44 | |
% 169.11/25.44 | End of split
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #165 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.11/25.44 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.11/25.44 (2) ~ (e3 = e1)
% 169.11/25.44 (3) ~ (e1 = e0)
% 169.11/25.44 (4) op(e2, e3) = all_52_1
% 169.11/25.44 (5) all_56_12 = e2
% 169.11/25.44 (6) op(e2, e3) = e2
% 169.11/25.44 (7) ~ (e3 = e0)
% 169.11/25.44 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.11/25.44 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.11/25.44 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.11/25.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.11/25.44 (10) ~ (e2 = e0)
% 169.11/25.44 (11) all_58_3 = e3
% 169.11/25.44 (12) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.11/25.44 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.11/25.44 (13) ~ (e2 = e1)
% 169.11/25.44 (14) all_56_12 = e3
% 169.11/25.44 (15) ~ (e3 = e2)
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | COMBINE_EQS: (5), (14) imply:
% 169.11/25.44 | (16) e3 = e2
% 169.11/25.44 |
% 169.11/25.44 | SIMP: (16) implies:
% 169.11/25.44 | (17) e3 = e2
% 169.11/25.44 |
% 169.11/25.44 | COMBINE_EQS: (11), (17) imply:
% 169.11/25.44 | (18) all_58_3 = e2
% 169.11/25.44 |
% 169.11/25.44 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (15),
% 169.11/25.44 | (18) are inconsistent by sub-proof #665.
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #166 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) all_56_10 = e3
% 169.11/25.44 (2) all_56_10 = e0
% 169.11/25.44 (3) ~ (e3 = e0)
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | COMBINE_EQS: (1), (2) imply:
% 169.11/25.44 | (4) e3 = e0
% 169.11/25.44 |
% 169.11/25.44 | SIMP: (4) implies:
% 169.11/25.44 | (5) e3 = e0
% 169.11/25.44 |
% 169.11/25.44 | REDUCE: (3), (5) imply:
% 169.11/25.44 | (6) $false
% 169.11/25.44 |
% 169.11/25.44 | CLOSE: (6) is inconsistent.
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #167 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) all_56_0 = e2
% 169.11/25.44 (2) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 =
% 169.11/25.44 e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4)))
% 169.11/25.44 & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.11/25.44 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.11/25.44 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.11/25.44 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.11/25.44 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.44 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.11/25.44 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.11/25.44 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.11/25.44 (3) op(e1, e2) = all_52_6
% 169.11/25.44 (4) ~ (all_52_6 = e2)
% 169.11/25.44 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.11/25.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.11/25.44 (6) all_56_12 = e3
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | BETA: splitting (2) gives:
% 169.11/25.44 |
% 169.11/25.44 | Case 1:
% 169.11/25.44 | |
% 169.11/25.44 | | (7) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.11/25.44 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.11/25.44 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.11/25.44 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | (
% 169.11/25.44 | | ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 169.11/25.44 | |
% 169.11/25.44 | | ALPHA: (7) implies:
% 169.11/25.44 | | (8) op(e1, e2) = e2
% 169.11/25.44 | |
% 169.11/25.44 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #986.
% 169.11/25.44 | |
% 169.11/25.44 | Case 2:
% 169.11/25.44 | |
% 169.11/25.44 | | (9) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 169.11/25.44 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.11/25.44 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.11/25.44 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 169.11/25.44 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 169.11/25.44 | |
% 169.11/25.44 | | ALPHA: (9) implies:
% 169.11/25.44 | | (10) ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.11/25.44 | | $i(all_56_0))
% 169.11/25.44 | |
% 169.11/25.44 | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #368.
% 169.11/25.44 | |
% 169.11/25.44 | End of split
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #168 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) ~ (all_6_2 = e1)
% 169.11/25.44 (2) all_54_10 = all_6_2
% 169.11/25.44 (3) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 169.11/25.44 (4) ~ (e3 = e1)
% 169.11/25.44 (5) all_56_14 = all_6_2
% 169.11/25.44 (6) op(e1, e3) = all_52_2
% 169.11/25.44 (7) ~ (all_6_2 = e2)
% 169.11/25.44 (8) ~ (all_6_2 = e0)
% 169.11/25.44 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.11/25.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.11/25.44 (10) op(e1, e3) = e3
% 169.11/25.44 (11) ~ (all_56_14 = e3) | (all_56_2 = e1 & op(e1, e3) = e1)
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | BETA: splitting (11) gives:
% 169.11/25.44 |
% 169.11/25.44 | Case 1:
% 169.11/25.44 | |
% 169.11/25.44 | | (12) ~ (all_56_14 = e3)
% 169.11/25.44 | |
% 169.11/25.44 | | REDUCE: (5), (12) imply:
% 169.11/25.44 | | (13) ~ (all_6_2 = e3)
% 169.11/25.44 | |
% 169.11/25.44 | | REF_CLOSE: (1), (2), (3), (7), (8), (13) are inconsistent by sub-proof #978.
% 169.11/25.44 | |
% 169.11/25.44 | Case 2:
% 169.11/25.44 | |
% 169.11/25.44 | | (14) all_56_2 = e1 & op(e1, e3) = e1
% 169.11/25.44 | |
% 169.11/25.44 | | ALPHA: (14) implies:
% 169.11/25.44 | | (15) op(e1, e3) = e1
% 169.11/25.44 | |
% 169.11/25.44 | | REF_CLOSE: (4), (6), (9), (10), (15) are inconsistent by sub-proof #750.
% 169.11/25.44 | |
% 169.11/25.44 | End of split
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #169 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.11/25.44 $i(all_56_9))
% 169.11/25.44 (2) all_56_10 = e0
% 169.11/25.44 (3) all_56_9 = e3
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | BETA: splitting (1) gives:
% 169.11/25.44 |
% 169.11/25.44 | Case 1:
% 169.11/25.44 | |
% 169.11/25.44 | | (4) ~ (all_56_10 = e0)
% 169.11/25.44 | |
% 169.11/25.44 | | REDUCE: (2), (4) imply:
% 169.11/25.44 | | (5) $false
% 169.11/25.44 | |
% 169.11/25.44 | | CLOSE: (5) is inconsistent.
% 169.11/25.44 | |
% 169.11/25.44 | Case 2:
% 169.11/25.44 | |
% 169.11/25.44 | | (6) ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 & $i(all_56_9)
% 169.11/25.44 | |
% 169.11/25.44 | | ALPHA: (6) implies:
% 169.11/25.44 | | (7) ~ (all_56_9 = e3)
% 169.11/25.44 | |
% 169.11/25.44 | | REDUCE: (3), (7) imply:
% 169.11/25.44 | | (8) $false
% 169.11/25.44 | |
% 169.11/25.44 | | CLOSE: (8) is inconsistent.
% 169.11/25.44 | |
% 169.11/25.44 | End of split
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #170 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) all_56_14 = e3
% 169.11/25.44 (2) all_56_14 = all_6_2
% 169.11/25.44 (3) ~ (all_52_6 = all_6_2)
% 169.11/25.44 (4) ~ (all_52_6 = e2)
% 169.11/25.44 (5) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 169.11/25.44 (6) ~ (all_52_6 = e1)
% 169.11/25.44 (7) ~ (all_52_6 = e0)
% 169.11/25.44 (8) all_54_9 = all_52_6
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | COMBINE_EQS: (1), (2) imply:
% 169.11/25.44 | (9) all_6_2 = e3
% 169.11/25.44 |
% 169.11/25.44 | SIMP: (9) implies:
% 169.11/25.44 | (10) all_6_2 = e3
% 169.11/25.44 |
% 169.11/25.44 | REDUCE: (3), (10) imply:
% 169.11/25.44 | (11) ~ (all_52_6 = e3)
% 169.11/25.44 |
% 169.11/25.44 | BETA: splitting (5) gives:
% 169.11/25.44 |
% 169.11/25.44 | Case 1:
% 169.11/25.44 | |
% 169.11/25.44 | | (12) all_54_9 = e3
% 169.11/25.44 | |
% 169.11/25.44 | | REF_CLOSE: (8), (11), (12) are inconsistent by sub-proof #741.
% 169.11/25.44 | |
% 169.11/25.44 | Case 2:
% 169.11/25.44 | |
% 169.11/25.44 | | (13) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 169.11/25.44 | |
% 169.11/25.44 | | BETA: splitting (13) gives:
% 169.11/25.44 | |
% 169.11/25.44 | | Case 1:
% 169.11/25.44 | | |
% 169.11/25.44 | | | (14) all_54_9 = e2
% 169.11/25.44 | | |
% 169.11/25.44 | | | REF_CLOSE: (4), (8), (14) are inconsistent by sub-proof #740.
% 169.11/25.44 | | |
% 169.11/25.44 | | Case 2:
% 169.11/25.44 | | |
% 169.11/25.44 | | | (15) all_54_9 = e1 | all_54_9 = e0
% 169.11/25.44 | | |
% 169.11/25.44 | | | REF_CLOSE: (6), (7), (8), (15) are inconsistent by sub-proof #171.
% 169.11/25.44 | | |
% 169.11/25.44 | | End of split
% 169.11/25.44 | |
% 169.11/25.44 | End of split
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #171 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) all_54_9 = e1 | all_54_9 = e0
% 169.11/25.44 (2) all_54_9 = all_52_6
% 169.11/25.44 (3) ~ (all_52_6 = e1)
% 169.11/25.44 (4) ~ (all_52_6 = e0)
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | BETA: splitting (1) gives:
% 169.11/25.44 |
% 169.11/25.44 | Case 1:
% 169.11/25.44 | |
% 169.11/25.44 | | (5) all_54_9 = e1
% 169.11/25.44 | |
% 169.11/25.44 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #739.
% 169.11/25.44 | |
% 169.11/25.44 | Case 2:
% 169.11/25.44 | |
% 169.11/25.44 | | (6) all_54_9 = e0
% 169.11/25.44 | |
% 169.11/25.44 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #601.
% 169.11/25.44 | |
% 169.11/25.44 | End of split
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #172 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) all_54_7 = all_52_13
% 169.11/25.44 (2) all_54_7 = e1
% 169.11/25.44 (3) ~ (all_52_13 = e1)
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | COMBINE_EQS: (1), (2) imply:
% 169.11/25.44 | (4) all_52_13 = e1
% 169.11/25.44 |
% 169.11/25.44 | SIMP: (4) implies:
% 169.11/25.44 | (5) all_52_13 = e1
% 169.11/25.44 |
% 169.11/25.44 | REDUCE: (3), (5) imply:
% 169.11/25.44 | (6) $false
% 169.11/25.44 |
% 169.11/25.44 | CLOSE: (6) is inconsistent.
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.44
% 169.11/25.44 Sub-proof #173 shows that the following formulas are inconsistent:
% 169.11/25.44 ----------------------------------------------------------------
% 169.11/25.44 (1) all_58_12 = e2
% 169.11/25.44 (2) ~ (e3 = e1)
% 169.11/25.44 (3) all_58_13 = e3
% 169.11/25.44 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 169.11/25.44 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.11/25.44 (5) ~ (e1 = e0)
% 169.11/25.44 (6) op(e0, e0) = e0
% 169.11/25.44 (7) all_58_14 = e0
% 169.11/25.44 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.11/25.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.11/25.44 (9) ~ (e2 = e1)
% 169.11/25.44
% 169.11/25.44 Begin of proof
% 169.11/25.44 |
% 169.11/25.44 | BETA: splitting (4) gives:
% 169.11/25.44 |
% 169.11/25.44 | Case 1:
% 169.11/25.44 | |
% 169.11/25.44 | | (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.11/25.44 | | e1)
% 169.11/25.44 | |
% 169.11/25.44 | | BETA: splitting (10) gives:
% 169.11/25.44 | |
% 169.11/25.44 | | Case 1:
% 169.11/25.44 | | |
% 169.11/25.44 | | | (11) all_58_12 = e1 & op(e0, e3) = e1
% 169.11/25.44 | | |
% 169.11/25.44 | | | ALPHA: (11) implies:
% 169.11/25.44 | | | (12) all_58_12 = e1
% 169.11/25.44 | | |
% 169.11/25.44 | | | REF_CLOSE: (1), (9), (12) are inconsistent by sub-proof #862.
% 169.11/25.44 | | |
% 169.11/25.44 | | Case 2:
% 169.11/25.44 | | |
% 169.11/25.44 | | | (13) all_58_13 = e1 & op(e0, e2) = e1
% 169.11/25.44 | | |
% 169.11/25.44 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #709.
% 169.11/25.44 | | |
% 169.11/25.44 | | End of split
% 169.11/25.44 | |
% 169.11/25.44 | Case 2:
% 169.11/25.44 | |
% 169.11/25.44 | | (14) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.11/25.44 | | e1)
% 169.11/25.44 | |
% 169.11/25.44 | | BETA: splitting (14) gives:
% 169.11/25.44 | |
% 169.11/25.44 | | Case 1:
% 169.11/25.44 | | |
% 169.11/25.44 | | | (15) all_58_14 = e1 & op(e0, e1) = e1
% 169.11/25.44 | | |
% 169.11/25.44 | | | ALPHA: (15) implies:
% 169.11/25.44 | | | (16) all_58_14 = e1
% 169.11/25.44 | | |
% 169.11/25.44 | | | REF_CLOSE: (5), (7), (16) are inconsistent by sub-proof #586.
% 169.11/25.44 | | |
% 169.11/25.44 | | Case 2:
% 169.11/25.44 | | |
% 169.11/25.44 | | | (17) all_58_15 = e1 & op(e0, e0) = e1
% 169.11/25.44 | | |
% 169.11/25.44 | | | ALPHA: (17) implies:
% 169.11/25.44 | | | (18) op(e0, e0) = e1
% 169.11/25.44 | | |
% 169.11/25.44 | | | REF_CLOSE: (5), (6), (8), (18) are inconsistent by sub-proof #204.
% 169.11/25.44 | | |
% 169.11/25.44 | | End of split
% 169.11/25.44 | |
% 169.11/25.44 | End of split
% 169.11/25.44 |
% 169.11/25.44 End of proof
% 169.11/25.45
% 169.11/25.45 Sub-proof #174 shows that the following formulas are inconsistent:
% 169.11/25.45 ----------------------------------------------------------------
% 169.11/25.45 (1) op(e2, e1) = all_52_9
% 169.11/25.45 (2) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.11/25.45 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.11/25.45 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.11/25.45 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.11/25.45 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.11/25.45 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.11/25.45 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.45 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.11/25.45 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.11/25.45 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 169.11/25.45 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 169.11/25.45 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.11/25.45 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.11/25.45 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.11/25.45 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.11/25.45 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 169.11/25.45 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.11/25.45 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.11/25.45 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.11/25.45 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.11/25.45 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.11/25.45 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.45 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.11/25.45 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.11/25.45 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 169.11/25.45 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 169.11/25.45 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.11/25.45 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.11/25.45 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.11/25.45 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.11/25.45 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.11/25.45 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.45 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.11/25.45 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.11/25.45 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 169.11/25.45 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 169.11/25.45 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.11/25.45 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.11/25.45 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.11/25.45 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.11/25.45 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 169.11/25.45 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.11/25.45 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.11/25.45 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.11/25.45 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 169.11/25.45 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.11/25.45 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.11/25.45 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 169.11/25.45 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.11/25.45 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 169.11/25.45 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.11/25.45 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.11/25.45 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.11/25.45 (4) all_58_2 = e3
% 169.11/25.45 (5) ~ (all_52_13 = e3)
% 169.11/25.45 (6) ~ (all_4_2 = e2)
% 169.11/25.45 (7) all_56_2 = e1
% 169.11/25.45 (8) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.11/25.45 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.11/25.45 (9) ~ (all_8_2 = e3)
% 169.11/25.45 (10) all_56_14 = e3
% 169.11/25.45 (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.11/25.45 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.11/25.45 (12) ~ (e3 = e1)
% 169.11/25.45 (13) all_58_13 = e3
% 169.11/25.45 (14) ~ (all_52_13 = e0)
% 169.11/25.45 (15) op(e1, e3) = all_52_2
% 169.11/25.45 (16) ~ (e1 = e0)
% 169.11/25.45 (17) op(e1, e2) = all_52_6
% 169.11/25.45 (18) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.11/25.45 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.11/25.45 (19) all_58_7 = e0
% 169.11/25.45 (20) ~ (all_52_14 = e0)
% 169.11/25.45 (21) op(e2, e2) = all_8_2
% 169.11/25.45 (22) all_56_12 = all_8_2
% 169.11/25.45 (23) ~ (e3 = e0)
% 169.11/25.45 (24) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.11/25.45 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.11/25.45 (25) op(e1, e2) = e0
% 169.11/25.45 (26) op(e0, e0) = all_4_2
% 169.11/25.45 (27) ~ (all_52_4 = e3)
% 169.11/25.45 (28) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.11/25.45 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.11/25.45 (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.11/25.45 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.11/25.45 (30) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.11/25.45 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.11/25.45 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.11/25.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.11/25.45 (32) ~ (e2 = e0)
% 169.11/25.45 (33) op(e1, e0) = all_52_14
% 169.11/25.45 (34) all_58_9 = e3
% 169.11/25.45 (35) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.11/25.45 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.11/25.45 (36) ~ (e2 = e1)
% 169.11/25.45 (37) op(e2, e1) = e0
% 169.11/25.45 (38) op(e3, e2) = all_52_4
% 169.11/25.45 (39) ~ (all_8_2 = e1)
% 169.11/25.45 (40) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.11/25.45 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 169.11/25.45 (41) all_56_15 = e0
% 169.11/25.45 (42) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.11/25.45 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.11/25.45 (43) op(e1, e3) = e1
% 169.11/25.45 (44) op(e2, e0) = all_52_13
% 169.11/25.45 (45) all_58_0 = e0
% 169.11/25.45 (46) ~ (e3 = e2)
% 169.11/25.45
% 169.11/25.45 Begin of proof
% 169.11/25.45 |
% 169.11/25.45 | BETA: splitting (8) gives:
% 169.11/25.45 |
% 169.11/25.45 | Case 1:
% 169.11/25.45 | |
% 169.11/25.45 | | (47) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.11/25.45 | | e1)
% 169.11/25.45 | |
% 169.11/25.45 | | BETA: splitting (47) gives:
% 169.11/25.45 | |
% 169.11/25.45 | | Case 1:
% 169.11/25.45 | | |
% 169.11/25.45 | | | (48) all_58_1 = e1 & op(e3, e2) = e1
% 169.11/25.45 | | |
% 169.11/25.45 | | | ALPHA: (48) implies:
% 169.11/25.45 | | | (49) op(e3, e2) = e1
% 169.11/25.45 | | |
% 169.11/25.45 | | | BETA: splitting (28) gives:
% 169.11/25.45 | | |
% 169.11/25.45 | | | Case 1:
% 169.11/25.45 | | | |
% 169.11/25.45 | | | | (50) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 169.11/25.45 | | | | = e2)
% 169.11/25.45 | | | |
% 169.11/25.45 | | | | BETA: splitting (50) gives:
% 169.11/25.45 | | | |
% 169.11/25.45 | | | | Case 1:
% 169.11/25.45 | | | | |
% 169.11/25.45 | | | | | (51) all_58_1 = e2 & op(e3, e2) = e2
% 169.11/25.45 | | | | |
% 169.11/25.45 | | | | | ALPHA: (51) implies:
% 169.11/25.45 | | | | | (52) op(e3, e2) = e2
% 169.11/25.45 | | | | |
% 169.11/25.45 | | | | | REF_CLOSE: (31), (36), (49), (52) are inconsistent by sub-proof #180.
% 169.11/25.45 | | | | |
% 169.11/25.45 | | | | Case 2:
% 169.11/25.45 | | | | |
% 169.11/25.45 | | | | | (53) all_58_3 = e2 & op(e2, e2) = e2
% 169.11/25.45 | | | | |
% 169.11/25.45 | | | | | ALPHA: (53) implies:
% 169.11/25.45 | | | | | (54) all_58_3 = e2
% 169.11/25.45 | | | | | (55) op(e2, e2) = e2
% 169.11/25.45 | | | | |
% 169.11/25.45 | | | | | BETA: splitting (42) gives:
% 169.11/25.45 | | | | |
% 169.11/25.45 | | | | | Case 1:
% 169.11/25.45 | | | | | |
% 169.11/25.45 | | | | | | (56) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 169.11/25.45 | | | | | | e2) = e2)
% 169.11/25.45 | | | | | |
% 169.11/25.45 | | | | | | BETA: splitting (56) gives:
% 169.11/25.45 | | | | | |
% 169.11/25.45 | | | | | | Case 1:
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | | (57) all_58_0 = e2 & op(e3, e3) = e2
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | | REF_CLOSE: (32), (45), (57) are inconsistent by sub-proof #390.
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | Case 2:
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | | (58) all_58_1 = e2 & op(e3, e2) = e2
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | | ALPHA: (58) implies:
% 169.11/25.45 | | | | | | | (59) op(e3, e2) = e2
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | | REF_CLOSE: (31), (36), (49), (59) are inconsistent by sub-proof
% 169.11/25.45 | | | | | | | #180.
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | End of split
% 169.11/25.45 | | | | | |
% 169.11/25.45 | | | | | Case 2:
% 169.11/25.45 | | | | | |
% 169.11/25.45 | | | | | | (60) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 169.11/25.45 | | | | | | e0) = e2)
% 169.11/25.45 | | | | | |
% 169.11/25.45 | | | | | | BETA: splitting (60) gives:
% 169.11/25.45 | | | | | |
% 169.11/25.45 | | | | | | Case 1:
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | | (61) all_58_4 = e2 & op(e3, e1) = e2
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | | ALPHA: (61) implies:
% 169.11/25.45 | | | | | | | (62) all_58_4 = e2
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | | BETA: splitting (3) gives:
% 169.11/25.45 | | | | | | |
% 169.11/25.45 | | | | | | | Case 1:
% 169.11/25.45 | | | | | | | |
% 169.11/25.45 | | | | | | | | (63) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 169.11/25.45 | | | | | | | | op(e2, e2) = e1)
% 169.11/25.45 | | | | | | | |
% 169.11/25.45 | | | | | | | | BETA: splitting (63) gives:
% 169.11/25.45 | | | | | | | |
% 169.11/25.45 | | | | | | | | Case 1:
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | (64) all_58_2 = e1 & op(e2, e3) = e1
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | ALPHA: (64) implies:
% 169.11/25.45 | | | | | | | | | (65) all_58_2 = e1
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | REF_CLOSE: (4), (12), (65) are inconsistent by sub-proof #938.
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | Case 2:
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | (66) all_58_3 = e1 & op(e2, e2) = e1
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | REF_CLOSE: (21), (31), (39), (66) are inconsistent by
% 169.11/25.45 | | | | | | | | | sub-proof #498.
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | End of split
% 169.11/25.45 | | | | | | | |
% 169.11/25.45 | | | | | | | Case 2:
% 169.11/25.45 | | | | | | | |
% 169.11/25.45 | | | | | | | | (67) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 &
% 169.11/25.45 | | | | | | | | op(e2, e0) = e1)
% 169.11/25.45 | | | | | | | |
% 169.11/25.45 | | | | | | | | BETA: splitting (67) gives:
% 169.11/25.45 | | | | | | | |
% 169.11/25.45 | | | | | | | | Case 1:
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | (68) all_58_5 = e1 & op(e2, e1) = e1
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | ALPHA: (68) implies:
% 169.11/25.45 | | | | | | | | | (69) op(e2, e1) = e1
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | REF_CLOSE: (16), (31), (37), (69) are inconsistent by
% 169.11/25.45 | | | | | | | | | sub-proof #911.
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | Case 2:
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | (70) all_58_10 = e1 & op(e2, e0) = e1
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | ALPHA: (70) implies:
% 169.11/25.45 | | | | | | | | | (71) op(e2, e0) = e1
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | BETA: splitting (18) gives:
% 169.11/25.45 | | | | | | | | |
% 169.11/25.45 | | | | | | | | | Case 1:
% 169.11/25.45 | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | (72) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2
% 169.11/25.45 | | | | | | | | | | & op(e2, e0) = e2)
% 169.11/25.45 | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | BETA: splitting (72) gives:
% 169.11/25.45 | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | Case 1:
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | (73) all_58_9 = e2 & op(e3, e0) = e2
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | ALPHA: (73) implies:
% 169.11/25.45 | | | | | | | | | | | (74) all_58_9 = e2
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | REF_CLOSE: (11), (12), (16), (23), (27), (29), (30), (31),
% 169.11/25.45 | | | | | | | | | | | (32), (36), (38), (46), (62), (74) are
% 169.11/25.45 | | | | | | | | | | | inconsistent by sub-proof #939.
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | Case 2:
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | (75) all_58_10 = e2 & op(e2, e0) = e2
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | ALPHA: (75) implies:
% 169.11/25.45 | | | | | | | | | | | (76) all_58_10 = e2
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | REF_CLOSE: (3), (9), (12), (16), (21), (23), (24), (31),
% 169.11/25.45 | | | | | | | | | | | (32), (35), (36), (40), (46), (54), (76) are
% 169.11/25.45 | | | | | | | | | | | inconsistent by sub-proof #908.
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | End of split
% 169.11/25.45 | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | Case 2:
% 169.11/25.45 | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | (77) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2
% 169.11/25.45 | | | | | | | | | | & op(e0, e0) = e2)
% 169.11/25.45 | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | BETA: splitting (77) gives:
% 169.11/25.45 | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | Case 1:
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | (78) all_58_11 = e2 & op(e1, e0) = e2
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | ALPHA: (78) implies:
% 169.11/25.45 | | | | | | | | | | | (79) op(e1, e0) = e2
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | GROUND_INST: instantiating (31) with all_52_14, e2, e0, e1,
% 169.11/25.45 | | | | | | | | | | | simplifying with (33), (79) gives:
% 169.11/25.45 | | | | | | | | | | | (80) all_52_14 = e2
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | GROUND_INST: instantiating (31) with all_52_6, e0, e2, e1,
% 169.11/25.45 | | | | | | | | | | | simplifying with (17), (25) gives:
% 169.11/25.45 | | | | | | | | | | | (81) all_52_6 = e0
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | GROUND_INST: instantiating (31) with all_52_2, e1, e3, e1,
% 169.11/25.45 | | | | | | | | | | | simplifying with (15), (43) gives:
% 169.11/25.45 | | | | | | | | | | | (82) all_52_2 = e1
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | GROUND_INST: instantiating (31) with all_52_13, e1, e0, e2,
% 169.11/25.45 | | | | | | | | | | | simplifying with (44), (71) gives:
% 169.11/25.45 | | | | | | | | | | | (83) all_52_13 = e1
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | GROUND_INST: instantiating (31) with all_52_9, e0, e1, e2,
% 169.11/25.45 | | | | | | | | | | | simplifying with (1), (37) gives:
% 169.11/25.45 | | | | | | | | | | | (84) all_52_9 = e0
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | GROUND_INST: instantiating (31) with all_8_2, e2, e2, e2,
% 169.11/25.45 | | | | | | | | | | | simplifying with (21), (55) gives:
% 169.11/25.45 | | | | | | | | | | | (85) all_8_2 = e2
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | COMBINE_EQS: (22), (85) imply:
% 169.11/25.45 | | | | | | | | | | | (86) all_56_12 = e2
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | REDUCE: (5), (83) imply:
% 169.11/25.45 | | | | | | | | | | | (87) ~ (e3 = e1)
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | BETA: splitting (2) gives:
% 169.11/25.45 | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | Case 1:
% 169.11/25.45 | | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | | (88) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 169.11/25.45 | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.11/25.45 | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.11/25.45 | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.11/25.45 | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.11/25.45 | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.11/25.45 | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.11/25.45 | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.11/25.45 | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 169.11/25.45 | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 169.11/25.45 | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.11/25.45 | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.11/25.45 | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.11/25.45 | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.11/25.45 | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.11/25.45 | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.11/25.45 | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.11/25.45 | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 169.11/25.45 | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 169.11/25.45 | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 169.11/25.45 | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 169.11/25.45 | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.11/25.45 | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 169.11/25.45 | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 169.11/25.45 | | | | | | | | | | | | $i(all_56_6))))
% 169.11/25.45 | | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | | BETA: splitting (88) gives:
% 169.11/25.45 | | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | | Case 1:
% 169.11/25.45 | | | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | | | (89) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 169.11/25.45 | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.11/25.45 | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.11/25.45 | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.11/25.45 | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.11/25.45 | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.11/25.45 | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.11/25.45 | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.11/25.45 | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.11/25.45 | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.11/25.45 | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.45 | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.11/25.45 | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.11/25.45 | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.11/25.45 | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.11/25.45 | | | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | | | REF_CLOSE: (7), (10), (86), (89) are inconsistent by
% 169.11/25.45 | | | | | | | | | | | | | sub-proof #176.
% 169.11/25.45 | | | | | | | | | | | | |
% 169.11/25.45 | | | | | | | | | | | | Case 2:
% 169.11/25.45 | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | (90) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 169.11/25.46 | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.11/25.46 | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.11/25.46 | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.11/25.46 | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.11/25.46 | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 169.11/25.46 | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 169.11/25.46 | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 169.11/25.46 | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_6))))
% 169.11/25.46 | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | BETA: splitting (90) gives:
% 169.11/25.46 | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | Case 1:
% 169.11/25.46 | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | (91) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 169.11/25.46 | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.11/25.46 | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.11/25.46 | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.11/25.46 | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 169.11/25.46 | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | ALPHA: (91) implies:
% 169.11/25.46 | | | | | | | | | | | | | | (92) op(e1, e3) = e3
% 169.11/25.46 | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | REF_CLOSE: (12), (15), (31), (43), (92) are inconsistent by
% 169.11/25.46 | | | | | | | | | | | | | | sub-proof #750.
% 169.11/25.46 | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | Case 2:
% 169.11/25.46 | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | (93) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 169.11/25.46 | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.11/25.46 | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.11/25.46 | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.11/25.46 | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.11/25.46 | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.11/25.46 | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 169.11/25.46 | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.11/25.46 | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.11/25.46 | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.11/25.46 | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.11/25.46 | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 169.11/25.46 | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | Case 1:
% 169.11/25.46 | | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | | (94) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 169.11/25.46 | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.11/25.46 | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.11/25.46 | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.11/25.46 | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 169.11/25.46 | | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 169.11/25.46 | | | | | | | | | | | | | | | (95) op(e1, e2) = e2
% 169.11/25.46 | | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | | REF_CLOSE: (25), (31), (32), (95) are inconsistent by
% 169.11/25.46 | | | | | | | | | | | | | | | sub-proof #175.
% 169.11/25.46 | | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | Case 2:
% 169.11/25.46 | | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | | (96) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 169.11/25.46 | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.11/25.46 | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.11/25.46 | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.11/25.46 | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 169.11/25.46 | | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 169.11/25.46 | | | | | | | | | | | | | | | (97) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.11/25.46 | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))
% 169.11/25.46 | | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | | REF_CLOSE: (7), (10), (97) are inconsistent by sub-proof
% 169.11/25.46 | | | | | | | | | | | | | | | #485.
% 169.11/25.46 | | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | | End of split
% 169.11/25.46 | | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | End of split
% 169.11/25.46 | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | End of split
% 169.11/25.46 | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | Case 2:
% 169.11/25.46 | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | (98) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 169.11/25.46 | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.11/25.46 | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.11/25.46 | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.11/25.46 | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.11/25.46 | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.11/25.46 | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.11/25.46 | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.11/25.46 | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 169.11/25.46 | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.11/25.46 | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.11/25.46 | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.11/25.46 | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.11/25.46 | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.11/25.46 | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.11/25.46 | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.11/25.46 | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.11/25.46 | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 169.11/25.46 | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.11/25.46 | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.11/25.46 | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.11/25.46 | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.11/25.46 | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 169.11/25.46 | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 169.11/25.46 | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.11/25.46 | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | BETA: splitting (98) gives:
% 169.11/25.46 | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | Case 1:
% 169.11/25.46 | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | (99) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 169.11/25.46 | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.11/25.46 | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.11/25.46 | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.11/25.46 | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.11/25.46 | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.11/25.46 | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | REF_CLOSE: (7), (10), (16), (31), (37), (99) are inconsistent
% 169.11/25.46 | | | | | | | | | | | | | by sub-proof #291.
% 169.11/25.46 | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | Case 2:
% 169.11/25.46 | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | (100) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.11/25.46 | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.11/25.46 | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.11/25.46 | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.11/25.46 | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.11/25.46 | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 169.11/25.46 | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.11/25.46 | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.11/25.46 | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 169.11/25.46 | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 169.11/25.46 | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.11/25.46 | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | | REF_CLOSE: (16), (31), (32), (41), (71), (79), (100) are
% 169.11/25.46 | | | | | | | | | | | | | inconsistent by sub-proof #196.
% 169.11/25.46 | | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | | End of split
% 169.11/25.46 | | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | End of split
% 169.11/25.46 | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | Case 2:
% 169.11/25.46 | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | (101) all_58_15 = e2 & op(e0, e0) = e2
% 169.11/25.46 | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | | REF_CLOSE: (6), (26), (31), (101) are inconsistent by
% 169.11/25.46 | | | | | | | | | | | sub-proof #854.
% 169.11/25.46 | | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | | End of split
% 169.11/25.46 | | | | | | | | | |
% 169.11/25.46 | | | | | | | | | End of split
% 169.11/25.46 | | | | | | | | |
% 169.11/25.46 | | | | | | | | End of split
% 169.11/25.46 | | | | | | | |
% 169.11/25.46 | | | | | | | End of split
% 169.11/25.46 | | | | | | |
% 169.11/25.46 | | | | | | Case 2:
% 169.11/25.46 | | | | | | |
% 169.11/25.46 | | | | | | | (102) all_58_9 = e2 & op(e3, e0) = e2
% 169.11/25.46 | | | | | | |
% 169.11/25.46 | | | | | | | REF_CLOSE: (34), (46), (102) are inconsistent by sub-proof #205.
% 169.11/25.46 | | | | | | |
% 169.11/25.46 | | | | | | End of split
% 169.11/25.46 | | | | | |
% 169.11/25.46 | | | | | End of split
% 169.11/25.46 | | | | |
% 169.11/25.46 | | | | End of split
% 169.11/25.46 | | | |
% 169.11/25.46 | | | Case 2:
% 169.11/25.46 | | | |
% 169.11/25.46 | | | | (103) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0,
% 169.11/25.46 | | | | e2) = e2)
% 169.11/25.46 | | | |
% 169.11/25.46 | | | | BETA: splitting (103) gives:
% 169.11/25.46 | | | |
% 169.11/25.46 | | | | Case 1:
% 169.11/25.46 | | | | |
% 169.11/25.46 | | | | | (104) all_58_7 = e2 & op(e1, e2) = e2
% 169.11/25.46 | | | | |
% 169.11/25.46 | | | | | REF_CLOSE: (19), (32), (104) are inconsistent by sub-proof #468.
% 169.11/25.46 | | | | |
% 169.11/25.46 | | | | Case 2:
% 169.11/25.46 | | | | |
% 169.11/25.46 | | | | | (105) all_58_13 = e2 & op(e0, e2) = e2
% 169.11/25.46 | | | | |
% 169.11/25.46 | | | | | REF_CLOSE: (13), (46), (105) are inconsistent by sub-proof #861.
% 169.11/25.46 | | | | |
% 169.11/25.46 | | | | End of split
% 169.11/25.46 | | | |
% 169.11/25.46 | | | End of split
% 169.11/25.46 | | |
% 169.11/25.46 | | Case 2:
% 169.11/25.46 | | |
% 169.11/25.46 | | | (106) all_58_3 = e1 & op(e2, e2) = e1
% 169.13/25.46 | | |
% 169.13/25.46 | | | REF_CLOSE: (21), (31), (39), (106) are inconsistent by sub-proof #498.
% 169.13/25.46 | | |
% 169.13/25.46 | | End of split
% 169.13/25.46 | |
% 169.13/25.46 | Case 2:
% 169.13/25.46 | |
% 169.13/25.46 | | (107) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.13/25.46 | | e1)
% 169.13/25.46 | |
% 169.13/25.46 | | REF_CLOSE: (12), (13), (16), (19), (107) are inconsistent by sub-proof #193.
% 169.13/25.46 | |
% 169.13/25.46 | End of split
% 169.13/25.46 |
% 169.13/25.46 End of proof
% 169.13/25.46
% 169.13/25.46 Sub-proof #175 shows that the following formulas are inconsistent:
% 169.13/25.46 ----------------------------------------------------------------
% 169.13/25.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.46 (2) op(e1, e2) = e2
% 169.13/25.46 (3) op(e1, e2) = e0
% 169.13/25.46 (4) ~ (e2 = e0)
% 169.13/25.46
% 169.13/25.46 Begin of proof
% 169.13/25.46 |
% 169.13/25.46 | GROUND_INST: instantiating (1) with e0, e2, e2, e1, simplifying with (2), (3)
% 169.13/25.46 | gives:
% 169.13/25.46 | (5) e2 = e0
% 169.13/25.46 |
% 169.13/25.46 | REDUCE: (4), (5) imply:
% 169.13/25.46 | (6) $false
% 169.13/25.46 |
% 169.13/25.46 | CLOSE: (6) is inconsistent.
% 169.13/25.46 |
% 169.13/25.46 End of proof
% 169.13/25.46
% 169.13/25.46 Sub-proof #176 shows that the following formulas are inconsistent:
% 169.13/25.46 ----------------------------------------------------------------
% 169.13/25.46 (1) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.13/25.46 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.13/25.46 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.13/25.46 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.13/25.46 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.13/25.46 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.13/25.46 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.13/25.46 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.13/25.46 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.13/25.46 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.13/25.46 (2) all_56_12 = e2
% 169.13/25.46 (3) all_56_14 = e3
% 169.13/25.46 (4) all_56_2 = e1
% 169.13/25.46
% 169.13/25.46 Begin of proof
% 169.13/25.46 |
% 169.13/25.46 | BETA: splitting (1) gives:
% 169.13/25.46 |
% 169.13/25.46 | Case 1:
% 169.13/25.46 | |
% 169.13/25.46 | | (5) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 169.13/25.46 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 169.13/25.46 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 169.13/25.46 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 169.13/25.46 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 169.13/25.46 | |
% 169.13/25.46 | | ALPHA: (5) implies:
% 169.13/25.46 | | (6) ~ (all_56_12 = e2)
% 169.13/25.46 | |
% 169.13/25.46 | | REDUCE: (2), (6) imply:
% 169.13/25.46 | | (7) $false
% 169.13/25.46 | |
% 169.13/25.46 | | CLOSE: (7) is inconsistent.
% 169.13/25.46 | |
% 169.13/25.46 | Case 2:
% 169.13/25.46 | |
% 169.13/25.46 | | (8) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.13/25.46 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.13/25.46 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.13/25.46 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 169.13/25.46 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 169.13/25.46 | |
% 169.13/25.46 | | ALPHA: (8) implies:
% 169.13/25.46 | | (9) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.13/25.46 | | $i(all_56_2))
% 169.13/25.46 | |
% 169.13/25.46 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #485.
% 169.13/25.46 | |
% 169.13/25.46 | End of split
% 169.13/25.46 |
% 169.13/25.46 End of proof
% 169.13/25.46
% 169.13/25.46 Sub-proof #177 shows that the following formulas are inconsistent:
% 169.13/25.46 ----------------------------------------------------------------
% 169.13/25.46 (1) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 169.13/25.46 (2) op(e1, e3) = all_52_2
% 169.13/25.46 (3) op(e1, e2) = all_52_6
% 169.13/25.46 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.46 (5) ~ (all_52_6 = e3)
% 169.13/25.46 (6) ~ (all_52_2 = e3)
% 169.13/25.46
% 169.13/25.46 Begin of proof
% 169.13/25.46 |
% 169.13/25.46 | BETA: splitting (1) gives:
% 169.13/25.46 |
% 169.13/25.46 | Case 1:
% 169.13/25.46 | |
% 169.13/25.46 | | (7) all_58_6 = e3 & op(e1, e3) = e3
% 169.13/25.46 | |
% 169.13/25.46 | | ALPHA: (7) implies:
% 169.13/25.46 | | (8) op(e1, e3) = e3
% 169.13/25.46 | |
% 169.13/25.46 | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #987.
% 169.13/25.46 | |
% 169.13/25.46 | Case 2:
% 169.13/25.46 | |
% 169.13/25.46 | | (9) all_58_7 = e3 & op(e1, e2) = e3
% 169.13/25.46 | |
% 169.13/25.46 | | ALPHA: (9) implies:
% 169.13/25.46 | | (10) op(e1, e2) = e3
% 169.13/25.46 | |
% 169.13/25.46 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #668.
% 169.13/25.46 | |
% 169.13/25.46 | End of split
% 169.13/25.46 |
% 169.13/25.46 End of proof
% 169.13/25.46
% 169.13/25.46 Sub-proof #178 shows that the following formulas are inconsistent:
% 169.13/25.46 ----------------------------------------------------------------
% 169.13/25.46 (1) all_58_4 = e0 & op(e3, e1) = e0
% 169.13/25.46 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.46 (3) op(e3, e1) = all_52_8
% 169.13/25.46 (4) ~ (all_52_8 = e0)
% 169.13/25.46
% 169.13/25.46 Begin of proof
% 169.13/25.46 |
% 169.13/25.46 | ALPHA: (1) implies:
% 169.13/25.46 | (5) op(e3, e1) = e0
% 169.13/25.46 |
% 169.13/25.46 | GROUND_INST: instantiating (2) with all_52_8, e0, e1, e3, simplifying with
% 169.13/25.46 | (3), (5) gives:
% 169.13/25.46 | (6) all_52_8 = e0
% 169.13/25.46 |
% 169.13/25.46 | REDUCE: (4), (6) imply:
% 169.13/25.46 | (7) $false
% 169.13/25.46 |
% 169.13/25.46 | CLOSE: (7) is inconsistent.
% 169.13/25.46 |
% 169.13/25.46 End of proof
% 169.13/25.46
% 169.13/25.46 Sub-proof #179 shows that the following formulas are inconsistent:
% 169.13/25.46 ----------------------------------------------------------------
% 169.13/25.46 (1) ~ (e1 = e0)
% 169.13/25.46 (2) op(e0, e0) = e0
% 169.13/25.46 (3) all_58_11 = e0
% 169.13/25.46 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.46 (5) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.46
% 169.13/25.46 Begin of proof
% 169.13/25.46 |
% 169.13/25.46 | BETA: splitting (5) gives:
% 169.13/25.46 |
% 169.13/25.46 | Case 1:
% 169.13/25.46 | |
% 169.13/25.46 | | (6) all_58_11 = e1 & op(e1, e0) = e1
% 169.13/25.46 | |
% 169.13/25.46 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #354.
% 169.13/25.46 | |
% 169.13/25.46 | Case 2:
% 169.13/25.46 | |
% 169.13/25.46 | | (7) all_58_15 = e1 & op(e0, e0) = e1
% 169.13/25.46 | |
% 169.13/25.46 | | ALPHA: (7) implies:
% 169.13/25.46 | | (8) op(e0, e0) = e1
% 169.13/25.46 | |
% 169.13/25.46 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #204.
% 169.13/25.46 | |
% 169.13/25.46 | End of split
% 169.13/25.46 |
% 169.13/25.46 End of proof
% 169.13/25.46
% 169.13/25.46 Sub-proof #180 shows that the following formulas are inconsistent:
% 169.13/25.46 ----------------------------------------------------------------
% 169.13/25.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.46 (2) op(e3, e2) = e2
% 169.13/25.46 (3) op(e3, e2) = e1
% 169.13/25.46 (4) ~ (e2 = e1)
% 169.13/25.46
% 169.13/25.46 Begin of proof
% 169.13/25.46 |
% 169.13/25.46 | GROUND_INST: instantiating (1) with e1, e2, e2, e3, simplifying with (2), (3)
% 169.13/25.46 | gives:
% 169.13/25.46 | (5) e2 = e1
% 169.13/25.46 |
% 169.13/25.46 | REDUCE: (4), (5) imply:
% 169.13/25.46 | (6) $false
% 169.13/25.46 |
% 169.13/25.46 | CLOSE: (6) is inconsistent.
% 169.13/25.46 |
% 169.13/25.46 End of proof
% 169.13/25.46
% 169.13/25.46 Sub-proof #181 shows that the following formulas are inconsistent:
% 169.13/25.46 ----------------------------------------------------------------
% 169.13/25.46 (1) op(e2, e1) = all_52_9
% 169.13/25.46 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.13/25.46 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.46 (3) ~ (all_52_1 = e0)
% 169.13/25.46 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.46 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.13/25.46 (5) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.13/25.46 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.13/25.46 (6) ~ (all_6_2 = e3)
% 169.13/25.46 (7) ( ~ (all_42_0 = e3) & op(all_42_1, e2) = all_42_0 & op(e0, e2) = all_42_1
% 169.13/25.46 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) & op(e0, e2) =
% 169.13/25.46 all_42_1 & $i(all_42_1))
% 169.13/25.46 (8) ~ (e3 = e1)
% 169.13/25.46 (9) ~ (e1 = e0)
% 169.13/25.46 (10) op(e0, e0) = e0
% 169.13/25.46 (11) op(e2, e3) = all_52_1
% 169.13/25.46 (12) ~ (all_6_2 = e2)
% 169.13/25.46 (13) op(e1, e1) = all_6_2
% 169.13/25.46 (14) ~ (e3 = e0)
% 169.13/25.46 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.46 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.47 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.47 (17) ~ (e2 = e0)
% 169.13/25.47 (18) all_58_1 = e2 & op(e3, e2) = e2
% 169.13/25.47 (19) ~ (all_52_9 = e0)
% 169.13/25.47 (20) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.13/25.47 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.13/25.47 (21) all_58_9 = e3
% 169.13/25.47 (22) ~ (e2 = e1)
% 169.13/25.47 (23) op(e1, e2) = e3
% 169.13/25.47 (24) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.13/25.47 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.13/25.47 (25) op(e2, e0) = e2
% 169.13/25.47 (26) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.13/25.47 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.13/25.47 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.13/25.47 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.13/25.47 (27) op(e2, e0) = all_52_13
% 169.13/25.47 (28) ~ (e3 = e2)
% 169.13/25.47
% 169.13/25.47 Begin of proof
% 169.13/25.47 |
% 169.13/25.47 | ALPHA: (18) implies:
% 169.13/25.47 | (29) all_58_1 = e2
% 169.13/25.47 |
% 169.13/25.47 | BETA: splitting (4) gives:
% 169.13/25.47 |
% 169.13/25.47 | Case 1:
% 169.13/25.47 | |
% 169.13/25.47 | | (30) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.13/25.47 | | e1)
% 169.13/25.47 | |
% 169.13/25.47 | | BETA: splitting (30) gives:
% 169.13/25.47 | |
% 169.13/25.47 | | Case 1:
% 169.13/25.47 | | |
% 169.13/25.47 | | | (31) all_58_1 = e1 & op(e3, e2) = e1
% 169.13/25.47 | | |
% 169.13/25.47 | | | REF_CLOSE: (22), (29), (31) are inconsistent by sub-proof #899.
% 169.13/25.47 | | |
% 169.13/25.47 | | Case 2:
% 169.13/25.47 | | |
% 169.13/25.47 | | | (32) all_58_3 = e1 & op(e2, e2) = e1
% 169.13/25.47 | | |
% 169.13/25.47 | | | REF_CLOSE: (1), (3), (9), (11), (15), (16), (17), (19), (25), (27), (32)
% 169.13/25.47 | | | are inconsistent by sub-proof #507.
% 169.13/25.47 | | |
% 169.13/25.47 | | End of split
% 169.13/25.47 | |
% 169.13/25.47 | Case 2:
% 169.13/25.47 | |
% 169.13/25.47 | | (33) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.13/25.47 | | e1)
% 169.13/25.47 | |
% 169.13/25.47 | | BETA: splitting (33) gives:
% 169.13/25.47 | |
% 169.13/25.47 | | Case 1:
% 169.13/25.47 | | |
% 169.13/25.47 | | | (34) all_58_7 = e1 & op(e1, e2) = e1
% 169.13/25.47 | | |
% 169.13/25.47 | | | REF_CLOSE: (2), (5), (6), (8), (9), (10), (12), (13), (14), (16), (17),
% 169.13/25.47 | | | (20), (21), (22), (24), (25), (26), (27), (28), (34) are
% 169.13/25.47 | | | inconsistent by sub-proof #182.
% 169.13/25.47 | | |
% 169.13/25.47 | | Case 2:
% 169.13/25.47 | | |
% 169.13/25.47 | | | (35) all_58_13 = e1 & op(e0, e2) = e1
% 169.13/25.47 | | |
% 169.13/25.47 | | | ALPHA: (35) implies:
% 169.13/25.47 | | | (36) op(e0, e2) = e1
% 169.13/25.47 | | |
% 169.13/25.47 | | | BETA: splitting (7) gives:
% 169.13/25.47 | | |
% 169.13/25.47 | | | Case 1:
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | (37) ~ (all_42_0 = e3) & op(all_42_1, e2) = all_42_0 & op(e0, e2) =
% 169.13/25.47 | | | | all_42_1 & $i(all_42_0) & $i(all_42_1)
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | ALPHA: (37) implies:
% 169.13/25.47 | | | | (38) ~ (all_42_0 = e3)
% 169.13/25.47 | | | | (39) op(e0, e2) = all_42_1
% 169.13/25.47 | | | | (40) op(all_42_1, e2) = all_42_0
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | GROUND_INST: instantiating (16) with e1, all_42_1, e2, e0, simplifying
% 169.13/25.47 | | | | with (36), (39) gives:
% 169.13/25.47 | | | | (41) all_42_1 = e1
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | REDUCE: (40), (41) imply:
% 169.13/25.47 | | | | (42) op(e1, e2) = all_42_0
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | GROUND_INST: instantiating (16) with e3, all_42_0, e2, e1, simplifying
% 169.13/25.47 | | | | with (23), (42) gives:
% 169.13/25.47 | | | | (43) all_42_0 = e3
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | REDUCE: (38), (43) imply:
% 169.13/25.47 | | | | (44) $false
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | CLOSE: (44) is inconsistent.
% 169.13/25.47 | | | |
% 169.13/25.47 | | | Case 2:
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | (45) ~ (all_42_1 = e1) & op(e0, e2) = all_42_1 & $i(all_42_1)
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | ALPHA: (45) implies:
% 169.13/25.47 | | | | (46) ~ (all_42_1 = e1)
% 169.13/25.47 | | | | (47) op(e0, e2) = all_42_1
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | GROUND_INST: instantiating (16) with e1, all_42_1, e2, e0, simplifying
% 169.13/25.47 | | | | with (36), (47) gives:
% 169.13/25.47 | | | | (48) all_42_1 = e1
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | REDUCE: (46), (48) imply:
% 169.13/25.47 | | | | (49) $false
% 169.13/25.47 | | | |
% 169.13/25.47 | | | | CLOSE: (49) is inconsistent.
% 169.13/25.47 | | | |
% 169.13/25.47 | | | End of split
% 169.13/25.47 | | |
% 169.13/25.47 | | End of split
% 169.13/25.47 | |
% 169.13/25.47 | End of split
% 169.13/25.47 |
% 169.13/25.47 End of proof
% 169.13/25.47
% 169.13/25.47 Sub-proof #182 shows that the following formulas are inconsistent:
% 169.13/25.47 ----------------------------------------------------------------
% 169.13/25.47 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.13/25.47 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.47 (2) all_58_7 = e1 & op(e1, e2) = e1
% 169.13/25.47 (3) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.13/25.47 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.13/25.47 (4) ~ (all_6_2 = e3)
% 169.13/25.47 (5) ~ (e3 = e1)
% 169.13/25.47 (6) ~ (e1 = e0)
% 169.13/25.47 (7) op(e0, e0) = e0
% 169.13/25.47 (8) ~ (all_6_2 = e2)
% 169.13/25.47 (9) op(e1, e1) = all_6_2
% 169.13/25.47 (10) ~ (e3 = e0)
% 169.13/25.47 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.47 (12) ~ (e2 = e0)
% 169.13/25.47 (13) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.13/25.47 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.13/25.47 (14) all_58_9 = e3
% 169.13/25.47 (15) ~ (e2 = e1)
% 169.13/25.47 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.13/25.47 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.13/25.47 (17) op(e2, e0) = e2
% 169.13/25.47 (18) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.13/25.47 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.13/25.47 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.13/25.47 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.13/25.47 (19) op(e2, e0) = all_52_13
% 169.13/25.47 (20) ~ (e3 = e2)
% 169.13/25.47
% 169.13/25.47 Begin of proof
% 169.13/25.47 |
% 169.13/25.47 | ALPHA: (2) implies:
% 169.13/25.47 | (21) all_58_7 = e1
% 169.13/25.47 |
% 169.13/25.47 | BETA: splitting (13) gives:
% 169.13/25.47 |
% 169.13/25.47 | Case 1:
% 169.13/25.47 | |
% 169.13/25.47 | | (22) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 169.13/25.47 | | e3)
% 169.13/25.47 | |
% 169.13/25.47 | | BETA: splitting (22) gives:
% 169.13/25.47 | |
% 169.13/25.47 | | Case 1:
% 169.13/25.47 | | |
% 169.13/25.47 | | | (23) all_58_6 = e3 & op(e1, e3) = e3
% 169.13/25.47 | | |
% 169.13/25.47 | | | ALPHA: (23) implies:
% 169.13/25.47 | | | (24) all_58_6 = e3
% 169.13/25.47 | | |
% 169.13/25.47 | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (12), (15), (16),
% 169.13/25.47 | | | (17), (18), (19), (20), (21), (24) are inconsistent by
% 169.13/25.47 | | | sub-proof #185.
% 169.13/25.47 | | |
% 169.13/25.47 | | Case 2:
% 169.13/25.47 | | |
% 169.13/25.47 | | | (25) all_58_7 = e3 & op(e1, e2) = e3
% 169.13/25.47 | | |
% 169.13/25.47 | | | REF_CLOSE: (5), (21), (25) are inconsistent by sub-proof #183.
% 169.13/25.47 | | |
% 169.13/25.47 | | End of split
% 169.13/25.47 | |
% 169.13/25.47 | Case 2:
% 169.13/25.47 | |
% 169.13/25.47 | | (26) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 169.13/25.47 | | e3)
% 169.13/25.47 | |
% 169.13/25.47 | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (11), (14), (15), (17), (26) are
% 169.13/25.47 | | inconsistent by sub-proof #186.
% 169.13/25.47 | |
% 169.13/25.47 | End of split
% 169.13/25.47 |
% 169.13/25.47 End of proof
% 169.13/25.47
% 169.13/25.47 Sub-proof #183 shows that the following formulas are inconsistent:
% 169.13/25.47 ----------------------------------------------------------------
% 169.13/25.47 (1) all_58_7 = e3 & op(e1, e2) = e3
% 169.13/25.47 (2) all_58_7 = e1
% 169.13/25.47 (3) ~ (e3 = e1)
% 169.13/25.47
% 169.13/25.47 Begin of proof
% 169.13/25.47 |
% 169.13/25.47 | ALPHA: (1) implies:
% 169.13/25.47 | (4) all_58_7 = e3
% 169.13/25.47 |
% 169.13/25.47 | COMBINE_EQS: (2), (4) imply:
% 169.13/25.47 | (5) e3 = e1
% 169.13/25.47 |
% 169.13/25.47 | REDUCE: (3), (5) imply:
% 169.13/25.47 | (6) $false
% 169.13/25.47 |
% 169.13/25.47 | CLOSE: (6) is inconsistent.
% 169.13/25.47 |
% 169.13/25.47 End of proof
% 169.13/25.47
% 169.13/25.47 Sub-proof #184 shows that the following formulas are inconsistent:
% 169.13/25.47 ----------------------------------------------------------------
% 169.13/25.47 (1) ~ (all_24_1 = e1) & op(e0, e3) = all_24_1 & $i(all_24_1)
% 169.13/25.47 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.47 (3) op(e0, e3) = all_10_1
% 169.13/25.47 (4) op(e0, e3) = e1
% 169.13/25.47
% 169.13/25.47 Begin of proof
% 169.13/25.47 |
% 169.13/25.47 | ALPHA: (1) implies:
% 169.13/25.47 | (5) ~ (all_24_1 = e1)
% 169.13/25.47 | (6) op(e0, e3) = all_24_1
% 169.13/25.47 |
% 169.13/25.47 | GROUND_INST: instantiating (2) with all_10_1, all_24_1, e3, e0, simplifying
% 169.13/25.47 | with (3), (6) gives:
% 169.13/25.47 | (7) all_24_1 = all_10_1
% 169.13/25.47 |
% 169.13/25.47 | GROUND_INST: instantiating (2) with e1, all_24_1, e3, e0, simplifying with
% 169.13/25.47 | (4), (6) gives:
% 169.13/25.47 | (8) all_24_1 = e1
% 169.13/25.47 |
% 169.13/25.47 | COMBINE_EQS: (7), (8) imply:
% 169.13/25.47 | (9) all_10_1 = e1
% 169.13/25.47 |
% 169.13/25.47 | REDUCE: (5), (8) imply:
% 169.13/25.47 | (10) $false
% 169.13/25.47 |
% 169.13/25.47 | CLOSE: (10) is inconsistent.
% 169.13/25.47 |
% 169.13/25.47 End of proof
% 169.13/25.47
% 169.13/25.47 Sub-proof #185 shows that the following formulas are inconsistent:
% 169.13/25.47 ----------------------------------------------------------------
% 169.13/25.47 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.13/25.47 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.47 (2) all_58_7 = e1
% 169.13/25.47 (3) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.13/25.47 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.13/25.47 (4) ~ (e3 = e1)
% 169.13/25.47 (5) all_58_6 = e3
% 169.13/25.47 (6) ~ (e1 = e0)
% 169.13/25.47 (7) ~ (all_6_2 = e2)
% 169.13/25.47 (8) op(e1, e1) = all_6_2
% 169.13/25.47 (9) ~ (e3 = e0)
% 169.13/25.47 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.47 (11) ~ (e2 = e0)
% 169.13/25.47 (12) ~ (e2 = e1)
% 169.13/25.47 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.13/25.47 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.13/25.47 (14) op(e2, e0) = e2
% 169.13/25.47 (15) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.13/25.47 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.13/25.47 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.13/25.47 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.13/25.47 (16) op(e2, e0) = all_52_13
% 169.13/25.47 (17) ~ (e3 = e2)
% 169.13/25.47
% 169.13/25.47 Begin of proof
% 169.13/25.47 |
% 169.13/25.47 | BETA: splitting (3) gives:
% 169.13/25.47 |
% 169.13/25.47 | Case 1:
% 169.13/25.47 | |
% 169.13/25.47 | | (18) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 169.13/25.47 | | e2)
% 169.13/25.47 | |
% 169.13/25.47 | | BETA: splitting (18) gives:
% 169.13/25.47 | |
% 169.13/25.47 | | Case 1:
% 169.13/25.47 | | |
% 169.13/25.47 | | | (19) all_58_6 = e2 & op(e1, e3) = e2
% 169.13/25.47 | | |
% 169.13/25.47 | | | REF_CLOSE: (5), (17), (19) are inconsistent by sub-proof #189.
% 169.13/25.47 | | |
% 169.13/25.47 | | Case 2:
% 169.13/25.47 | | |
% 169.13/25.47 | | | (20) all_58_7 = e2 & op(e1, e2) = e2
% 169.13/25.47 | | |
% 169.13/25.47 | | | ALPHA: (20) implies:
% 169.13/25.47 | | | (21) all_58_7 = e2
% 169.13/25.47 | | |
% 169.13/25.47 | | | COMBINE_EQS: (2), (21) imply:
% 169.13/25.47 | | | (22) e2 = e1
% 169.13/25.47 | | |
% 169.13/25.47 | | | REDUCE: (12), (22) imply:
% 169.13/25.47 | | | (23) $false
% 169.13/25.47 | | |
% 169.13/25.47 | | | CLOSE: (23) is inconsistent.
% 169.13/25.47 | | |
% 169.13/25.47 | | End of split
% 169.13/25.47 | |
% 169.13/25.47 | Case 2:
% 169.13/25.47 | |
% 169.13/25.47 | | (24) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 169.13/25.47 | | e2)
% 169.13/25.47 | |
% 169.13/25.47 | | REF_CLOSE: (1), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 169.13/25.47 | | (16), (17), (24) are inconsistent by sub-proof #502.
% 169.13/25.47 | |
% 169.13/25.47 | End of split
% 169.13/25.47 |
% 169.13/25.47 End of proof
% 169.13/25.47
% 169.13/25.47 Sub-proof #186 shows that the following formulas are inconsistent:
% 169.13/25.47 ----------------------------------------------------------------
% 169.13/25.47 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.13/25.47 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.47 (2) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.13/25.47 (3) ~ (all_6_2 = e3)
% 169.13/25.47 (4) ~ (e3 = e1)
% 169.13/25.47 (5) ~ (e1 = e0)
% 169.13/25.47 (6) op(e0, e0) = e0
% 169.13/25.47 (7) op(e1, e1) = all_6_2
% 169.13/25.47 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.47 (9) all_58_9 = e3
% 169.13/25.47 (10) ~ (e2 = e1)
% 169.13/25.47 (11) op(e2, e0) = e2
% 169.13/25.47
% 169.13/25.47 Begin of proof
% 169.13/25.47 |
% 169.13/25.47 | BETA: splitting (2) gives:
% 169.13/25.47 |
% 169.13/25.47 | Case 1:
% 169.13/25.47 | |
% 169.13/25.47 | | (12) all_58_8 = e3 & op(e1, e1) = e3
% 169.13/25.47 | |
% 169.13/25.47 | | REF_CLOSE: (3), (7), (8), (12) are inconsistent by sub-proof #961.
% 169.13/25.47 | |
% 169.13/25.47 | Case 2:
% 169.13/25.47 | |
% 169.13/25.47 | | (13) all_58_11 = e3 & op(e1, e0) = e3
% 169.13/25.47 | |
% 169.13/25.47 | | ALPHA: (13) implies:
% 169.13/25.47 | | (14) all_58_11 = e3
% 169.13/25.47 | |
% 169.13/25.47 | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (11), (14) are inconsistent
% 169.13/25.47 | | by sub-proof #203.
% 169.13/25.47 | |
% 169.13/25.47 | End of split
% 169.13/25.47 |
% 169.13/25.47 End of proof
% 169.13/25.47
% 169.13/25.47 Sub-proof #187 shows that the following formulas are inconsistent:
% 169.13/25.47 ----------------------------------------------------------------
% 169.13/25.47 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.13/25.47 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.47 (2) all_58_6 = e1
% 169.13/25.47 (3) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.13/25.47 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.13/25.47 (4) ~ (e3 = e1)
% 169.13/25.47 (5) ~ (e1 = e0)
% 169.13/25.47 (6) ~ (all_6_2 = e2)
% 169.13/25.47 (7) op(e1, e1) = all_6_2
% 169.13/25.47 (8) ~ (e3 = e0)
% 169.13/25.47 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.47 (10) ~ (e2 = e0)
% 169.13/25.47 (11) ~ (e2 = e1)
% 169.13/25.47 (12) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.13/25.47 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.13/25.47 (13) op(e2, e0) = e2
% 169.13/25.47 (14) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.13/25.47 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.13/25.47 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.13/25.47 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.13/25.47 (15) all_58_7 = e3
% 169.13/25.47 (16) op(e2, e0) = all_52_13
% 169.13/25.47 (17) ~ (e3 = e2)
% 169.13/25.47
% 169.13/25.47 Begin of proof
% 169.13/25.47 |
% 169.13/25.47 | BETA: splitting (3) gives:
% 169.13/25.47 |
% 169.13/25.47 | Case 1:
% 169.13/25.47 | |
% 169.13/25.47 | | (18) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 169.13/25.47 | | e2)
% 169.13/25.47 | |
% 169.13/25.47 | | BETA: splitting (18) gives:
% 169.13/25.47 | |
% 169.13/25.47 | | Case 1:
% 169.13/25.47 | | |
% 169.13/25.47 | | | (19) all_58_6 = e2 & op(e1, e3) = e2
% 169.13/25.47 | | |
% 169.13/25.47 | | | REF_CLOSE: (2), (11), (19) are inconsistent by sub-proof #715.
% 169.13/25.47 | | |
% 169.13/25.47 | | Case 2:
% 169.13/25.47 | | |
% 169.13/25.47 | | | (20) all_58_7 = e2 & op(e1, e2) = e2
% 169.13/25.47 | | |
% 169.13/25.47 | | | REF_CLOSE: (15), (17), (20) are inconsistent by sub-proof #754.
% 169.13/25.47 | | |
% 169.13/25.47 | | End of split
% 169.13/25.47 | |
% 169.13/25.47 | Case 2:
% 169.13/25.47 | |
% 169.13/25.47 | | (21) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 169.13/25.47 | | e2)
% 169.13/25.47 | |
% 169.13/25.47 | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 169.13/25.47 | | (16), (17), (21) are inconsistent by sub-proof #502.
% 169.13/25.47 | |
% 169.13/25.47 | End of split
% 169.13/25.47 |
% 169.13/25.47 End of proof
% 169.13/25.47
% 169.13/25.47 Sub-proof #188 shows that the following formulas are inconsistent:
% 169.13/25.47 ----------------------------------------------------------------
% 169.13/25.47 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.47 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.47 (2) ~ (all_8_2 = e3)
% 169.13/25.47 (3) ~ (e3 = e1)
% 169.13/25.47 (4) all_58_2 = e2 & op(e2, e3) = e2
% 169.13/25.47 (5) ~ (e1 = e0)
% 169.13/25.48 (6) op(e2, e3) = all_52_1
% 169.13/25.48 (7) op(e2, e2) = all_8_2
% 169.13/25.48 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.48 (9) all_58_3 = e0
% 169.13/25.48 (10) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.48 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.48 (11) ~ (e2 = e1)
% 169.13/25.48 (12) op(e2, e0) = e2
% 169.13/25.48 (13) ~ (e3 = e2)
% 169.13/25.48
% 169.13/25.48 Begin of proof
% 169.13/25.48 |
% 169.13/25.48 | ALPHA: (4) implies:
% 169.13/25.48 | (14) op(e2, e3) = e2
% 169.13/25.48 |
% 169.13/25.48 | BETA: splitting (1) gives:
% 169.13/25.48 |
% 169.13/25.48 | Case 1:
% 169.13/25.48 | |
% 169.13/25.48 | | (15) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.13/25.48 | | e1)
% 169.13/25.48 | |
% 169.13/25.48 | | BETA: splitting (15) gives:
% 169.13/25.48 | |
% 169.13/25.48 | | Case 1:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (16) all_58_2 = e1 & op(e2, e3) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (16) implies:
% 169.13/25.48 | | | (17) op(e2, e3) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | REF_CLOSE: (6), (8), (11), (14), (17) are inconsistent by sub-proof #784.
% 169.13/25.48 | | |
% 169.13/25.48 | | Case 2:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (18) all_58_3 = e1 & op(e2, e2) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (18) implies:
% 169.13/25.48 | | | (19) all_58_3 = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | COMBINE_EQS: (9), (19) imply:
% 169.13/25.48 | | | (20) e1 = e0
% 169.13/25.48 | | |
% 169.13/25.48 | | | REDUCE: (5), (20) imply:
% 169.13/25.48 | | | (21) $false
% 169.13/25.48 | | |
% 169.13/25.48 | | | CLOSE: (21) is inconsistent.
% 169.13/25.48 | | |
% 169.13/25.48 | | End of split
% 169.13/25.48 | |
% 169.13/25.48 | Case 2:
% 169.13/25.48 | |
% 169.13/25.48 | | (22) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 169.13/25.48 | | e1)
% 169.13/25.48 | |
% 169.13/25.48 | | BETA: splitting (22) gives:
% 169.13/25.48 | |
% 169.13/25.48 | | Case 1:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (23) all_58_5 = e1 & op(e2, e1) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (23) implies:
% 169.13/25.48 | | | (24) all_58_5 = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | BETA: splitting (10) gives:
% 169.13/25.48 | | |
% 169.13/25.48 | | | Case 1:
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | (25) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2)
% 169.13/25.48 | | | | = e3)
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | BETA: splitting (25) gives:
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | Case 1:
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | (26) all_58_2 = e3 & op(e2, e3) = e3
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | ALPHA: (26) implies:
% 169.13/25.48 | | | | | (27) op(e2, e3) = e3
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | REF_CLOSE: (6), (8), (13), (14), (27) are inconsistent by sub-proof
% 169.13/25.48 | | | | | #462.
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | Case 2:
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | (28) all_58_3 = e3 & op(e2, e2) = e3
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | REF_CLOSE: (2), (7), (8), (28) are inconsistent by sub-proof #973.
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | End of split
% 169.13/25.48 | | | |
% 169.13/25.48 | | | Case 2:
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | (29) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0)
% 169.13/25.48 | | | | = e3)
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | BETA: splitting (29) gives:
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | Case 1:
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | (30) all_58_5 = e3 & op(e2, e1) = e3
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | ALPHA: (30) implies:
% 169.13/25.48 | | | | | (31) all_58_5 = e3
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | REF_CLOSE: (3), (24), (31) are inconsistent by sub-proof #920.
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | Case 2:
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | (32) all_58_10 = e3 & op(e2, e0) = e3
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | ALPHA: (32) implies:
% 169.13/25.48 | | | | | (33) op(e2, e0) = e3
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | REF_CLOSE: (8), (12), (13), (33) are inconsistent by sub-proof #682.
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | End of split
% 169.13/25.48 | | | |
% 169.13/25.48 | | | End of split
% 169.13/25.48 | | |
% 169.13/25.48 | | Case 2:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (34) all_58_10 = e1 & op(e2, e0) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (34) implies:
% 169.13/25.48 | | | (35) op(e2, e0) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | REF_CLOSE: (8), (11), (12), (35) are inconsistent by sub-proof #526.
% 169.13/25.48 | | |
% 169.13/25.48 | | End of split
% 169.13/25.48 | |
% 169.13/25.48 | End of split
% 169.13/25.48 |
% 169.13/25.48 End of proof
% 169.13/25.48
% 169.13/25.48 Sub-proof #189 shows that the following formulas are inconsistent:
% 169.13/25.48 ----------------------------------------------------------------
% 169.13/25.48 (1) all_58_6 = e2 & op(e1, e3) = e2
% 169.13/25.48 (2) all_58_6 = e3
% 169.13/25.48 (3) ~ (e3 = e2)
% 169.13/25.48
% 169.13/25.48 Begin of proof
% 169.13/25.48 |
% 169.13/25.48 | ALPHA: (1) implies:
% 169.13/25.48 | (4) all_58_6 = e2
% 169.13/25.48 |
% 169.13/25.48 | COMBINE_EQS: (2), (4) imply:
% 169.13/25.48 | (5) e3 = e2
% 169.13/25.48 |
% 169.13/25.48 | REDUCE: (3), (5) imply:
% 169.13/25.48 | (6) $false
% 169.13/25.48 |
% 169.13/25.48 | CLOSE: (6) is inconsistent.
% 169.13/25.48 |
% 169.13/25.48 End of proof
% 169.13/25.48
% 169.13/25.48 Sub-proof #190 shows that the following formulas are inconsistent:
% 169.13/25.48 ----------------------------------------------------------------
% 169.13/25.48 (1) op(e2, e1) = all_52_9
% 169.13/25.48 (2) ~ (all_52_1 = e0)
% 169.13/25.48 (3) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.48 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.13/25.48 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.48 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.13/25.48 (5) ~ (all_8_2 = e3)
% 169.13/25.48 (6) ~ (e3 = e1)
% 169.13/25.48 (7) ~ (e1 = e0)
% 169.13/25.48 (8) op(e2, e3) = all_52_1
% 169.13/25.48 (9) all_58_7 = e0
% 169.13/25.48 (10) op(e2, e2) = all_8_2
% 169.13/25.48 (11) ~ (e3 = e0)
% 169.13/25.48 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.48 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.48 (13) ~ (all_52_4 = e3)
% 169.13/25.48 (14) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.13/25.48 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.13/25.48 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.48 (16) ~ (e2 = e0)
% 169.13/25.48 (17) ~ (all_52_9 = e0)
% 169.13/25.48 (18) ~ (e2 = e1)
% 169.13/25.48 (19) op(e3, e2) = all_52_4
% 169.13/25.48 (20) op(e2, e0) = e2
% 169.13/25.48 (21) op(e2, e0) = all_52_13
% 169.13/25.48 (22) ~ (e3 = e2)
% 169.13/25.48
% 169.13/25.48 Begin of proof
% 169.13/25.48 |
% 169.13/25.48 | BETA: splitting (3) gives:
% 169.13/25.48 |
% 169.13/25.48 | Case 1:
% 169.13/25.48 | |
% 169.13/25.48 | | (23) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 169.13/25.48 | | e3)
% 169.13/25.48 | |
% 169.13/25.48 | | REF_CLOSE: (5), (10), (13), (15), (19), (23) are inconsistent by sub-proof
% 169.13/25.48 | | #972.
% 169.13/25.48 | |
% 169.13/25.48 | Case 2:
% 169.13/25.48 | |
% 169.13/25.48 | | (24) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 169.13/25.48 | | e3)
% 169.13/25.48 | |
% 169.13/25.48 | | BETA: splitting (24) gives:
% 169.13/25.48 | |
% 169.13/25.48 | | Case 1:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (25) all_58_7 = e3 & op(e1, e2) = e3
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (25) implies:
% 169.13/25.48 | | | (26) all_58_7 = e3
% 169.13/25.48 | | |
% 169.13/25.48 | | | REF_CLOSE: (9), (11), (26) are inconsistent by sub-proof #748.
% 169.13/25.48 | | |
% 169.13/25.48 | | Case 2:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (27) all_58_13 = e3 & op(e0, e2) = e3
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (27) implies:
% 169.13/25.48 | | | (28) all_58_13 = e3
% 169.13/25.48 | | |
% 169.13/25.48 | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (12), (14), (15), (16),
% 169.13/25.48 | | | (17), (18), (20), (21), (22), (28) are inconsistent by
% 169.13/25.48 | | | sub-proof #191.
% 169.13/25.48 | | |
% 169.13/25.48 | | End of split
% 169.13/25.48 | |
% 169.13/25.48 | End of split
% 169.13/25.48 |
% 169.13/25.48 End of proof
% 169.13/25.48
% 169.13/25.48 Sub-proof #191 shows that the following formulas are inconsistent:
% 169.13/25.48 ----------------------------------------------------------------
% 169.13/25.48 (1) op(e2, e1) = all_52_9
% 169.13/25.48 (2) ~ (all_52_1 = e0)
% 169.13/25.48 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.48 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.13/25.48 (4) ~ (e3 = e1)
% 169.13/25.48 (5) all_58_13 = e3
% 169.13/25.48 (6) ~ (e1 = e0)
% 169.13/25.48 (7) op(e2, e3) = all_52_1
% 169.13/25.48 (8) all_58_7 = e0
% 169.13/25.48 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.48 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.48 (10) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.13/25.48 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.13/25.48 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.48 (12) ~ (e2 = e0)
% 169.13/25.48 (13) ~ (all_52_9 = e0)
% 169.13/25.48 (14) ~ (e2 = e1)
% 169.13/25.48 (15) op(e2, e0) = e2
% 169.13/25.48 (16) op(e2, e0) = all_52_13
% 169.13/25.48 (17) ~ (e3 = e2)
% 169.13/25.48
% 169.13/25.48 Begin of proof
% 169.13/25.48 |
% 169.13/25.48 | BETA: splitting (10) gives:
% 169.13/25.48 |
% 169.13/25.48 | Case 1:
% 169.13/25.48 | |
% 169.13/25.48 | | (18) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 169.13/25.48 | | e2)
% 169.13/25.48 | |
% 169.13/25.48 | | BETA: splitting (18) gives:
% 169.13/25.48 | |
% 169.13/25.48 | | Case 1:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (19) all_58_1 = e2 & op(e3, e2) = e2
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (19) implies:
% 169.13/25.48 | | | (20) all_58_1 = e2
% 169.13/25.48 | | |
% 169.13/25.48 | | | BETA: splitting (3) gives:
% 169.13/25.48 | | |
% 169.13/25.48 | | | Case 1:
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | (21) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 169.13/25.48 | | | | = e1)
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | BETA: splitting (21) gives:
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | Case 1:
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | (22) all_58_1 = e1 & op(e3, e2) = e1
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | REF_CLOSE: (14), (20), (22) are inconsistent by sub-proof #899.
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | Case 2:
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | (23) all_58_3 = e1 & op(e2, e2) = e1
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | REF_CLOSE: (1), (2), (6), (7), (9), (11), (12), (13), (15), (16), (23)
% 169.13/25.48 | | | | | are inconsistent by sub-proof #507.
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | End of split
% 169.13/25.48 | | | |
% 169.13/25.48 | | | Case 2:
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | (24) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 169.13/25.48 | | | | = e1)
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | REF_CLOSE: (4), (5), (6), (8), (24) are inconsistent by sub-proof #193.
% 169.13/25.48 | | | |
% 169.13/25.48 | | | End of split
% 169.13/25.48 | | |
% 169.13/25.48 | | Case 2:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (25) all_58_3 = e2 & op(e2, e2) = e2
% 169.13/25.48 | | |
% 169.13/25.48 | | | REF_CLOSE: (1), (2), (7), (9), (11), (12), (13), (15), (16), (25) are
% 169.13/25.48 | | | inconsistent by sub-proof #484.
% 169.13/25.48 | | |
% 169.13/25.48 | | End of split
% 169.13/25.48 | |
% 169.13/25.48 | Case 2:
% 169.13/25.48 | |
% 169.13/25.48 | | (26) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 169.13/25.48 | | e2)
% 169.13/25.48 | |
% 169.13/25.48 | | BETA: splitting (26) gives:
% 169.13/25.48 | |
% 169.13/25.48 | | Case 1:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (27) all_58_7 = e2 & op(e1, e2) = e2
% 169.13/25.48 | | |
% 169.13/25.48 | | | REF_CLOSE: (8), (12), (27) are inconsistent by sub-proof #468.
% 169.13/25.48 | | |
% 169.13/25.48 | | Case 2:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (28) all_58_13 = e2 & op(e0, e2) = e2
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (28) implies:
% 169.13/25.48 | | | (29) all_58_13 = e2
% 169.13/25.48 | | |
% 169.13/25.48 | | | REF_CLOSE: (5), (17), (29) are inconsistent by sub-proof #192.
% 169.13/25.48 | | |
% 169.13/25.48 | | End of split
% 169.13/25.48 | |
% 169.13/25.48 | End of split
% 169.13/25.48 |
% 169.13/25.48 End of proof
% 169.13/25.48
% 169.13/25.48 Sub-proof #192 shows that the following formulas are inconsistent:
% 169.13/25.48 ----------------------------------------------------------------
% 169.13/25.48 (1) all_58_13 = e3
% 169.13/25.48 (2) all_58_13 = e2
% 169.13/25.48 (3) ~ (e3 = e2)
% 169.13/25.48
% 169.13/25.48 Begin of proof
% 169.13/25.48 |
% 169.13/25.48 | COMBINE_EQS: (1), (2) imply:
% 169.13/25.48 | (4) e3 = e2
% 169.13/25.48 |
% 169.13/25.48 | SIMP: (4) implies:
% 169.13/25.48 | (5) e3 = e2
% 169.13/25.48 |
% 169.13/25.48 | REDUCE: (3), (5) imply:
% 169.13/25.48 | (6) $false
% 169.13/25.48 |
% 169.13/25.48 | CLOSE: (6) is inconsistent.
% 169.13/25.48 |
% 169.13/25.48 End of proof
% 169.13/25.48
% 169.13/25.48 Sub-proof #193 shows that the following formulas are inconsistent:
% 169.13/25.48 ----------------------------------------------------------------
% 169.13/25.48 (1) ~ (e3 = e1)
% 169.13/25.48 (2) all_58_13 = e3
% 169.13/25.48 (3) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.13/25.48 (4) ~ (e1 = e0)
% 169.13/25.48 (5) all_58_7 = e0
% 169.13/25.48
% 169.13/25.48 Begin of proof
% 169.13/25.48 |
% 169.13/25.48 | BETA: splitting (3) gives:
% 169.13/25.48 |
% 169.13/25.48 | Case 1:
% 169.13/25.48 | |
% 169.13/25.48 | | (6) all_58_7 = e1 & op(e1, e2) = e1
% 169.13/25.48 | |
% 169.13/25.48 | | ALPHA: (6) implies:
% 169.13/25.48 | | (7) all_58_7 = e1
% 169.13/25.48 | |
% 169.13/25.48 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #710.
% 169.13/25.48 | |
% 169.13/25.48 | Case 2:
% 169.13/25.48 | |
% 169.13/25.48 | | (8) all_58_13 = e1 & op(e0, e2) = e1
% 169.13/25.48 | |
% 169.13/25.48 | | ALPHA: (8) implies:
% 169.13/25.48 | | (9) all_58_13 = e1
% 169.13/25.48 | |
% 169.13/25.48 | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #194.
% 169.13/25.48 | |
% 169.13/25.48 | End of split
% 169.13/25.48 |
% 169.13/25.48 End of proof
% 169.13/25.48
% 169.13/25.48 Sub-proof #194 shows that the following formulas are inconsistent:
% 169.13/25.48 ----------------------------------------------------------------
% 169.13/25.48 (1) all_58_13 = e3
% 169.13/25.48 (2) all_58_13 = e1
% 169.13/25.48 (3) ~ (e3 = e1)
% 169.13/25.48
% 169.13/25.48 Begin of proof
% 169.13/25.48 |
% 169.13/25.48 | COMBINE_EQS: (1), (2) imply:
% 169.13/25.48 | (4) e3 = e1
% 169.13/25.48 |
% 169.13/25.48 | SIMP: (4) implies:
% 169.13/25.48 | (5) e3 = e1
% 169.13/25.48 |
% 169.13/25.48 | REDUCE: (3), (5) imply:
% 169.13/25.48 | (6) $false
% 169.13/25.48 |
% 169.13/25.48 | CLOSE: (6) is inconsistent.
% 169.13/25.48 |
% 169.13/25.48 End of proof
% 169.13/25.48
% 169.13/25.48 Sub-proof #195 shows that the following formulas are inconsistent:
% 169.13/25.48 ----------------------------------------------------------------
% 169.13/25.48 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.13/25.48 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.48 (2) ~ (all_4_2 = e2)
% 169.13/25.48 (3) ~ (e3 = e1)
% 169.13/25.48 (4) ~ (e1 = e0)
% 169.13/25.48 (5) op(e0, e0) = e0
% 169.13/25.48 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.13/25.48 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.13/25.48 (7) op(e2, e0) = e0
% 169.13/25.48 (8) op(e0, e0) = all_4_2
% 169.13/25.48 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.48 (10) ~ (e2 = e0)
% 169.13/25.48 (11) all_58_9 = e3
% 169.13/25.48 (12) ~ (e2 = e1)
% 169.13/25.48 (13) op(e2, e0) = all_52_13
% 169.13/25.48 (14) ~ (e3 = e2)
% 169.13/25.48
% 169.13/25.48 Begin of proof
% 169.13/25.48 |
% 169.13/25.48 | BETA: splitting (1) gives:
% 169.13/25.48 |
% 169.13/25.48 | Case 1:
% 169.13/25.48 | |
% 169.13/25.48 | | (15) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 169.13/25.48 | | e1)
% 169.13/25.48 | |
% 169.13/25.48 | | BETA: splitting (15) gives:
% 169.13/25.48 | |
% 169.13/25.48 | | Case 1:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (16) all_58_9 = e1 & op(e3, e0) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | REF_CLOSE: (3), (11), (16) are inconsistent by sub-proof #836.
% 169.13/25.48 | | |
% 169.13/25.48 | | Case 2:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (17) all_58_10 = e1 & op(e2, e0) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (17) implies:
% 169.13/25.48 | | | (18) op(e2, e0) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | REF_CLOSE: (4), (7), (9), (18) are inconsistent by sub-proof #849.
% 169.13/25.48 | | |
% 169.13/25.48 | | End of split
% 169.13/25.48 | |
% 169.13/25.48 | Case 2:
% 169.13/25.48 | |
% 169.13/25.48 | | (19) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.13/25.48 | | e1)
% 169.13/25.48 | |
% 169.13/25.48 | | BETA: splitting (19) gives:
% 169.13/25.48 | |
% 169.13/25.48 | | Case 1:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (20) all_58_11 = e1 & op(e1, e0) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (20) implies:
% 169.13/25.48 | | | (21) all_58_11 = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | BETA: splitting (6) gives:
% 169.13/25.48 | | |
% 169.13/25.48 | | | Case 1:
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | (22) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 169.13/25.48 | | | | = e2)
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | BETA: splitting (22) gives:
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | Case 1:
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | (23) all_58_9 = e2 & op(e3, e0) = e2
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | REF_CLOSE: (11), (14), (23) are inconsistent by sub-proof #205.
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | Case 2:
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | (24) all_58_10 = e2 & op(e2, e0) = e2
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | ALPHA: (24) implies:
% 169.13/25.48 | | | | | (25) op(e2, e0) = e2
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | | REF_CLOSE: (7), (9), (10), (13), (25) are inconsistent by sub-proof
% 169.13/25.48 | | | | | #684.
% 169.13/25.48 | | | | |
% 169.13/25.48 | | | | End of split
% 169.13/25.48 | | | |
% 169.13/25.48 | | | Case 2:
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | (26) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 169.13/25.48 | | | | e0) = e2)
% 169.13/25.48 | | | |
% 169.13/25.48 | | | | REF_CLOSE: (2), (8), (9), (12), (21), (26) are inconsistent by sub-proof
% 169.13/25.48 | | | | #514.
% 169.13/25.48 | | | |
% 169.13/25.48 | | | End of split
% 169.13/25.48 | | |
% 169.13/25.48 | | Case 2:
% 169.13/25.48 | | |
% 169.13/25.48 | | | (27) all_58_15 = e1 & op(e0, e0) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | ALPHA: (27) implies:
% 169.13/25.48 | | | (28) op(e0, e0) = e1
% 169.13/25.48 | | |
% 169.13/25.48 | | | REF_CLOSE: (4), (5), (9), (28) are inconsistent by sub-proof #204.
% 169.13/25.48 | | |
% 169.13/25.48 | | End of split
% 169.13/25.48 | |
% 169.13/25.48 | End of split
% 169.13/25.48 |
% 169.13/25.48 End of proof
% 169.13/25.48
% 169.13/25.48 Sub-proof #196 shows that the following formulas are inconsistent:
% 169.13/25.48 ----------------------------------------------------------------
% 169.13/25.48 (1) op(e1, e0) = e2
% 169.13/25.48 (2) ~ (e1 = e0)
% 169.13/25.48 (3) op(e2, e0) = e1
% 169.13/25.49 (4) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10
% 169.13/25.49 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 169.13/25.49 $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 169.13/25.49 op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.13/25.49 (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))) |
% 169.13/25.49 (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10
% 169.13/25.49 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.13/25.49 $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.13/25.49 op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.13/25.49 (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~
% 169.13/25.49 (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3,
% 169.13/25.49 e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.13/25.49 (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~
% 169.13/25.49 (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.13/25.49 $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 169.13/25.49 e2 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.13/25.49 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.49 (6) ~ (e2 = e0)
% 169.13/25.49 (7) all_56_15 = e0
% 169.13/25.49
% 169.13/25.49 Begin of proof
% 169.13/25.49 |
% 169.13/25.49 | BETA: splitting (4) gives:
% 169.13/25.49 |
% 169.13/25.49 | Case 1:
% 169.13/25.49 | |
% 169.13/25.49 | | (8) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) = e0 & ( ~
% 169.13/25.49 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 169.13/25.49 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 169.13/25.49 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 169.13/25.49 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 169.13/25.49 | |
% 169.13/25.49 | | ALPHA: (8) implies:
% 169.13/25.49 | | (9) op(e2, e0) = e0
% 169.13/25.49 | |
% 169.13/25.49 | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #849.
% 169.13/25.49 | |
% 169.13/25.49 | Case 2:
% 169.13/25.49 | |
% 169.13/25.49 | | (10) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.13/25.49 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.13/25.49 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.13/25.49 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 169.13/25.49 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8))))
% 169.13/25.49 | | | ( ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3)
% 169.13/25.49 | | & op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 =
% 169.13/25.49 | | e0) | ( ~ (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.13/25.49 | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1)
% 169.13/25.49 | | & op(e1, e0) = all_56_13 & $i(all_56_13))) & ((all_56_6 = e3 &
% 169.13/25.49 | | op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 169.13/25.49 | | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.13/25.49 | |
% 169.13/25.49 | | BETA: splitting (10) gives:
% 169.13/25.49 | |
% 169.13/25.49 | | Case 1:
% 169.13/25.49 | | |
% 169.13/25.49 | | | (11) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.13/25.49 | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.13/25.49 | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.13/25.49 | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 169.13/25.49 | | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 169.13/25.49 | | |
% 169.13/25.49 | | | ALPHA: (11) implies:
% 169.13/25.49 | | | (12) op(e1, e0) = e0
% 169.13/25.49 | | |
% 169.13/25.49 | | | REF_CLOSE: (1), (5), (6), (12) are inconsistent by sub-proof #197.
% 169.13/25.49 | | |
% 169.13/25.49 | | Case 2:
% 169.13/25.49 | | |
% 169.13/25.49 | | | (13) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 169.13/25.49 | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0)
% 169.13/25.49 | | | | ( ~ (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.13/25.49 | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1)
% 169.13/25.49 | | | & op(e1, e0) = all_56_13 & $i(all_56_13))) & ((all_56_6 = e3 &
% 169.13/25.49 | | | op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 169.13/25.49 | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 169.13/25.49 | | |
% 169.13/25.49 | | | ALPHA: (13) implies:
% 169.13/25.49 | | | (14) ~ (all_56_15 = e0)
% 169.13/25.49 | | |
% 169.13/25.49 | | | REDUCE: (7), (14) imply:
% 169.13/25.49 | | | (15) $false
% 169.13/25.49 | | |
% 169.13/25.49 | | | CLOSE: (15) is inconsistent.
% 169.13/25.49 | | |
% 169.13/25.49 | | End of split
% 169.13/25.49 | |
% 169.13/25.49 | End of split
% 169.13/25.49 |
% 169.13/25.49 End of proof
% 169.13/25.49
% 169.13/25.49 Sub-proof #197 shows that the following formulas are inconsistent:
% 169.13/25.49 ----------------------------------------------------------------
% 169.13/25.49 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.49 (2) op(e1, e0) = e2
% 169.13/25.49 (3) op(e1, e0) = e0
% 169.13/25.49 (4) ~ (e2 = e0)
% 169.13/25.49
% 169.13/25.49 Begin of proof
% 169.13/25.49 |
% 169.13/25.49 | GROUND_INST: instantiating (1) with e0, e2, e0, e1, simplifying with (2), (3)
% 169.13/25.49 | gives:
% 169.13/25.49 | (5) e2 = e0
% 169.13/25.49 |
% 169.13/25.49 | REDUCE: (4), (5) imply:
% 169.13/25.49 | (6) $false
% 169.13/25.49 |
% 169.13/25.49 | CLOSE: (6) is inconsistent.
% 169.13/25.49 |
% 169.13/25.49 End of proof
% 169.13/25.49
% 169.13/25.49 Sub-proof #198 shows that the following formulas are inconsistent:
% 169.13/25.49 ----------------------------------------------------------------
% 169.13/25.49 (1) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 =
% 169.13/25.49 e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) &
% 169.13/25.49 ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.13/25.49 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.13/25.49 e3) = all_56_6 & $i(all_56_6)))
% 169.13/25.49 (2) all_56_9 = e3
% 169.13/25.49 (3) ~ (e3 = e0)
% 169.13/25.49
% 169.13/25.49 Begin of proof
% 169.13/25.49 |
% 169.13/25.49 | ALPHA: (1) implies:
% 169.13/25.49 | (4) all_56_9 = e0
% 169.13/25.49 |
% 169.13/25.49 | COMBINE_EQS: (2), (4) imply:
% 169.13/25.49 | (5) e3 = e0
% 169.13/25.49 |
% 169.13/25.49 | REDUCE: (3), (5) imply:
% 169.13/25.49 | (6) $false
% 169.13/25.49 |
% 169.13/25.49 | CLOSE: (6) is inconsistent.
% 169.13/25.49 |
% 169.13/25.49 End of proof
% 169.13/25.49
% 169.13/25.49 Sub-proof #199 shows that the following formulas are inconsistent:
% 169.13/25.49 ----------------------------------------------------------------
% 169.13/25.49 (1) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 =
% 169.13/25.49 e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4)))
% 169.13/25.49 & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.13/25.49 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.13/25.49 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.13/25.49 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.13/25.49 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.13/25.49 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.13/25.49 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.13/25.49 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.13/25.49 (2) op(e1, e2) = all_52_6
% 169.13/25.49 (3) ~ (all_52_6 = e2)
% 169.13/25.49 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.49 (5) ~ (e2 = e1)
% 169.13/25.49 (6) op(e3, e1) = e2
% 169.13/25.49
% 169.13/25.49 Begin of proof
% 169.13/25.49 |
% 169.13/25.49 | BETA: splitting (1) gives:
% 169.13/25.49 |
% 169.13/25.49 | Case 1:
% 169.13/25.49 | |
% 169.13/25.49 | | (7) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.13/25.49 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.13/25.49 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.13/25.49 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | (
% 169.13/25.49 | | ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 169.13/25.49 | |
% 169.13/25.49 | | ALPHA: (7) implies:
% 169.13/25.49 | | (8) op(e1, e2) = e2
% 169.13/25.49 | |
% 169.13/25.49 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #986.
% 169.13/25.49 | |
% 169.13/25.49 | Case 2:
% 169.13/25.49 | |
% 169.13/25.49 | | (9) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 169.13/25.49 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.13/25.49 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.13/25.49 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 169.13/25.49 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 169.13/25.49 | |
% 169.13/25.49 | | ALPHA: (9) implies:
% 169.13/25.49 | | (10) op(e3, e1) = e1
% 169.13/25.49 | |
% 169.13/25.49 | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #212.
% 169.13/25.49 | |
% 169.13/25.49 | End of split
% 169.13/25.49 |
% 169.13/25.49 End of proof
% 169.13/25.49
% 169.13/25.49 Sub-proof #200 shows that the following formulas are inconsistent:
% 169.13/25.49 ----------------------------------------------------------------
% 169.13/25.49 (1) all_56_12 = e2
% 169.13/25.49 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.49 (3) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.13/25.49 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.13/25.49 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.13/25.49 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.13/25.49 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.13/25.49 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.13/25.49 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.13/25.49 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.13/25.49 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.13/25.49 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.13/25.49 (4) ~ (all_52_4 = e2)
% 169.13/25.49 (5) op(e3, e2) = all_52_4
% 169.13/25.49
% 169.13/25.49 Begin of proof
% 169.13/25.49 |
% 169.13/25.49 | BETA: splitting (3) gives:
% 169.13/25.49 |
% 169.13/25.49 | Case 1:
% 169.13/25.49 | |
% 169.13/25.49 | | (6) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 169.13/25.49 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 169.13/25.49 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 169.13/25.49 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 169.13/25.49 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 169.13/25.49 | |
% 169.13/25.49 | | ALPHA: (6) implies:
% 169.13/25.49 | | (7) ~ (all_56_12 = e2)
% 169.13/25.49 | |
% 169.13/25.49 | | REDUCE: (1), (7) imply:
% 169.13/25.49 | | (8) $false
% 169.13/25.49 | |
% 169.13/25.49 | | CLOSE: (8) is inconsistent.
% 169.13/25.49 | |
% 169.13/25.49 | Case 2:
% 169.13/25.49 | |
% 169.13/25.49 | | (9) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.13/25.49 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.13/25.49 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.13/25.49 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 169.13/25.49 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 169.13/25.49 | |
% 169.13/25.49 | | ALPHA: (9) implies:
% 169.13/25.49 | | (10) op(e3, e2) = e2
% 169.13/25.49 | |
% 169.13/25.49 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #993.
% 169.13/25.49 | |
% 169.13/25.49 | End of split
% 169.13/25.49 |
% 169.13/25.49 End of proof
% 169.13/25.49
% 169.13/25.49 Sub-proof #201 shows that the following formulas are inconsistent:
% 169.13/25.49 ----------------------------------------------------------------
% 169.13/25.49 (1) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.13/25.49 (2) ~ (all_6_2 = e2)
% 169.13/25.49 (3) op(e1, e1) = all_6_2
% 169.13/25.49 (4) all_58_14 = e3
% 169.13/25.49 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.49 (6) ~ (e3 = e2)
% 169.13/25.49
% 169.13/25.49 Begin of proof
% 169.13/25.49 |
% 169.13/25.49 | BETA: splitting (1) gives:
% 169.13/25.49 |
% 169.13/25.49 | Case 1:
% 169.13/25.49 | |
% 169.13/25.49 | | (7) all_58_8 = e2 & op(e1, e1) = e2
% 169.13/25.49 | |
% 169.13/25.49 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #845.
% 169.13/25.49 | |
% 169.13/25.49 | Case 2:
% 169.13/25.49 | |
% 169.13/25.49 | | (8) all_58_14 = e2 & op(e0, e1) = e2
% 169.13/25.49 | |
% 169.13/25.49 | | ALPHA: (8) implies:
% 169.13/25.49 | | (9) all_58_14 = e2
% 169.13/25.49 | |
% 169.13/25.49 | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #855.
% 169.13/25.49 | |
% 169.13/25.49 | End of split
% 169.13/25.49 |
% 169.13/25.49 End of proof
% 169.13/25.49
% 169.13/25.49 Sub-proof #202 shows that the following formulas are inconsistent:
% 169.13/25.49 ----------------------------------------------------------------
% 169.13/25.49 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.13/25.49 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.49 (2) ~ (all_4_2 = e2)
% 169.13/25.49 (3) ~ (e3 = e1)
% 169.13/25.49 (4) ~ (e1 = e0)
% 169.13/25.49 (5) op(e0, e0) = e0
% 169.13/25.49 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.13/25.49 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.13/25.49 (7) op(e0, e0) = all_4_2
% 169.13/25.49 (8) all_58_11 = e3
% 169.13/25.49 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.49 (10) all_58_9 = e3
% 169.13/25.49 (11) ~ (e2 = e1)
% 169.13/25.49 (12) ~ (e3 = e2)
% 169.13/25.49
% 169.13/25.49 Begin of proof
% 169.13/25.49 |
% 169.13/25.49 | BETA: splitting (6) gives:
% 169.13/25.49 |
% 169.13/25.49 | Case 1:
% 169.13/25.49 | |
% 169.13/25.49 | | (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 169.13/25.49 | | e2)
% 169.13/25.49 | |
% 169.13/25.49 | | BETA: splitting (13) gives:
% 169.13/25.49 | |
% 169.13/25.49 | | Case 1:
% 169.13/25.49 | | |
% 169.13/25.49 | | | (14) all_58_9 = e2 & op(e3, e0) = e2
% 169.13/25.49 | | |
% 169.13/25.49 | | | REF_CLOSE: (10), (12), (14) are inconsistent by sub-proof #205.
% 169.13/25.49 | | |
% 169.13/25.49 | | Case 2:
% 169.13/25.49 | | |
% 169.13/25.49 | | | (15) all_58_10 = e2 & op(e2, e0) = e2
% 169.13/25.49 | | |
% 169.13/25.49 | | | ALPHA: (15) implies:
% 169.13/25.49 | | | (16) op(e2, e0) = e2
% 169.13/25.49 | | |
% 169.13/25.49 | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (16) are inconsistent
% 169.13/25.49 | | | by sub-proof #203.
% 169.13/25.49 | | |
% 169.13/25.49 | | End of split
% 169.13/25.49 | |
% 169.13/25.49 | Case 2:
% 169.13/25.49 | |
% 169.13/25.49 | | (17) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.13/25.49 | | e2)
% 169.13/25.49 | |
% 169.13/25.49 | | BETA: splitting (17) gives:
% 169.13/25.49 | |
% 169.13/25.49 | | Case 1:
% 169.13/25.49 | | |
% 169.13/25.49 | | | (18) all_58_11 = e2 & op(e1, e0) = e2
% 169.13/25.49 | | |
% 169.13/25.49 | | | ALPHA: (18) implies:
% 169.13/25.49 | | | (19) all_58_11 = e2
% 169.13/25.49 | | |
% 169.13/25.49 | | | COMBINE_EQS: (8), (19) imply:
% 169.13/25.49 | | | (20) e3 = e2
% 169.13/25.49 | | |
% 169.13/25.49 | | | REDUCE: (12), (20) imply:
% 169.13/25.49 | | | (21) $false
% 169.13/25.49 | | |
% 169.13/25.49 | | | CLOSE: (21) is inconsistent.
% 169.13/25.49 | | |
% 169.13/25.49 | | Case 2:
% 169.13/25.49 | | |
% 169.13/25.49 | | | (22) all_58_15 = e2 & op(e0, e0) = e2
% 169.13/25.49 | | |
% 169.13/25.49 | | | REF_CLOSE: (2), (7), (9), (22) are inconsistent by sub-proof #854.
% 169.13/25.49 | | |
% 169.13/25.49 | | End of split
% 169.13/25.49 | |
% 169.13/25.49 | End of split
% 169.13/25.49 |
% 169.13/25.49 End of proof
% 169.13/25.49
% 169.13/25.49 Sub-proof #203 shows that the following formulas are inconsistent:
% 169.13/25.49 ----------------------------------------------------------------
% 169.13/25.49 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.13/25.49 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.49 (2) ~ (e3 = e1)
% 169.13/25.49 (3) ~ (e1 = e0)
% 169.13/25.49 (4) op(e0, e0) = e0
% 169.13/25.49 (5) all_58_11 = e3
% 169.13/25.49 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.49 (7) all_58_9 = e3
% 169.13/25.49 (8) ~ (e2 = e1)
% 169.13/25.49 (9) op(e2, e0) = e2
% 169.13/25.49
% 169.13/25.49 Begin of proof
% 169.13/25.49 |
% 169.13/25.49 | BETA: splitting (1) gives:
% 169.13/25.49 |
% 169.13/25.49 | Case 1:
% 169.13/25.49 | |
% 169.13/25.49 | | (10) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 169.13/25.49 | | e1)
% 169.13/25.49 | |
% 169.13/25.49 | | BETA: splitting (10) gives:
% 169.13/25.49 | |
% 169.13/25.49 | | Case 1:
% 169.13/25.49 | | |
% 169.13/25.49 | | | (11) all_58_9 = e1 & op(e3, e0) = e1
% 169.13/25.49 | | |
% 169.13/25.49 | | | ALPHA: (11) implies:
% 169.13/25.49 | | | (12) all_58_9 = e1
% 169.13/25.49 | | |
% 169.13/25.49 | | | REF_CLOSE: (2), (7), (12) are inconsistent by sub-proof #896.
% 169.13/25.49 | | |
% 169.13/25.49 | | Case 2:
% 169.13/25.49 | | |
% 169.13/25.49 | | | (13) all_58_10 = e1 & op(e2, e0) = e1
% 169.13/25.49 | | |
% 169.13/25.49 | | | ALPHA: (13) implies:
% 169.13/25.49 | | | (14) op(e2, e0) = e1
% 169.13/25.49 | | |
% 169.13/25.49 | | | REF_CLOSE: (6), (8), (9), (14) are inconsistent by sub-proof #526.
% 169.13/25.49 | | |
% 169.13/25.49 | | End of split
% 169.13/25.49 | |
% 169.13/25.49 | Case 2:
% 169.13/25.49 | |
% 169.13/25.49 | | (15) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.13/25.49 | | e1)
% 169.13/25.49 | |
% 169.13/25.49 | | BETA: splitting (15) gives:
% 169.13/25.49 | |
% 169.13/25.49 | | Case 1:
% 169.13/25.49 | | |
% 169.13/25.49 | | | (16) all_58_11 = e1 & op(e1, e0) = e1
% 169.13/25.49 | | |
% 169.13/25.49 | | | ALPHA: (16) implies:
% 169.13/25.49 | | | (17) all_58_11 = e1
% 169.13/25.49 | | |
% 169.13/25.49 | | | REF_CLOSE: (2), (5), (17) are inconsistent by sub-proof #755.
% 169.13/25.49 | | |
% 169.13/25.49 | | Case 2:
% 169.13/25.49 | | |
% 169.13/25.49 | | | (18) all_58_15 = e1 & op(e0, e0) = e1
% 169.13/25.49 | | |
% 169.13/25.49 | | | ALPHA: (18) implies:
% 169.13/25.49 | | | (19) op(e0, e0) = e1
% 169.13/25.49 | | |
% 169.13/25.49 | | | REF_CLOSE: (3), (4), (6), (19) are inconsistent by sub-proof #204.
% 169.13/25.49 | | |
% 169.13/25.49 | | End of split
% 169.13/25.49 | |
% 169.13/25.49 | End of split
% 169.13/25.49 |
% 169.13/25.49 End of proof
% 169.13/25.49
% 169.13/25.49 Sub-proof #204 shows that the following formulas are inconsistent:
% 169.13/25.49 ----------------------------------------------------------------
% 169.13/25.49 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.49 (2) op(e0, e0) = e1
% 169.13/25.49 (3) op(e0, e0) = e0
% 169.13/25.49 (4) ~ (e1 = e0)
% 169.13/25.49
% 169.13/25.49 Begin of proof
% 169.13/25.49 |
% 169.13/25.49 | GROUND_INST: instantiating (1) with e0, e1, e0, e0, simplifying with (2), (3)
% 169.13/25.49 | gives:
% 169.13/25.49 | (5) e1 = e0
% 169.13/25.49 |
% 169.13/25.49 | REDUCE: (4), (5) imply:
% 169.13/25.49 | (6) $false
% 169.13/25.49 |
% 169.13/25.49 | CLOSE: (6) is inconsistent.
% 169.13/25.49 |
% 169.13/25.49 End of proof
% 169.13/25.49
% 169.13/25.49 Sub-proof #205 shows that the following formulas are inconsistent:
% 169.13/25.49 ----------------------------------------------------------------
% 169.13/25.49 (1) all_58_9 = e2 & op(e3, e0) = e2
% 169.13/25.49 (2) all_58_9 = e3
% 169.13/25.49 (3) ~ (e3 = e2)
% 169.13/25.49
% 169.13/25.49 Begin of proof
% 169.13/25.49 |
% 169.13/25.49 | ALPHA: (1) implies:
% 169.13/25.49 | (4) all_58_9 = e2
% 169.13/25.49 |
% 169.13/25.49 | COMBINE_EQS: (2), (4) imply:
% 169.13/25.49 | (5) e3 = e2
% 169.13/25.49 |
% 169.13/25.49 | REDUCE: (3), (5) imply:
% 169.13/25.49 | (6) $false
% 169.13/25.49 |
% 169.13/25.49 | CLOSE: (6) is inconsistent.
% 169.13/25.49 |
% 169.13/25.49 End of proof
% 169.13/25.49
% 169.13/25.49 Sub-proof #206 shows that the following formulas are inconsistent:
% 169.13/25.49 ----------------------------------------------------------------
% 169.13/25.49 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.49 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.50 (2) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 169.13/25.50 (3) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 169.13/25.50 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 169.13/25.50 (4) ~ (all_8_2 = e3)
% 169.13/25.50 (5) op(e3, e3) = e0
% 169.13/25.50 (6) ~ (e3 = e1)
% 169.13/25.50 (7) all_58_6 = e3
% 169.13/25.50 (8) op(e1, e3) = all_52_2
% 169.13/25.50 (9) ~ (e1 = e0)
% 169.13/25.50 (10) ~ (all_52_6 = all_8_2)
% 169.13/25.50 (11) op(e1, e2) = all_52_6
% 169.13/25.50 (12) op(e2, e3) = all_52_1
% 169.13/25.50 (13) ( ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 & op(e0, e3) =
% 169.13/25.50 all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e0,
% 169.13/25.50 e3) = all_10_1 & $i(all_10_1))
% 169.13/25.50 (14) ~ (all_8_2 = e0)
% 169.13/25.50 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.13/25.50 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.13/25.50 (16) ~ (e3 = e0)
% 169.13/25.50 (17) ~ (all_52_7 = all_8_2)
% 169.13/25.50 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.50 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.50 (19) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.13/25.50 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.13/25.50 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.50 (21) ~ (all_52_4 = all_8_2)
% 169.13/25.50 (22) op(e1, e3) = e3
% 169.13/25.50 (23) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.50 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.50 (24) all_54_5 = all_8_2
% 169.13/25.50 (25) ( ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0 & op(e0, e3) =
% 169.13/25.50 all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0,
% 169.13/25.50 e3) = all_24_1 & $i(all_24_1))
% 169.13/25.50 (26) op(e3, e2) = all_52_4
% 169.13/25.50 (27) ~ (all_8_2 = e1)
% 169.13/25.50 (28) op(e0, e2) = all_52_7
% 169.13/25.50 (29) all_58_0 = e0
% 169.13/25.50
% 169.13/25.50 Begin of proof
% 169.13/25.50 |
% 169.13/25.50 | BETA: splitting (2) gives:
% 169.13/25.50 |
% 169.13/25.50 | Case 1:
% 169.13/25.50 | |
% 169.13/25.50 | | (30) all_54_5 = e3
% 169.13/25.50 | |
% 169.13/25.50 | | REF_CLOSE: (4), (24), (30) are inconsistent by sub-proof #667.
% 169.13/25.50 | |
% 169.13/25.50 | Case 2:
% 169.13/25.50 | |
% 169.13/25.50 | | (31) ~ (all_54_5 = e3)
% 169.13/25.50 | | (32) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 169.13/25.50 | |
% 169.13/25.50 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.13/25.50 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 169.13/25.50 | | (25), (26), (27), (28), (29), (32) are inconsistent by sub-proof
% 169.13/25.50 | | #207.
% 169.13/25.50 | |
% 169.13/25.50 | End of split
% 169.13/25.50 |
% 169.13/25.50 End of proof
% 169.13/25.50
% 169.13/25.50 Sub-proof #207 shows that the following formulas are inconsistent:
% 169.13/25.50 ----------------------------------------------------------------
% 169.13/25.50 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.50 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.50 (2) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 169.13/25.50 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 169.13/25.50 (3) ~ (all_8_2 = e3)
% 169.13/25.50 (4) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 169.13/25.50 (5) op(e3, e3) = e0
% 169.13/25.50 (6) ~ (e3 = e1)
% 169.13/25.50 (7) all_58_6 = e3
% 169.13/25.50 (8) op(e1, e3) = all_52_2
% 169.13/25.50 (9) ~ (e1 = e0)
% 169.13/25.50 (10) ~ (all_52_6 = all_8_2)
% 169.13/25.50 (11) op(e1, e2) = all_52_6
% 169.13/25.50 (12) op(e2, e3) = all_52_1
% 169.13/25.50 (13) ( ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 & op(e0, e3) =
% 169.13/25.50 all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e0,
% 169.13/25.50 e3) = all_10_1 & $i(all_10_1))
% 169.13/25.50 (14) ~ (all_8_2 = e0)
% 169.13/25.50 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.13/25.50 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.13/25.50 (16) ~ (e3 = e0)
% 169.13/25.50 (17) ~ (all_52_7 = all_8_2)
% 169.13/25.50 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.50 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.50 (19) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.13/25.50 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.13/25.50 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.50 (21) ~ (all_52_4 = all_8_2)
% 169.13/25.50 (22) op(e1, e3) = e3
% 169.13/25.50 (23) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.50 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.50 (24) all_54_5 = all_8_2
% 169.13/25.50 (25) ( ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0 & op(e0, e3) =
% 169.13/25.50 all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0,
% 169.13/25.50 e3) = all_24_1 & $i(all_24_1))
% 169.13/25.50 (26) op(e3, e2) = all_52_4
% 169.13/25.50 (27) ~ (all_8_2 = e1)
% 169.13/25.50 (28) op(e0, e2) = all_52_7
% 169.13/25.50 (29) all_58_0 = e0
% 169.13/25.50
% 169.13/25.50 Begin of proof
% 169.13/25.50 |
% 169.13/25.50 | BETA: splitting (4) gives:
% 169.13/25.50 |
% 169.13/25.50 | Case 1:
% 169.13/25.50 | |
% 169.13/25.50 | | (30) all_54_5 = e2
% 169.13/25.50 | |
% 169.13/25.50 | | COMBINE_EQS: (24), (30) imply:
% 169.13/25.50 | | (31) all_8_2 = e2
% 169.13/25.50 | |
% 169.13/25.50 | | SIMP: (31) implies:
% 169.13/25.50 | | (32) all_8_2 = e2
% 169.13/25.50 | |
% 169.13/25.50 | | REDUCE: (21), (32) imply:
% 169.13/25.50 | | (33) ~ (all_52_4 = e2)
% 169.13/25.50 | |
% 169.13/25.50 | | REDUCE: (10), (32) imply:
% 169.13/25.50 | | (34) ~ (all_52_6 = e2)
% 169.13/25.50 | |
% 169.13/25.50 | | REDUCE: (17), (32) imply:
% 169.13/25.50 | | (35) ~ (all_52_7 = e2)
% 169.13/25.50 | |
% 169.13/25.50 | | REDUCE: (3), (32) imply:
% 169.13/25.50 | | (36) ~ (e3 = e2)
% 169.13/25.50 | |
% 169.13/25.50 | | SIMP: (36) implies:
% 169.13/25.50 | | (37) ~ (e3 = e2)
% 169.13/25.50 | |
% 169.13/25.50 | | REDUCE: (27), (32) imply:
% 169.13/25.50 | | (38) ~ (e2 = e1)
% 169.13/25.50 | |
% 169.13/25.50 | | REDUCE: (14), (32) imply:
% 169.13/25.50 | | (39) ~ (e2 = e0)
% 169.13/25.50 | |
% 169.13/25.50 | | BETA: splitting (2) gives:
% 169.13/25.50 | |
% 169.13/25.50 | | Case 1:
% 169.13/25.50 | | |
% 169.13/25.50 | | | (40) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 169.13/25.50 | | | e2)
% 169.13/25.50 | | |
% 169.13/25.50 | | | BETA: splitting (40) gives:
% 169.13/25.50 | | |
% 169.13/25.50 | | | Case 1:
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | (41) all_58_0 = e2 & op(e3, e3) = e2
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | REF_CLOSE: (29), (39), (41) are inconsistent by sub-proof #390.
% 169.13/25.50 | | | |
% 169.13/25.50 | | | Case 2:
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | (42) all_58_2 = e2 & op(e2, e3) = e2
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | REF_CLOSE: (1), (6), (9), (11), (12), (16), (18), (19), (20), (23),
% 169.13/25.50 | | | | (26), (28), (33), (34), (35), (37), (38), (39), (42) are
% 169.13/25.50 | | | | inconsistent by sub-proof #664.
% 169.13/25.50 | | | |
% 169.13/25.50 | | | End of split
% 169.13/25.50 | | |
% 169.13/25.50 | | Case 2:
% 169.13/25.50 | | |
% 169.13/25.50 | | | (43) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 169.13/25.50 | | | e2)
% 169.13/25.50 | | |
% 169.13/25.50 | | | BETA: splitting (43) gives:
% 169.13/25.50 | | |
% 169.13/25.50 | | | Case 1:
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | (44) all_58_6 = e2 & op(e1, e3) = e2
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | ALPHA: (44) implies:
% 169.13/25.50 | | | | (45) all_58_6 = e2
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | REF_CLOSE: (7), (37), (45) are inconsistent by sub-proof #822.
% 169.13/25.50 | | | |
% 169.13/25.50 | | | Case 2:
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | (46) all_58_12 = e2 & op(e0, e3) = e2
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | ALPHA: (46) implies:
% 169.13/25.50 | | | | (47) all_58_12 = e2
% 169.13/25.50 | | | | (48) op(e0, e3) = e2
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | BETA: splitting (15) gives:
% 169.13/25.50 | | | |
% 169.13/25.50 | | | | Case 1:
% 169.13/25.50 | | | | |
% 169.13/25.50 | | | | | (49) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 169.13/25.50 | | | | | e3) = e1)
% 169.13/25.50 | | | | |
% 169.13/25.50 | | | | | REF_CLOSE: (5), (9), (13), (20), (25), (48), (49) are inconsistent by
% 169.13/25.50 | | | | | sub-proof #208.
% 169.13/25.50 | | | | |
% 169.13/25.50 | | | | Case 2:
% 169.13/25.50 | | | | |
% 169.13/25.50 | | | | | (50) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 169.13/25.50 | | | | | e3) = e1)
% 169.13/25.50 | | | | |
% 169.13/25.50 | | | | | BETA: splitting (50) gives:
% 169.13/25.50 | | | | |
% 169.13/25.50 | | | | | Case 1:
% 169.13/25.50 | | | | | |
% 169.13/25.50 | | | | | | (51) all_58_6 = e1 & op(e1, e3) = e1
% 169.13/25.50 | | | | | |
% 169.13/25.50 | | | | | | ALPHA: (51) implies:
% 169.13/25.50 | | | | | | (52) op(e1, e3) = e1
% 169.13/25.50 | | | | | |
% 169.13/25.50 | | | | | | REF_CLOSE: (6), (8), (20), (22), (52) are inconsistent by sub-proof
% 169.13/25.50 | | | | | | #750.
% 169.13/25.50 | | | | | |
% 169.13/25.50 | | | | | Case 2:
% 169.13/25.50 | | | | | |
% 169.13/25.50 | | | | | | (53) all_58_12 = e1 & op(e0, e3) = e1
% 169.13/25.50 | | | | | |
% 169.13/25.50 | | | | | | ALPHA: (53) implies:
% 169.13/25.50 | | | | | | (54) all_58_12 = e1
% 169.13/25.50 | | | | | |
% 169.13/25.50 | | | | | | REF_CLOSE: (38), (47), (54) are inconsistent by sub-proof #862.
% 169.13/25.50 | | | | | |
% 169.13/25.50 | | | | | End of split
% 169.13/25.50 | | | | |
% 169.13/25.50 | | | | End of split
% 169.13/25.50 | | | |
% 169.13/25.50 | | | End of split
% 169.13/25.50 | | |
% 169.13/25.50 | | End of split
% 169.13/25.50 | |
% 169.13/25.50 | Case 2:
% 169.13/25.50 | |
% 169.13/25.50 | | (55) all_54_5 = e1 | all_54_5 = e0
% 169.13/25.50 | |
% 169.13/25.50 | | REF_CLOSE: (14), (24), (27), (55) are inconsistent by sub-proof #735.
% 169.13/25.50 | |
% 169.13/25.50 | End of split
% 169.13/25.50 |
% 169.13/25.50 End of proof
% 169.13/25.50
% 169.13/25.50 Sub-proof #208 shows that the following formulas are inconsistent:
% 169.13/25.50 ----------------------------------------------------------------
% 169.13/25.50 (1) op(e3, e3) = e0
% 169.13/25.50 (2) ~ (e1 = e0)
% 169.13/25.50 (3) op(e0, e3) = e2
% 169.13/25.50 (4) ( ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 & op(e0, e3) = all_10_1
% 169.13/25.50 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e0, e3) =
% 169.13/25.50 all_10_1 & $i(all_10_1))
% 169.13/25.50 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 169.13/25.50 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.50 (7) ( ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0 & op(e0, e3) = all_24_1
% 169.13/25.50 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0, e3) =
% 169.13/25.50 all_24_1 & $i(all_24_1))
% 169.13/25.50
% 169.13/25.50 Begin of proof
% 169.13/25.50 |
% 169.13/25.50 | BETA: splitting (5) gives:
% 169.13/25.50 |
% 169.13/25.50 | Case 1:
% 169.13/25.50 | |
% 169.13/25.50 | | (8) all_58_0 = e1 & op(e3, e3) = e1
% 169.13/25.50 | |
% 169.13/25.50 | | ALPHA: (8) implies:
% 169.13/25.50 | | (9) op(e3, e3) = e1
% 169.13/25.50 | |
% 169.13/25.50 | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #907.
% 169.13/25.50 | |
% 169.13/25.50 | Case 2:
% 169.13/25.50 | |
% 169.13/25.50 | | (10) all_58_2 = e1 & op(e2, e3) = e1
% 169.13/25.50 | |
% 169.13/25.50 | | ALPHA: (10) implies:
% 169.13/25.50 | | (11) op(e2, e3) = e1
% 169.13/25.50 | |
% 169.13/25.50 | | REF_CLOSE: (3), (4), (6), (7), (11) are inconsistent by sub-proof #209.
% 169.13/25.50 | |
% 169.13/25.50 | End of split
% 169.13/25.50 |
% 169.13/25.50 End of proof
% 169.13/25.50
% 169.13/25.50 Sub-proof #209 shows that the following formulas are inconsistent:
% 169.13/25.50 ----------------------------------------------------------------
% 169.13/25.50 (1) op(e0, e3) = e2
% 169.13/25.50 (2) ( ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 & op(e0, e3) = all_10_1
% 169.13/25.50 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e0, e3) =
% 169.13/25.50 all_10_1 & $i(all_10_1))
% 169.13/25.50 (3) op(e2, e3) = e1
% 169.13/25.50 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.50 (5) ( ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0 & op(e0, e3) = all_24_1
% 169.13/25.50 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0, e3) =
% 169.13/25.50 all_24_1 & $i(all_24_1))
% 169.13/25.50
% 169.13/25.50 Begin of proof
% 169.13/25.50 |
% 169.13/25.50 | BETA: splitting (5) gives:
% 169.13/25.50 |
% 169.13/25.50 | Case 1:
% 169.13/25.50 | |
% 169.13/25.50 | | (6) ~ (all_24_0 = e2) & op(all_24_1, e3) = all_24_0 & op(e0, e3) =
% 169.13/25.50 | | all_24_1 & $i(all_24_0) & $i(all_24_1)
% 169.13/25.50 | |
% 169.13/25.50 | | ALPHA: (6) implies:
% 169.13/25.50 | | (7) op(e0, e3) = all_24_1
% 169.13/25.50 | | (8) op(all_24_1, e3) = all_24_0
% 169.13/25.50 | |
% 169.13/25.50 | | BETA: splitting (2) gives:
% 169.13/25.50 | |
% 169.13/25.50 | | Case 1:
% 169.13/25.50 | | |
% 169.13/25.50 | | | (9) ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 & op(e0, e3) =
% 169.13/25.50 | | | all_10_1 & $i(all_10_0) & $i(all_10_1)
% 169.13/25.50 | | |
% 169.13/25.50 | | | ALPHA: (9) implies:
% 169.13/25.50 | | | (10) ~ (all_10_0 = e1)
% 169.13/25.50 | | | (11) op(e0, e3) = all_10_1
% 169.13/25.50 | | | (12) op(all_10_1, e3) = all_10_0
% 169.13/25.50 | | |
% 169.13/25.50 | | | GROUND_INST: instantiating (4) with all_10_1, all_24_1, e3, e0,
% 169.13/25.50 | | | simplifying with (7), (11) gives:
% 169.13/25.50 | | | (13) all_24_1 = all_10_1
% 169.13/25.50 | | |
% 169.13/25.50 | | | GROUND_INST: instantiating (4) with e2, all_24_1, e3, e0, simplifying with
% 169.13/25.50 | | | (1), (7) gives:
% 169.13/25.50 | | | (14) all_24_1 = e2
% 169.13/25.50 | | |
% 169.13/25.50 | | | COMBINE_EQS: (13), (14) imply:
% 169.13/25.50 | | | (15) all_10_1 = e2
% 169.13/25.50 | | |
% 169.13/25.50 | | | SIMP: (15) implies:
% 169.13/25.50 | | | (16) all_10_1 = e2
% 169.13/25.50 | | |
% 169.13/25.50 | | | REDUCE: (8), (14) imply:
% 169.13/25.50 | | | (17) op(e2, e3) = all_24_0
% 169.13/25.50 | | |
% 169.13/25.50 | | | REDUCE: (12), (16) imply:
% 169.13/25.50 | | | (18) op(e2, e3) = all_10_0
% 169.13/25.50 | | |
% 169.13/25.50 | | | GROUND_INST: instantiating (4) with e1, all_24_0, e3, e2, simplifying with
% 169.13/25.50 | | | (3), (17) gives:
% 169.13/25.50 | | | (19) all_24_0 = e1
% 169.13/25.50 | | |
% 169.13/25.50 | | | GROUND_INST: instantiating (4) with all_10_0, all_24_0, e3, e2,
% 169.13/25.50 | | | simplifying with (17), (18) gives:
% 169.13/25.50 | | | (20) all_24_0 = all_10_0
% 169.13/25.50 | | |
% 169.13/25.50 | | | COMBINE_EQS: (19), (20) imply:
% 169.13/25.50 | | | (21) all_10_0 = e1
% 169.13/25.50 | | |
% 169.13/25.50 | | | SIMP: (21) implies:
% 169.13/25.50 | | | (22) all_10_0 = e1
% 169.13/25.50 | | |
% 169.13/25.50 | | | REDUCE: (10), (22) imply:
% 169.13/25.50 | | | (23) $false
% 169.13/25.50 | | |
% 169.13/25.50 | | | CLOSE: (23) is inconsistent.
% 169.13/25.50 | | |
% 169.13/25.50 | | Case 2:
% 169.13/25.50 | | |
% 169.13/25.50 | | | (24) ~ (all_10_1 = e2) & op(e0, e3) = all_10_1 & $i(all_10_1)
% 169.13/25.50 | | |
% 169.13/25.50 | | | REF_CLOSE: (1), (4), (7), (24) are inconsistent by sub-proof #210.
% 169.13/25.50 | | |
% 169.13/25.50 | | End of split
% 169.13/25.50 | |
% 169.13/25.50 | Case 2:
% 169.13/25.50 | |
% 169.13/25.50 | | (25) ~ (all_24_1 = e1) & op(e0, e3) = all_24_1 & $i(all_24_1)
% 169.13/25.50 | |
% 169.13/25.50 | | ALPHA: (25) implies:
% 169.13/25.50 | | (26) op(e0, e3) = all_24_1
% 169.13/25.50 | |
% 169.13/25.50 | | BETA: splitting (2) gives:
% 169.13/25.50 | |
% 169.13/25.50 | | Case 1:
% 169.13/25.50 | | |
% 169.13/25.50 | | | (27) ~ (all_10_0 = e1) & op(all_10_1, e3) = all_10_0 & op(e0, e3) =
% 169.13/25.50 | | | all_10_1 & $i(all_10_0) & $i(all_10_1)
% 169.13/25.50 | | |
% 169.13/25.50 | | | ALPHA: (27) implies:
% 169.13/25.50 | | | (28) ~ (all_10_0 = e1)
% 169.13/25.50 | | | (29) op(e0, e3) = all_10_1
% 169.13/25.50 | | | (30) op(all_10_1, e3) = all_10_0
% 169.13/25.50 | | |
% 169.13/25.50 | | | GROUND_INST: instantiating (4) with all_10_1, all_24_1, e3, e0,
% 169.13/25.50 | | | simplifying with (26), (29) gives:
% 169.13/25.50 | | | (31) all_24_1 = all_10_1
% 169.13/25.50 | | |
% 169.13/25.50 | | | GROUND_INST: instantiating (4) with e2, all_24_1, e3, e0, simplifying with
% 169.13/25.50 | | | (1), (26) gives:
% 169.13/25.50 | | | (32) all_24_1 = e2
% 169.13/25.50 | | |
% 169.13/25.50 | | | COMBINE_EQS: (31), (32) imply:
% 169.13/25.50 | | | (33) all_10_1 = e2
% 169.13/25.50 | | |
% 169.13/25.50 | | | SIMP: (33) implies:
% 169.13/25.50 | | | (34) all_10_1 = e2
% 169.13/25.50 | | |
% 169.13/25.50 | | | REDUCE: (30), (34) imply:
% 169.13/25.50 | | | (35) op(e2, e3) = all_10_0
% 169.13/25.50 | | |
% 169.13/25.50 | | | GROUND_INST: instantiating (4) with e1, all_10_0, e3, e2, simplifying with
% 169.13/25.50 | | | (3), (35) gives:
% 169.13/25.50 | | | (36) all_10_0 = e1
% 169.13/25.50 | | |
% 169.13/25.50 | | | REDUCE: (28), (36) imply:
% 169.13/25.50 | | | (37) $false
% 169.13/25.50 | | |
% 169.13/25.50 | | | CLOSE: (37) is inconsistent.
% 169.13/25.50 | | |
% 169.13/25.50 | | Case 2:
% 169.13/25.50 | | |
% 169.13/25.50 | | | (38) ~ (all_10_1 = e2) & op(e0, e3) = all_10_1 & $i(all_10_1)
% 169.13/25.50 | | |
% 169.13/25.50 | | | REF_CLOSE: (1), (4), (26), (38) are inconsistent by sub-proof #210.
% 169.13/25.50 | | |
% 169.13/25.50 | | End of split
% 169.13/25.50 | |
% 169.13/25.50 | End of split
% 169.13/25.50 |
% 169.13/25.50 End of proof
% 169.13/25.50
% 169.13/25.50 Sub-proof #210 shows that the following formulas are inconsistent:
% 169.13/25.50 ----------------------------------------------------------------
% 169.13/25.50 (1) ~ (all_10_1 = e2) & op(e0, e3) = all_10_1 & $i(all_10_1)
% 169.13/25.51 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.51 (3) op(e0, e3) = all_24_1
% 169.13/25.51 (4) op(e0, e3) = e2
% 169.13/25.51
% 169.13/25.51 Begin of proof
% 169.13/25.51 |
% 169.13/25.51 | ALPHA: (1) implies:
% 169.13/25.51 | (5) ~ (all_10_1 = e2)
% 169.13/25.51 | (6) op(e0, e3) = all_10_1
% 169.13/25.51 |
% 169.13/25.51 | GROUND_INST: instantiating (2) with all_10_1, all_24_1, e3, e0, simplifying
% 169.13/25.51 | with (3), (6) gives:
% 169.13/25.51 | (7) all_24_1 = all_10_1
% 169.13/25.51 |
% 169.13/25.51 | GROUND_INST: instantiating (2) with e2, all_24_1, e3, e0, simplifying with
% 169.13/25.51 | (3), (4) gives:
% 169.13/25.51 | (8) all_24_1 = e2
% 169.13/25.51 |
% 169.13/25.51 | COMBINE_EQS: (7), (8) imply:
% 169.13/25.51 | (9) all_10_1 = e2
% 169.13/25.51 |
% 169.13/25.51 | SIMP: (9) implies:
% 169.13/25.51 | (10) all_10_1 = e2
% 169.13/25.51 |
% 169.13/25.51 | REDUCE: (5), (10) imply:
% 169.13/25.51 | (11) $false
% 169.13/25.51 |
% 169.13/25.51 | CLOSE: (11) is inconsistent.
% 169.13/25.51 |
% 169.13/25.51 End of proof
% 169.13/25.51
% 169.13/25.51 Sub-proof #211 shows that the following formulas are inconsistent:
% 169.13/25.51 ----------------------------------------------------------------
% 169.13/25.51 (1) op(e3, e3) = e0
% 169.13/25.51 (2) ~ (e3 = e1)
% 169.13/25.51 (3) ~ (e1 = e0)
% 169.13/25.51 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.13/25.51 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.13/25.51 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.51 (6) all_58_9 = e3
% 169.13/25.51 (7) ~ (e2 = e1)
% 169.13/25.51 (8) all_58_1 = e0
% 169.13/25.51 (9) op(e3, e1) = e2
% 169.13/25.51
% 169.13/25.51 Begin of proof
% 169.13/25.51 |
% 169.13/25.51 | BETA: splitting (4) gives:
% 169.13/25.51 |
% 169.13/25.51 | Case 1:
% 169.13/25.51 | |
% 169.13/25.51 | | (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 169.13/25.51 | | e1)
% 169.13/25.51 | |
% 169.13/25.51 | | BETA: splitting (10) gives:
% 169.13/25.51 | |
% 169.13/25.51 | | Case 1:
% 169.13/25.51 | | |
% 169.13/25.51 | | | (11) all_58_0 = e1 & op(e3, e3) = e1
% 169.13/25.51 | | |
% 169.13/25.51 | | | ALPHA: (11) implies:
% 169.13/25.51 | | | (12) op(e3, e3) = e1
% 169.13/25.51 | | |
% 169.13/25.51 | | | REF_CLOSE: (1), (3), (5), (12) are inconsistent by sub-proof #907.
% 169.13/25.51 | | |
% 169.13/25.51 | | Case 2:
% 169.13/25.51 | | |
% 169.13/25.51 | | | (13) all_58_1 = e1 & op(e3, e2) = e1
% 169.13/25.51 | | |
% 169.13/25.51 | | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #658.
% 169.13/25.51 | | |
% 169.13/25.51 | | End of split
% 169.13/25.51 | |
% 169.13/25.51 | Case 2:
% 169.13/25.51 | |
% 169.13/25.51 | | (14) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 169.13/25.51 | | e1)
% 169.13/25.51 | |
% 169.13/25.51 | | BETA: splitting (14) gives:
% 169.13/25.51 | |
% 169.13/25.51 | | Case 1:
% 169.13/25.51 | | |
% 169.13/25.51 | | | (15) all_58_4 = e1 & op(e3, e1) = e1
% 169.13/25.51 | | |
% 169.13/25.51 | | | ALPHA: (15) implies:
% 169.13/25.51 | | | (16) op(e3, e1) = e1
% 169.13/25.51 | | |
% 169.13/25.51 | | | REF_CLOSE: (5), (7), (9), (16) are inconsistent by sub-proof #212.
% 169.13/25.51 | | |
% 169.13/25.51 | | Case 2:
% 169.13/25.51 | | |
% 169.13/25.51 | | | (17) all_58_9 = e1 & op(e3, e0) = e1
% 169.13/25.51 | | |
% 169.13/25.51 | | | ALPHA: (17) implies:
% 169.13/25.51 | | | (18) all_58_9 = e1
% 169.13/25.51 | | |
% 169.13/25.51 | | | REF_CLOSE: (2), (6), (18) are inconsistent by sub-proof #896.
% 169.13/25.51 | | |
% 169.13/25.51 | | End of split
% 169.13/25.51 | |
% 169.13/25.51 | End of split
% 169.13/25.51 |
% 169.13/25.51 End of proof
% 169.13/25.51
% 169.13/25.51 Sub-proof #212 shows that the following formulas are inconsistent:
% 169.13/25.51 ----------------------------------------------------------------
% 169.13/25.51 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.51 (2) op(e3, e1) = e2
% 169.13/25.51 (3) op(e3, e1) = e1
% 169.13/25.51 (4) ~ (e2 = e1)
% 169.13/25.51
% 169.13/25.51 Begin of proof
% 169.13/25.51 |
% 169.13/25.51 | GROUND_INST: instantiating (1) with e2, e1, e1, e3, simplifying with (2), (3)
% 169.13/25.51 | gives:
% 169.13/25.51 | (5) e2 = e1
% 169.13/25.51 |
% 169.13/25.51 | REDUCE: (4), (5) imply:
% 169.13/25.51 | (6) $false
% 169.13/25.51 |
% 169.13/25.51 | CLOSE: (6) is inconsistent.
% 169.13/25.51 |
% 169.13/25.51 End of proof
% 169.13/25.51
% 169.13/25.51 Sub-proof #213 shows that the following formulas are inconsistent:
% 169.13/25.51 ----------------------------------------------------------------
% 169.13/25.51 (1) op(e3, e1) = all_52_8
% 169.13/25.51 (2) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 169.13/25.51 (3) ~ (e3 = e0)
% 169.13/25.51 (4) ~ (all_52_8 = e3)
% 169.13/25.51 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.51 (6) all_58_5 = e0
% 169.13/25.51
% 169.13/25.51 Begin of proof
% 169.13/25.51 |
% 169.13/25.51 | BETA: splitting (2) gives:
% 169.13/25.51 |
% 169.13/25.51 | Case 1:
% 169.13/25.51 | |
% 169.13/25.51 | | (7) all_58_4 = e3 & op(e3, e1) = e3
% 169.13/25.51 | |
% 169.13/25.51 | | ALPHA: (7) implies:
% 169.13/25.51 | | (8) op(e3, e1) = e3
% 169.13/25.51 | |
% 169.13/25.51 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #975.
% 169.13/25.51 | |
% 169.13/25.51 | Case 2:
% 169.13/25.51 | |
% 169.13/25.51 | | (9) all_58_5 = e3 & op(e2, e1) = e3
% 169.13/25.51 | |
% 169.13/25.51 | | ALPHA: (9) implies:
% 169.13/25.51 | | (10) all_58_5 = e3
% 169.13/25.51 | |
% 169.13/25.51 | | REF_CLOSE: (3), (6), (10) are inconsistent by sub-proof #919.
% 169.13/25.51 | |
% 169.13/25.51 | End of split
% 169.13/25.51 |
% 169.13/25.51 End of proof
% 169.13/25.51
% 169.13/25.51 Sub-proof #214 shows that the following formulas are inconsistent:
% 169.13/25.51 ----------------------------------------------------------------
% 169.13/25.51 (1) op(e2, e1) = all_52_9
% 169.13/25.51 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.51 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.51 (3) ~ (all_52_13 = e3)
% 169.13/25.51 (4) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 169.13/25.51 (5) ~ (all_8_2 = e3)
% 169.13/25.51 (6) ~ (all_52_13 = all_8_2)
% 169.13/25.51 (7) ~ (all_52_13 = e0)
% 169.13/25.51 (8) ~ (all_52_6 = all_8_2)
% 169.13/25.51 (9) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 169.13/25.51 (10) all_58_3 = e0 & op(e2, e2) = e0
% 169.13/25.51 (11) op(e1, e2) = all_52_6
% 169.13/25.51 (12) op(e2, e3) = all_52_1
% 169.13/25.51 (13) ~ (all_8_2 = e0)
% 169.13/25.51 (14) ~ (e3 = e0)
% 169.13/25.51 (15) ~ (all_52_7 = all_8_2)
% 169.13/25.51 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.51 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.51 (17) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.13/25.51 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.13/25.51 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.51 (19) ~ (all_52_4 = all_8_2)
% 169.13/25.51 (20) ~ (all_52_9 = all_8_2)
% 169.13/25.51 (21) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.51 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.51 (22) all_54_5 = all_8_2
% 169.13/25.51 (23) op(e3, e2) = all_52_4
% 169.13/25.51 (24) ~ (all_8_2 = e1)
% 169.13/25.51 (25) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.13/25.51 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 169.13/25.51 (26) op(e0, e2) = all_52_7
% 169.13/25.51 (27) all_54_7 = all_52_13
% 169.13/25.51 (28) op(e2, e0) = all_52_13
% 169.13/25.51
% 169.13/25.51 Begin of proof
% 169.13/25.51 |
% 169.13/25.51 | ALPHA: (10) implies:
% 169.13/25.51 | (29) all_58_3 = e0
% 169.13/25.51 |
% 169.13/25.51 | BETA: splitting (4) gives:
% 169.13/25.51 |
% 169.13/25.51 | Case 1:
% 169.13/25.51 | |
% 169.13/25.51 | | (30) all_54_5 = e3
% 169.13/25.51 | |
% 169.13/25.51 | | REF_CLOSE: (5), (22), (30) are inconsistent by sub-proof #667.
% 169.13/25.51 | |
% 169.13/25.51 | Case 2:
% 169.13/25.51 | |
% 169.13/25.51 | | (31) ~ (all_54_5 = e3)
% 169.13/25.51 | | (32) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 169.13/25.51 | |
% 169.13/25.51 | | BETA: splitting (32) gives:
% 169.13/25.51 | |
% 169.13/25.51 | | Case 1:
% 169.13/25.51 | | |
% 169.13/25.51 | | | (33) all_54_5 = e2
% 169.13/25.51 | | |
% 169.13/25.51 | | | COMBINE_EQS: (22), (33) imply:
% 169.13/25.51 | | | (34) all_8_2 = e2
% 169.13/25.51 | | |
% 169.13/25.51 | | | SIMP: (34) implies:
% 169.13/25.51 | | | (35) all_8_2 = e2
% 169.13/25.51 | | |
% 169.13/25.51 | | | REDUCE: (19), (35) imply:
% 169.13/25.51 | | | (36) ~ (all_52_4 = e2)
% 169.13/25.51 | | |
% 169.13/25.51 | | | REDUCE: (8), (35) imply:
% 169.13/25.51 | | | (37) ~ (all_52_6 = e2)
% 169.13/25.51 | | |
% 169.13/25.51 | | | REDUCE: (15), (35) imply:
% 169.13/25.51 | | | (38) ~ (all_52_7 = e2)
% 169.13/25.51 | | |
% 169.13/25.51 | | | REDUCE: (20), (35) imply:
% 169.13/25.51 | | | (39) ~ (all_52_9 = e2)
% 169.13/25.51 | | |
% 169.13/25.51 | | | REDUCE: (6), (35) imply:
% 169.13/25.51 | | | (40) ~ (all_52_13 = e2)
% 169.13/25.51 | | |
% 169.13/25.51 | | | REDUCE: (5), (35) imply:
% 169.13/25.51 | | | (41) ~ (e3 = e2)
% 169.13/25.51 | | |
% 169.13/25.51 | | | SIMP: (41) implies:
% 169.13/25.51 | | | (42) ~ (e3 = e2)
% 169.13/25.51 | | |
% 169.13/25.51 | | | REDUCE: (13), (35) imply:
% 169.13/25.51 | | | (43) ~ (e2 = e0)
% 169.13/25.51 | | |
% 169.13/25.51 | | | BETA: splitting (9) gives:
% 169.13/25.51 | | |
% 169.13/25.51 | | | Case 1:
% 169.13/25.51 | | | |
% 169.13/25.51 | | | | (44) all_54_7 = e3
% 169.13/25.51 | | | |
% 169.13/25.51 | | | | REF_CLOSE: (3), (27), (44) are inconsistent by sub-proof #533.
% 169.13/25.51 | | | |
% 169.13/25.51 | | | Case 2:
% 169.13/25.51 | | | |
% 169.13/25.51 | | | | (45) ~ (all_54_7 = e3)
% 169.13/25.51 | | | | (46) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 169.13/25.51 | | | |
% 169.13/25.51 | | | | BETA: splitting (46) gives:
% 169.13/25.51 | | | |
% 169.13/25.51 | | | | Case 1:
% 169.13/25.51 | | | | |
% 169.13/25.51 | | | | | (47) all_54_7 = e2
% 169.13/25.51 | | | | |
% 169.13/25.51 | | | | | REF_CLOSE: (27), (40), (47) are inconsistent by sub-proof #532.
% 169.13/25.51 | | | | |
% 169.13/25.51 | | | | Case 2:
% 169.13/25.51 | | | | |
% 169.13/25.51 | | | | | (48) ~ (all_54_7 = e2)
% 169.13/25.51 | | | | | (49) all_54_7 = e1 | all_54_7 = e0
% 169.13/25.51 | | | | |
% 169.13/25.51 | | | | | BETA: splitting (49) gives:
% 169.13/25.51 | | | | |
% 169.13/25.51 | | | | | Case 1:
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | (50) all_54_7 = e1
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | COMBINE_EQS: (27), (50) imply:
% 169.13/25.51 | | | | | | (51) all_52_13 = e1
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | SIMP: (51) implies:
% 169.13/25.51 | | | | | | (52) all_52_13 = e1
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | REDUCE: (3), (52) imply:
% 169.13/25.51 | | | | | | (53) ~ (e3 = e1)
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | SIMP: (53) implies:
% 169.13/25.51 | | | | | | (54) ~ (e3 = e1)
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | REDUCE: (40), (52) imply:
% 169.13/25.51 | | | | | | (55) ~ (e2 = e1)
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | SIMP: (55) implies:
% 169.13/25.51 | | | | | | (56) ~ (e2 = e1)
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | REDUCE: (7), (52) imply:
% 169.13/25.51 | | | | | | (57) ~ (e1 = e0)
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | REDUCE: (28), (52) imply:
% 169.13/25.51 | | | | | | (58) op(e2, e0) = e1
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | REF_CLOSE: (1), (2), (11), (12), (14), (16), (17), (18), (21), (23),
% 169.13/25.51 | | | | | | (25), (26), (29), (36), (37), (38), (39), (42), (43),
% 169.13/25.51 | | | | | | (54), (56), (57), (58) are inconsistent by sub-proof
% 169.13/25.51 | | | | | | #215.
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | Case 2:
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | (59) all_54_7 = e0
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | | REF_CLOSE: (7), (27), (59) are inconsistent by sub-proof #529.
% 169.13/25.51 | | | | | |
% 169.13/25.51 | | | | | End of split
% 169.13/25.51 | | | | |
% 169.13/25.51 | | | | End of split
% 169.13/25.51 | | | |
% 169.13/25.51 | | | End of split
% 169.13/25.51 | | |
% 169.13/25.51 | | Case 2:
% 169.13/25.51 | | |
% 169.13/25.51 | | | (60) all_54_5 = e1 | all_54_5 = e0
% 169.13/25.51 | | |
% 169.13/25.51 | | | REF_CLOSE: (13), (22), (24), (60) are inconsistent by sub-proof #735.
% 169.13/25.51 | | |
% 169.13/25.51 | | End of split
% 169.13/25.51 | |
% 169.13/25.51 | End of split
% 169.13/25.51 |
% 169.13/25.51 End of proof
% 169.13/25.51
% 169.13/25.51 Sub-proof #215 shows that the following formulas are inconsistent:
% 169.13/25.51 ----------------------------------------------------------------
% 169.13/25.51 (1) op(e2, e1) = all_52_9
% 169.13/25.51 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.51 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.51 (3) ~ (e3 = e1)
% 169.13/25.51 (4) ~ (e1 = e0)
% 169.13/25.51 (5) op(e1, e2) = all_52_6
% 169.13/25.51 (6) op(e2, e3) = all_52_1
% 169.13/25.51 (7) ~ (all_52_6 = e2)
% 169.13/25.51 (8) ~ (e3 = e0)
% 169.13/25.51 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.51 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.51 (10) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.13/25.51 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.13/25.51 (11) op(e2, e0) = e1
% 169.13/25.51 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.51 (13) ~ (e2 = e0)
% 169.13/25.51 (14) all_58_3 = e0
% 169.13/25.51 (15) ~ (all_52_7 = e2)
% 169.13/25.51 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.51 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.51 (17) ~ (e2 = e1)
% 169.13/25.51 (18) ~ (all_52_4 = e2)
% 169.13/25.51 (19) op(e3, e2) = all_52_4
% 169.13/25.51 (20) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.13/25.51 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 169.13/25.51 (21) op(e0, e2) = all_52_7
% 169.13/25.51 (22) ~ (all_52_9 = e2)
% 169.13/25.51 (23) ~ (e3 = e2)
% 169.13/25.51
% 169.13/25.51 Begin of proof
% 169.13/25.51 |
% 169.13/25.51 | BETA: splitting (20) gives:
% 169.13/25.51 |
% 169.13/25.51 | Case 1:
% 169.13/25.51 | |
% 169.13/25.51 | | (24) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 169.13/25.51 | | e2)
% 169.13/25.51 | |
% 169.13/25.51 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 169.13/25.51 | | (15), (16), (17), (18), (19), (21), (23), (24) are inconsistent
% 169.13/25.51 | | by sub-proof #216.
% 169.13/25.51 | |
% 169.13/25.51 | Case 2:
% 169.13/25.51 | |
% 169.13/25.51 | | (25) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 169.13/25.51 | | e2)
% 169.13/25.51 | |
% 169.13/25.51 | | BETA: splitting (25) gives:
% 169.13/25.51 | |
% 169.13/25.51 | | Case 1:
% 169.13/25.51 | | |
% 169.13/25.51 | | | (26) all_58_5 = e2 & op(e2, e1) = e2
% 169.13/25.51 | | |
% 169.13/25.51 | | | ALPHA: (26) implies:
% 169.13/25.51 | | | (27) op(e2, e1) = e2
% 169.13/25.51 | | |
% 169.13/25.51 | | | REF_CLOSE: (1), (12), (22), (27) are inconsistent by sub-proof #571.
% 169.13/25.51 | | |
% 169.13/25.51 | | Case 2:
% 169.13/25.51 | | |
% 169.13/25.51 | | | (28) all_58_10 = e2 & op(e2, e0) = e2
% 169.13/25.51 | | |
% 169.13/25.51 | | | ALPHA: (28) implies:
% 169.13/25.51 | | | (29) op(e2, e0) = e2
% 169.13/25.51 | | |
% 169.13/25.51 | | | REF_CLOSE: (11), (12), (17), (29) are inconsistent by sub-proof #526.
% 169.13/25.51 | | |
% 169.13/25.51 | | End of split
% 169.13/25.51 | |
% 169.13/25.51 | End of split
% 169.13/25.51 |
% 169.13/25.51 End of proof
% 169.13/25.51
% 169.13/25.51 Sub-proof #216 shows that the following formulas are inconsistent:
% 169.13/25.51 ----------------------------------------------------------------
% 169.13/25.51 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.51 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.51 (2) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 169.13/25.51 (3) ~ (e3 = e1)
% 169.13/25.51 (4) ~ (e1 = e0)
% 169.13/25.51 (5) op(e1, e2) = all_52_6
% 169.13/25.51 (6) op(e2, e3) = all_52_1
% 169.13/25.51 (7) ~ (all_52_6 = e2)
% 169.13/25.51 (8) ~ (e3 = e0)
% 169.13/25.51 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.51 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.51 (10) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.13/25.51 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.13/25.51 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.51 (12) ~ (e2 = e0)
% 169.13/25.51 (13) all_58_3 = e0
% 169.13/25.51 (14) ~ (all_52_7 = e2)
% 169.13/25.51 (15) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.51 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.51 (16) ~ (e2 = e1)
% 169.13/25.51 (17) ~ (all_52_4 = e2)
% 169.13/25.51 (18) op(e3, e2) = all_52_4
% 169.13/25.51 (19) op(e0, e2) = all_52_7
% 169.13/25.51 (20) ~ (e3 = e2)
% 169.13/25.51
% 169.13/25.51 Begin of proof
% 169.13/25.51 |
% 169.13/25.51 | BETA: splitting (2) gives:
% 169.13/25.51 |
% 169.13/25.51 | Case 1:
% 169.13/25.51 | |
% 169.13/25.51 | | (21) all_58_2 = e2 & op(e2, e3) = e2
% 169.13/25.51 | |
% 169.13/25.51 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 169.13/25.51 | | (15), (16), (17), (18), (19), (20), (21) are inconsistent by
% 169.13/25.51 | | sub-proof #664.
% 169.13/25.51 | |
% 169.13/25.51 | Case 2:
% 169.13/25.51 | |
% 169.13/25.52 | | (22) all_58_3 = e2 & op(e2, e2) = e2
% 169.13/25.52 | |
% 169.13/25.52 | | ALPHA: (22) implies:
% 169.13/25.52 | | (23) all_58_3 = e2
% 169.13/25.52 | |
% 169.13/25.52 | | REF_CLOSE: (12), (13), (23) are inconsistent by sub-proof #843.
% 169.13/25.52 | |
% 169.13/25.52 | End of split
% 169.13/25.52 |
% 169.13/25.52 End of proof
% 169.13/25.52
% 169.13/25.52 Sub-proof #217 shows that the following formulas are inconsistent:
% 169.13/25.52 ----------------------------------------------------------------
% 169.13/25.52 (1) op(e3, e3) = e0
% 169.13/25.52 (2) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 169.13/25.52 (3) ~ (e3 = e0)
% 169.13/25.52 (4) ~ (all_52_4 = e3)
% 169.13/25.52 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.52 (6) op(e3, e2) = all_52_4
% 169.13/25.52
% 169.13/25.52 Begin of proof
% 169.13/25.52 |
% 169.13/25.52 | BETA: splitting (2) gives:
% 169.13/25.52 |
% 169.13/25.52 | Case 1:
% 169.13/25.52 | |
% 169.13/25.52 | | (7) all_58_0 = e3 & op(e3, e3) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | ALPHA: (7) implies:
% 169.13/25.52 | | (8) op(e3, e3) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #949.
% 169.13/25.52 | |
% 169.13/25.52 | Case 2:
% 169.13/25.52 | |
% 169.13/25.52 | | (9) all_58_1 = e3 & op(e3, e2) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | ALPHA: (9) implies:
% 169.13/25.52 | | (10) op(e3, e2) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #974.
% 169.13/25.52 | |
% 169.13/25.52 | End of split
% 169.13/25.52 |
% 169.13/25.52 End of proof
% 169.13/25.52
% 169.13/25.52 Sub-proof #218 shows that the following formulas are inconsistent:
% 169.13/25.52 ----------------------------------------------------------------
% 169.13/25.52 (1) op(e2, e1) = all_52_9
% 169.13/25.52 (2) ~ (all_52_9 = e3)
% 169.13/25.52 (3) ~ (all_52_13 = e3)
% 169.13/25.52 (4) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.52 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.52 (6) op(e2, e0) = all_52_13
% 169.13/25.52
% 169.13/25.52 Begin of proof
% 169.13/25.52 |
% 169.13/25.52 | BETA: splitting (4) gives:
% 169.13/25.52 |
% 169.13/25.52 | Case 1:
% 169.13/25.52 | |
% 169.13/25.52 | | (7) all_58_5 = e3 & op(e2, e1) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | ALPHA: (7) implies:
% 169.13/25.52 | | (8) op(e2, e1) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #951.
% 169.13/25.52 | |
% 169.13/25.52 | Case 2:
% 169.13/25.52 | |
% 169.13/25.52 | | (9) all_58_10 = e3 & op(e2, e0) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | ALPHA: (9) implies:
% 169.13/25.52 | | (10) op(e2, e0) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #562.
% 169.13/25.52 | |
% 169.13/25.52 | End of split
% 169.13/25.52 |
% 169.13/25.52 End of proof
% 169.13/25.52
% 169.13/25.52 Sub-proof #219 shows that the following formulas are inconsistent:
% 169.13/25.52 ----------------------------------------------------------------
% 169.13/25.52 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.13/25.52 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.52 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.52 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.52 (3) ~ (all_52_13 = e3)
% 169.13/25.52 (4) all_58_2 = e2
% 169.13/25.52 (5) op(e0, e0) = e2
% 169.13/25.52 (6) ~ (e3 = e1)
% 169.13/25.52 (7) ~ (e1 = e0)
% 169.13/25.52 (8) all_58_11 = e2
% 169.13/25.52 (9) op(e2, e3) = all_52_1
% 169.13/25.52 (10) op(e2, e3) = e2
% 169.13/25.52 (11) ~ (e3 = e0)
% 169.13/25.52 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.52 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.52 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.52 (14) ~ (e2 = e0)
% 169.13/25.52 (15) all_58_3 = e3
% 169.13/25.52 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.52 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.52 (17) ~ (e2 = e1)
% 169.13/25.52 (18) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.13/25.52 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.13/25.52 (19) all_58_9 = e2 & op(e3, e0) = e2
% 169.13/25.52 (20) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.13/25.52 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.13/25.52 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.13/25.52 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.13/25.52 (21) op(e2, e0) = all_52_13
% 169.13/25.52 (22) ~ (e3 = e2)
% 169.13/25.52
% 169.13/25.52 Begin of proof
% 169.13/25.52 |
% 169.13/25.52 | ALPHA: (19) implies:
% 169.13/25.52 | (23) all_58_9 = e2
% 169.13/25.52 |
% 169.13/25.52 | BETA: splitting (18) gives:
% 169.13/25.52 |
% 169.13/25.52 | Case 1:
% 169.13/25.52 | |
% 169.13/25.52 | | (24) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 169.13/25.52 | | e3)
% 169.13/25.52 | |
% 169.13/25.52 | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 169.13/25.52 | | (16), (17), (21), (22), (23), (24) are inconsistent by sub-proof
% 169.13/25.52 | | #222.
% 169.13/25.52 | |
% 169.13/25.52 | Case 2:
% 169.13/25.52 | |
% 169.13/25.52 | | (25) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.13/25.52 | | e3)
% 169.13/25.52 | |
% 169.13/25.52 | | BETA: splitting (25) gives:
% 169.13/25.52 | |
% 169.13/25.52 | | Case 1:
% 169.13/25.52 | | |
% 169.13/25.52 | | | (26) all_58_11 = e3 & op(e1, e0) = e3
% 169.13/25.52 | | |
% 169.13/25.52 | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 169.13/25.52 | | | (15), (16), (17), (22), (26) are inconsistent by sub-proof
% 169.13/25.52 | | | #221.
% 169.13/25.52 | | |
% 169.13/25.52 | | Case 2:
% 169.13/25.52 | | |
% 169.13/25.52 | | | (27) all_58_15 = e3 & op(e0, e0) = e3
% 169.13/25.52 | | |
% 169.13/25.52 | | | ALPHA: (27) implies:
% 169.13/25.52 | | | (28) all_58_15 = e3
% 169.13/25.52 | | |
% 169.13/25.52 | | | BETA: splitting (18) gives:
% 169.13/25.52 | | |
% 169.13/25.52 | | | Case 1:
% 169.13/25.52 | | | |
% 169.13/25.52 | | | | (29) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0)
% 169.13/25.52 | | | | = e3)
% 169.13/25.52 | | | |
% 169.13/25.52 | | | | REF_CLOSE: (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 169.13/25.52 | | | | (15), (16), (17), (21), (22), (23), (29) are inconsistent by
% 169.13/25.52 | | | | sub-proof #222.
% 169.13/25.52 | | | |
% 169.13/25.52 | | | Case 2:
% 169.13/25.52 | | | |
% 169.13/25.52 | | | |
% 169.13/25.52 | | | | BETA: splitting (25) gives:
% 169.13/25.52 | | | |
% 169.13/25.52 | | | | Case 1:
% 169.13/25.52 | | | | |
% 169.13/25.52 | | | | | (30) all_58_11 = e3 & op(e1, e0) = e3
% 169.13/25.52 | | | | |
% 169.13/25.52 | | | | | ALPHA: (30) implies:
% 169.13/25.52 | | | | | (31) all_58_11 = e3
% 169.13/25.52 | | | | |
% 169.13/25.52 | | | | | REF_CLOSE: (1), (6), (7), (11), (14), (17), (20), (23), (28), (31) are
% 169.13/25.52 | | | | | inconsistent by sub-proof #374.
% 169.13/25.52 | | | | |
% 169.13/25.52 | | | | Case 2:
% 169.13/25.52 | | | | |
% 169.13/25.52 | | | | |
% 169.13/25.52 | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 169.13/25.52 | | | | | (15), (16), (17), (22), (27) are inconsistent by sub-proof
% 169.13/25.52 | | | | | #220.
% 169.13/25.52 | | | | |
% 169.13/25.52 | | | | End of split
% 169.13/25.52 | | | |
% 169.13/25.52 | | | End of split
% 169.13/25.52 | | |
% 169.13/25.52 | | End of split
% 169.13/25.52 | |
% 169.13/25.52 | End of split
% 169.13/25.52 |
% 169.13/25.52 End of proof
% 169.13/25.52
% 169.13/25.52 Sub-proof #220 shows that the following formulas are inconsistent:
% 169.13/25.52 ----------------------------------------------------------------
% 169.13/25.52 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.52 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.52 (2) all_58_2 = e2
% 169.13/25.52 (3) op(e0, e0) = e2
% 169.13/25.52 (4) ~ (e3 = e1)
% 169.13/25.52 (5) ~ (e1 = e0)
% 169.13/25.52 (6) op(e2, e3) = all_52_1
% 169.13/25.52 (7) op(e2, e3) = e2
% 169.13/25.52 (8) ~ (e3 = e0)
% 169.13/25.52 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.52 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.52 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.52 (11) ~ (e2 = e0)
% 169.13/25.52 (12) all_58_15 = e3 & op(e0, e0) = e3
% 169.13/25.52 (13) all_58_3 = e3
% 169.13/25.52 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.52 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.52 (15) ~ (e2 = e1)
% 169.13/25.52 (16) ~ (e3 = e2)
% 169.13/25.52
% 169.13/25.52 Begin of proof
% 169.13/25.52 |
% 169.13/25.52 | ALPHA: (12) implies:
% 169.13/25.52 | (17) op(e0, e0) = e3
% 169.13/25.52 |
% 169.13/25.52 | GROUND_INST: instantiating (10) with e2, e3, e0, e0, simplifying with (3),
% 169.13/25.52 | (17) gives:
% 169.13/25.52 | (18) e3 = e2
% 169.13/25.52 |
% 169.13/25.52 | COMBINE_EQS: (13), (18) imply:
% 169.13/25.52 | (19) all_58_3 = e2
% 169.13/25.52 |
% 169.13/25.52 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (14), (15),
% 169.13/25.52 | (16), (19) are inconsistent by sub-proof #779.
% 169.13/25.52 |
% 169.13/25.52 End of proof
% 169.13/25.52
% 169.13/25.52 Sub-proof #221 shows that the following formulas are inconsistent:
% 169.13/25.52 ----------------------------------------------------------------
% 169.13/25.52 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.52 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.52 (2) all_58_2 = e2
% 169.13/25.52 (3) ~ (e3 = e1)
% 169.13/25.52 (4) ~ (e1 = e0)
% 169.13/25.52 (5) all_58_11 = e2
% 169.13/25.52 (6) op(e2, e3) = all_52_1
% 169.13/25.52 (7) all_58_11 = e3 & op(e1, e0) = e3
% 169.13/25.52 (8) op(e2, e3) = e2
% 169.13/25.52 (9) ~ (e3 = e0)
% 169.13/25.52 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.52 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.52 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.52 (12) ~ (e2 = e0)
% 169.13/25.52 (13) all_58_3 = e3
% 169.13/25.52 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.52 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.52 (15) ~ (e2 = e1)
% 169.13/25.52 (16) ~ (e3 = e2)
% 169.13/25.52
% 169.13/25.52 Begin of proof
% 169.13/25.52 |
% 169.13/25.52 | ALPHA: (7) implies:
% 169.13/25.52 | (17) all_58_11 = e3
% 169.13/25.52 |
% 169.13/25.52 | COMBINE_EQS: (5), (17) imply:
% 169.13/25.52 | (18) e3 = e2
% 169.13/25.52 |
% 169.13/25.52 | COMBINE_EQS: (13), (18) imply:
% 169.13/25.52 | (19) all_58_3 = e2
% 169.13/25.52 |
% 169.13/25.52 | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (14), (15),
% 169.13/25.52 | (16), (19) are inconsistent by sub-proof #779.
% 169.13/25.52 |
% 169.13/25.52 End of proof
% 169.13/25.52
% 169.13/25.52 Sub-proof #222 shows that the following formulas are inconsistent:
% 169.13/25.52 ----------------------------------------------------------------
% 169.13/25.52 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.52 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.52 (2) ~ (all_52_13 = e3)
% 169.13/25.52 (3) all_58_9 = e2
% 169.13/25.52 (4) all_58_2 = e2
% 169.13/25.52 (5) ~ (e3 = e1)
% 169.13/25.52 (6) ~ (e1 = e0)
% 169.13/25.52 (7) op(e2, e3) = all_52_1
% 169.13/25.52 (8) op(e2, e3) = e2
% 169.13/25.52 (9) ~ (e3 = e0)
% 169.13/25.52 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.52 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.52 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.52 (12) ~ (e2 = e0)
% 169.13/25.52 (13) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.52 (14) all_58_3 = e3
% 169.13/25.52 (15) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.52 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.52 (16) ~ (e2 = e1)
% 169.13/25.52 (17) op(e2, e0) = all_52_13
% 169.13/25.52 (18) ~ (e3 = e2)
% 169.13/25.52
% 169.13/25.52 Begin of proof
% 169.13/25.52 |
% 169.13/25.52 | BETA: splitting (13) gives:
% 169.13/25.52 |
% 169.13/25.52 | Case 1:
% 169.13/25.52 | |
% 169.13/25.52 | | (19) all_58_9 = e3 & op(e3, e0) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | ALPHA: (19) implies:
% 169.13/25.52 | | (20) all_58_9 = e3
% 169.13/25.52 | |
% 169.13/25.52 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 169.13/25.52 | | (15), (16), (18), (20) are inconsistent by sub-proof #451.
% 169.13/25.52 | |
% 169.13/25.52 | Case 2:
% 169.13/25.52 | |
% 169.13/25.52 | | (21) all_58_10 = e3 & op(e2, e0) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | ALPHA: (21) implies:
% 169.13/25.52 | | (22) op(e2, e0) = e3
% 169.13/25.52 | |
% 169.13/25.52 | | REF_CLOSE: (2), (11), (17), (22) are inconsistent by sub-proof #562.
% 169.13/25.52 | |
% 169.13/25.52 | End of split
% 169.13/25.52 |
% 169.13/25.52 End of proof
% 169.13/25.52
% 169.13/25.52 Sub-proof #223 shows that the following formulas are inconsistent:
% 169.13/25.52 ----------------------------------------------------------------
% 169.13/25.52 (1) op(e2, e1) = all_52_9
% 169.13/25.52 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.13/25.52 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.13/25.52 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.52 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.13/25.52 (4) all_58_14 = e2
% 169.13/25.52 (5) ~ (all_52_9 = e3)
% 169.13/25.52 (6) ~ (all_52_13 = e3)
% 169.13/25.52 (7) all_58_7 = e2
% 169.13/25.52 (8) all_58_15 = e2
% 169.13/25.52 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.13/25.52 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.13/25.52 (10) all_58_2 = e2
% 169.13/25.52 (11) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.13/25.52 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.13/25.52 (12) ~ (e3 = e1)
% 169.13/25.52 (13) op(e1, e3) = all_52_2
% 169.13/25.52 (14) ~ (e1 = e0)
% 169.13/25.52 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.13/25.52 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.13/25.52 (16) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.13/25.52 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.13/25.52 (17) op(e2, e3) = all_52_1
% 169.13/25.52 (18) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.13/25.52 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.13/25.52 (19) op(e2, e3) = e2
% 169.13/25.52 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.13/25.52 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.13/25.52 (21) ~ (e3 = e0)
% 169.13/25.52 (22) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.13/25.52 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.13/25.52 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.13/25.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.13/25.52 (24) ~ (e2 = e0)
% 169.13/25.52 (25) all_58_12 = e3
% 169.13/25.52 (26) all_58_3 = e3
% 169.13/25.52 (27) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.13/25.52 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.13/25.52 (28) ~ (e2 = e1)
% 169.13/25.52 (29) op(e0, e1) = e2
% 169.13/25.52 (30) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.13/25.52 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.13/25.52 (31) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.13/25.52 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.13/25.52 (32) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.13/25.52 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.13/25.52 (33) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.13/25.52 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.13/25.52 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.13/25.52 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.13/25.52 (34) op(e2, e0) = all_52_13
% 169.13/25.52 (35) ~ (e3 = e2)
% 169.13/25.52
% 169.13/25.52 Begin of proof
% 169.13/25.52 |
% 169.13/25.52 | BETA: splitting (33) gives:
% 169.13/25.52 |
% 169.13/25.52 | Case 1:
% 169.13/25.52 | |
% 169.13/25.52 | | (36) all_58_15 = e0 & op(e0, e0) = e0
% 169.13/25.52 | |
% 169.13/25.52 | | ALPHA: (36) implies:
% 169.13/25.52 | | (37) all_58_15 = e0
% 169.13/25.52 | |
% 169.13/25.52 | | REF_CLOSE: (8), (24), (37) are inconsistent by sub-proof #725.
% 169.13/25.52 | |
% 169.13/25.52 | Case 2:
% 169.13/25.52 | |
% 169.13/25.53 | | (38) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 169.13/25.53 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 169.13/25.53 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 169.13/25.53 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.13/25.53 | |
% 169.13/25.53 | | ALPHA: (38) implies:
% 169.13/25.53 | | (39) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.13/25.53 | | e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.13/25.53 | |
% 169.13/25.53 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.13/25.53 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 169.13/25.53 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 169.13/25.53 | | (35), (39) are inconsistent by sub-proof #224.
% 169.13/25.53 | |
% 169.13/25.53 | End of split
% 169.13/25.53 |
% 169.13/25.53 End of proof
% 169.13/25.53
% 169.13/25.53 Sub-proof #224 shows that the following formulas are inconsistent:
% 169.13/25.53 ----------------------------------------------------------------
% 169.13/25.53 (1) op(e2, e1) = all_52_9
% 169.23/25.53 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.53 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.53 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.53 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.53 (4) all_58_14 = e2
% 169.23/25.53 (5) ~ (all_52_9 = e3)
% 169.23/25.53 (6) ~ (all_52_13 = e3)
% 169.23/25.53 (7) all_58_7 = e2
% 169.23/25.53 (8) all_58_15 = e2
% 169.23/25.53 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.53 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.53 (10) all_58_2 = e2
% 169.23/25.53 (11) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.53 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.53 (12) ~ (e3 = e1)
% 169.23/25.53 (13) op(e1, e3) = all_52_2
% 169.23/25.53 (14) ~ (e1 = e0)
% 169.23/25.53 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.53 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.53 (16) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.23/25.53 | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.53 (17) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.53 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.53 (18) op(e2, e3) = all_52_1
% 169.23/25.53 (19) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.53 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.53 (20) op(e2, e3) = e2
% 169.23/25.53 (21) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.53 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.53 (22) ~ (e3 = e0)
% 169.23/25.53 (23) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.53 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.53 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.53 (25) ~ (e2 = e0)
% 169.23/25.53 (26) all_58_12 = e3
% 169.23/25.53 (27) all_58_3 = e3
% 169.23/25.53 (28) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.53 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.53 (29) ~ (e2 = e1)
% 169.23/25.53 (30) op(e0, e1) = e2
% 169.23/25.53 (31) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.23/25.53 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.23/25.53 (32) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.23/25.53 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.23/25.53 (33) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.53 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.53 (34) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.53 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.23/25.53 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.23/25.53 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.23/25.53 (35) op(e2, e0) = all_52_13
% 169.23/25.53 (36) ~ (e3 = e2)
% 169.23/25.53
% 169.23/25.53 Begin of proof
% 169.23/25.53 |
% 169.23/25.53 | BETA: splitting (11) gives:
% 169.23/25.53 |
% 169.23/25.53 | Case 1:
% 169.23/25.53 | |
% 169.23/25.53 | | (37) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.23/25.53 | | e1)
% 169.23/25.53 | |
% 169.23/25.53 | | BETA: splitting (37) gives:
% 169.23/25.53 | |
% 169.23/25.53 | | Case 1:
% 169.23/25.53 | | |
% 169.23/25.53 | | | (38) all_58_1 = e1 & op(e3, e2) = e1
% 169.23/25.53 | | |
% 169.23/25.53 | | | ALPHA: (38) implies:
% 169.23/25.53 | | | (39) all_58_1 = e1
% 169.23/25.53 | | |
% 169.23/25.53 | | | BETA: splitting (32) gives:
% 169.23/25.53 | | |
% 169.23/25.53 | | | Case 1:
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | (40) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 169.23/25.53 | | | | = e2)
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | REF_CLOSE: (3), (9), (10), (12), (13), (14), (15), (18), (20), (21),
% 169.23/25.53 | | | | (22), (23), (24), (25), (26), (27), (28), (29), (36), (39),
% 169.23/25.53 | | | | (40) are inconsistent by sub-proof #227.
% 169.23/25.53 | | | |
% 169.23/25.53 | | | Case 2:
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | (41) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 169.23/25.53 | | | | = e2)
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | BETA: splitting (41) gives:
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | Case 1:
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | | (42) all_58_4 = e2 & op(e3, e1) = e2
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | | ALPHA: (42) implies:
% 169.23/25.53 | | | | | (43) all_58_4 = e2
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | | REF_CLOSE: (1), (3), (4), (5), (10), (12), (14), (17), (18), (19),
% 169.23/25.53 | | | | | (20), (22), (23), (24), (25), (27), (28), (29), (30), (33),
% 169.23/25.53 | | | | | (36), (43) are inconsistent by sub-proof #251.
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | Case 2:
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | | (44) all_58_9 = e2 & op(e3, e0) = e2
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | | ALPHA: (44) implies:
% 169.23/25.53 | | | | | (45) all_58_9 = e2
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | | REF_CLOSE: (2), (3), (6), (8), (10), (12), (14), (18), (20), (22),
% 169.23/25.53 | | | | | (23), (24), (25), (27), (28), (29), (31), (34), (35), (36),
% 169.23/25.53 | | | | | (45) are inconsistent by sub-proof #226.
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | End of split
% 169.23/25.53 | | | |
% 169.23/25.53 | | | End of split
% 169.23/25.53 | | |
% 169.23/25.53 | | Case 2:
% 169.23/25.53 | | |
% 169.23/25.53 | | | (46) all_58_3 = e1 & op(e2, e2) = e1
% 169.23/25.53 | | |
% 169.23/25.53 | | | REF_CLOSE: (12), (27), (46) are inconsistent by sub-proof #868.
% 169.23/25.53 | | |
% 169.23/25.53 | | End of split
% 169.23/25.53 | |
% 169.23/25.53 | Case 2:
% 169.23/25.53 | |
% 169.23/25.53 | | (47) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.23/25.53 | | e1)
% 169.23/25.53 | |
% 169.23/25.53 | | REF_CLOSE: (4), (7), (14), (16), (22), (25), (26), (29), (47) are
% 169.23/25.53 | | inconsistent by sub-proof #225.
% 169.23/25.53 | |
% 169.23/25.53 | End of split
% 169.23/25.53 |
% 169.23/25.53 End of proof
% 169.23/25.53
% 169.23/25.53 Sub-proof #225 shows that the following formulas are inconsistent:
% 169.23/25.53 ----------------------------------------------------------------
% 169.23/25.53 (1) all_58_14 = e2
% 169.23/25.53 (2) all_58_7 = e2
% 169.23/25.53 (3) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.53 (4) ~ (e1 = e0)
% 169.23/25.53 (5) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 169.23/25.53 (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.53 (6) ~ (e3 = e0)
% 169.23/25.53 (7) ~ (e2 = e0)
% 169.23/25.53 (8) all_58_12 = e3
% 169.23/25.53 (9) ~ (e2 = e1)
% 169.23/25.53
% 169.23/25.53 Begin of proof
% 169.23/25.53 |
% 169.23/25.53 | BETA: splitting (3) gives:
% 169.23/25.53 |
% 169.23/25.53 | Case 1:
% 169.23/25.53 | |
% 169.23/25.53 | | (10) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.53 | |
% 169.23/25.53 | | ALPHA: (10) implies:
% 169.23/25.53 | | (11) all_58_7 = e1
% 169.23/25.53 | |
% 169.23/25.53 | | REF_CLOSE: (2), (9), (11) are inconsistent by sub-proof #494.
% 169.23/25.53 | |
% 169.23/25.53 | Case 2:
% 169.23/25.53 | |
% 169.23/25.53 | | (12) all_58_13 = e1 & op(e0, e2) = e1
% 169.23/25.53 | |
% 169.23/25.53 | | ALPHA: (12) implies:
% 169.23/25.53 | | (13) all_58_13 = e1
% 169.23/25.53 | |
% 169.23/25.53 | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (13) are inconsistent by sub-proof
% 169.23/25.53 | | #545.
% 169.23/25.53 | |
% 169.23/25.53 | End of split
% 169.23/25.53 |
% 169.23/25.53 End of proof
% 169.23/25.53
% 169.23/25.53 Sub-proof #226 shows that the following formulas are inconsistent:
% 169.23/25.53 ----------------------------------------------------------------
% 169.23/25.53 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.53 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.53 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.53 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.53 (3) ~ (all_52_13 = e3)
% 169.23/25.53 (4) all_58_15 = e2
% 169.23/25.53 (5) all_58_9 = e2
% 169.23/25.53 (6) all_58_2 = e2
% 169.23/25.53 (7) ~ (e3 = e1)
% 169.23/25.53 (8) ~ (e1 = e0)
% 169.23/25.53 (9) op(e2, e3) = all_52_1
% 169.23/25.53 (10) op(e2, e3) = e2
% 169.23/25.53 (11) ~ (e3 = e0)
% 169.23/25.53 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.53 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.53 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.53 (14) ~ (e2 = e0)
% 169.23/25.53 (15) all_58_3 = e3
% 169.23/25.53 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.53 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.53 (17) ~ (e2 = e1)
% 169.23/25.53 (18) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.23/25.53 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.23/25.53 (19) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.53 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.23/25.53 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.23/25.53 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.23/25.53 (20) op(e2, e0) = all_52_13
% 169.23/25.53 (21) ~ (e3 = e2)
% 169.23/25.53
% 169.23/25.53 Begin of proof
% 169.23/25.53 |
% 169.23/25.53 | BETA: splitting (18) gives:
% 169.23/25.53 |
% 169.23/25.53 | Case 1:
% 169.23/25.53 | |
% 169.23/25.53 | | (22) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 169.23/25.53 | | e3)
% 169.23/25.53 | |
% 169.23/25.53 | | BETA: splitting (22) gives:
% 169.23/25.53 | |
% 169.23/25.53 | | Case 1:
% 169.23/25.53 | | |
% 169.23/25.53 | | | (23) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.53 | | |
% 169.23/25.53 | | | ALPHA: (23) implies:
% 169.23/25.53 | | | (24) all_58_9 = e3
% 169.23/25.53 | | |
% 169.23/25.53 | | | COMBINE_EQS: (5), (24) imply:
% 169.23/25.53 | | | (25) e3 = e2
% 169.23/25.53 | | |
% 169.23/25.53 | | | COMBINE_EQS: (15), (25) imply:
% 169.23/25.53 | | | (26) all_58_3 = e2
% 169.23/25.53 | | |
% 169.23/25.53 | | | REF_CLOSE: (2), (6), (7), (8), (9), (10), (11), (12), (13), (14), (16),
% 169.23/25.53 | | | (17), (21), (26) are inconsistent by sub-proof #779.
% 169.23/25.53 | | |
% 169.23/25.53 | | Case 2:
% 169.23/25.53 | | |
% 169.23/25.53 | | | (27) all_58_10 = e3 & op(e2, e0) = e3
% 169.23/25.53 | | |
% 169.23/25.53 | | | ALPHA: (27) implies:
% 169.23/25.53 | | | (28) op(e2, e0) = e3
% 169.23/25.53 | | |
% 169.23/25.53 | | | REF_CLOSE: (3), (13), (20), (28) are inconsistent by sub-proof #562.
% 169.23/25.53 | | |
% 169.23/25.53 | | End of split
% 169.23/25.53 | |
% 169.23/25.53 | Case 2:
% 169.23/25.53 | |
% 169.23/25.53 | | (29) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.23/25.53 | | e3)
% 169.23/25.53 | |
% 169.23/25.53 | | BETA: splitting (29) gives:
% 169.23/25.53 | |
% 169.23/25.53 | | Case 1:
% 169.23/25.53 | | |
% 169.23/25.53 | | | (30) all_58_11 = e3 & op(e1, e0) = e3
% 169.23/25.53 | | |
% 169.23/25.53 | | | ALPHA: (30) implies:
% 169.23/25.53 | | | (31) all_58_11 = e3
% 169.23/25.53 | | |
% 169.23/25.53 | | | REF_CLOSE: (1), (4), (5), (7), (8), (11), (13), (14), (17), (19), (31) are
% 169.23/25.53 | | | inconsistent by sub-proof #719.
% 169.23/25.53 | | |
% 169.23/25.53 | | Case 2:
% 169.23/25.53 | | |
% 169.23/25.53 | | | (32) all_58_15 = e3 & op(e0, e0) = e3
% 169.23/25.53 | | |
% 169.23/25.53 | | | ALPHA: (32) implies:
% 169.23/25.53 | | | (33) all_58_15 = e3
% 169.23/25.53 | | |
% 169.23/25.53 | | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 169.23/25.53 | | | (15), (16), (17), (21), (33) are inconsistent by sub-proof
% 169.23/25.53 | | | #320.
% 169.23/25.53 | | |
% 169.23/25.53 | | End of split
% 169.23/25.53 | |
% 169.23/25.53 | End of split
% 169.23/25.53 |
% 169.23/25.53 End of proof
% 169.23/25.53
% 169.23/25.53 Sub-proof #227 shows that the following formulas are inconsistent:
% 169.23/25.53 ----------------------------------------------------------------
% 169.23/25.53 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.53 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.53 (2) all_58_1 = e1
% 169.23/25.53 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.53 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.53 (4) all_58_2 = e2
% 169.23/25.53 (5) ~ (e3 = e1)
% 169.23/25.53 (6) op(e1, e3) = all_52_2
% 169.23/25.53 (7) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 169.23/25.53 (8) ~ (e1 = e0)
% 169.23/25.53 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.53 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.53 (10) op(e2, e3) = all_52_1
% 169.23/25.53 (11) op(e2, e3) = e2
% 169.23/25.53 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.53 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.53 (13) ~ (e3 = e0)
% 169.23/25.53 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.53 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.53 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.53 (16) ~ (e2 = e0)
% 169.23/25.53 (17) all_58_12 = e3
% 169.23/25.53 (18) all_58_3 = e3
% 169.23/25.53 (19) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.53 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.53 (20) ~ (e2 = e1)
% 169.23/25.53 (21) ~ (e3 = e2)
% 169.23/25.53
% 169.23/25.53 Begin of proof
% 169.23/25.53 |
% 169.23/25.53 | BETA: splitting (7) gives:
% 169.23/25.53 |
% 169.23/25.53 | Case 1:
% 169.23/25.53 | |
% 169.23/25.53 | | (22) all_58_0 = e2 & op(e3, e3) = e2
% 169.23/25.53 | |
% 169.23/25.53 | | ALPHA: (22) implies:
% 169.23/25.53 | | (23) all_58_0 = e2
% 169.23/25.53 | |
% 169.23/25.53 | | BETA: splitting (12) gives:
% 169.23/25.53 | |
% 169.23/25.53 | | Case 1:
% 169.23/25.53 | | |
% 169.23/25.53 | | | (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 169.23/25.53 | | | e1)
% 169.23/25.53 | | |
% 169.23/25.53 | | | BETA: splitting (24) gives:
% 169.23/25.53 | | |
% 169.23/25.53 | | | Case 1:
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | (25) all_58_0 = e1 & op(e3, e3) = e1
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | REF_CLOSE: (20), (23), (25) are inconsistent by sub-proof #706.
% 169.23/25.53 | | | |
% 169.23/25.53 | | | Case 2:
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | (26) all_58_2 = e1 & op(e2, e3) = e1
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | ALPHA: (26) implies:
% 169.23/25.53 | | | | (27) op(e2, e3) = e1
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | REF_CLOSE: (10), (11), (15), (20), (27) are inconsistent by sub-proof
% 169.23/25.53 | | | | #784.
% 169.23/25.53 | | | |
% 169.23/25.53 | | | End of split
% 169.23/25.53 | | |
% 169.23/25.53 | | Case 2:
% 169.23/25.53 | | |
% 169.23/25.53 | | | (28) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 169.23/25.53 | | | e1)
% 169.23/25.53 | | |
% 169.23/25.53 | | | BETA: splitting (28) gives:
% 169.23/25.53 | | |
% 169.23/25.53 | | | Case 1:
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | (29) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | ALPHA: (29) implies:
% 169.23/25.53 | | | | (30) all_58_6 = e1
% 169.23/25.53 | | | | (31) op(e1, e3) = e1
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | BETA: splitting (3) gives:
% 169.23/25.53 | | | |
% 169.23/25.53 | | | | Case 1:
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | | (32) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 169.23/25.53 | | | | | e3) = e0)
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | | BETA: splitting (32) gives:
% 169.23/25.53 | | | | |
% 169.23/25.53 | | | | | Case 1:
% 169.23/25.53 | | | | | |
% 169.23/25.53 | | | | | | (33) all_58_0 = e0 & op(e3, e3) = e0
% 169.23/25.53 | | | | | |
% 169.23/25.53 | | | | | | REF_CLOSE: (16), (23), (33) are inconsistent by sub-proof #705.
% 169.23/25.53 | | | | | |
% 169.23/25.53 | | | | | Case 2:
% 169.23/25.53 | | | | | |
% 169.23/25.53 | | | | | | (34) all_58_2 = e0 & op(e2, e3) = e0
% 169.23/25.54 | | | | | |
% 169.23/25.54 | | | | | | REF_CLOSE: (10), (11), (15), (16), (34) are inconsistent by
% 169.23/25.54 | | | | | | sub-proof #782.
% 169.23/25.54 | | | | | |
% 169.23/25.54 | | | | | End of split
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | Case 2:
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | (35) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 169.23/25.54 | | | | | e3) = e0)
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | BETA: splitting (35) gives:
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | Case 1:
% 169.23/25.54 | | | | | |
% 169.23/25.54 | | | | | | (36) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.54 | | | | | |
% 169.23/25.54 | | | | | | ALPHA: (36) implies:
% 169.23/25.54 | | | | | | (37) op(e1, e3) = e0
% 169.23/25.54 | | | | | |
% 169.23/25.54 | | | | | | REF_CLOSE: (6), (8), (15), (31), (37) are inconsistent by sub-proof
% 169.23/25.54 | | | | | | #749.
% 169.23/25.54 | | | | | |
% 169.23/25.54 | | | | | Case 2:
% 169.23/25.54 | | | | | |
% 169.23/25.54 | | | | | | (38) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.54 | | | | | |
% 169.23/25.54 | | | | | | ALPHA: (38) implies:
% 169.23/25.54 | | | | | | (39) all_58_12 = e0
% 169.23/25.54 | | | | | |
% 169.23/25.54 | | | | | | REF_CLOSE: (1), (4), (5), (8), (9), (10), (11), (13), (14), (15),
% 169.23/25.54 | | | | | | (16), (18), (19), (20), (21), (23), (30), (39) are
% 169.23/25.54 | | | | | | inconsistent by sub-proof #245.
% 169.23/25.54 | | | | | |
% 169.23/25.54 | | | | | End of split
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | End of split
% 169.23/25.54 | | | |
% 169.23/25.54 | | | Case 2:
% 169.23/25.54 | | | |
% 169.23/25.54 | | | | (40) all_58_12 = e1 & op(e0, e3) = e1
% 169.23/25.54 | | | |
% 169.23/25.54 | | | | ALPHA: (40) implies:
% 169.23/25.54 | | | | (41) all_58_12 = e1
% 169.23/25.54 | | | |
% 169.23/25.54 | | | | REF_CLOSE: (5), (17), (41) are inconsistent by sub-proof #600.
% 169.23/25.54 | | | |
% 169.23/25.54 | | | End of split
% 169.23/25.54 | | |
% 169.23/25.54 | | End of split
% 169.23/25.54 | |
% 169.23/25.54 | Case 2:
% 169.23/25.54 | |
% 169.23/25.54 | | (42) all_58_1 = e2 & op(e3, e2) = e2
% 169.23/25.54 | |
% 169.23/25.54 | | REF_CLOSE: (2), (20), (42) are inconsistent by sub-proof #316.
% 169.23/25.54 | |
% 169.23/25.54 | End of split
% 169.23/25.54 |
% 169.23/25.54 End of proof
% 169.23/25.54
% 169.23/25.54 Sub-proof #228 shows that the following formulas are inconsistent:
% 169.23/25.54 ----------------------------------------------------------------
% 169.23/25.54 (1) all_58_7 = e2
% 169.23/25.54 (2) ~ (e3 = e1)
% 169.23/25.54 (3) op(e1, e3) = all_52_2
% 169.23/25.54 (4) ~ (e1 = e0)
% 169.23/25.54 (5) all_58_11 = e2
% 169.23/25.54 (6) ~ (e3 = e0)
% 169.23/25.54 (7) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.54 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.54 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.54 (9) ~ (e2 = e0)
% 169.23/25.54 (10) all_58_8 = e3
% 169.23/25.54 (11) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.54 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.54 (12) ~ (e2 = e1)
% 169.23/25.54
% 169.23/25.54 Begin of proof
% 169.23/25.54 |
% 169.23/25.54 | BETA: splitting (7) gives:
% 169.23/25.54 |
% 169.23/25.54 | Case 1:
% 169.23/25.54 | |
% 169.23/25.54 | | (13) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 169.23/25.54 | | e0)
% 169.23/25.54 | |
% 169.23/25.54 | | BETA: splitting (13) gives:
% 169.23/25.54 | |
% 169.23/25.54 | | Case 1:
% 169.23/25.54 | | |
% 169.23/25.54 | | | (14) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.54 | | |
% 169.23/25.54 | | | ALPHA: (14) implies:
% 169.23/25.54 | | | (15) op(e1, e3) = e0
% 169.23/25.54 | | |
% 169.23/25.54 | | | BETA: splitting (11) gives:
% 169.23/25.54 | | |
% 169.23/25.54 | | | Case 1:
% 169.23/25.54 | | | |
% 169.23/25.54 | | | | (16) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 169.23/25.54 | | | | = e1)
% 169.23/25.54 | | | |
% 169.23/25.54 | | | | BETA: splitting (16) gives:
% 169.23/25.54 | | | |
% 169.23/25.54 | | | | Case 1:
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | (17) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | ALPHA: (17) implies:
% 169.23/25.54 | | | | | (18) op(e1, e3) = e1
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | REF_CLOSE: (3), (4), (8), (15), (18) are inconsistent by sub-proof
% 169.23/25.54 | | | | | #749.
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | Case 2:
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | (19) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | REF_CLOSE: (1), (12), (19) are inconsistent by sub-proof #503.
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | End of split
% 169.23/25.54 | | | |
% 169.23/25.54 | | | Case 2:
% 169.23/25.54 | | | |
% 169.23/25.54 | | | | (20) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0)
% 169.23/25.54 | | | | = e1)
% 169.23/25.54 | | | |
% 169.23/25.54 | | | | BETA: splitting (20) gives:
% 169.23/25.54 | | | |
% 169.23/25.54 | | | | Case 1:
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | (21) all_58_8 = e1 & op(e1, e1) = e1
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | REF_CLOSE: (2), (10), (21) are inconsistent by sub-proof #478.
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | Case 2:
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | (22) all_58_11 = e1 & op(e1, e0) = e1
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | ALPHA: (22) implies:
% 169.23/25.54 | | | | | (23) all_58_11 = e1
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | | REF_CLOSE: (5), (12), (23) are inconsistent by sub-proof #832.
% 169.23/25.54 | | | | |
% 169.23/25.54 | | | | End of split
% 169.23/25.54 | | | |
% 169.23/25.54 | | | End of split
% 169.23/25.54 | | |
% 169.23/25.54 | | Case 2:
% 169.23/25.54 | | |
% 169.23/25.54 | | | (24) all_58_7 = e0 & op(e1, e2) = e0
% 169.23/25.54 | | |
% 169.23/25.54 | | | REF_CLOSE: (1), (9), (24) are inconsistent by sub-proof #363.
% 169.23/25.54 | | |
% 169.23/25.54 | | End of split
% 169.23/25.54 | |
% 169.23/25.54 | Case 2:
% 169.23/25.54 | |
% 169.23/25.54 | | (25) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 169.23/25.54 | | e0)
% 169.23/25.54 | |
% 169.23/25.54 | | BETA: splitting (25) gives:
% 169.23/25.54 | |
% 169.23/25.54 | | Case 1:
% 169.23/25.54 | | |
% 169.23/25.54 | | | (26) all_58_8 = e0 & op(e1, e1) = e0
% 169.23/25.54 | | |
% 169.23/25.54 | | | ALPHA: (26) implies:
% 169.23/25.54 | | | (27) all_58_8 = e0
% 169.23/25.54 | | |
% 169.23/25.54 | | | REF_CLOSE: (6), (10), (27) are inconsistent by sub-proof #480.
% 169.23/25.54 | | |
% 169.23/25.54 | | Case 2:
% 169.23/25.54 | | |
% 169.23/25.54 | | | (28) all_58_11 = e0 & op(e1, e0) = e0
% 169.23/25.54 | | |
% 169.23/25.54 | | | ALPHA: (28) implies:
% 169.23/25.54 | | | (29) all_58_11 = e0
% 169.23/25.54 | | |
% 169.23/25.54 | | | REF_CLOSE: (5), (9), (29) are inconsistent by sub-proof #879.
% 169.23/25.54 | | |
% 169.23/25.54 | | End of split
% 169.23/25.54 | |
% 169.23/25.54 | End of split
% 169.23/25.54 |
% 169.23/25.54 End of proof
% 169.23/25.54
% 169.23/25.54 Sub-proof #229 shows that the following formulas are inconsistent:
% 169.23/25.54 ----------------------------------------------------------------
% 169.23/25.54 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.54 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.54 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.54 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.54 (3) all_58_9 = e2
% 169.23/25.54 (4) all_58_2 = e2
% 169.23/25.54 (5) ~ (e3 = e1)
% 169.23/25.54 (6) ~ (e1 = e0)
% 169.23/25.54 (7) op(e2, e3) = all_52_1
% 169.23/25.54 (8) op(e2, e3) = e2
% 169.23/25.54 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.54 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.54 (10) ~ (e3 = e0)
% 169.23/25.54 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.54 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.54 (12) all_58_4 = e0
% 169.23/25.54 (13) ~ (all_52_4 = e3)
% 169.23/25.54 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.23/25.54 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.23/25.54 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.54 (16) ~ (e2 = e0)
% 169.23/25.54 (17) all_58_12 = e3
% 169.23/25.54 (18) all_58_3 = e3
% 169.23/25.54 (19) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.54 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.54 (20) ~ (e2 = e1)
% 169.23/25.54 (21) op(e3, e2) = all_52_4
% 169.23/25.54 (22) ~ (e3 = e2)
% 169.23/25.54
% 169.23/25.54 Begin of proof
% 169.23/25.54 |
% 169.23/25.54 | BETA: splitting (14) gives:
% 169.23/25.54 |
% 169.23/25.54 | Case 1:
% 169.23/25.54 | |
% 169.23/25.54 | | (23) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 169.23/25.54 | | e3)
% 169.23/25.54 | |
% 169.23/25.54 | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (13), (15), (16), (17), (20),
% 169.23/25.54 | | (21), (23) are inconsistent by sub-proof #413.
% 169.23/25.54 | |
% 169.23/25.54 | Case 2:
% 169.23/25.54 | |
% 169.23/25.54 | | (24) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 169.23/25.54 | | e3)
% 169.23/25.54 | |
% 169.23/25.54 | | BETA: splitting (24) gives:
% 169.23/25.54 | |
% 169.23/25.54 | | Case 1:
% 169.23/25.54 | | |
% 169.23/25.54 | | | (25) all_58_4 = e3 & op(e3, e1) = e3
% 169.23/25.54 | | |
% 169.23/25.54 | | | ALPHA: (25) implies:
% 169.23/25.54 | | | (26) all_58_4 = e3
% 169.23/25.54 | | |
% 169.23/25.54 | | | REF_CLOSE: (10), (12), (26) are inconsistent by sub-proof #894.
% 169.23/25.54 | | |
% 169.23/25.54 | | Case 2:
% 169.23/25.54 | | |
% 169.23/25.54 | | | (27) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.54 | | |
% 169.23/25.54 | | | ALPHA: (27) implies:
% 169.23/25.54 | | | (28) all_58_9 = e3
% 169.23/25.54 | | |
% 169.23/25.54 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (15), (16),
% 169.23/25.54 | | | (18), (19), (20), (22), (28) are inconsistent by sub-proof
% 169.23/25.54 | | | #451.
% 169.23/25.54 | | |
% 169.23/25.54 | | End of split
% 169.23/25.54 | |
% 169.23/25.54 | End of split
% 169.23/25.54 |
% 169.23/25.54 End of proof
% 169.23/25.54
% 169.23/25.54 Sub-proof #230 shows that the following formulas are inconsistent:
% 169.23/25.54 ----------------------------------------------------------------
% 169.23/25.54 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.23/25.54 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.23/25.54 (2) op(e2, e1) = all_52_9
% 169.23/25.54 (3) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.23/25.54 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.23/25.54 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.54 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.54 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.23/25.54 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.54 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.54 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.54 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.54 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 169.23/25.54 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.54 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.54 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.54 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.54 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.23/25.54 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.54 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.54 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.54 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.54 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.23/25.54 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.54 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.54 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.54 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.54 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 169.23/25.54 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 169.23/25.54 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.23/25.54 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.54 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.54 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.23/25.54 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.54 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.54 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.54 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.54 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 169.23/25.54 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 169.23/25.54 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.23/25.54 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.54 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.54 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.23/25.54 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.54 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.54 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.54 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.54 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 169.23/25.54 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.23/25.54 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.23/25.54 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 169.23/25.54 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.23/25.54 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 169.23/25.54 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.23/25.54 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.54 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.54 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.54 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.54 (6) ~ (all_52_9 = e3)
% 169.23/25.54 (7) ~ (all_52_13 = e3)
% 169.23/25.54 (8) all_58_7 = e2
% 169.23/25.54 (9) all_56_0 = e2
% 169.23/25.54 (10) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.54 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.54 (11) all_54_8 = all_52_2
% 169.23/25.54 (12) all_54_12 = all_52_3
% 169.23/25.54 (13) all_58_2 = e2
% 169.23/25.54 (14) all_54_6 = all_52_9
% 169.23/25.54 (15) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.54 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.54 (16) all_56_10 = all_10_2
% 169.23/25.54 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.23/25.54 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.54 (18) all_54_10 = all_6_2
% 169.23/25.54 (19) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 169.23/25.54 (20) op(e3, e3) = all_10_2
% 169.23/25.54 (21) ~ (all_52_3 = e2)
% 169.23/25.54 (22) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.54 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.54 (23) ~ (e3 = e1)
% 169.23/25.54 (24) all_56_14 = all_6_2
% 169.23/25.54 (25) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.54 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.23/25.54 e1)
% 169.23/25.54 (26) op(e1, e3) = all_52_2
% 169.23/25.54 (27) ~ (all_10_2 = e0)
% 169.23/25.54 (28) op(e3, e1) = all_52_8
% 169.23/25.54 (29) ~ (all_52_2 = all_52_6)
% 169.23/25.54 (30) ~ (e1 = e0)
% 169.23/25.54 (31) all_56_7 = e0
% 169.23/25.54 (32) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.23/25.54 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.23/25.54 e3)
% 169.23/25.54 (33) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.54 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.54 (34) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 169.23/25.54 (35) op(e1, e2) = all_52_6
% 169.23/25.54 (36) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 169.23/25.54 (37) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.54 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.54 (38) ~ (all_52_8 = all_10_2)
% 169.23/25.54 (39) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.23/25.54 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.23/25.54 (40) op(e2, e3) = all_52_1
% 169.23/25.54 (41) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.54 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.54 (42) ~ (all_52_3 = all_52_7)
% 169.23/25.54 (43) ~ (all_52_7 = e3)
% 169.23/25.54 (44) op(e0, e2) = e0
% 169.23/25.54 (45) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 169.23/25.54 (46) ~ (all_52_2 = all_6_2)
% 169.23/25.54 (47) op(e1, e1) = all_6_2
% 169.23/25.54 (48) ~ (all_52_4 = all_10_2)
% 169.23/25.54 (49) op(e2, e3) = e2
% 169.23/25.54 (50) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.54 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.54 (51) ~ (e3 = e0)
% 169.23/25.54 (52) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.54 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.54 (53) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.54 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.54 (54) ~ (all_52_13 = e2)
% 169.23/25.54 (55) ~ (all_52_9 = all_6_2)
% 169.23/25.54 (56) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.54 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.54 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.54 (57) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 169.23/25.54 (58) ~ (all_52_4 = e3)
% 169.23/25.54 (59) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.23/25.54 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.23/25.54 (60) ~ (all_52_3 = all_10_2)
% 169.23/25.54 (61) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.54 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.23/25.54 (62) ~ (all_52_8 = all_52_9)
% 169.23/25.54 (63) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.54 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.54 (64) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.23/25.54 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.23/25.54 (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.54 (66) ~ (all_52_8 = all_6_2)
% 169.23/25.54 (67) ~ (e2 = e0)
% 169.23/25.54 (68) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.54 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.54 (69) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.23/25.54 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.23/25.55 (70) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 169.23/25.55 (71) all_58_3 = e3
% 169.23/25.55 (72) ~ (all_52_7 = e2)
% 169.23/25.55 (73) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.55 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.55 (74) ~ (e2 = e1)
% 169.23/25.55 (75) ~ (all_56_14 = e3) | (all_56_2 = e1 & op(e1, e3) = e1)
% 169.23/25.55 (76) op(e3, e2) = all_52_4
% 169.23/25.55 (77) ~ (all_52_2 = all_10_2)
% 169.23/25.55 (78) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.23/25.55 (79) all_54_0 = all_10_2
% 169.23/25.55 (80) ~ (all_52_6 = e3)
% 169.23/25.55 (81) op(e0, e2) = all_52_7
% 169.23/25.55 (82) all_54_7 = all_52_13
% 169.23/25.55 (83) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.23/25.55 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.23/25.55 (84) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.23/25.55 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.23/25.55 (85) all_58_4 = e2
% 169.23/25.55 (86) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.55 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.55 (87) op(e1, e2) = e2
% 169.23/25.55 (88) all_56_12 = e3
% 169.23/25.55 (89) all_56_15 = e2
% 169.23/25.55 (90) ~ (all_52_9 = all_52_13)
% 169.23/25.55 (91) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.55 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.23/25.55 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.23/25.55 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.23/25.55 (92) ~ (all_52_2 = all_52_3)
% 169.23/25.55 (93) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.23/25.55 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.23/25.55 (94) op(e3, e1) = e2
% 169.23/25.55 (95) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.23/25.55 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.23/25.55 e2) = all_14_1 & $i(all_14_1))
% 169.23/25.55 (96) op(e2, e0) = all_52_13
% 169.23/25.55 (97) ~ (e3 = e2)
% 169.23/25.55
% 169.23/25.55 Begin of proof
% 169.23/25.55 |
% 169.23/25.55 | BETA: splitting (1) gives:
% 169.23/25.55 |
% 169.23/25.55 | Case 1:
% 169.23/25.55 | |
% 169.23/25.55 | | (98) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 169.23/25.55 | | e2)
% 169.23/25.55 | |
% 169.23/25.55 | | BETA: splitting (98) gives:
% 169.23/25.55 | |
% 169.23/25.55 | | Case 1:
% 169.23/25.55 | | |
% 169.23/25.55 | | | (99) all_58_12 = e2 & op(e0, e3) = e2
% 169.23/25.55 | | |
% 169.23/25.55 | | | ALPHA: (99) implies:
% 169.23/25.55 | | | (100) all_58_12 = e2
% 169.23/25.55 | | |
% 169.23/25.55 | | | REF_CLOSE: (5), (10), (13), (23), (30), (33), (40), (49), (50), (51),
% 169.23/25.55 | | | (52), (65), (67), (71), (73), (74), (97), (100) are
% 169.23/25.55 | | | inconsistent by sub-proof #433.
% 169.23/25.55 | | |
% 169.23/25.55 | | Case 2:
% 169.23/25.55 | | |
% 169.23/25.55 | | | (101) all_58_13 = e2 & op(e0, e2) = e2
% 169.23/25.55 | | |
% 169.23/25.55 | | | ALPHA: (101) implies:
% 169.23/25.55 | | | (102) all_58_13 = e2
% 169.23/25.55 | | |
% 169.23/25.55 | | | BETA: splitting (61) gives:
% 169.23/25.55 | | |
% 169.23/25.55 | | | Case 1:
% 169.23/25.55 | | | |
% 169.23/25.55 | | | | (103) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2)
% 169.23/25.55 | | | | = e0)
% 169.23/25.55 | | | |
% 169.23/25.55 | | | | BETA: splitting (103) gives:
% 169.23/25.55 | | | |
% 169.23/25.55 | | | | Case 1:
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | (104) all_58_1 = e0 & op(e3, e2) = e0
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | ALPHA: (104) implies:
% 169.23/25.55 | | | | | (105) op(e3, e2) = e0
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | BETA: splitting (15) gives:
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | Case 1:
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | (106) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2,
% 169.23/25.55 | | | | | | e2) = e1)
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | BETA: splitting (106) gives:
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | Case 1:
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | (107) all_58_1 = e1 & op(e3, e2) = e1
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | ALPHA: (107) implies:
% 169.23/25.55 | | | | | | | (108) all_58_1 = e1
% 169.23/25.55 | | | | | | | (109) op(e3, e2) = e1
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | REF_CLOSE: (30), (35), (51), (56), (61), (65), (67), (71), (76),
% 169.23/25.55 | | | | | | | (95), (102), (108), (109) are inconsistent by sub-proof
% 169.23/25.55 | | | | | | | #429.
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | Case 2:
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | (110) all_58_3 = e1 & op(e2, e2) = e1
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | ALPHA: (110) implies:
% 169.23/25.55 | | | | | | | (111) all_58_3 = e1
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | REF_CLOSE: (23), (71), (111) are inconsistent by sub-proof #328.
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | End of split
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | Case 2:
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | (112) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 169.23/25.55 | | | | | | op(e0, e2) = e1)
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | BETA: splitting (112) gives:
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | Case 1:
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | (113) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | ALPHA: (113) implies:
% 169.23/25.55 | | | | | | | (114) all_58_7 = e1
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | REF_CLOSE: (8), (74), (114) are inconsistent by sub-proof #494.
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | Case 2:
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | (115) all_58_13 = e1 & op(e0, e2) = e1
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | ALPHA: (115) implies:
% 169.23/25.55 | | | | | | | (116) op(e0, e2) = e1
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | REF_CLOSE: (56), (65), (105), (116) are inconsistent by sub-proof
% 169.23/25.55 | | | | | | | #443.
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | End of split
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | End of split
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | Case 2:
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | (117) all_58_3 = e0 & op(e2, e2) = e0
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | REF_CLOSE: (51), (71), (117) are inconsistent by sub-proof #869.
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | End of split
% 169.23/25.55 | | | |
% 169.23/25.55 | | | Case 2:
% 169.23/25.55 | | | |
% 169.23/25.55 | | | | (118) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0,
% 169.23/25.55 | | | | e2) = e0)
% 169.23/25.55 | | | |
% 169.23/25.55 | | | | REF_CLOSE: (8), (67), (102), (118) are inconsistent by sub-proof #264.
% 169.23/25.55 | | | |
% 169.23/25.55 | | | End of split
% 169.23/25.55 | | |
% 169.23/25.55 | | End of split
% 169.23/25.55 | |
% 169.23/25.55 | Case 2:
% 169.23/25.55 | |
% 169.23/25.55 | | (119) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.23/25.55 | | e2)
% 169.23/25.55 | |
% 169.23/25.55 | | BETA: splitting (119) gives:
% 169.23/25.55 | |
% 169.23/25.55 | | Case 1:
% 169.23/25.55 | | |
% 169.23/25.55 | | | (120) all_58_14 = e2 & op(e0, e1) = e2
% 169.23/25.55 | | |
% 169.23/25.55 | | | ALPHA: (120) implies:
% 169.23/25.55 | | | (121) all_58_14 = e2
% 169.23/25.55 | | | (122) op(e0, e1) = e2
% 169.23/25.55 | | |
% 169.23/25.55 | | | REF_CLOSE: (2), (5), (6), (13), (23), (30), (37), (40), (41), (49), (51),
% 169.23/25.55 | | | (52), (65), (67), (71), (73), (74), (85), (86), (97), (121),
% 169.23/25.55 | | | (122) are inconsistent by sub-proof #251.
% 169.23/25.55 | | |
% 169.23/25.55 | | Case 2:
% 169.23/25.55 | | |
% 169.23/25.55 | | | (123) all_58_15 = e2 & op(e0, e0) = e2
% 169.23/25.55 | | |
% 169.23/25.55 | | | ALPHA: (123) implies:
% 169.23/25.55 | | | (124) all_58_15 = e2
% 169.23/25.55 | | |
% 169.23/25.55 | | | GROUND_INST: instantiating (65) with all_52_7, e0, e2, e0, simplifying
% 169.23/25.55 | | | with (44), (81) gives:
% 169.23/25.55 | | | (125) all_52_7 = e0
% 169.23/25.55 | | |
% 169.23/25.55 | | | GROUND_INST: instantiating (65) with all_52_6, e2, e2, e1, simplifying
% 169.23/25.55 | | | with (35), (87) gives:
% 169.23/25.55 | | | (126) all_52_6 = e2
% 169.23/25.55 | | |
% 169.23/25.55 | | | GROUND_INST: instantiating (65) with all_52_8, e2, e1, e3, simplifying
% 169.23/25.55 | | | with (28), (94) gives:
% 169.23/25.55 | | | (127) all_52_8 = e2
% 169.23/25.55 | | |
% 169.23/25.55 | | | REDUCE: (29), (126) imply:
% 169.23/25.55 | | | (128) ~ (all_52_2 = e2)
% 169.23/25.55 | | |
% 169.23/25.55 | | | REDUCE: (42), (125) imply:
% 169.23/25.55 | | | (129) ~ (all_52_3 = e0)
% 169.23/25.55 | | |
% 169.23/25.55 | | | REDUCE: (80), (126) imply:
% 169.23/25.55 | | | (130) ~ (e3 = e2)
% 169.23/25.55 | | |
% 169.23/25.55 | | | REDUCE: (43), (125) imply:
% 169.23/25.55 | | | (131) ~ (e3 = e0)
% 169.23/25.55 | | |
% 169.23/25.55 | | | REDUCE: (72), (125) imply:
% 169.23/25.55 | | | (132) ~ (e2 = e0)
% 169.23/25.55 | | |
% 169.23/25.55 | | | REDUCE: (62), (127) imply:
% 169.23/25.55 | | | (133) ~ (all_52_9 = e2)
% 169.23/25.55 | | |
% 169.23/25.55 | | | SIMP: (133) implies:
% 169.23/25.55 | | | (134) ~ (all_52_9 = e2)
% 169.23/25.55 | | |
% 169.23/25.55 | | | REDUCE: (38), (127) imply:
% 169.23/25.55 | | | (135) ~ (all_10_2 = e2)
% 169.23/25.55 | | |
% 169.23/25.55 | | | SIMP: (135) implies:
% 169.23/25.55 | | | (136) ~ (all_10_2 = e2)
% 169.23/25.55 | | |
% 169.23/25.55 | | | REDUCE: (66), (127) imply:
% 169.23/25.55 | | | (137) ~ (all_6_2 = e2)
% 169.23/25.55 | | |
% 169.23/25.55 | | | SIMP: (137) implies:
% 169.23/25.55 | | | (138) ~ (all_6_2 = e2)
% 169.23/25.55 | | |
% 169.23/25.55 | | | BETA: splitting (70) gives:
% 169.23/25.55 | | |
% 169.23/25.55 | | | Case 1:
% 169.23/25.55 | | | |
% 169.23/25.55 | | | | (139) ~ (all_56_10 = e1)
% 169.23/25.55 | | | |
% 169.23/25.55 | | | | REDUCE: (16), (139) imply:
% 169.23/25.55 | | | | (140) ~ (all_10_2 = e1)
% 169.23/25.55 | | | |
% 169.23/25.55 | | | | BETA: splitting (78) gives:
% 169.23/25.55 | | | |
% 169.23/25.55 | | | | Case 1:
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | (141) all_54_0 = e3
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | COMBINE_EQS: (79), (141) imply:
% 169.23/25.55 | | | | | (142) all_10_2 = e3
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | SIMP: (142) implies:
% 169.23/25.55 | | | | | (143) all_10_2 = e3
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | REDUCE: (77), (143) imply:
% 169.23/25.55 | | | | | (144) ~ (all_52_2 = e3)
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | REDUCE: (60), (143) imply:
% 169.23/25.55 | | | | | (145) ~ (all_52_3 = e3)
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | REDUCE: (20), (143) imply:
% 169.23/25.55 | | | | | (146) op(e3, e3) = e3
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | BETA: splitting (57) gives:
% 169.23/25.55 | | | | |
% 169.23/25.55 | | | | | Case 1:
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | (147) all_54_12 = e3
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | REF_CLOSE: (12), (145), (147) are inconsistent by sub-proof #738.
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | Case 2:
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | (148) ~ (all_54_12 = e3)
% 169.23/25.55 | | | | | | (149) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | BETA: splitting (149) gives:
% 169.23/25.55 | | | | | |
% 169.23/25.55 | | | | | | Case 1:
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | (150) all_54_12 = e2
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | REF_CLOSE: (12), (21), (150) are inconsistent by sub-proof #676.
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | Case 2:
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | (151) ~ (all_54_12 = e2)
% 169.23/25.55 | | | | | | | (152) all_54_12 = e1 | all_54_12 = e0
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | BETA: splitting (152) gives:
% 169.23/25.55 | | | | | | |
% 169.23/25.55 | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | |
% 169.23/25.55 | | | | | | | | (153) all_54_12 = e1
% 169.23/25.55 | | | | | | | |
% 169.23/25.55 | | | | | | | | COMBINE_EQS: (12), (153) imply:
% 169.23/25.55 | | | | | | | | (154) all_52_3 = e1
% 169.23/25.55 | | | | | | | |
% 169.23/25.55 | | | | | | | | SIMP: (154) implies:
% 169.23/25.55 | | | | | | | | (155) all_52_3 = e1
% 169.23/25.55 | | | | | | | |
% 169.23/25.55 | | | | | | | | REDUCE: (92), (155) imply:
% 169.23/25.55 | | | | | | | | (156) ~ (all_52_2 = e1)
% 169.23/25.55 | | | | | | | |
% 169.23/25.55 | | | | | | | | REDUCE: (145), (155) imply:
% 169.23/25.55 | | | | | | | | (157) ~ (e3 = e1)
% 169.23/25.55 | | | | | | | |
% 169.23/25.55 | | | | | | | | REDUCE: (21), (155) imply:
% 169.23/25.55 | | | | | | | | (158) ~ (e2 = e1)
% 169.23/25.55 | | | | | | | |
% 169.23/25.55 | | | | | | | | BETA: splitting (91) gives:
% 169.23/25.55 | | | | | | | |
% 169.23/25.55 | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | |
% 169.23/25.55 | | | | | | | | | (159) all_58_15 = e0 & op(e0, e0) = e0
% 169.23/25.55 | | | | | | | | |
% 169.23/25.55 | | | | | | | | | REF_CLOSE: (67), (124), (159) are inconsistent by sub-proof
% 169.23/25.55 | | | | | | | | | #874.
% 169.23/25.55 | | | | | | | | |
% 169.23/25.55 | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | |
% 169.23/25.55 | | | | | | | | | (160) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 169.23/25.55 | | | | | | | | | & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.23/25.55 | | | | | | | | | = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 169.23/25.55 | | | | | | | | | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 169.23/25.55 | | | | | | | | | e0 & op(e0, e1) = e0))
% 169.23/25.55 | | | | | | | | |
% 169.23/25.55 | | | | | | | | | ALPHA: (160) implies:
% 169.23/25.55 | | | | | | | | | (161) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0
% 169.23/25.55 | | | | | | | | | & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 169.23/25.55 | | | | | | | | | e0)
% 169.23/25.55 | | | | | | | | |
% 169.23/25.55 | | | | | | | | | BETA: splitting (161) gives:
% 169.23/25.55 | | | | | | | | |
% 169.23/25.55 | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | (162) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.55 | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | ALPHA: (162) implies:
% 169.23/25.55 | | | | | | | | | | (163) all_58_12 = e0
% 169.23/25.55 | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | BETA: splitting (75) gives:
% 169.23/25.55 | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | (164) ~ (all_56_14 = e3)
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | REDUCE: (24), (164) imply:
% 169.23/25.55 | | | | | | | | | | | (165) ~ (all_6_2 = e3)
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (13), (15), (17),
% 169.23/25.55 | | | | | | | | | | | (22), (23), (25), (26), (30), (33), (37), (40),
% 169.23/25.55 | | | | | | | | | | | (41), (47), (49), (50), (51), (52), (53), (56),
% 169.23/25.55 | | | | | | | | | | | (58), (63), (64), (65), (67), (68), (69), (71),
% 169.23/25.55 | | | | | | | | | | | (73), (74), (76), (85), (86), (93), (97), (124),
% 169.23/25.55 | | | | | | | | | | | (138), (146), (163), (165) are inconsistent by
% 169.23/25.55 | | | | | | | | | | | sub-proof #243.
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | (166) all_56_14 = e3
% 169.23/25.55 | | | | | | | | | | | (167) all_56_2 = e1 & op(e1, e3) = e1
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | ALPHA: (167) implies:
% 169.23/25.55 | | | | | | | | | | | (168) op(e1, e3) = e1
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | COMBINE_EQS: (24), (166) imply:
% 169.23/25.55 | | | | | | | | | | | (169) all_6_2 = e3
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | SIMP: (169) implies:
% 169.23/25.55 | | | | | | | | | | | (170) all_6_2 = e3
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | REDUCE: (47), (170) imply:
% 169.23/25.55 | | | | | | | | | | | (171) op(e1, e1) = e3
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | BETA: splitting (64) gives:
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | (172) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 169.23/25.55 | | | | | | | | | | | | & op(e3, e2) = e3)
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (10), (13), (17), (20), (22), (23),
% 169.23/25.55 | | | | | | | | | | | | (25), (26), (27), (30), (32), (33), (37), (40),
% 169.23/25.55 | | | | | | | | | | | | (41), (43), (49), (50), (51), (52), (53), (56),
% 169.23/25.55 | | | | | | | | | | | | (58), (63), (65), (67), (68), (71), (73), (74),
% 169.23/25.55 | | | | | | | | | | | | (76), (78), (79), (81), (83), (85), (86), (96),
% 169.23/25.55 | | | | | | | | | | | | (97), (124), (136), (140), (168), (171), (172) are
% 169.23/25.55 | | | | | | | | | | | | inconsistent by sub-proof #242.
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | (173) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 169.23/25.55 | | | | | | | | | | | | & op(e3, e0) = e3)
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | BETA: splitting (173) gives:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | (174) all_58_4 = e3 & op(e3, e1) = e3
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | ALPHA: (174) implies:
% 169.23/25.55 | | | | | | | | | | | | | (175) all_58_4 = e3
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (10), (13), (15), (17), (20), (22),
% 169.23/25.55 | | | | | | | | | | | | | (23), (25), (26), (27), (30), (32), (33), (37),
% 169.23/25.55 | | | | | | | | | | | | | (39), (40), (41), (43), (49), (50), (51), (52),
% 169.23/25.55 | | | | | | | | | | | | | (53), (59), (61), (63), (65), (67), (68), (69),
% 169.23/25.55 | | | | | | | | | | | | | (71), (73), (74), (78), (79), (81), (83), (84),
% 169.23/25.55 | | | | | | | | | | | | | (86), (91), (93), (96), (97), (136), (140), (168),
% 169.23/25.55 | | | | | | | | | | | | | (171), (175) are inconsistent by sub-proof #302.
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | (176) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | REF_CLOSE: (8), (15), (22), (23), (30), (51), (56), (65),
% 169.23/25.55 | | | | | | | | | | | | | (67), (71), (74), (85), (146), (176) are
% 169.23/25.55 | | | | | | | | | | | | | inconsistent by sub-proof #247.
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | End of split
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | End of split
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | End of split
% 169.23/25.55 | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | (177) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 169.23/25.55 | | | | | | | | | | e0 & op(e0, e1) = e0)
% 169.23/25.55 | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | BETA: splitting (177) gives:
% 169.23/25.55 | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | (178) all_58_13 = e0 & op(e0, e2) = e0
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | ALPHA: (178) implies:
% 169.23/25.55 | | | | | | | | | | | (179) all_58_13 = e0
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | BETA: splitting (75) gives:
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | (180) ~ (all_56_14 = e3)
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | REDUCE: (24), (180) imply:
% 169.23/25.55 | | | | | | | | | | | | (181) ~ (all_6_2 = e3)
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | BETA: splitting (37) gives:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | (182) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 169.23/25.55 | | | | | | | | | | | | | & op(e2, e1) = e3)
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (13), (23), (30), (40), (49), (51),
% 169.23/25.55 | | | | | | | | | | | | | (52), (65), (67), (71), (73), (74), (85), (97),
% 169.23/25.55 | | | | | | | | | | | | | (182) are inconsistent by sub-proof #347.
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | (183) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 169.23/25.55 | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | BETA: splitting (183) gives:
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | | (184) all_58_8 = e3 & op(e1, e1) = e3
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | | REF_CLOSE: (47), (65), (181), (184) are inconsistent by
% 169.23/25.55 | | | | | | | | | | | | | | sub-proof #961.
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | | (185) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | | ALPHA: (185) implies:
% 169.23/25.55 | | | | | | | | | | | | | | (186) all_58_14 = e3
% 169.23/25.55 | | | | | | | | | | | | | | (187) op(e0, e1) = e3
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 169.23/25.55 | | | | | | | | | | | | | | (11), (13), (14), (15), (17), (18), (19), (22),
% 169.23/25.55 | | | | | | | | | | | | | | (23), (24), (25), (26), (30), (31), (33), (34),
% 169.23/25.55 | | | | | | | | | | | | | | (36), (37), (40), (41), (45), (46), (47), (49),
% 169.23/25.55 | | | | | | | | | | | | | | (50), (51), (52), (53), (54), (55), (56), (58),
% 169.23/25.55 | | | | | | | | | | | | | | (63), (64), (65), (67), (68), (69), (71), (73),
% 169.23/25.55 | | | | | | | | | | | | | | (74), (76), (82), (85), (86), (88), (89), (90),
% 169.23/25.55 | | | | | | | | | | | | | | (93), (97), (124), (128), (134), (138), (144),
% 169.23/25.55 | | | | | | | | | | | | | | (146), (156), (179), (181), (186), (187) are
% 169.23/25.55 | | | | | | | | | | | | | | inconsistent by sub-proof #235.
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | End of split
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | End of split
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | (188) all_56_14 = e3
% 169.23/25.55 | | | | | | | | | | | | (189) all_56_2 = e1 & op(e1, e3) = e1
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | ALPHA: (189) implies:
% 169.23/25.55 | | | | | | | | | | | | (190) op(e1, e3) = e1
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | COMBINE_EQS: (24), (188) imply:
% 169.23/25.55 | | | | | | | | | | | | (191) all_6_2 = e3
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | SIMP: (191) implies:
% 169.23/25.55 | | | | | | | | | | | | (192) all_6_2 = e3
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | REDUCE: (47), (192) imply:
% 169.23/25.55 | | | | | | | | | | | | (193) op(e1, e1) = e3
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | BETA: splitting (64) gives:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | (194) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 169.23/25.55 | | | | | | | | | | | | | & op(e3, e2) = e3)
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (10), (13), (17), (20), (22), (23),
% 169.23/25.55 | | | | | | | | | | | | | (25), (26), (27), (30), (32), (33), (37), (40),
% 169.23/25.55 | | | | | | | | | | | | | (41), (43), (49), (50), (51), (52), (53), (56),
% 169.23/25.55 | | | | | | | | | | | | | (58), (63), (65), (67), (68), (71), (73), (74),
% 169.23/25.55 | | | | | | | | | | | | | (76), (78), (79), (81), (83), (85), (86), (96),
% 169.23/25.55 | | | | | | | | | | | | | (97), (124), (136), (140), (190), (193), (194) are
% 169.23/25.55 | | | | | | | | | | | | | inconsistent by sub-proof #242.
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | (195) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 169.23/25.55 | | | | | | | | | | | | | & op(e3, e0) = e3)
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | BETA: splitting (195) gives:
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | | (196) all_58_4 = e3 & op(e3, e1) = e3
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | | ALPHA: (196) implies:
% 169.23/25.55 | | | | | | | | | | | | | | (197) all_58_4 = e3
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (10), (13), (15), (17), (20), (22),
% 169.23/25.55 | | | | | | | | | | | | | | (23), (25), (26), (27), (30), (32), (33), (37),
% 169.23/25.55 | | | | | | | | | | | | | | (39), (40), (41), (43), (49), (50), (51), (52),
% 169.23/25.55 | | | | | | | | | | | | | | (53), (59), (61), (63), (65), (67), (68), (69),
% 169.23/25.55 | | | | | | | | | | | | | | (71), (73), (74), (78), (79), (81), (83), (84),
% 169.23/25.55 | | | | | | | | | | | | | | (86), (91), (93), (96), (97), (136), (140), (190),
% 169.23/25.55 | | | | | | | | | | | | | | (193), (197) are inconsistent by sub-proof #302.
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | | (198) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | | REF_CLOSE: (8), (15), (22), (23), (30), (51), (65), (67),
% 169.23/25.55 | | | | | | | | | | | | | | (71), (74), (85), (146), (179), (198) are
% 169.23/25.55 | | | | | | | | | | | | | | inconsistent by sub-proof #241.
% 169.23/25.55 | | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | End of split
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | End of split
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | End of split
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | (199) all_58_14 = e0 & op(e0, e1) = e0
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | ALPHA: (199) implies:
% 169.23/25.55 | | | | | | | | | | | (200) all_58_14 = e0
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | BETA: splitting (75) gives:
% 169.23/25.55 | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | (201) ~ (all_56_14 = e3)
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | REDUCE: (24), (201) imply:
% 169.23/25.55 | | | | | | | | | | | | (202) ~ (all_6_2 = e3)
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | BETA: splitting (37) gives:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | Case 1:
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | (203) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 169.23/25.55 | | | | | | | | | | | | | & op(e2, e1) = e3)
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (13), (23), (30), (40), (49), (51),
% 169.23/25.55 | | | | | | | | | | | | | (52), (65), (67), (71), (73), (74), (85), (97),
% 169.23/25.55 | | | | | | | | | | | | | (203) are inconsistent by sub-proof #347.
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | (204) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 169.23/25.55 | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | | REF_CLOSE: (47), (51), (65), (200), (202), (204) are
% 169.23/25.55 | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 169.23/25.55 | | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | End of split
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | Case 2:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | (205) all_56_14 = e3
% 169.23/25.55 | | | | | | | | | | | | (206) all_56_2 = e1 & op(e1, e3) = e1
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | ALPHA: (206) implies:
% 169.23/25.55 | | | | | | | | | | | | (207) op(e1, e3) = e1
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | COMBINE_EQS: (24), (205) imply:
% 169.23/25.55 | | | | | | | | | | | | (208) all_6_2 = e3
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | SIMP: (208) implies:
% 169.23/25.55 | | | | | | | | | | | | (209) all_6_2 = e3
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | BETA: splitting (10) gives:
% 169.23/25.55 | | | | | | | | | | | |
% 169.23/25.55 | | | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | (210) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 169.23/25.56 | | | | | | | | | | | | | & op(e2, e3) = e0)
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | REF_CLOSE: (40), (49), (51), (65), (67), (146), (210) are
% 169.23/25.56 | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | (211) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 169.23/25.56 | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | BETA: splitting (211) gives:
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | (212) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | ALPHA: (212) implies:
% 169.23/25.56 | | | | | | | | | | | | | | (213) op(e1, e3) = e0
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | REF_CLOSE: (26), (30), (65), (207), (213) are inconsistent by
% 169.23/25.56 | | | | | | | | | | | | | | sub-proof #749.
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | (214) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | ALPHA: (214) implies:
% 169.23/25.56 | | | | | | | | | | | | | | (215) all_58_12 = e0
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (23), (30), (32), (40), (43), (49),
% 169.23/25.56 | | | | | | | | | | | | | | (51), (52), (65), (67), (71), (73), (74), (81),
% 169.23/25.56 | | | | | | | | | | | | | | (97), (124), (200), (215) are inconsistent by
% 169.23/25.56 | | | | | | | | | | | | | | sub-proof #298.
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | End of split
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | (216) all_54_12 = e0
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | REF_CLOSE: (12), (129), (216) are inconsistent by sub-proof
% 169.23/25.56 | | | | | | | | #653.
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | End of split
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | End of split
% 169.23/25.56 | | | | | |
% 169.23/25.56 | | | | | End of split
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | Case 2:
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | (217) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | REF_CLOSE: (27), (79), (136), (140), (217) are inconsistent by
% 169.23/25.56 | | | | | sub-proof #958.
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | End of split
% 169.23/25.56 | | | |
% 169.23/25.56 | | | Case 2:
% 169.23/25.56 | | | |
% 169.23/25.56 | | | | (218) all_56_10 = e1
% 169.23/25.56 | | | |
% 169.23/25.56 | | | | COMBINE_EQS: (16), (218) imply:
% 169.23/25.56 | | | | (219) all_10_2 = e1
% 169.23/25.56 | | | |
% 169.23/25.56 | | | | REDUCE: (77), (219) imply:
% 169.23/25.56 | | | | (220) ~ (all_52_2 = e1)
% 169.23/25.56 | | | |
% 169.23/25.56 | | | | REDUCE: (60), (219) imply:
% 169.23/25.56 | | | | (221) ~ (all_52_3 = e1)
% 169.23/25.56 | | | |
% 169.23/25.56 | | | | REDUCE: (136), (219) imply:
% 169.23/25.56 | | | | (222) ~ (e2 = e1)
% 169.23/25.56 | | | |
% 169.23/25.56 | | | | REDUCE: (20), (219) imply:
% 169.23/25.56 | | | | (223) op(e3, e3) = e1
% 169.23/25.56 | | | |
% 169.23/25.56 | | | | BETA: splitting (75) gives:
% 169.23/25.56 | | | |
% 169.23/25.56 | | | | Case 1:
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | (224) ~ (all_56_14 = e3)
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | REDUCE: (24), (224) imply:
% 169.23/25.56 | | | | | (225) ~ (all_6_2 = e3)
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | BETA: splitting (22) gives:
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | Case 1:
% 169.23/25.56 | | | | | |
% 169.23/25.56 | | | | | | (226) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 169.23/25.56 | | | | | | e2) = e0)
% 169.23/25.56 | | | | | |
% 169.23/25.56 | | | | | | BETA: splitting (226) gives:
% 169.23/25.56 | | | | | |
% 169.23/25.56 | | | | | | Case 1:
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | (227) all_58_0 = e0 & op(e3, e3) = e0
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | ALPHA: (227) implies:
% 169.23/25.56 | | | | | | | (228) op(e3, e3) = e0
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | REF_CLOSE: (30), (65), (223), (228) are inconsistent by sub-proof
% 169.23/25.56 | | | | | | | #907.
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | Case 2:
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | (229) all_58_1 = e0 & op(e3, e2) = e0
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | ALPHA: (229) implies:
% 169.23/25.56 | | | | | | | (230) all_58_1 = e0
% 169.23/25.56 | | | | | | | (231) op(e3, e2) = e0
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | BETA: splitting (32) gives:
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | (232) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 169.23/25.56 | | | | | | | | op(e0, e2) = e3)
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | BETA: splitting (232) gives:
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | (233) all_58_12 = e3 & op(e0, e3) = e3
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | ALPHA: (233) implies:
% 169.23/25.56 | | | | | | | | | (234) all_58_12 = e3
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | BETA: splitting (64) gives:
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | (235) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 169.23/25.56 | | | | | | | | | | & op(e3, e2) = e3)
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | REF_CLOSE: (10), (23), (30), (40), (49), (50), (51), (58),
% 169.23/25.56 | | | | | | | | | | (65), (67), (74), (76), (234), (235) are
% 169.23/25.56 | | | | | | | | | | inconsistent by sub-proof #413.
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | (236) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 169.23/25.56 | | | | | | | | | | & op(e3, e0) = e3)
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | BETA: splitting (236) gives:
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | (237) all_58_4 = e3 & op(e3, e1) = e3
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | ALPHA: (237) implies:
% 169.23/25.56 | | | | | | | | | | | (238) all_58_4 = e3
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | REF_CLOSE: (5), (13), (23), (30), (40), (49), (51), (52),
% 169.23/25.56 | | | | | | | | | | | (65), (67), (71), (73), (74), (85), (97), (238)
% 169.23/25.56 | | | | | | | | | | | are inconsistent by sub-proof #452.
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | (239) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | ALPHA: (239) implies:
% 169.23/25.56 | | | | | | | | | | | (240) all_58_9 = e3
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | BETA: splitting (37) gives:
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | (241) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 169.23/25.56 | | | | | | | | | | | | & op(e2, e1) = e3)
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (10), (13), (22), (23), (30), (33),
% 169.23/25.56 | | | | | | | | | | | | (40), (49), (50), (51), (52), (63), (65), (67),
% 169.23/25.56 | | | | | | | | | | | | (71), (73), (74), (84), (97), (234), (240), (241)
% 169.23/25.56 | | | | | | | | | | | | are inconsistent by sub-proof #234.
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | (242) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 169.23/25.56 | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | BETA: splitting (242) gives:
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | (243) all_58_8 = e3 & op(e1, e1) = e3
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | REF_CLOSE: (47), (65), (225), (243) are inconsistent by
% 169.23/25.56 | | | | | | | | | | | | | sub-proof #961.
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | (244) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | REF_CLOSE: (5), (8), (13), (15), (23), (30), (40), (47),
% 169.23/25.56 | | | | | | | | | | | | | (49), (51), (52), (56), (65), (67), (71), (73),
% 169.23/25.56 | | | | | | | | | | | | | (74), (85), (93), (97), (138), (230), (231), (244)
% 169.23/25.56 | | | | | | | | | | | | | are inconsistent by sub-proof #233.
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | (245) all_58_13 = e3 & op(e0, e2) = e3
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | REF_CLOSE: (43), (65), (81), (245) are inconsistent by
% 169.23/25.56 | | | | | | | | | sub-proof #962.
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | End of split
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | (246) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 169.23/25.56 | | | | | | | | op(e0, e0) = e3)
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | BETA: splitting (246) gives:
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | (247) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | REF_CLOSE: (5), (8), (13), (15), (23), (30), (40), (47), (49),
% 169.23/25.56 | | | | | | | | | (51), (52), (56), (65), (67), (71), (73), (74),
% 169.23/25.56 | | | | | | | | | (85), (93), (97), (138), (230), (231), (247) are
% 169.23/25.56 | | | | | | | | | inconsistent by sub-proof #233.
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | (248) all_58_15 = e3 & op(e0, e0) = e3
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | REF_CLOSE: (5), (13), (23), (30), (40), (49), (51), (52),
% 169.23/25.56 | | | | | | | | | (65), (67), (71), (73), (74), (97), (124), (248)
% 169.23/25.56 | | | | | | | | | are inconsistent by sub-proof #359.
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | End of split
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | End of split
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | End of split
% 169.23/25.56 | | | | | |
% 169.23/25.56 | | | | | Case 2:
% 169.23/25.56 | | | | | |
% 169.23/25.56 | | | | | | (249) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 169.23/25.56 | | | | | | e0) = e0)
% 169.23/25.56 | | | | | |
% 169.23/25.56 | | | | | | BETA: splitting (249) gives:
% 169.23/25.56 | | | | | |
% 169.23/25.56 | | | | | | Case 1:
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | (250) all_58_4 = e0 & op(e3, e1) = e0
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | REF_CLOSE: (67), (85), (250) are inconsistent by sub-proof #946.
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | Case 2:
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | (251) all_58_9 = e0 & op(e3, e0) = e0
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | ALPHA: (251) implies:
% 169.23/25.56 | | | | | | | (252) all_58_9 = e0
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | BETA: splitting (57) gives:
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | (253) all_54_12 = e3
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | COMBINE_EQS: (12), (253) imply:
% 169.23/25.56 | | | | | | | | (254) all_52_3 = e3
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | SIMP: (254) implies:
% 169.23/25.56 | | | | | | | | (255) all_52_3 = e3
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | REDUCE: (92), (255) imply:
% 169.23/25.56 | | | | | | | | (256) ~ (all_52_2 = e3)
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | BETA: splitting (32) gives:
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | (257) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3
% 169.23/25.56 | | | | | | | | | & op(e0, e2) = e3)
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | BETA: splitting (257) gives:
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | (258) all_58_12 = e3 & op(e0, e3) = e3
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | ALPHA: (258) implies:
% 169.23/25.56 | | | | | | | | | | (259) all_58_12 = e3
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | BETA: splitting (64) gives:
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | (260) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 169.23/25.56 | | | | | | | | | | | & op(e3, e2) = e3)
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | REF_CLOSE: (10), (23), (30), (40), (49), (50), (51), (58),
% 169.23/25.56 | | | | | | | | | | | (65), (67), (74), (76), (259), (260) are
% 169.23/25.56 | | | | | | | | | | | inconsistent by sub-proof #413.
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | (261) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 169.23/25.56 | | | | | | | | | | | & op(e3, e0) = e3)
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | BETA: splitting (261) gives:
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | (262) all_58_4 = e3 & op(e3, e1) = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | REF_CLOSE: (5), (13), (23), (30), (40), (49), (51), (52),
% 169.23/25.56 | | | | | | | | | | | | (65), (67), (71), (73), (74), (85), (97), (262)
% 169.23/25.56 | | | | | | | | | | | | are inconsistent by sub-proof #348.
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | (263) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | ALPHA: (263) implies:
% 169.23/25.56 | | | | | | | | | | | | (264) all_58_9 = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | REF_CLOSE: (51), (252), (264) are inconsistent by sub-proof
% 169.23/25.56 | | | | | | | | | | | | #835.
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | (265) all_58_13 = e3 & op(e0, e2) = e3
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | REF_CLOSE: (43), (65), (81), (265) are inconsistent by
% 169.23/25.56 | | | | | | | | | | sub-proof #962.
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | (266) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3
% 169.23/25.56 | | | | | | | | | & op(e0, e0) = e3)
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | BETA: splitting (266) gives:
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | (267) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | ALPHA: (267) implies:
% 169.23/25.56 | | | | | | | | | | (268) all_58_14 = e3
% 169.23/25.56 | | | | | | | | | | (269) op(e0, e1) = e3
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | BETA: splitting (64) gives:
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | (270) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 169.23/25.56 | | | | | | | | | | | & op(e3, e2) = e3)
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | BETA: splitting (270) gives:
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | (271) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | ALPHA: (271) implies:
% 169.23/25.56 | | | | | | | | | | | | (272) op(e3, e3) = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | BETA: splitting (91) gives:
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | (273) all_58_15 = e0 & op(e0, e0) = e0
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | REF_CLOSE: (67), (124), (273) are inconsistent by sub-proof
% 169.23/25.56 | | | | | | | | | | | | | #874.
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | (274) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 169.23/25.56 | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 169.23/25.56 | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 169.23/25.56 | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.23/25.56 | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | ALPHA: (274) implies:
% 169.23/25.56 | | | | | | | | | | | | | (275) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 169.23/25.56 | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 169.23/25.56 | | | | | | | | | | | | | e1) = e0)
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | BETA: splitting (275) gives:
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | (276) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | ALPHA: (276) implies:
% 169.23/25.56 | | | | | | | | | | | | | | (277) all_58_12 = e0
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (13), (15), (17),
% 169.23/25.56 | | | | | | | | | | | | | | (22), (23), (25), (26), (30), (33), (37), (40),
% 169.23/25.56 | | | | | | | | | | | | | | (41), (47), (49), (50), (51), (52), (53), (56),
% 169.23/25.56 | | | | | | | | | | | | | | (58), (63), (64), (65), (67), (68), (69), (71),
% 169.23/25.56 | | | | | | | | | | | | | | (73), (74), (76), (85), (86), (93), (97), (124),
% 169.23/25.56 | | | | | | | | | | | | | | (138), (225), (272), (277) are inconsistent by
% 169.23/25.56 | | | | | | | | | | | | | | sub-proof #243.
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | (278) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 169.23/25.56 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | | (279) all_58_13 = e0 & op(e0, e2) = e0
% 169.23/25.56 | | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 169.23/25.56 | | | | | | | | | | | | | | | (280) all_58_13 = e0
% 169.23/25.56 | | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 169.23/25.56 | | | | | | | | | | | | | | | (11), (13), (14), (15), (17), (18), (19), (22),
% 169.23/25.56 | | | | | | | | | | | | | | | (23), (24), (25), (26), (30), (31), (33), (34),
% 169.23/25.56 | | | | | | | | | | | | | | | (36), (37), (40), (41), (45), (46), (47), (49),
% 169.23/25.56 | | | | | | | | | | | | | | | (50), (51), (52), (53), (54), (55), (56), (58),
% 169.23/25.56 | | | | | | | | | | | | | | | (63), (64), (65), (67), (68), (69), (71), (73),
% 169.23/25.56 | | | | | | | | | | | | | | | (74), (76), (82), (85), (86), (88), (89), (90),
% 169.23/25.56 | | | | | | | | | | | | | | | (93), (97), (124), (128), (134), (138), (220),
% 169.23/25.56 | | | | | | | | | | | | | | | (225), (256), (268), (269), (272), (280) are
% 169.23/25.56 | | | | | | | | | | | | | | | inconsistent by sub-proof #235.
% 169.23/25.56 | | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | | (281) all_58_14 = e0 & op(e0, e1) = e0
% 169.23/25.56 | | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 169.23/25.56 | | | | | | | | | | | | | | | (282) all_58_14 = e0
% 169.23/25.56 | | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (13), (23), (30), (37), (40), (47),
% 169.23/25.56 | | | | | | | | | | | | | | | (49), (51), (52), (65), (67), (71), (73), (74),
% 169.23/25.56 | | | | | | | | | | | | | | | (85), (97), (225), (282) are inconsistent by
% 169.23/25.56 | | | | | | | | | | | | | | | sub-proof #236.
% 169.23/25.56 | | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | (283) all_58_1 = e3 & op(e3, e2) = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | ALPHA: (283) implies:
% 169.23/25.56 | | | | | | | | | | | | (284) op(e3, e2) = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | REF_CLOSE: (58), (65), (76), (284) are inconsistent by
% 169.23/25.56 | | | | | | | | | | | | sub-proof #974.
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | (285) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 169.23/25.56 | | | | | | | | | | | & op(e3, e0) = e3)
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | BETA: splitting (285) gives:
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | Case 1:
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | (286) all_58_4 = e3 & op(e3, e1) = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | ALPHA: (286) implies:
% 169.23/25.56 | | | | | | | | | | | | (287) all_58_4 = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | REF_CLOSE: (5), (13), (23), (30), (40), (41), (49), (51),
% 169.23/25.56 | | | | | | | | | | | | (52), (65), (67), (71), (73), (74), (86), (93),
% 169.23/25.56 | | | | | | | | | | | | (97), (268), (287) are inconsistent by sub-proof
% 169.23/25.56 | | | | | | | | | | | | #375.
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | (288) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | ALPHA: (288) implies:
% 169.23/25.56 | | | | | | | | | | | | (289) all_58_9 = e3
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | COMBINE_EQS: (252), (289) imply:
% 169.23/25.56 | | | | | | | | | | | | (290) e3 = e0
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | SIMP: (290) implies:
% 169.23/25.56 | | | | | | | | | | | | (291) e3 = e0
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | COMBINE_EQS: (268), (291) imply:
% 169.23/25.56 | | | | | | | | | | | | (292) all_58_14 = e0
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (13), (23), (30), (37), (40), (47),
% 169.23/25.56 | | | | | | | | | | | | (49), (51), (52), (65), (67), (71), (73), (74),
% 169.23/25.56 | | | | | | | | | | | | (85), (97), (225), (292) are inconsistent by
% 169.23/25.56 | | | | | | | | | | | | sub-proof #236.
% 169.23/25.56 | | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | (293) all_58_15 = e3 & op(e0, e0) = e3
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | | REF_CLOSE: (5), (13), (23), (30), (40), (49), (51), (52),
% 169.23/25.56 | | | | | | | | | | (65), (67), (71), (73), (74), (97), (124), (293)
% 169.23/25.56 | | | | | | | | | | are inconsistent by sub-proof #359.
% 169.23/25.56 | | | | | | | | | |
% 169.23/25.56 | | | | | | | | | End of split
% 169.23/25.56 | | | | | | | | |
% 169.23/25.56 | | | | | | | | End of split
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | Case 2:
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | (294) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | | REF_CLOSE: (12), (21), (129), (221), (294) are inconsistent by
% 169.23/25.56 | | | | | | | | sub-proof #675.
% 169.23/25.56 | | | | | | | |
% 169.23/25.56 | | | | | | | End of split
% 169.23/25.56 | | | | | | |
% 169.23/25.56 | | | | | | End of split
% 169.23/25.56 | | | | | |
% 169.23/25.56 | | | | | End of split
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | Case 2:
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | (295) all_56_14 = e3
% 169.23/25.56 | | | | | (296) all_56_2 = e1 & op(e1, e3) = e1
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | ALPHA: (296) implies:
% 169.23/25.56 | | | | | (297) op(e1, e3) = e1
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | COMBINE_EQS: (24), (295) imply:
% 169.23/25.56 | | | | | (298) all_6_2 = e3
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | SIMP: (298) implies:
% 169.23/25.56 | | | | | (299) all_6_2 = e3
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | REDUCE: (46), (299) imply:
% 169.23/25.56 | | | | | (300) ~ (all_52_2 = e3)
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | | REF_CLOSE: (11), (26), (36), (65), (128), (220), (297), (300) are
% 169.23/25.56 | | | | | inconsistent by sub-proof #231.
% 169.23/25.56 | | | | |
% 169.23/25.56 | | | | End of split
% 169.23/25.56 | | | |
% 169.23/25.56 | | | End of split
% 169.23/25.56 | | |
% 169.23/25.56 | | End of split
% 169.23/25.56 | |
% 169.23/25.56 | End of split
% 169.23/25.56 |
% 169.23/25.56 End of proof
% 169.23/25.56
% 169.23/25.56 Sub-proof #231 shows that the following formulas are inconsistent:
% 169.23/25.56 ----------------------------------------------------------------
% 169.23/25.56 (1) all_54_8 = all_52_2
% 169.23/25.56 (2) op(e1, e3) = all_52_2
% 169.23/25.56 (3) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 169.23/25.56 (4) ~ (all_52_2 = e1)
% 169.23/25.56 (5) ~ (all_52_2 = e2)
% 169.23/25.56 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.56 (7) op(e1, e3) = e1
% 169.23/25.56 (8) ~ (all_52_2 = e3)
% 169.23/25.56
% 169.23/25.56 Begin of proof
% 169.23/25.56 |
% 169.23/25.56 | BETA: splitting (3) gives:
% 169.23/25.56 |
% 169.23/25.56 | Case 1:
% 169.23/25.56 | |
% 169.23/25.56 | | (9) all_54_8 = e3
% 169.23/25.56 | |
% 169.23/25.56 | | COMBINE_EQS: (1), (9) imply:
% 169.23/25.56 | | (10) all_52_2 = e3
% 169.23/25.56 | |
% 169.23/25.56 | | REDUCE: (8), (10) imply:
% 169.23/25.56 | | (11) $false
% 169.23/25.56 | |
% 169.23/25.56 | | CLOSE: (11) is inconsistent.
% 169.23/25.56 | |
% 169.23/25.56 | Case 2:
% 169.23/25.56 | |
% 169.23/25.57 | | (12) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 169.23/25.57 | |
% 169.23/25.57 | | BETA: splitting (12) gives:
% 169.23/25.57 | |
% 169.23/25.57 | | Case 1:
% 169.23/25.57 | | |
% 169.23/25.57 | | | (13) all_54_8 = e2
% 169.23/25.57 | | |
% 169.23/25.57 | | | COMBINE_EQS: (1), (13) imply:
% 169.23/25.57 | | | (14) all_52_2 = e2
% 169.23/25.57 | | |
% 169.23/25.57 | | | REDUCE: (5), (14) imply:
% 169.23/25.57 | | | (15) $false
% 169.23/25.57 | | |
% 169.23/25.57 | | | CLOSE: (15) is inconsistent.
% 169.23/25.57 | | |
% 169.23/25.57 | | Case 2:
% 169.23/25.57 | | |
% 169.23/25.57 | | | (16) all_54_8 = e1 | all_54_8 = e0
% 169.23/25.57 | | |
% 169.23/25.57 | | | REF_CLOSE: (1), (2), (4), (6), (7), (16) are inconsistent by sub-proof
% 169.23/25.57 | | | #232.
% 169.23/25.57 | | |
% 169.23/25.57 | | End of split
% 169.23/25.57 | |
% 169.23/25.57 | End of split
% 169.23/25.57 |
% 169.23/25.57 End of proof
% 169.23/25.57
% 169.23/25.57 Sub-proof #232 shows that the following formulas are inconsistent:
% 169.23/25.57 ----------------------------------------------------------------
% 169.23/25.57 (1) all_54_8 = all_52_2
% 169.23/25.57 (2) all_54_8 = e1 | all_54_8 = e0
% 169.23/25.57 (3) op(e1, e3) = all_52_2
% 169.23/25.57 (4) ~ (all_52_2 = e1)
% 169.23/25.57 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.57 (6) op(e1, e3) = e1
% 169.23/25.57
% 169.23/25.57 Begin of proof
% 169.23/25.57 |
% 169.23/25.57 | BETA: splitting (2) gives:
% 169.23/25.57 |
% 169.23/25.57 | Case 1:
% 169.23/25.57 | |
% 169.23/25.57 | | (7) all_54_8 = e1
% 169.23/25.57 | |
% 169.23/25.57 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #689.
% 169.23/25.57 | |
% 169.23/25.57 | Case 2:
% 169.23/25.57 | |
% 169.23/25.57 | | (8) all_54_8 = e0
% 169.23/25.57 | |
% 169.23/25.57 | | COMBINE_EQS: (1), (8) imply:
% 169.23/25.57 | | (9) all_52_2 = e0
% 169.23/25.57 | |
% 169.23/25.57 | | SIMP: (9) implies:
% 169.23/25.57 | | (10) all_52_2 = e0
% 169.23/25.57 | |
% 169.23/25.57 | | REDUCE: (4), (10) imply:
% 169.23/25.57 | | (11) ~ (e1 = e0)
% 169.23/25.57 | |
% 169.23/25.57 | | SIMP: (11) implies:
% 169.23/25.57 | | (12) ~ (e1 = e0)
% 169.23/25.57 | |
% 169.23/25.57 | | REDUCE: (3), (10) imply:
% 169.23/25.57 | | (13) op(e1, e3) = e0
% 169.23/25.57 | |
% 169.23/25.57 | | REF_CLOSE: (3), (5), (6), (12), (13) are inconsistent by sub-proof #749.
% 169.23/25.57 | |
% 169.23/25.57 | End of split
% 169.23/25.57 |
% 169.23/25.57 End of proof
% 169.23/25.57
% 169.23/25.57 Sub-proof #233 shows that the following formulas are inconsistent:
% 169.23/25.57 ----------------------------------------------------------------
% 169.23/25.57 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.57 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.57 (2) all_58_7 = e2
% 169.23/25.57 (3) all_58_2 = e2
% 169.23/25.57 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.57 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.57 (5) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.57 (6) ~ (e3 = e1)
% 169.23/25.57 (7) ~ (e1 = e0)
% 169.23/25.57 (8) op(e2, e3) = all_52_1
% 169.23/25.57 (9) ~ (all_6_2 = e2)
% 169.23/25.57 (10) op(e1, e1) = all_6_2
% 169.23/25.57 (11) op(e2, e3) = e2
% 169.23/25.57 (12) ~ (e3 = e0)
% 169.23/25.57 (13) op(e3, e2) = e0
% 169.23/25.57 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.57 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.57 (15) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.57 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.57 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.57 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.57 (17) ~ (e2 = e0)
% 169.23/25.57 (18) all_58_3 = e3
% 169.23/25.57 (19) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.57 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.57 (20) ~ (e2 = e1)
% 169.23/25.57 (21) all_58_4 = e2
% 169.23/25.57 (22) all_58_1 = e0
% 169.23/25.57 (23) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.23/25.57 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.23/25.57 (24) ~ (e3 = e2)
% 169.23/25.57
% 169.23/25.57 Begin of proof
% 169.23/25.57 |
% 169.23/25.57 | ALPHA: (5) implies:
% 169.23/25.57 | (25) all_58_14 = e3
% 169.23/25.57 |
% 169.23/25.57 | BETA: splitting (15) gives:
% 169.23/25.57 |
% 169.23/25.57 | Case 1:
% 169.23/25.57 | |
% 169.23/25.57 | | (26) ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.57 | | all_22_1 & $i(all_22_0) & $i(all_22_1)
% 169.23/25.57 | |
% 169.23/25.57 | | ALPHA: (26) implies:
% 169.23/25.57 | | (27) ~ (all_22_0 = e1)
% 169.23/25.57 | | (28) op(e3, e2) = all_22_1
% 169.23/25.57 | | (29) op(all_22_1, e2) = all_22_0
% 169.23/25.57 | |
% 169.23/25.57 | | BETA: splitting (4) gives:
% 169.23/25.57 | |
% 169.23/25.57 | | Case 1:
% 169.23/25.57 | | |
% 169.23/25.57 | | | (30) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.23/25.57 | | | e1)
% 169.23/25.57 | | |
% 169.23/25.57 | | | BETA: splitting (30) gives:
% 169.23/25.57 | | |
% 169.23/25.57 | | | Case 1:
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | (31) all_58_1 = e1 & op(e3, e2) = e1
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | REF_CLOSE: (7), (22), (31) are inconsistent by sub-proof #658.
% 169.23/25.57 | | | |
% 169.23/25.57 | | | Case 2:
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | (32) all_58_3 = e1 & op(e2, e2) = e1
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | REF_CLOSE: (6), (18), (32) are inconsistent by sub-proof #868.
% 169.23/25.57 | | | |
% 169.23/25.57 | | | End of split
% 169.23/25.57 | | |
% 169.23/25.57 | | Case 2:
% 169.23/25.57 | | |
% 169.23/25.57 | | | (33) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.23/25.57 | | | e1)
% 169.23/25.57 | | |
% 169.23/25.57 | | | BETA: splitting (33) gives:
% 169.23/25.57 | | |
% 169.23/25.57 | | | Case 1:
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | (34) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | ALPHA: (34) implies:
% 169.23/25.57 | | | | (35) all_58_7 = e1
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | COMBINE_EQS: (2), (35) imply:
% 169.23/25.57 | | | | (36) e2 = e1
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | COMBINE_EQS: (21), (36) imply:
% 169.23/25.57 | | | | (37) all_58_4 = e1
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (12), (14), (16),
% 169.23/25.57 | | | | (17), (18), (19), (20), (23), (24), (25), (37) are
% 169.23/25.57 | | | | inconsistent by sub-proof #408.
% 169.23/25.57 | | | |
% 169.23/25.57 | | | Case 2:
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | (38) all_58_13 = e1 & op(e0, e2) = e1
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | ALPHA: (38) implies:
% 169.23/25.57 | | | | (39) op(e0, e2) = e1
% 169.23/25.57 | | | |
% 169.23/25.57 | | | | REF_CLOSE: (13), (16), (27), (28), (29), (39) are inconsistent by
% 169.23/25.57 | | | | sub-proof #445.
% 169.23/25.57 | | | |
% 169.23/25.57 | | | End of split
% 169.23/25.57 | | |
% 169.23/25.57 | | End of split
% 169.23/25.57 | |
% 169.23/25.57 | Case 2:
% 169.23/25.57 | |
% 169.23/25.57 | | (40) ~ (all_22_1 = e0) & op(e3, e2) = all_22_1 & $i(all_22_1)
% 169.23/25.57 | |
% 169.23/25.57 | | REF_CLOSE: (13), (16), (40) are inconsistent by sub-proof #444.
% 169.23/25.57 | |
% 169.23/25.57 | End of split
% 169.23/25.57 |
% 169.23/25.57 End of proof
% 169.23/25.57
% 169.23/25.57 Sub-proof #234 shows that the following formulas are inconsistent:
% 169.23/25.57 ----------------------------------------------------------------
% 169.23/25.57 (1) op(e2, e1) = all_52_9
% 169.23/25.57 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.57 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.57 (3) ~ (all_52_9 = e3)
% 169.23/25.57 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.57 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.57 (5) all_58_2 = e2
% 169.23/25.57 (6) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.57 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.57 (7) ~ (e3 = e1)
% 169.23/25.57 (8) ~ (e1 = e0)
% 169.23/25.57 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.57 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.57 (10) op(e2, e3) = all_52_1
% 169.23/25.57 (11) op(e2, e3) = e2
% 169.23/25.57 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.57 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.57 (13) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 169.23/25.57 (14) ~ (e3 = e0)
% 169.23/25.57 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.57 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.57 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.57 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.57 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.57 (18) ~ (e2 = e0)
% 169.23/25.57 (19) all_58_12 = e3
% 169.23/25.57 (20) all_58_3 = e3
% 169.23/25.57 (21) all_58_9 = e3
% 169.23/25.57 (22) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.57 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.57 (23) ~ (e2 = e1)
% 169.23/25.57 (24) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.23/25.57 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.23/25.57 (25) ~ (e3 = e2)
% 169.23/25.57
% 169.23/25.57 Begin of proof
% 169.23/25.57 |
% 169.23/25.57 | BETA: splitting (13) gives:
% 169.23/25.57 |
% 169.23/25.57 | Case 1:
% 169.23/25.57 | |
% 169.23/25.57 | | (26) all_58_4 = e3 & op(e3, e1) = e3
% 169.23/25.57 | |
% 169.23/25.57 | | ALPHA: (26) implies:
% 169.23/25.57 | | (27) all_58_4 = e3
% 169.23/25.57 | |
% 169.23/25.57 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 169.23/25.57 | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (27)
% 169.23/25.57 | | are inconsistent by sub-proof #388.
% 169.23/25.57 | |
% 169.23/25.57 | Case 2:
% 169.23/25.57 | |
% 169.23/25.57 | | (28) all_58_5 = e3 & op(e2, e1) = e3
% 169.23/25.57 | |
% 169.23/25.57 | | ALPHA: (28) implies:
% 169.23/25.57 | | (29) op(e2, e1) = e3
% 169.23/25.57 | |
% 169.23/25.57 | | REF_CLOSE: (1), (3), (17), (29) are inconsistent by sub-proof #951.
% 169.23/25.57 | |
% 169.23/25.57 | End of split
% 169.23/25.57 |
% 169.23/25.57 End of proof
% 169.23/25.57
% 169.23/25.57 Sub-proof #235 shows that the following formulas are inconsistent:
% 169.23/25.57 ----------------------------------------------------------------
% 169.23/25.57 (1) op(e2, e1) = all_52_9
% 169.23/25.57 (2) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.23/25.57 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.23/25.57 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.57 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.57 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.23/25.57 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.57 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.57 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.57 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.57 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 169.23/25.57 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.57 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.57 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.57 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.57 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.23/25.57 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.57 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.57 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.57 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.57 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.23/25.57 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.57 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.57 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.57 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.57 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 169.23/25.57 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 169.23/25.57 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.23/25.57 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.57 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.57 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.23/25.57 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.57 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.57 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.57 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.57 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 169.23/25.57 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 169.23/25.57 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.23/25.57 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.57 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.57 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.23/25.57 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.57 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.57 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.57 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.57 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 169.23/25.57 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.23/25.57 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.23/25.57 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 169.23/25.57 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.23/25.57 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 169.23/25.57 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.23/25.57 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.57 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.57 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.57 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.57 (5) op(e0, e1) = e3
% 169.23/25.57 (6) ~ (all_52_9 = e3)
% 169.23/25.57 (7) ~ (all_52_13 = e3)
% 169.23/25.57 (8) all_58_7 = e2
% 169.23/25.57 (9) all_58_15 = e2
% 169.23/25.57 (10) all_56_0 = e2
% 169.23/25.57 (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.57 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.57 (12) all_54_8 = all_52_2
% 169.23/25.57 (13) all_58_2 = e2
% 169.23/25.57 (14) all_54_6 = all_52_9
% 169.23/25.57 (15) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.57 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.57 (16) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.23/25.57 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.57 (17) ~ (all_6_2 = e3)
% 169.23/25.57 (18) all_54_10 = all_6_2
% 169.23/25.57 (19) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 169.23/25.57 (20) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.57 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.57 (21) ~ (e3 = e1)
% 169.23/25.57 (22) all_56_14 = all_6_2
% 169.23/25.57 (23) all_58_13 = e0
% 169.23/25.57 (24) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.57 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.23/25.57 e1)
% 169.23/25.57 (25) op(e1, e3) = all_52_2
% 169.23/25.57 (26) ~ (e1 = e0)
% 169.23/25.57 (27) all_56_7 = e0
% 169.23/25.57 (28) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.57 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.57 (29) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 169.23/25.57 (30) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 169.23/25.57 (31) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.57 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.57 (32) op(e2, e3) = all_52_1
% 169.23/25.57 (33) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.57 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.57 (34) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 169.23/25.57 (35) ~ (all_52_2 = all_6_2)
% 169.23/25.57 (36) ~ (all_6_2 = e2)
% 169.23/25.57 (37) op(e1, e1) = all_6_2
% 169.23/25.57 (38) op(e2, e3) = e2
% 169.23/25.57 (39) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.57 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.57 (40) ~ (e3 = e0)
% 169.23/25.57 (41) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.57 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.57 (42) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.57 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.57 (43) ~ (all_52_13 = e2)
% 169.23/25.57 (44) ~ (all_52_9 = all_6_2)
% 169.23/25.57 (45) ~ (all_52_2 = e1)
% 169.23/25.57 (46) ~ (all_52_2 = e2)
% 169.23/25.58 (47) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.58 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.58 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.58 (48) all_58_14 = e3
% 169.23/25.58 (49) ~ (all_52_4 = e3)
% 169.23/25.58 (50) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.58 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.58 (51) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.23/25.58 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.23/25.58 (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.58 (53) ~ (e2 = e0)
% 169.23/25.58 (54) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.58 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.58 (55) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.23/25.58 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.23/25.58 (56) all_58_3 = e3
% 169.23/25.58 (57) op(e3, e3) = e3
% 169.23/25.58 (58) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.58 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.58 (59) ~ (e2 = e1)
% 169.23/25.58 (60) op(e3, e2) = all_52_4
% 169.23/25.58 (61) all_54_7 = all_52_13
% 169.23/25.58 (62) all_58_4 = e2
% 169.23/25.58 (63) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.58 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.58 (64) all_56_12 = e3
% 169.23/25.58 (65) all_56_15 = e2
% 169.23/25.58 (66) ~ (all_52_9 = e2)
% 169.23/25.58 (67) ~ (all_52_9 = all_52_13)
% 169.23/25.58 (68) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.23/25.58 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.23/25.58 (69) ~ (all_52_2 = e3)
% 169.23/25.58 (70) ~ (e3 = e2)
% 169.23/25.58
% 169.23/25.58 Begin of proof
% 169.23/25.58 |
% 169.23/25.58 | BETA: splitting (39) gives:
% 169.23/25.58 |
% 169.23/25.58 | Case 1:
% 169.23/25.58 | |
% 169.23/25.58 | | (71) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 169.23/25.58 | | e1)
% 169.23/25.58 | |
% 169.23/25.58 | | BETA: splitting (71) gives:
% 169.23/25.58 | |
% 169.23/25.58 | | Case 1:
% 169.23/25.58 | | |
% 169.23/25.58 | | | (72) all_58_0 = e1 & op(e3, e3) = e1
% 169.23/25.58 | | |
% 169.23/25.58 | | | ALPHA: (72) implies:
% 169.23/25.58 | | | (73) all_58_0 = e1
% 169.23/25.58 | | |
% 169.23/25.58 | | | REF_CLOSE: (4), (8), (13), (15), (20), (21), (23), (26), (32), (33), (38),
% 169.23/25.58 | | | (40), (41), (48), (49), (51), (52), (53), (56), (57), (58),
% 169.23/25.58 | | | (59), (60), (62), (63), (68), (70), (73) are inconsistent by
% 169.23/25.58 | | | sub-proof #239.
% 169.23/25.58 | | |
% 169.23/25.58 | | Case 2:
% 169.23/25.58 | | |
% 169.23/25.58 | | | (74) all_58_2 = e1 & op(e2, e3) = e1
% 169.23/25.58 | | |
% 169.23/25.58 | | | ALPHA: (74) implies:
% 169.23/25.58 | | | (75) op(e2, e3) = e1
% 169.23/25.58 | | |
% 169.23/25.58 | | | REF_CLOSE: (32), (38), (52), (59), (75) are inconsistent by sub-proof
% 169.23/25.58 | | | #784.
% 169.23/25.58 | | |
% 169.23/25.58 | | End of split
% 169.23/25.58 | |
% 169.23/25.58 | Case 2:
% 169.23/25.58 | |
% 169.23/25.58 | | (76) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 169.23/25.58 | | e1)
% 169.23/25.58 | |
% 169.23/25.58 | | BETA: splitting (76) gives:
% 169.23/25.58 | |
% 169.23/25.58 | | Case 1:
% 169.23/25.58 | | |
% 169.23/25.58 | | | (77) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.58 | | |
% 169.23/25.58 | | | REF_CLOSE: (3), (4), (8), (9), (11), (13), (16), (20), (21), (24), (25),
% 169.23/25.58 | | | (26), (28), (31), (32), (33), (36), (37), (38), (39), (40),
% 169.23/25.58 | | | (41), (42), (47), (48), (49), (50), (51), (52), (53), (54),
% 169.23/25.58 | | | (55), (56), (57), (58), (59), (60), (62), (63), (68), (70),
% 169.23/25.58 | | | (77) are inconsistent by sub-proof #244.
% 169.23/25.58 | | |
% 169.23/25.58 | | Case 2:
% 169.23/25.58 | | |
% 169.23/25.58 | | | (78) all_58_12 = e1 & op(e0, e3) = e1
% 169.23/25.58 | | |
% 169.23/25.58 | | | ALPHA: (78) implies:
% 169.23/25.58 | | | (79) all_58_12 = e1
% 169.23/25.58 | | | (80) op(e0, e3) = e1
% 169.23/25.58 | | |
% 169.23/25.58 | | | BETA: splitting (30) gives:
% 169.23/25.58 | | |
% 169.23/25.58 | | | Case 1:
% 169.23/25.58 | | | |
% 169.23/25.58 | | | | (81) all_54_8 = e3
% 169.23/25.58 | | | |
% 169.23/25.58 | | | | COMBINE_EQS: (12), (81) imply:
% 169.23/25.58 | | | | (82) all_52_2 = e3
% 169.23/25.58 | | | |
% 169.23/25.58 | | | | REDUCE: (69), (82) imply:
% 169.23/25.58 | | | | (83) $false
% 169.23/25.58 | | | |
% 169.23/25.58 | | | | CLOSE: (83) is inconsistent.
% 169.23/25.58 | | | |
% 169.23/25.58 | | | Case 2:
% 169.23/25.58 | | | |
% 169.23/25.58 | | | | (84) ~ (all_54_8 = e3)
% 169.23/25.58 | | | | (85) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 169.23/25.58 | | | |
% 169.23/25.58 | | | | BETA: splitting (51) gives:
% 169.23/25.58 | | | |
% 169.23/25.58 | | | | Case 1:
% 169.23/25.58 | | | | |
% 169.23/25.58 | | | | | (86) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 169.23/25.58 | | | | | e2) = e3)
% 169.23/25.58 | | | | |
% 169.23/25.58 | | | | | BETA: splitting (86) gives:
% 169.23/25.58 | | | | |
% 169.23/25.58 | | | | | Case 1:
% 169.23/25.58 | | | | | |
% 169.23/25.58 | | | | | | (87) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.58 | | | | | |
% 169.23/25.58 | | | | | | ALPHA: (87) implies:
% 169.23/25.58 | | | | | | (88) all_58_0 = e3
% 169.23/25.58 | | | | | |
% 169.23/25.58 | | | | | | BETA: splitting (55) gives:
% 169.23/25.58 | | | | | |
% 169.23/25.58 | | | | | | Case 1:
% 169.23/25.58 | | | | | | |
% 169.23/25.58 | | | | | | | (89) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 &
% 169.23/25.58 | | | | | | | op(e1, e2) = e3)
% 169.23/25.58 | | | | | | |
% 169.23/25.58 | | | | | | | BETA: splitting (89) gives:
% 169.23/25.58 | | | | | | |
% 169.23/25.58 | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | (90) all_58_6 = e3 & op(e1, e3) = e3
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | ALPHA: (90) implies:
% 169.23/25.58 | | | | | | | | (91) all_58_6 = e3
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | BETA: splitting (11) gives:
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | | (92) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 169.23/25.58 | | | | | | | | | op(e2, e3) = e0)
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | | REF_CLOSE: (32), (38), (40), (52), (53), (57), (92) are
% 169.23/25.58 | | | | | | | | | inconsistent by sub-proof #460.
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | | (93) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 169.23/25.58 | | | | | | | | | op(e0, e3) = e0)
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | | BETA: splitting (93) gives:
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | (94) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | REF_CLOSE: (40), (91), (94) are inconsistent by sub-proof
% 169.23/25.58 | | | | | | | | | | #559.
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | (95) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | ALPHA: (95) implies:
% 169.23/25.58 | | | | | | | | | | (96) all_58_12 = e0
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | REF_CLOSE: (26), (79), (96) are inconsistent by sub-proof
% 169.23/25.58 | | | | | | | | | | #873.
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | End of split
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | End of split
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | (97) all_58_7 = e3 & op(e1, e2) = e3
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | ALPHA: (97) implies:
% 169.23/25.58 | | | | | | | | (98) all_58_7 = e3
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | REF_CLOSE: (4), (8), (13), (21), (26), (32), (38), (40), (41),
% 169.23/25.58 | | | | | | | | (52), (53), (56), (58), (59), (70), (98) are
% 169.23/25.58 | | | | | | | | inconsistent by sub-proof #399.
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | End of split
% 169.23/25.58 | | | | | | |
% 169.23/25.58 | | | | | | Case 2:
% 169.23/25.58 | | | | | | |
% 169.23/25.58 | | | | | | | (99) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 &
% 169.23/25.58 | | | | | | | op(e1, e0) = e3)
% 169.23/25.58 | | | | | | |
% 169.23/25.58 | | | | | | | BETA: splitting (99) gives:
% 169.23/25.58 | | | | | | |
% 169.23/25.58 | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | (100) all_58_8 = e3 & op(e1, e1) = e3
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | ALPHA: (100) implies:
% 169.23/25.58 | | | | | | | | (101) all_58_8 = e3
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | REF_CLOSE: (21), (26), (33), (40), (48), (53), (59), (62), (63),
% 169.23/25.58 | | | | | | | | (101) are inconsistent by sub-proof #422.
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | (102) all_58_11 = e3 & op(e1, e0) = e3
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | ALPHA: (102) implies:
% 169.23/25.58 | | | | | | | | (103) all_58_11 = e3
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | BETA: splitting (85) gives:
% 169.23/25.58 | | | | | | | |
% 169.23/25.58 | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | | (104) all_54_8 = e2
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | | REF_CLOSE: (12), (46), (104) are inconsistent by sub-proof
% 169.23/25.58 | | | | | | | | | #259.
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | | (105) ~ (all_54_8 = e2)
% 169.23/25.58 | | | | | | | | | (106) all_54_8 = e1 | all_54_8 = e0
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | | BETA: splitting (54) gives:
% 169.23/25.58 | | | | | | | | |
% 169.23/25.58 | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | (107) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 169.23/25.58 | | | | | | | | | | & op(e1, e2) = e1)
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | BETA: splitting (107) gives:
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | (108) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | REF_CLOSE: (3), (4), (8), (9), (11), (13), (16), (20), (21),
% 169.23/25.58 | | | | | | | | | | | (24), (25), (26), (28), (31), (32), (33), (36),
% 169.23/25.58 | | | | | | | | | | | (37), (38), (39), (40), (41), (42), (47), (48),
% 169.23/25.58 | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 169.23/25.58 | | | | | | | | | | | (57), (58), (59), (60), (62), (63), (68), (70),
% 169.23/25.58 | | | | | | | | | | | (108) are inconsistent by sub-proof #244.
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | (109) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | ALPHA: (109) implies:
% 169.23/25.58 | | | | | | | | | | | (110) all_58_7 = e1
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | COMBINE_EQS: (8), (110) imply:
% 169.23/25.58 | | | | | | | | | | | (111) e2 = e1
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | SIMP: (111) implies:
% 169.23/25.58 | | | | | | | | | | | (112) e2 = e1
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | COMBINE_EQS: (62), (112) imply:
% 169.23/25.58 | | | | | | | | | | | (113) all_58_4 = e1
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | REF_CLOSE: (4), (13), (21), (26), (32), (36), (37), (38),
% 169.23/25.58 | | | | | | | | | | | (40), (41), (48), (52), (53), (56), (58), (59),
% 169.23/25.58 | | | | | | | | | | | (68), (70), (113) are inconsistent by sub-proof
% 169.23/25.58 | | | | | | | | | | | #408.
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | End of split
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | (114) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1
% 169.23/25.58 | | | | | | | | | | & op(e1, e0) = e1)
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | BETA: splitting (114) gives:
% 169.23/25.58 | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | (115) all_58_8 = e1 & op(e1, e1) = e1
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | ALPHA: (115) implies:
% 169.23/25.58 | | | | | | | | | | | (116) all_58_8 = e1
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | BETA: splitting (106) gives:
% 169.23/25.58 | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | (117) all_54_8 = e1
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | REF_CLOSE: (12), (45), (117) are inconsistent by sub-proof
% 169.23/25.58 | | | | | | | | | | | | #689.
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | (118) all_54_8 = e0
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | COMBINE_EQS: (12), (118) imply:
% 169.23/25.58 | | | | | | | | | | | | (119) all_52_2 = e0
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | SIMP: (119) implies:
% 169.23/25.58 | | | | | | | | | | | | (120) all_52_2 = e0
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | REDUCE: (35), (120) imply:
% 169.23/25.58 | | | | | | | | | | | | (121) ~ (all_6_2 = e0)
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | SIMP: (121) implies:
% 169.23/25.58 | | | | | | | | | | | | (122) ~ (all_6_2 = e0)
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | REDUCE: (69), (120) imply:
% 169.23/25.58 | | | | | | | | | | | | (123) ~ (e3 = e0)
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | REDUCE: (46), (120) imply:
% 169.23/25.58 | | | | | | | | | | | | (124) ~ (e2 = e0)
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | REDUCE: (45), (120) imply:
% 169.23/25.58 | | | | | | | | | | | | (125) ~ (e1 = e0)
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | BETA: splitting (33) gives:
% 169.23/25.58 | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | (126) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 169.23/25.58 | | | | | | | | | | | | | & op(e2, e1) = e0)
% 169.23/25.58 | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | BETA: splitting (126) gives:
% 169.23/25.58 | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | (127) all_58_4 = e0 & op(e3, e1) = e0
% 169.23/25.58 | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | REF_CLOSE: (53), (62), (127) are inconsistent by sub-proof
% 169.23/25.58 | | | | | | | | | | | | | | #902.
% 169.23/25.58 | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | (128) all_58_5 = e0 & op(e2, e1) = e0
% 169.23/25.58 | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | ALPHA: (128) implies:
% 169.23/25.58 | | | | | | | | | | | | | | (129) op(e2, e1) = e0
% 169.23/25.58 | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 169.23/25.58 | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | (130) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 169.23/25.58 | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 169.23/25.58 | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 169.23/25.58 | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | (131) all_58_2 = e1 & op(e2, e3) = e1
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 169.23/25.58 | | | | | | | | | | | | | | | | (132) op(e2, e3) = e1
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | REF_CLOSE: (32), (38), (52), (59), (132) are inconsistent by
% 169.23/25.58 | | | | | | | | | | | | | | | | sub-proof #784.
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | (133) all_58_3 = e1 & op(e2, e2) = e1
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 169.23/25.58 | | | | | | | | | | | | | | | | (134) all_58_3 = e1
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | COMBINE_EQS: (56), (134) imply:
% 169.23/25.58 | | | | | | | | | | | | | | | | (135) e3 = e1
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (135) imply:
% 169.23/25.58 | | | | | | | | | | | | | | | | (136) all_58_0 = e1
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (13), (15), (20), (21), (23), (26),
% 169.23/25.58 | | | | | | | | | | | | | | | | (32), (33), (38), (40), (41), (48), (49), (51),
% 169.23/25.58 | | | | | | | | | | | | | | | | (52), (53), (56), (57), (58), (59), (60), (62),
% 169.23/25.58 | | | | | | | | | | | | | | | | (63), (68), (70), (136) are inconsistent by
% 169.23/25.58 | | | | | | | | | | | | | | | | sub-proof #239.
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | End of split
% 169.23/25.58 | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | (137) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 169.23/25.58 | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 169.23/25.58 | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 169.23/25.58 | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | (138) all_58_5 = e1 & op(e2, e1) = e1
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 169.23/25.58 | | | | | | | | | | | | | | | | (139) op(e2, e1) = e1
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | REF_CLOSE: (26), (52), (129), (139) are inconsistent by
% 169.23/25.58 | | | | | | | | | | | | | | | | sub-proof #911.
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | (140) all_58_10 = e1 & op(e2, e0) = e1
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 169.23/25.58 | | | | | | | | | | | | | | | | (141) op(e2, e0) = e1
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 169.23/25.58 | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | | (142) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 169.23/25.58 | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.23/25.58 | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.23/25.58 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.23/25.58 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.58 | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 169.23/25.58 | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.23/25.58 | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.23/25.58 | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.23/25.58 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.58 | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 169.23/25.58 | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 169.23/25.58 | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 169.23/25.58 | | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 169.23/25.58 | | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.58 | | | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | | | (143) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 169.23/25.58 | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.23/25.58 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.23/25.58 | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.23/25.58 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.23/25.58 | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.23/25.58 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.58 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.23/25.58 | | | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (32), (38), (52), (64), (70), (143) are
% 169.23/25.58 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #367.
% 169.23/25.58 | | | | | | | | | | | | | | | | | |
% 169.23/25.58 | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.58 | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (144) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 169.23/25.59 | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (145) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (146) ~ (all_56_14 = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | REDUCE: (22), (146) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (147) ~ (all_6_2 = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (19), (36), (122), (147) are
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #978.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (148) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (149) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (150) ~ (all_56_14 = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (150) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (151) ~ (all_6_2 = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (19), (36), (122), (151) are
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #978.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (152) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (153) ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | e3) = all_56_0 & $i(all_56_0))
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (64), (153) are inconsistent by sub-proof
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | #368.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | (154) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.23/25.59 | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.23/25.59 | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.23/25.59 | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 169.23/25.59 | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 169.23/25.59 | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 169.23/25.59 | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.23/25.59 | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (155) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.23/25.59 | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (26), (52), (64), (129), (155) are
% 169.23/25.59 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #238.
% 169.23/25.59 | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (156) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 169.23/25.59 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.23/25.59 | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (157) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (158) op(e2, e0) = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (52), (141), (158) are inconsistent by
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | sub-proof #849.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (159) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (160) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (161) ~ (all_56_14 = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (161) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (162) ~ (all_6_2 = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (19), (36), (122), (162) are
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #978.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (163) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (164) ~ (all_56_15 = e0)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | (165) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | (166) all_56_6 = e3 & op(e0, e3) = e3
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | (167) op(e0, e3) = e3
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | (168) all_54_10 = e3
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (168) are inconsistent by sub-proof
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | #982.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | (169) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | (170) all_54_10 = e2
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (36), (170) are inconsistent by sub-proof
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | #981.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | (171) all_54_10 = e1 | all_54_10 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | (172) all_54_10 = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (172) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | (173) all_6_2 = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (173) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | (174) all_6_2 = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (174) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | (175) ~ (all_52_9 = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_54_6 = e3
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (176) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_52_9 = e3
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (177) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | (178) $false
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (178) is inconsistent.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | (179) ~ (all_54_6 = e3)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | (180) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (181) all_54_6 = e2
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (181) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (182) all_52_9 = e2
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (182) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (183) $false
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (183) is inconsistent.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (184) ~ (all_54_6 = e2)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_54_6 = e1 | all_54_6 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_54_6 = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (186) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (187) all_52_9 = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (175), (187) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (188) $false
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (188) is inconsistent.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_54_6 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (189) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_52_9 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (190) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (191) ~ (all_52_13 = e0)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (191) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | (192) ~ (all_52_13 = e0)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_54_7 = e3
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (193) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) all_52_13 = e3
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (194) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) $false
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (195) is inconsistent.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) ~ (all_54_7 = e3)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_54_7 = e2
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (198) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_52_13 = e2
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (199) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) $false
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (200) is inconsistent.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) ~ (all_54_7 = e2)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) all_54_7 = e1 | all_54_7 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_54_7 = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (203) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) all_52_13 = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (204) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) ~ (e3 = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (204) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) ~ (e2 = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with e1, e3, e3, e0,
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (80), (167) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) e3 = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (207) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) all_58_0 = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (13), (15), (20), (21), (23), (26),
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (32), (33), (38), (40), (41), (48), (49), (51),
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (53), (56), (57), (58), (59), (60), (62),
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (63), (68), (70), (208) are inconsistent by
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #239.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_54_7 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (209) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_52_13 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (192), (210) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) $false
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (211) is inconsistent.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | (212) all_54_10 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (122), (212) are inconsistent by sub-proof
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | | #979.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | (213) (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = e1)
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | (214) all_56_7 = e2 & op(e0, e2) = e2
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | (215) all_56_7 = e2
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (215) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | (216) e2 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | SIMP: (216) implies:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | (217) e2 = e0
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (53), (217) imply:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | (218) $false
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (218) is inconsistent.
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | (219) all_56_8 = e1 & op(e0, e1) = e1
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.59 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | (220) op(e0, e1) = e1
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | (221) all_54_10 = e3
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (221) are inconsistent by sub-proof
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | #982.
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | (222) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | (223) all_54_10 = e2
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (36), (223) are inconsistent by sub-proof
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | #981.
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | (224) all_54_10 = e1 | all_54_10 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_54_10 = e1
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (225) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_6_2 = e1
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (226) implies:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_6_2 = e1
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (44), (227) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | (228) ~ (all_52_9 = e1)
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_54_6 = e3
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (229) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (230) all_52_9 = e3
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (230) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (231) $false
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent.
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (232) ~ (all_54_6 = e3)
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (233) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_54_6 = e2
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (234) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_52_9 = e2
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (66), (235) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) $false
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (236) is inconsistent.
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) ~ (all_54_6 = e2)
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_54_6 = e1 | all_54_6 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) all_54_6 = e1
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (239) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) all_52_9 = e1
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (228), (240) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) $false
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (241) is inconsistent.
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_54_6 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (242) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) all_52_9 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (67), (243) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) ~ (all_52_13 = e0)
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (244) implies:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) ~ (all_52_13 = e0)
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) all_54_7 = e3
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (246) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_52_13 = e3
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (247) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) $false
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (248) is inconsistent.
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) ~ (all_54_7 = e3)
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_54_7 = e2
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (251) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_52_13 = e2
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (252) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) $false
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (253) is inconsistent.
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) ~ (all_54_7 = e2)
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_54_7 = e1 | all_54_7 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_54_7 = e1
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (256) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_52_13 = e1
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (257) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (258) ~ (e3 = e1)
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (43), (257) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (259) ~ (e2 = e1)
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (52) with e1, e3, e1, e0,
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (5), (220) gives:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260) e3 = e1
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (260) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) all_58_0 = e1
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (13), (15), (20), (21), (23), (26),
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (32), (33), (38), (40), (41), (48), (49), (51),
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (52), (53), (56), (57), (58), (59), (60), (62),
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (63), (68), (70), (261) are inconsistent by
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #239.
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) all_54_7 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (262) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_52_13 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (245), (263) imply:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) $false
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (264) is inconsistent.
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_54_10 = e0
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (122), (265) are inconsistent by sub-proof
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | | #979.
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | (266) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 169.23/25.60 | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 169.23/25.60 | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | BETA: splitting (266) gives:
% 169.23/25.60 | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | Case 1:
% 169.23/25.60 | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | (267) all_58_8 = e0 & op(e1, e1) = e0
% 169.23/25.60 | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | REF_CLOSE: (26), (116), (267) are inconsistent by sub-proof
% 169.23/25.60 | | | | | | | | | | | | | | #718.
% 169.23/25.60 | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | (268) all_58_14 = e0 & op(e0, e1) = e0
% 169.23/25.60 | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | ALPHA: (268) implies:
% 169.23/25.60 | | | | | | | | | | | | | | (269) all_58_14 = e0
% 169.23/25.60 | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (6), (13), (17), (21), (26), (31), (32),
% 169.23/25.60 | | | | | | | | | | | | | | (37), (38), (40), (41), (52), (53), (56), (58),
% 169.23/25.60 | | | | | | | | | | | | | | (59), (62), (70), (269) are inconsistent by
% 169.23/25.60 | | | | | | | | | | | | | | sub-proof #236.
% 169.23/25.60 | | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | Case 2:
% 169.23/25.60 | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | (270) all_58_11 = e1 & op(e1, e0) = e1
% 169.23/25.60 | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | ALPHA: (270) implies:
% 169.23/25.60 | | | | | | | | | | | (271) all_58_11 = e1
% 169.23/25.60 | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | COMBINE_EQS: (103), (271) imply:
% 169.23/25.60 | | | | | | | | | | | (272) e3 = e1
% 169.23/25.60 | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | COMBINE_EQS: (88), (272) imply:
% 169.23/25.60 | | | | | | | | | | | (273) all_58_0 = e1
% 169.23/25.60 | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | | REF_CLOSE: (4), (8), (13), (15), (20), (21), (23), (26),
% 169.23/25.60 | | | | | | | | | | | (32), (33), (38), (40), (41), (48), (49), (51),
% 169.23/25.60 | | | | | | | | | | | (52), (53), (56), (57), (58), (59), (60), (62),
% 169.23/25.60 | | | | | | | | | | | (63), (68), (70), (273) are inconsistent by
% 169.23/25.60 | | | | | | | | | | | sub-proof #239.
% 169.23/25.60 | | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | | |
% 169.23/25.60 | | | | | | | | | End of split
% 169.23/25.60 | | | | | | | | |
% 169.23/25.60 | | | | | | | | End of split
% 169.23/25.60 | | | | | | | |
% 169.23/25.60 | | | | | | | End of split
% 169.23/25.60 | | | | | | |
% 169.23/25.60 | | | | | | End of split
% 169.23/25.60 | | | | | |
% 169.23/25.60 | | | | | Case 2:
% 169.23/25.60 | | | | | |
% 169.23/25.60 | | | | | | (274) all_58_1 = e3 & op(e3, e2) = e3
% 169.23/25.60 | | | | | |
% 169.23/25.60 | | | | | | ALPHA: (274) implies:
% 169.23/25.60 | | | | | | (275) op(e3, e2) = e3
% 169.23/25.60 | | | | | |
% 169.23/25.60 | | | | | | REF_CLOSE: (49), (52), (60), (275) are inconsistent by sub-proof
% 169.23/25.60 | | | | | | #974.
% 169.23/25.60 | | | | | |
% 169.23/25.60 | | | | | End of split
% 169.23/25.60 | | | | |
% 169.23/25.60 | | | | Case 2:
% 169.23/25.60 | | | | |
% 169.23/25.60 | | | | | (276) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 169.23/25.60 | | | | | e0) = e3)
% 169.23/25.60 | | | | |
% 169.23/25.60 | | | | | REF_CLOSE: (4), (8), (13), (15), (20), (21), (23), (26), (32), (33),
% 169.23/25.60 | | | | | (38), (40), (41), (48), (52), (53), (56), (57), (58), (59),
% 169.23/25.60 | | | | | (62), (63), (68), (70), (276) are inconsistent by sub-proof
% 169.23/25.60 | | | | | #240.
% 169.23/25.60 | | | | |
% 169.23/25.60 | | | | End of split
% 169.23/25.60 | | | |
% 169.23/25.60 | | | End of split
% 169.23/25.60 | | |
% 169.23/25.60 | | End of split
% 169.23/25.60 | |
% 169.23/25.60 | End of split
% 169.23/25.60 |
% 169.23/25.60 End of proof
% 169.23/25.60
% 169.23/25.60 Sub-proof #236 shows that the following formulas are inconsistent:
% 169.23/25.60 ----------------------------------------------------------------
% 169.23/25.60 (1) op(e2, e1) = all_52_9
% 169.23/25.60 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.60 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.60 (3) ~ (all_52_9 = e3)
% 169.23/25.60 (4) all_58_2 = e2
% 169.23/25.60 (5) ~ (all_6_2 = e3)
% 169.23/25.60 (6) ~ (e3 = e1)
% 169.23/25.60 (7) ~ (e1 = e0)
% 169.23/25.60 (8) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.60 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.60 (9) op(e2, e3) = all_52_1
% 169.23/25.60 (10) op(e1, e1) = all_6_2
% 169.23/25.60 (11) op(e2, e3) = e2
% 169.23/25.60 (12) ~ (e3 = e0)
% 169.23/25.60 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.60 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.60 (14) all_58_14 = e0
% 169.23/25.60 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.60 (16) ~ (e2 = e0)
% 169.23/25.60 (17) all_58_3 = e3
% 169.23/25.60 (18) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.60 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.60 (19) ~ (e2 = e1)
% 169.23/25.60 (20) all_58_4 = e2
% 169.23/25.60 (21) ~ (e3 = e2)
% 169.23/25.60
% 169.23/25.60 Begin of proof
% 169.23/25.60 |
% 169.23/25.60 | BETA: splitting (8) gives:
% 169.23/25.60 |
% 169.23/25.60 | Case 1:
% 169.23/25.60 | |
% 169.23/25.60 | | (22) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 169.23/25.60 | | e3)
% 169.23/25.60 | |
% 169.23/25.60 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (11), (12), (13), (15), (16),
% 169.23/25.60 | | (17), (18), (19), (20), (21), (22) are inconsistent by sub-proof
% 169.23/25.60 | | #347.
% 169.23/25.60 | |
% 169.23/25.60 | Case 2:
% 169.23/25.60 | |
% 169.23/25.60 | | (23) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 169.23/25.60 | | e3)
% 169.23/25.60 | |
% 169.23/25.60 | | REF_CLOSE: (5), (10), (12), (14), (15), (23) are inconsistent by sub-proof
% 169.23/25.60 | | #237.
% 169.23/25.60 | |
% 169.23/25.60 | End of split
% 169.23/25.60 |
% 169.23/25.60 End of proof
% 169.23/25.60
% 169.23/25.60 Sub-proof #237 shows that the following formulas are inconsistent:
% 169.23/25.60 ----------------------------------------------------------------
% 169.23/25.60 (1) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.60 (2) ~ (all_6_2 = e3)
% 169.23/25.60 (3) op(e1, e1) = all_6_2
% 169.23/25.60 (4) ~ (e3 = e0)
% 169.23/25.60 (5) all_58_14 = e0
% 169.23/25.60 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.60
% 169.23/25.60 Begin of proof
% 169.23/25.60 |
% 169.23/25.60 | BETA: splitting (1) gives:
% 169.23/25.60 |
% 169.23/25.60 | Case 1:
% 169.23/25.60 | |
% 169.23/25.60 | | (7) all_58_8 = e3 & op(e1, e1) = e3
% 169.23/25.60 | |
% 169.23/25.60 | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #961.
% 169.23/25.60 | |
% 169.23/25.60 | Case 2:
% 169.23/25.60 | |
% 169.23/25.60 | | (8) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.60 | |
% 169.23/25.60 | | ALPHA: (8) implies:
% 169.23/25.60 | | (9) all_58_14 = e3
% 169.23/25.60 | |
% 169.23/25.60 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #423.
% 169.23/25.60 | |
% 169.23/25.60 | End of split
% 169.23/25.60 |
% 169.23/25.60 End of proof
% 169.23/25.60
% 169.23/25.60 Sub-proof #238 shows that the following formulas are inconsistent:
% 169.23/25.60 ----------------------------------------------------------------
% 169.23/25.60 (1) all_56_0 = e2
% 169.23/25.60 (2) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 =
% 169.23/25.60 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.23/25.60 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.60 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.60 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.23/25.60 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.60 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.60 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.60 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.60 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.23/25.60 (3) ~ (e1 = e0)
% 169.23/25.60 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.60 (5) op(e2, e1) = e0
% 169.23/25.60 (6) all_56_12 = e3
% 169.23/25.60
% 169.23/25.60 Begin of proof
% 169.23/25.60 |
% 169.23/25.60 | BETA: splitting (2) gives:
% 169.23/25.60 |
% 169.23/25.60 | Case 1:
% 169.23/25.60 | |
% 169.23/25.60 | | (7) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~
% 169.23/25.60 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 169.23/25.60 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 169.23/25.60 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 169.23/25.60 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 169.23/25.60 | |
% 169.23/25.60 | | ALPHA: (7) implies:
% 169.23/25.60 | | (8) op(e2, e1) = e1
% 169.23/25.60 | |
% 169.23/25.60 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #911.
% 169.23/25.60 | |
% 169.23/25.60 | Case 2:
% 169.23/25.60 | |
% 169.23/25.60 | | (9) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.23/25.60 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.23/25.60 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.23/25.60 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 169.23/25.60 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 169.23/25.60 | |
% 169.23/25.60 | | ALPHA: (9) implies:
% 169.23/25.60 | | (10) ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.23/25.60 | | $i(all_56_0))
% 169.23/25.60 | |
% 169.23/25.60 | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #368.
% 169.23/25.60 | |
% 169.23/25.60 | End of split
% 169.23/25.60 |
% 169.23/25.60 End of proof
% 169.23/25.60
% 169.23/25.60 Sub-proof #239 shows that the following formulas are inconsistent:
% 169.23/25.60 ----------------------------------------------------------------
% 169.23/25.60 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.60 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.60 (2) all_58_7 = e2
% 169.23/25.60 (3) all_58_2 = e2
% 169.23/25.60 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.60 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.60 (5) all_58_0 = e1
% 169.23/25.60 (6) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.60 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.60 (7) ~ (e3 = e1)
% 169.23/25.60 (8) all_58_13 = e0
% 169.23/25.60 (9) ~ (e1 = e0)
% 169.23/25.60 (10) op(e2, e3) = all_52_1
% 169.23/25.60 (11) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.60 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.60 (12) op(e2, e3) = e2
% 169.23/25.60 (13) ~ (e3 = e0)
% 169.23/25.60 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.60 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.60 (15) all_58_14 = e3
% 169.23/25.60 (16) ~ (all_52_4 = e3)
% 169.23/25.60 (17) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.23/25.60 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.23/25.60 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.60 (19) ~ (e2 = e0)
% 169.23/25.60 (20) all_58_3 = e3
% 169.23/25.60 (21) op(e3, e3) = e3
% 169.23/25.60 (22) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.60 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.60 (23) ~ (e2 = e1)
% 169.23/25.60 (24) op(e3, e2) = all_52_4
% 169.23/25.60 (25) all_58_4 = e2
% 169.23/25.60 (26) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.60 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.60 (27) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.23/25.60 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.23/25.60 (28) ~ (e3 = e2)
% 169.23/25.60
% 169.23/25.60 Begin of proof
% 169.23/25.60 |
% 169.23/25.60 | BETA: splitting (17) gives:
% 169.23/25.60 |
% 169.23/25.60 | Case 1:
% 169.23/25.60 | |
% 169.23/25.61 | | (29) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 169.23/25.61 | | e3)
% 169.23/25.61 | |
% 169.23/25.61 | | REF_CLOSE: (5), (7), (16), (18), (24), (29) are inconsistent by sub-proof
% 169.23/25.61 | | #250.
% 169.23/25.61 | |
% 169.23/25.61 | Case 2:
% 169.23/25.61 | |
% 169.23/25.61 | | (30) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 169.23/25.61 | | e3)
% 169.23/25.61 | |
% 169.23/25.61 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.23/25.61 | | (14), (15), (18), (19), (20), (21), (22), (23), (25), (26), (27),
% 169.23/25.61 | | (28), (30) are inconsistent by sub-proof #240.
% 169.23/25.61 | |
% 169.23/25.61 | End of split
% 169.23/25.61 |
% 169.23/25.61 End of proof
% 169.23/25.61
% 169.23/25.61 Sub-proof #240 shows that the following formulas are inconsistent:
% 169.23/25.61 ----------------------------------------------------------------
% 169.23/25.61 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.61 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.61 (2) all_58_7 = e2
% 169.23/25.61 (3) all_58_2 = e2
% 169.23/25.61 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.61 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.61 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.61 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.61 (6) ~ (e3 = e1)
% 169.23/25.61 (7) all_58_13 = e0
% 169.23/25.61 (8) ~ (e1 = e0)
% 169.23/25.61 (9) op(e2, e3) = all_52_1
% 169.23/25.61 (10) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.61 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.61 (11) op(e2, e3) = e2
% 169.23/25.61 (12) ~ (e3 = e0)
% 169.23/25.61 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.61 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.61 (14) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.23/25.61 (15) all_58_14 = e3
% 169.23/25.61 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.61 (17) ~ (e2 = e0)
% 169.23/25.61 (18) all_58_3 = e3
% 169.23/25.61 (19) op(e3, e3) = e3
% 169.23/25.61 (20) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.61 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.61 (21) ~ (e2 = e1)
% 169.23/25.61 (22) all_58_4 = e2
% 169.23/25.61 (23) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.61 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.61 (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.23/25.61 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.23/25.61 (25) ~ (e3 = e2)
% 169.23/25.61
% 169.23/25.61 Begin of proof
% 169.23/25.61 |
% 169.23/25.61 | BETA: splitting (14) gives:
% 169.23/25.61 |
% 169.23/25.61 | Case 1:
% 169.23/25.61 | |
% 169.23/25.61 | | (26) all_58_4 = e3 & op(e3, e1) = e3
% 169.23/25.61 | |
% 169.23/25.61 | | ALPHA: (26) implies:
% 169.23/25.61 | | (27) all_58_4 = e3
% 169.23/25.61 | |
% 169.23/25.61 | | REF_CLOSE: (1), (3), (6), (8), (9), (10), (11), (12), (13), (15), (16),
% 169.23/25.61 | | (17), (18), (20), (21), (23), (24), (25), (27) are inconsistent
% 169.23/25.61 | | by sub-proof #375.
% 169.23/25.61 | |
% 169.23/25.61 | Case 2:
% 169.23/25.61 | |
% 169.23/25.61 | | (28) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.61 | |
% 169.23/25.61 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (12), (16), (17), (18), (19), (21),
% 169.23/25.61 | | (22), (28) are inconsistent by sub-proof #241.
% 169.23/25.61 | |
% 169.23/25.61 | End of split
% 169.23/25.61 |
% 169.23/25.61 End of proof
% 169.23/25.61
% 169.23/25.61 Sub-proof #241 shows that the following formulas are inconsistent:
% 169.23/25.61 ----------------------------------------------------------------
% 169.23/25.61 (1) all_58_7 = e2
% 169.23/25.61 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.61 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.61 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.61 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.61 (4) ~ (e3 = e1)
% 169.23/25.61 (5) all_58_13 = e0
% 169.23/25.61 (6) ~ (e1 = e0)
% 169.23/25.61 (7) ~ (e3 = e0)
% 169.23/25.61 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.61 (9) ~ (e2 = e0)
% 169.23/25.61 (10) all_58_3 = e3
% 169.23/25.61 (11) op(e3, e3) = e3
% 169.23/25.61 (12) ~ (e2 = e1)
% 169.23/25.61 (13) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.61 (14) all_58_4 = e2
% 169.23/25.61
% 169.23/25.61 Begin of proof
% 169.23/25.61 |
% 169.23/25.61 | ALPHA: (13) implies:
% 169.23/25.61 | (15) all_58_9 = e3
% 169.23/25.61 |
% 169.23/25.61 | BETA: splitting (2) gives:
% 169.23/25.61 |
% 169.23/25.61 | Case 1:
% 169.23/25.61 | |
% 169.23/25.61 | | (16) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.23/25.61 | | e1)
% 169.23/25.61 | |
% 169.23/25.61 | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (11), (14), (15), (16) are
% 169.23/25.61 | | inconsistent by sub-proof #248.
% 169.23/25.61 | |
% 169.23/25.61 | Case 2:
% 169.23/25.61 | |
% 169.23/25.61 | | (17) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.23/25.61 | | e1)
% 169.23/25.61 | |
% 169.23/25.61 | | BETA: splitting (17) gives:
% 169.23/25.61 | |
% 169.23/25.61 | | Case 1:
% 169.23/25.61 | | |
% 169.23/25.61 | | | (18) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.61 | | |
% 169.23/25.61 | | | REF_CLOSE: (1), (12), (18) are inconsistent by sub-proof #503.
% 169.23/25.61 | | |
% 169.23/25.61 | | Case 2:
% 169.23/25.61 | | |
% 169.23/25.61 | | | (19) all_58_13 = e1 & op(e0, e2) = e1
% 169.23/25.61 | | |
% 169.23/25.61 | | | ALPHA: (19) implies:
% 169.23/25.61 | | | (20) all_58_13 = e1
% 169.23/25.61 | | |
% 169.23/25.61 | | | COMBINE_EQS: (5), (20) imply:
% 169.23/25.61 | | | (21) e1 = e0
% 169.23/25.61 | | |
% 169.23/25.61 | | | REDUCE: (6), (21) imply:
% 169.23/25.61 | | | (22) $false
% 169.23/25.61 | | |
% 169.23/25.61 | | | CLOSE: (22) is inconsistent.
% 169.23/25.61 | | |
% 169.23/25.61 | | End of split
% 169.23/25.61 | |
% 169.23/25.61 | End of split
% 169.23/25.61 |
% 169.23/25.61 End of proof
% 169.23/25.61
% 169.23/25.61 Sub-proof #242 shows that the following formulas are inconsistent:
% 169.23/25.61 ----------------------------------------------------------------
% 169.23/25.61 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.61 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.61 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.61 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.61 (3) ~ (all_52_13 = e3)
% 169.23/25.61 (4) all_58_15 = e2
% 169.23/25.61 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.61 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.61 (6) all_58_2 = e2
% 169.23/25.61 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.23/25.61 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.61 (8) op(e3, e3) = all_10_2
% 169.23/25.61 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.61 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.61 (10) ~ (e3 = e1)
% 169.23/25.61 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.61 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.23/25.61 e1)
% 169.23/25.61 (12) op(e1, e3) = all_52_2
% 169.23/25.61 (13) ~ (all_10_2 = e0)
% 169.23/25.61 (14) ~ (e1 = e0)
% 169.23/25.61 (15) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.23/25.61 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.23/25.61 e3)
% 169.23/25.61 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.61 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.61 (17) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.61 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.61 (18) op(e2, e3) = all_52_1
% 169.23/25.61 (19) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.61 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.61 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 169.23/25.61 (21) ~ (all_52_7 = e3)
% 169.23/25.61 (22) op(e2, e3) = e2
% 169.23/25.61 (23) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.61 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.61 (24) ~ (e3 = e0)
% 169.23/25.61 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.61 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.61 (26) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.61 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.61 (27) op(e1, e1) = e3
% 169.23/25.61 (28) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.61 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.61 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.61 (29) ~ (all_52_4 = e3)
% 169.23/25.61 (30) ~ (all_10_2 = e1)
% 169.23/25.61 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.61 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.61 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.61 (33) ~ (e2 = e0)
% 169.23/25.61 (34) ~ (all_10_2 = e2)
% 169.23/25.61 (35) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.61 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.61 (36) all_58_3 = e3
% 169.23/25.61 (37) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.61 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.61 (38) ~ (e2 = e1)
% 169.23/25.61 (39) op(e3, e2) = all_52_4
% 169.23/25.61 (40) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.23/25.61 (41) all_54_0 = all_10_2
% 169.23/25.61 (42) op(e0, e2) = all_52_7
% 169.23/25.61 (43) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.23/25.61 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.23/25.61 (44) all_58_4 = e2
% 169.23/25.61 (45) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.61 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.61 (46) op(e1, e3) = e1
% 169.23/25.61 (47) op(e2, e0) = all_52_13
% 169.23/25.61 (48) ~ (e3 = e2)
% 169.23/25.61
% 169.23/25.61 Begin of proof
% 169.23/25.61 |
% 169.23/25.61 | BETA: splitting (20) gives:
% 169.23/25.61 |
% 169.23/25.61 | Case 1:
% 169.23/25.61 | |
% 169.23/25.61 | | (49) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.61 | |
% 169.23/25.61 | | ALPHA: (49) implies:
% 169.23/25.61 | | (50) all_58_0 = e3
% 169.23/25.61 | |
% 169.23/25.61 | | BETA: splitting (15) gives:
% 169.23/25.61 | |
% 169.23/25.61 | | Case 1:
% 169.23/25.61 | | |
% 169.23/25.61 | | | (51) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2)
% 169.23/25.61 | | | = e3)
% 169.23/25.61 | | |
% 169.23/25.61 | | | BETA: splitting (51) gives:
% 169.23/25.61 | | |
% 169.23/25.61 | | | Case 1:
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | (52) all_58_12 = e3 & op(e0, e3) = e3
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | ALPHA: (52) implies:
% 169.23/25.61 | | | | (53) all_58_12 = e3
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | REF_CLOSE: (5), (10), (14), (18), (22), (23), (24), (32), (33), (38),
% 169.23/25.61 | | | | (50), (53) are inconsistent by sub-proof #414.
% 169.23/25.61 | | | |
% 169.23/25.61 | | | Case 2:
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | (54) all_58_13 = e3 & op(e0, e2) = e3
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | REF_CLOSE: (21), (32), (42), (54) are inconsistent by sub-proof #962.
% 169.23/25.61 | | | |
% 169.23/25.61 | | | End of split
% 169.23/25.61 | | |
% 169.23/25.61 | | Case 2:
% 169.23/25.61 | | |
% 169.23/25.61 | | | (55) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0)
% 169.23/25.61 | | | = e3)
% 169.23/25.61 | | |
% 169.23/25.61 | | | BETA: splitting (55) gives:
% 169.23/25.61 | | |
% 169.23/25.61 | | | Case 1:
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | (56) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | ALPHA: (56) implies:
% 169.23/25.61 | | | | (57) all_58_14 = e3
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12),
% 169.23/25.61 | | | | (13), (14), (16), (17), (18), (19), (22), (23), (25), (26),
% 169.23/25.61 | | | | (27), (28), (30), (31), (32), (33), (34), (35), (36), (37),
% 169.23/25.61 | | | | (38), (40), (41), (43), (44), (45), (46), (47), (57) are
% 169.23/25.61 | | | | inconsistent by sub-proof #260.
% 169.23/25.61 | | | |
% 169.23/25.61 | | | Case 2:
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | (58) all_58_15 = e3 & op(e0, e0) = e3
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | ALPHA: (58) implies:
% 169.23/25.61 | | | | (59) all_58_15 = e3
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | REF_CLOSE: (2), (4), (6), (10), (14), (18), (22), (24), (25), (32),
% 169.23/25.61 | | | | (33), (36), (37), (38), (48), (59) are inconsistent by
% 169.23/25.61 | | | | sub-proof #320.
% 169.23/25.61 | | | |
% 169.23/25.61 | | | End of split
% 169.23/25.61 | | |
% 169.23/25.61 | | End of split
% 169.23/25.61 | |
% 169.23/25.61 | Case 2:
% 169.23/25.61 | |
% 169.23/25.61 | | (60) all_58_1 = e3 & op(e3, e2) = e3
% 169.23/25.61 | |
% 169.23/25.61 | | ALPHA: (60) implies:
% 169.23/25.61 | | (61) op(e3, e2) = e3
% 169.23/25.61 | |
% 169.23/25.61 | | REF_CLOSE: (29), (32), (39), (61) are inconsistent by sub-proof #974.
% 169.23/25.61 | |
% 169.23/25.61 | End of split
% 169.23/25.61 |
% 169.23/25.61 End of proof
% 169.23/25.61
% 169.23/25.61 Sub-proof #243 shows that the following formulas are inconsistent:
% 169.23/25.61 ----------------------------------------------------------------
% 169.23/25.61 (1) op(e2, e1) = all_52_9
% 169.23/25.61 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.61 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.61 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.61 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.61 (4) ~ (all_52_9 = e3)
% 169.23/25.61 (5) all_58_7 = e2
% 169.23/25.61 (6) all_58_15 = e2
% 169.23/25.61 (7) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.61 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.61 (8) all_58_2 = e2
% 169.23/25.61 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.61 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.61 (10) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.23/25.61 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.61 (11) ~ (all_6_2 = e3)
% 169.23/25.61 (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.61 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.61 (13) ~ (e3 = e1)
% 169.23/25.61 (14) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.61 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.23/25.61 e1)
% 169.23/25.61 (15) op(e1, e3) = all_52_2
% 169.23/25.61 (16) ~ (e1 = e0)
% 169.23/25.61 (17) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.61 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.61 (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.61 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.61 (19) op(e2, e3) = all_52_1
% 169.23/25.61 (20) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.61 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.61 (21) ~ (all_6_2 = e2)
% 169.23/25.61 (22) op(e1, e1) = all_6_2
% 169.23/25.61 (23) op(e2, e3) = e2
% 169.23/25.61 (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.61 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.61 (25) ~ (e3 = e0)
% 169.23/25.61 (26) all_58_12 = e0
% 169.23/25.61 (27) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.61 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.61 (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.61 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.61 (29) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.61 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.61 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.61 (30) ~ (all_52_4 = e3)
% 169.23/25.61 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.61 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.61 (32) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.23/25.61 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.23/25.61 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.61 (34) ~ (e2 = e0)
% 169.23/25.61 (35) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.61 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.61 (36) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.23/25.61 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.23/25.61 (37) all_58_3 = e3
% 169.23/25.61 (38) op(e3, e3) = e3
% 169.23/25.61 (39) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.61 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.61 (40) ~ (e2 = e1)
% 169.23/25.61 (41) op(e3, e2) = all_52_4
% 169.23/25.61 (42) all_58_4 = e2
% 169.23/25.61 (43) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.61 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.61 (44) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.23/25.61 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.23/25.61 (45) ~ (e3 = e2)
% 169.23/25.61
% 169.23/25.61 Begin of proof
% 169.23/25.61 |
% 169.23/25.61 | BETA: splitting (18) gives:
% 169.23/25.61 |
% 169.23/25.61 | Case 1:
% 169.23/25.61 | |
% 169.23/25.61 | | (46) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 169.23/25.61 | | e3)
% 169.23/25.61 | |
% 169.23/25.61 | | REF_CLOSE: (1), (3), (4), (8), (13), (16), (19), (23), (25), (27), (33),
% 169.23/25.61 | | (34), (37), (39), (40), (42), (45), (46) are inconsistent by
% 169.23/25.61 | | sub-proof #347.
% 169.23/25.61 | |
% 169.23/25.61 | Case 2:
% 169.23/25.61 | |
% 169.23/25.61 | | (47) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 169.23/25.61 | | e3)
% 169.23/25.61 | |
% 169.23/25.61 | | BETA: splitting (47) gives:
% 169.23/25.61 | |
% 169.23/25.61 | | Case 1:
% 169.23/25.61 | | |
% 169.23/25.61 | | | (48) all_58_8 = e3 & op(e1, e1) = e3
% 169.23/25.61 | | |
% 169.23/25.61 | | | REF_CLOSE: (11), (22), (33), (48) are inconsistent by sub-proof #961.
% 169.23/25.61 | | |
% 169.23/25.61 | | Case 2:
% 169.23/25.61 | | |
% 169.23/25.61 | | | (49) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.61 | | |
% 169.23/25.61 | | | ALPHA: (49) implies:
% 169.23/25.61 | | | (50) all_58_14 = e3
% 169.23/25.61 | | |
% 169.23/25.61 | | | BETA: splitting (24) gives:
% 169.23/25.61 | | |
% 169.23/25.61 | | | Case 1:
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | (51) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 169.23/25.61 | | | | = e1)
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | BETA: splitting (51) gives:
% 169.23/25.61 | | | |
% 169.23/25.61 | | | | Case 1:
% 169.23/25.61 | | | | |
% 169.23/25.61 | | | | | (52) all_58_0 = e1 & op(e3, e3) = e1
% 169.23/25.61 | | | | |
% 169.23/25.61 | | | | | ALPHA: (52) implies:
% 169.23/25.61 | | | | | (53) all_58_0 = e1
% 169.23/25.61 | | | | |
% 169.23/25.61 | | | | | BETA: splitting (32) gives:
% 169.23/25.61 | | | | |
% 169.23/25.61 | | | | | Case 1:
% 169.23/25.61 | | | | | |
% 169.23/25.62 | | | | | | (54) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3,
% 169.23/25.62 | | | | | | e2) = e3)
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | | REF_CLOSE: (13), (30), (33), (41), (53), (54) are inconsistent by
% 169.23/25.62 | | | | | | sub-proof #250.
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | Case 2:
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | | (55) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3,
% 169.23/25.62 | | | | | | e0) = e3)
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | | BETA: splitting (55) gives:
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | | Case 1:
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | (56) all_58_4 = e3 & op(e3, e1) = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | ALPHA: (56) implies:
% 169.23/25.62 | | | | | | | (57) all_58_4 = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | REF_CLOSE: (3), (8), (13), (16), (19), (20), (23), (25), (27),
% 169.23/25.62 | | | | | | | (33), (34), (37), (39), (40), (43), (44), (45), (50),
% 169.23/25.62 | | | | | | | (57) are inconsistent by sub-proof #375.
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | Case 2:
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | (58) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | REF_CLOSE: (5), (9), (12), (13), (16), (25), (29), (33), (34),
% 169.23/25.62 | | | | | | | (37), (38), (40), (42), (58) are inconsistent by
% 169.23/25.62 | | | | | | | sub-proof #247.
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | End of split
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | End of split
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | Case 2:
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | (59) all_58_2 = e1 & op(e2, e3) = e1
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | ALPHA: (59) implies:
% 169.23/25.62 | | | | | (60) op(e2, e3) = e1
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | REF_CLOSE: (19), (23), (33), (40), (60) are inconsistent by sub-proof
% 169.23/25.62 | | | | | #784.
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | End of split
% 169.23/25.62 | | | |
% 169.23/25.62 | | | Case 2:
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | (61) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 169.23/25.62 | | | | = e1)
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | BETA: splitting (61) gives:
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | Case 1:
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | (62) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (10), (12), (13), (14), (15),
% 169.23/25.62 | | | | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 169.23/25.62 | | | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 169.23/25.62 | | | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (50),
% 169.23/25.62 | | | | | (62) are inconsistent by sub-proof #244.
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | Case 2:
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | (63) all_58_12 = e1 & op(e0, e3) = e1
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | REF_CLOSE: (16), (26), (63) are inconsistent by sub-proof #773.
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | End of split
% 169.23/25.62 | | | |
% 169.23/25.62 | | | End of split
% 169.23/25.62 | | |
% 169.23/25.62 | | End of split
% 169.23/25.62 | |
% 169.23/25.62 | End of split
% 169.23/25.62 |
% 169.23/25.62 End of proof
% 169.23/25.62
% 169.23/25.62 Sub-proof #244 shows that the following formulas are inconsistent:
% 169.23/25.62 ----------------------------------------------------------------
% 169.23/25.62 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.62 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.62 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.62 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.62 (3) all_58_7 = e2
% 169.23/25.62 (4) all_58_15 = e2
% 169.23/25.62 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.62 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.62 (6) all_58_2 = e2
% 169.23/25.62 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.23/25.62 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.62 (8) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.62 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.62 (9) ~ (e3 = e1)
% 169.23/25.62 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.62 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.23/25.62 e1)
% 169.23/25.62 (11) op(e1, e3) = all_52_2
% 169.23/25.62 (12) ~ (e1 = e0)
% 169.23/25.62 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.62 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.62 (14) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.62 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.62 (15) op(e2, e3) = all_52_1
% 169.23/25.62 (16) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.62 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.62 (17) ~ (all_6_2 = e2)
% 169.23/25.62 (18) op(e1, e1) = all_6_2
% 169.23/25.62 (19) op(e2, e3) = e2
% 169.23/25.62 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.62 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.62 (21) ~ (e3 = e0)
% 169.23/25.62 (22) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.62 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.62 (23) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.62 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.62 (24) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.62 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.62 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.62 (25) all_58_14 = e3
% 169.23/25.62 (26) ~ (all_52_4 = e3)
% 169.23/25.62 (27) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.62 (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.62 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.62 (29) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.23/25.62 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.23/25.62 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.62 (31) ~ (e2 = e0)
% 169.23/25.62 (32) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.62 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.62 (33) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.23/25.62 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.23/25.62 (34) all_58_3 = e3
% 169.23/25.62 (35) op(e3, e3) = e3
% 169.23/25.62 (36) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.62 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.62 (37) ~ (e2 = e1)
% 169.23/25.62 (38) op(e3, e2) = all_52_4
% 169.23/25.62 (39) all_58_4 = e2
% 169.23/25.62 (40) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.62 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.62 (41) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.23/25.62 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.23/25.62 (42) ~ (e3 = e2)
% 169.23/25.62
% 169.23/25.62 Begin of proof
% 169.23/25.62 |
% 169.23/25.62 | ALPHA: (27) implies:
% 169.23/25.62 | (43) all_58_6 = e1
% 169.23/25.62 | (44) op(e1, e3) = e1
% 169.23/25.62 |
% 169.23/25.62 | BETA: splitting (29) gives:
% 169.23/25.62 |
% 169.23/25.62 | Case 1:
% 169.23/25.62 | |
% 169.23/25.62 | | (45) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 169.23/25.62 | | e3)
% 169.23/25.62 | |
% 169.23/25.62 | | BETA: splitting (45) gives:
% 169.23/25.62 | |
% 169.23/25.62 | | Case 1:
% 169.23/25.62 | | |
% 169.23/25.62 | | | (46) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | ALPHA: (46) implies:
% 169.23/25.62 | | | (47) all_58_0 = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | BETA: splitting (5) gives:
% 169.23/25.62 | | |
% 169.23/25.62 | | | Case 1:
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | (48) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 169.23/25.62 | | | | = e0)
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | REF_CLOSE: (15), (19), (21), (30), (31), (35), (48) are inconsistent by
% 169.23/25.62 | | | | sub-proof #460.
% 169.23/25.62 | | | |
% 169.23/25.62 | | | Case 2:
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | (49) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 169.23/25.62 | | | | = e0)
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | BETA: splitting (49) gives:
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | Case 1:
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | (50) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | ALPHA: (50) implies:
% 169.23/25.62 | | | | | (51) op(e1, e3) = e0
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | REF_CLOSE: (11), (12), (30), (44), (51) are inconsistent by sub-proof
% 169.23/25.62 | | | | | #749.
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | Case 2:
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | (52) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | ALPHA: (52) implies:
% 169.23/25.62 | | | | | (53) all_58_12 = e0
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | BETA: splitting (33) gives:
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | Case 1:
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | | (54) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 169.23/25.62 | | | | | | e2) = e3)
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | | BETA: splitting (54) gives:
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | | Case 1:
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | (55) all_58_6 = e3 & op(e1, e3) = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | ALPHA: (55) implies:
% 169.23/25.62 | | | | | | | (56) all_58_6 = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | REF_CLOSE: (5), (6), (9), (12), (13), (15), (19), (20), (21),
% 169.23/25.62 | | | | | | | (30), (31), (37), (42), (47), (53), (56) are
% 169.23/25.62 | | | | | | | inconsistent by sub-proof #454.
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | Case 2:
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | (57) all_58_7 = e3 & op(e1, e2) = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | ALPHA: (57) implies:
% 169.23/25.62 | | | | | | | (58) all_58_7 = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | COMBINE_EQS: (3), (58) imply:
% 169.23/25.62 | | | | | | | (59) e3 = e2
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | SIMP: (59) implies:
% 169.23/25.62 | | | | | | | (60) e3 = e2
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | COMBINE_EQS: (47), (60) imply:
% 169.23/25.62 | | | | | | | (61) all_58_0 = e2
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | REF_CLOSE: (2), (6), (9), (12), (13), (15), (19), (21), (22),
% 169.23/25.62 | | | | | | | (30), (31), (34), (36), (37), (42), (43), (53), (61)
% 169.23/25.62 | | | | | | | are inconsistent by sub-proof #245.
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | End of split
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | Case 2:
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | | (62) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 169.23/25.62 | | | | | | e0) = e3)
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | | BETA: splitting (62) gives:
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | | Case 1:
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | (63) all_58_8 = e3 & op(e1, e1) = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | ALPHA: (63) implies:
% 169.23/25.62 | | | | | | | (64) all_58_8 = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | REF_CLOSE: (9), (12), (16), (21), (25), (31), (37), (39), (40),
% 169.23/25.62 | | | | | | | (64) are inconsistent by sub-proof #422.
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | Case 2:
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | (65) all_58_11 = e3 & op(e1, e0) = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | ALPHA: (65) implies:
% 169.23/25.62 | | | | | | | (66) all_58_11 = e3
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | BETA: splitting (40) gives:
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | | Case 1:
% 169.23/25.62 | | | | | | | |
% 169.23/25.62 | | | | | | | | (67) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 &
% 169.23/25.62 | | | | | | | | op(e2, e1) = e1)
% 169.23/25.62 | | | | | | | |
% 169.23/25.62 | | | | | | | | BETA: splitting (67) gives:
% 169.23/25.62 | | | | | | | |
% 169.23/25.62 | | | | | | | | Case 1:
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | (68) all_58_4 = e1 & op(e3, e1) = e1
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | ALPHA: (68) implies:
% 169.23/25.62 | | | | | | | | | (69) all_58_4 = e1
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | REF_CLOSE: (2), (6), (9), (12), (15), (17), (18), (19), (21),
% 169.23/25.62 | | | | | | | | | (22), (25), (30), (31), (34), (36), (37), (41),
% 169.23/25.62 | | | | | | | | | (42), (69) are inconsistent by sub-proof #408.
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | Case 2:
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | (70) all_58_5 = e1 & op(e2, e1) = e1
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | ALPHA: (70) implies:
% 169.23/25.62 | | | | | | | | | (71) all_58_5 = e1
% 169.23/25.62 | | | | | | | | | (72) op(e2, e1) = e1
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11),
% 169.23/25.62 | | | | | | | | | (12), (13), (14), (15), (16), (19), (20), (21),
% 169.23/25.62 | | | | | | | | | (22), (23), (24), (25), (30), (31), (32), (34),
% 169.23/25.62 | | | | | | | | | (35), (36), (37), (39), (42), (44), (47), (66),
% 169.23/25.62 | | | | | | | | | (71), (72) are inconsistent by sub-proof #261.
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | End of split
% 169.23/25.62 | | | | | | | |
% 169.23/25.62 | | | | | | | Case 2:
% 169.23/25.62 | | | | | | | |
% 169.23/25.62 | | | | | | | | (73) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 169.23/25.62 | | | | | | | | op(e0, e1) = e1)
% 169.23/25.62 | | | | | | | |
% 169.23/25.62 | | | | | | | | BETA: splitting (73) gives:
% 169.23/25.62 | | | | | | | |
% 169.23/25.62 | | | | | | | | Case 1:
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | (74) all_58_8 = e1 & op(e1, e1) = e1
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | ALPHA: (74) implies:
% 169.23/25.62 | | | | | | | | | (75) all_58_8 = e1
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | BETA: splitting (23) gives:
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | Case 1:
% 169.23/25.62 | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | (76) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 169.23/25.62 | | | | | | | | | | op(e1, e2) = e0)
% 169.23/25.62 | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | BETA: splitting (76) gives:
% 169.23/25.62 | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | Case 1:
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | | (77) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | | REF_CLOSE: (12), (43), (77) are inconsistent by sub-proof
% 169.23/25.62 | | | | | | | | | | | #457.
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | Case 2:
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | | (78) all_58_7 = e0 & op(e1, e2) = e0
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | | REF_CLOSE: (3), (31), (78) are inconsistent by sub-proof
% 169.23/25.62 | | | | | | | | | | | #363.
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | End of split
% 169.23/25.62 | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | Case 2:
% 169.23/25.62 | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | (79) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0
% 169.23/25.62 | | | | | | | | | | & op(e1, e0) = e0)
% 169.23/25.62 | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | BETA: splitting (79) gives:
% 169.23/25.62 | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | Case 1:
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | | (80) all_58_8 = e0 & op(e1, e1) = e0
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | | REF_CLOSE: (12), (75), (80) are inconsistent by sub-proof
% 169.23/25.62 | | | | | | | | | | | #718.
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | Case 2:
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | | (81) all_58_11 = e0 & op(e1, e0) = e0
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | | REF_CLOSE: (21), (66), (81) are inconsistent by sub-proof
% 169.23/25.62 | | | | | | | | | | | #724.
% 169.23/25.62 | | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | | End of split
% 169.23/25.62 | | | | | | | | | |
% 169.23/25.62 | | | | | | | | | End of split
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | Case 2:
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | (82) all_58_14 = e1 & op(e0, e1) = e1
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | ALPHA: (82) implies:
% 169.23/25.62 | | | | | | | | | (83) all_58_14 = e1
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | COMBINE_EQS: (25), (83) imply:
% 169.23/25.62 | | | | | | | | | (84) e3 = e1
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | COMBINE_EQS: (47), (84) imply:
% 169.23/25.62 | | | | | | | | | (85) all_58_0 = e1
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | | REF_CLOSE: (6), (9), (13), (21), (42), (43), (53), (85) are
% 169.23/25.62 | | | | | | | | | inconsistent by sub-proof #456.
% 169.23/25.62 | | | | | | | | |
% 169.23/25.62 | | | | | | | | End of split
% 169.23/25.62 | | | | | | | |
% 169.23/25.62 | | | | | | | End of split
% 169.23/25.62 | | | | | | |
% 169.23/25.62 | | | | | | End of split
% 169.23/25.62 | | | | | |
% 169.23/25.62 | | | | | End of split
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | End of split
% 169.23/25.62 | | | |
% 169.23/25.62 | | | End of split
% 169.23/25.62 | | |
% 169.23/25.62 | | Case 2:
% 169.23/25.62 | | |
% 169.23/25.62 | | | (86) all_58_1 = e3 & op(e3, e2) = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | ALPHA: (86) implies:
% 169.23/25.62 | | | (87) op(e3, e2) = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | REF_CLOSE: (26), (30), (38), (87) are inconsistent by sub-proof #974.
% 169.23/25.62 | | |
% 169.23/25.62 | | End of split
% 169.23/25.62 | |
% 169.23/25.62 | Case 2:
% 169.23/25.62 | |
% 169.23/25.62 | | (88) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 169.23/25.62 | | e3)
% 169.23/25.62 | |
% 169.23/25.62 | | BETA: splitting (88) gives:
% 169.23/25.62 | |
% 169.23/25.62 | | Case 1:
% 169.23/25.62 | | |
% 169.23/25.62 | | | (89) all_58_4 = e3 & op(e3, e1) = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | ALPHA: (89) implies:
% 169.23/25.62 | | | (90) all_58_4 = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | REF_CLOSE: (2), (6), (9), (12), (15), (16), (19), (21), (22), (25), (30),
% 169.23/25.62 | | | (31), (34), (36), (37), (40), (41), (42), (90) are inconsistent
% 169.23/25.62 | | | by sub-proof #375.
% 169.23/25.62 | | |
% 169.23/25.62 | | Case 2:
% 169.23/25.62 | | |
% 169.23/25.62 | | | (91) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | ALPHA: (91) implies:
% 169.23/25.62 | | | (92) all_58_9 = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | REF_CLOSE: (4), (5), (6), (8), (9), (10), (11), (12), (13), (15), (19),
% 169.23/25.62 | | | (20), (21), (24), (25), (28), (30), (31), (35), (37), (39),
% 169.23/25.62 | | | (42), (44), (92) are inconsistent by sub-proof #262.
% 169.23/25.62 | | |
% 169.23/25.62 | | End of split
% 169.23/25.62 | |
% 169.23/25.62 | End of split
% 169.23/25.62 |
% 169.23/25.62 End of proof
% 169.23/25.62
% 169.23/25.62 Sub-proof #245 shows that the following formulas are inconsistent:
% 169.23/25.62 ----------------------------------------------------------------
% 169.23/25.62 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.62 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.62 (2) all_58_2 = e2
% 169.23/25.62 (3) all_58_6 = e1
% 169.23/25.62 (4) ~ (e3 = e1)
% 169.23/25.62 (5) ~ (e1 = e0)
% 169.23/25.62 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.62 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.62 (7) op(e2, e3) = all_52_1
% 169.23/25.62 (8) op(e2, e3) = e2
% 169.23/25.62 (9) ~ (e3 = e0)
% 169.23/25.62 (10) all_58_12 = e0
% 169.23/25.62 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.62 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.62 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.62 (13) ~ (e2 = e0)
% 169.23/25.62 (14) all_58_0 = e2
% 169.23/25.62 (15) all_58_3 = e3
% 169.23/25.62 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.62 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.62 (17) ~ (e2 = e1)
% 169.23/25.62 (18) ~ (e3 = e2)
% 169.23/25.62
% 169.23/25.62 Begin of proof
% 169.23/25.62 |
% 169.23/25.62 | BETA: splitting (6) gives:
% 169.23/25.62 |
% 169.23/25.62 | Case 1:
% 169.23/25.62 | |
% 169.23/25.62 | | (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 169.23/25.62 | | e3)
% 169.23/25.62 | |
% 169.23/25.62 | | BETA: splitting (19) gives:
% 169.23/25.62 | |
% 169.23/25.62 | | Case 1:
% 169.23/25.62 | | |
% 169.23/25.62 | | | (20) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | ALPHA: (20) implies:
% 169.23/25.62 | | | (21) all_58_0 = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | COMBINE_EQS: (14), (21) imply:
% 169.23/25.62 | | | (22) e3 = e2
% 169.23/25.62 | | |
% 169.23/25.62 | | | SIMP: (22) implies:
% 169.23/25.62 | | | (23) e3 = e2
% 169.23/25.62 | | |
% 169.23/25.62 | | | COMBINE_EQS: (15), (23) imply:
% 169.23/25.62 | | | (24) all_58_3 = e2
% 169.23/25.62 | | |
% 169.23/25.62 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (11), (12), (13), (16),
% 169.23/25.62 | | | (17), (18), (24) are inconsistent by sub-proof #779.
% 169.23/25.62 | | |
% 169.23/25.62 | | Case 2:
% 169.23/25.62 | | |
% 169.23/25.62 | | | (25) all_58_2 = e3 & op(e2, e3) = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | ALPHA: (25) implies:
% 169.23/25.62 | | | (26) op(e2, e3) = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | REF_CLOSE: (7), (8), (12), (18), (26) are inconsistent by sub-proof #462.
% 169.23/25.62 | | |
% 169.23/25.62 | | End of split
% 169.23/25.62 | |
% 169.23/25.62 | Case 2:
% 169.23/25.62 | |
% 169.23/25.62 | | (27) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 169.23/25.62 | | e3)
% 169.23/25.62 | |
% 169.23/25.62 | | BETA: splitting (27) gives:
% 169.23/25.62 | |
% 169.23/25.62 | | Case 1:
% 169.23/25.62 | | |
% 169.23/25.62 | | | (28) all_58_6 = e3 & op(e1, e3) = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | REF_CLOSE: (3), (4), (28) are inconsistent by sub-proof #246.
% 169.23/25.62 | | |
% 169.23/25.62 | | Case 2:
% 169.23/25.62 | | |
% 169.23/25.62 | | | (29) all_58_12 = e3 & op(e0, e3) = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | ALPHA: (29) implies:
% 169.23/25.62 | | | (30) all_58_12 = e3
% 169.23/25.62 | | |
% 169.23/25.62 | | | REF_CLOSE: (9), (10), (30) are inconsistent by sub-proof #608.
% 169.23/25.62 | | |
% 169.23/25.62 | | End of split
% 169.23/25.62 | |
% 169.23/25.62 | End of split
% 169.23/25.62 |
% 169.23/25.62 End of proof
% 169.23/25.62
% 169.23/25.62 Sub-proof #246 shows that the following formulas are inconsistent:
% 169.23/25.62 ----------------------------------------------------------------
% 169.23/25.62 (1) all_58_6 = e3 & op(e1, e3) = e3
% 169.23/25.62 (2) all_58_6 = e1
% 169.23/25.62 (3) ~ (e3 = e1)
% 169.23/25.62
% 169.23/25.62 Begin of proof
% 169.23/25.62 |
% 169.23/25.62 | ALPHA: (1) implies:
% 169.23/25.62 | (4) all_58_6 = e3
% 169.23/25.62 |
% 169.23/25.62 | COMBINE_EQS: (2), (4) imply:
% 169.23/25.62 | (5) e3 = e1
% 169.23/25.62 |
% 169.23/25.62 | REDUCE: (3), (5) imply:
% 169.23/25.62 | (6) $false
% 169.23/25.62 |
% 169.23/25.62 | CLOSE: (6) is inconsistent.
% 169.23/25.62 |
% 169.23/25.62 End of proof
% 169.23/25.62
% 169.23/25.62 Sub-proof #247 shows that the following formulas are inconsistent:
% 169.23/25.62 ----------------------------------------------------------------
% 169.23/25.62 (1) all_58_7 = e2
% 169.23/25.62 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.62 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.62 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.62 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.62 (4) ~ (e3 = e1)
% 169.23/25.62 (5) ~ (e1 = e0)
% 169.23/25.62 (6) ~ (e3 = e0)
% 169.23/25.62 (7) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) = all_22_1
% 169.23/25.62 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2) =
% 169.23/25.62 all_22_1 & $i(all_22_1))
% 169.23/25.62 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.62 (9) ~ (e2 = e0)
% 169.23/25.62 (10) all_58_3 = e3
% 169.23/25.62 (11) op(e3, e3) = e3
% 169.23/25.62 (12) ~ (e2 = e1)
% 169.23/25.62 (13) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.62 (14) all_58_4 = e2
% 169.23/25.62
% 169.23/25.62 Begin of proof
% 169.23/25.62 |
% 169.23/25.62 | ALPHA: (13) implies:
% 169.23/25.62 | (15) all_58_9 = e3
% 169.23/25.62 |
% 169.23/25.62 | BETA: splitting (2) gives:
% 169.23/25.62 |
% 169.23/25.62 | Case 1:
% 169.23/25.62 | |
% 169.23/25.62 | | (16) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.23/25.62 | | e1)
% 169.23/25.62 | |
% 169.23/25.62 | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (14), (15), (16) are
% 169.23/25.62 | | inconsistent by sub-proof #248.
% 169.23/25.62 | |
% 169.23/25.62 | Case 2:
% 169.23/25.62 | |
% 169.23/25.62 | | (17) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.23/25.62 | | e1)
% 169.23/25.62 | |
% 169.23/25.62 | | BETA: splitting (17) gives:
% 169.23/25.62 | |
% 169.23/25.62 | | Case 1:
% 169.23/25.62 | | |
% 169.23/25.62 | | | (18) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.62 | | |
% 169.23/25.62 | | | REF_CLOSE: (1), (12), (18) are inconsistent by sub-proof #503.
% 169.23/25.62 | | |
% 169.23/25.62 | | Case 2:
% 169.23/25.62 | | |
% 169.23/25.62 | | | (19) all_58_13 = e1 & op(e0, e2) = e1
% 169.23/25.62 | | |
% 169.23/25.62 | | | ALPHA: (19) implies:
% 169.23/25.62 | | | (20) op(e0, e2) = e1
% 169.23/25.62 | | |
% 169.23/25.62 | | | BETA: splitting (3) gives:
% 169.23/25.62 | | |
% 169.23/25.62 | | | Case 1:
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | (21) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 169.23/25.62 | | | | = e0)
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | REF_CLOSE: (6), (7), (8), (11), (20), (21) are inconsistent by sub-proof
% 169.23/25.62 | | | | #295.
% 169.23/25.62 | | | |
% 169.23/25.62 | | | Case 2:
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | (22) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 169.23/25.62 | | | | = e0)
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | BETA: splitting (22) gives:
% 169.23/25.62 | | | |
% 169.23/25.62 | | | | Case 1:
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | (23) all_58_4 = e0 & op(e3, e1) = e0
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | REF_CLOSE: (9), (14), (23) are inconsistent by sub-proof #902.
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | Case 2:
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | (24) all_58_9 = e0 & op(e3, e0) = e0
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | | REF_CLOSE: (6), (15), (24) are inconsistent by sub-proof #901.
% 169.23/25.62 | | | | |
% 169.23/25.62 | | | | End of split
% 169.23/25.62 | | | |
% 169.23/25.62 | | | End of split
% 169.23/25.62 | | |
% 169.23/25.62 | | End of split
% 169.23/25.62 | |
% 169.23/25.62 | End of split
% 169.23/25.62 |
% 169.23/25.62 End of proof
% 169.23/25.62
% 169.23/25.62 Sub-proof #248 shows that the following formulas are inconsistent:
% 169.23/25.62 ----------------------------------------------------------------
% 169.23/25.62 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 169.23/25.62 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.62 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.62 (3) ~ (e3 = e1)
% 169.23/25.62 (4) ~ (e1 = e0)
% 169.23/25.62 (5) ~ (e3 = e0)
% 169.23/25.63 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.63 (7) ~ (e2 = e0)
% 169.23/25.63 (8) all_58_3 = e3
% 169.23/25.63 (9) op(e3, e3) = e3
% 169.23/25.63 (10) all_58_9 = e3
% 169.23/25.63 (11) all_58_4 = e2
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | BETA: splitting (1) gives:
% 169.23/25.63 |
% 169.23/25.63 | Case 1:
% 169.23/25.63 | |
% 169.23/25.63 | | (12) all_58_1 = e1 & op(e3, e2) = e1
% 169.23/25.63 | |
% 169.23/25.63 | | ALPHA: (12) implies:
% 169.23/25.63 | | (13) all_58_1 = e1
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (11), (13) are inconsistent
% 169.23/25.63 | | by sub-proof #249.
% 169.23/25.63 | |
% 169.23/25.63 | Case 2:
% 169.23/25.63 | |
% 169.23/25.63 | | (14) all_58_3 = e1 & op(e2, e2) = e1
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (3), (8), (14) are inconsistent by sub-proof #868.
% 169.23/25.63 | |
% 169.23/25.63 | End of split
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #249 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) all_58_1 = e1
% 169.23/25.63 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.63 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.63 (3) ~ (e1 = e0)
% 169.23/25.63 (4) ~ (e3 = e0)
% 169.23/25.63 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.63 (6) ~ (e2 = e0)
% 169.23/25.63 (7) op(e3, e3) = e3
% 169.23/25.63 (8) all_58_9 = e3
% 169.23/25.63 (9) all_58_4 = e2
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | BETA: splitting (2) gives:
% 169.23/25.63 |
% 169.23/25.63 | Case 1:
% 169.23/25.63 | |
% 169.23/25.63 | | (10) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 169.23/25.63 | | e0)
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (1), (3), (4), (5), (7), (10) are inconsistent by sub-proof #947.
% 169.23/25.63 | |
% 169.23/25.63 | Case 2:
% 169.23/25.63 | |
% 169.23/25.63 | | (11) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 169.23/25.63 | | e0)
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (4), (6), (8), (9), (11) are inconsistent by sub-proof #511.
% 169.23/25.63 | |
% 169.23/25.63 | End of split
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #250 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) all_58_0 = e1
% 169.23/25.63 (2) ~ (e3 = e1)
% 169.23/25.63 (3) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 169.23/25.63 (4) ~ (all_52_4 = e3)
% 169.23/25.63 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.63 (6) op(e3, e2) = all_52_4
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | BETA: splitting (3) gives:
% 169.23/25.63 |
% 169.23/25.63 | Case 1:
% 169.23/25.63 | |
% 169.23/25.63 | | (7) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #905.
% 169.23/25.63 | |
% 169.23/25.63 | Case 2:
% 169.23/25.63 | |
% 169.23/25.63 | | (8) all_58_1 = e3 & op(e3, e2) = e3
% 169.23/25.63 | |
% 169.23/25.63 | | ALPHA: (8) implies:
% 169.23/25.63 | | (9) op(e3, e2) = e3
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #974.
% 169.23/25.63 | |
% 169.23/25.63 | End of split
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #251 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) op(e2, e1) = all_52_9
% 169.23/25.63 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.63 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.63 (3) all_58_14 = e2
% 169.23/25.63 (4) ~ (all_52_9 = e3)
% 169.23/25.63 (5) all_58_2 = e2
% 169.23/25.63 (6) ~ (e3 = e1)
% 169.23/25.63 (7) ~ (e1 = e0)
% 169.23/25.63 (8) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.63 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.63 (9) op(e2, e3) = all_52_1
% 169.23/25.63 (10) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.63 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.63 (11) op(e2, e3) = e2
% 169.23/25.63 (12) ~ (e3 = e0)
% 169.23/25.63 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.63 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.63 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.63 (15) ~ (e2 = e0)
% 169.23/25.63 (16) all_58_3 = e3
% 169.23/25.63 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.63 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.63 (18) ~ (e2 = e1)
% 169.23/25.63 (19) op(e0, e1) = e2
% 169.23/25.63 (20) all_58_4 = e2
% 169.23/25.63 (21) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.63 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.63 (22) ~ (e3 = e2)
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | BETA: splitting (8) gives:
% 169.23/25.63 |
% 169.23/25.63 | Case 1:
% 169.23/25.63 | |
% 169.23/25.63 | | (23) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 169.23/25.63 | | e3)
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (12), (13), (14), (15),
% 169.23/25.63 | | (16), (17), (18), (20), (22), (23) are inconsistent by sub-proof
% 169.23/25.63 | | #347.
% 169.23/25.63 | |
% 169.23/25.63 | Case 2:
% 169.23/25.63 | |
% 169.23/25.63 | | (24) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 169.23/25.63 | | e3)
% 169.23/25.63 | |
% 169.23/25.63 | | BETA: splitting (24) gives:
% 169.23/25.63 | |
% 169.23/25.63 | | Case 1:
% 169.23/25.63 | | |
% 169.23/25.63 | | | (25) all_58_8 = e3 & op(e1, e1) = e3
% 169.23/25.63 | | |
% 169.23/25.63 | | | ALPHA: (25) implies:
% 169.23/25.63 | | | (26) all_58_8 = e3
% 169.23/25.63 | | |
% 169.23/25.63 | | | BETA: splitting (21) gives:
% 169.23/25.63 | | |
% 169.23/25.63 | | | Case 1:
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | (27) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 169.23/25.63 | | | | = e1)
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | BETA: splitting (27) gives:
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | Case 1:
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | (28) all_58_4 = e1 & op(e3, e1) = e1
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | REF_CLOSE: (18), (20), (28) are inconsistent by sub-proof #510.
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | Case 2:
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | (29) all_58_5 = e1 & op(e2, e1) = e1
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | ALPHA: (29) implies:
% 169.23/25.63 | | | | | (30) all_58_5 = e1
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | REF_CLOSE: (3), (6), (7), (8), (10), (12), (15), (20), (22), (30) are
% 169.23/25.63 | | | | | inconsistent by sub-proof #321.
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | End of split
% 169.23/25.63 | | | |
% 169.23/25.63 | | | Case 2:
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | (31) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 169.23/25.63 | | | | = e1)
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | BETA: splitting (31) gives:
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | Case 1:
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | (32) all_58_8 = e1 & op(e1, e1) = e1
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | REF_CLOSE: (6), (26), (32) are inconsistent by sub-proof #478.
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | Case 2:
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | (33) all_58_14 = e1 & op(e0, e1) = e1
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | ALPHA: (33) implies:
% 169.23/25.63 | | | | | (34) op(e0, e1) = e1
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | REF_CLOSE: (14), (18), (19), (34) are inconsistent by sub-proof #967.
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | End of split
% 169.23/25.63 | | | |
% 169.23/25.63 | | | End of split
% 169.23/25.63 | | |
% 169.23/25.63 | | Case 2:
% 169.23/25.63 | | |
% 169.23/25.63 | | | (35) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.63 | | |
% 169.23/25.63 | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (11), (12), (13), (14), (15),
% 169.23/25.63 | | | (16), (17), (18), (22), (35) are inconsistent by sub-proof
% 169.23/25.63 | | | #405.
% 169.23/25.63 | | |
% 169.23/25.63 | | End of split
% 169.23/25.63 | |
% 169.23/25.63 | End of split
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #252 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.63 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.63 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.63 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.63 (3) all_58_2 = e2
% 169.23/25.63 (4) ~ (e3 = e1)
% 169.23/25.63 (5) ~ (e1 = e0)
% 169.23/25.63 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.63 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.63 (7) op(e2, e3) = all_52_1
% 169.23/25.63 (8) op(e2, e3) = e2
% 169.23/25.63 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.63 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.63 (10) ~ (e3 = e0)
% 169.23/25.63 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.63 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.63 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.63 (13) ~ (e2 = e0)
% 169.23/25.63 (14) all_58_3 = e3
% 169.23/25.63 (15) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.63 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.63 (16) ~ (e2 = e1)
% 169.23/25.63 (17) all_58_6 = e2 & op(e1, e3) = e2
% 169.23/25.63 (18) ~ (e3 = e2)
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | ALPHA: (17) implies:
% 169.23/25.63 | (19) all_58_6 = e2
% 169.23/25.63 |
% 169.23/25.63 | BETA: splitting (9) gives:
% 169.23/25.63 |
% 169.23/25.63 | Case 1:
% 169.23/25.63 | |
% 169.23/25.63 | | (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 169.23/25.63 | | e1)
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 169.23/25.63 | | (14), (15), (16), (18), (19), (20) are inconsistent by sub-proof
% 169.23/25.63 | | #279.
% 169.23/25.63 | |
% 169.23/25.63 | Case 2:
% 169.23/25.63 | |
% 169.23/25.63 | | (21) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 169.23/25.63 | | e1)
% 169.23/25.63 | |
% 169.23/25.63 | | BETA: splitting (21) gives:
% 169.23/25.63 | |
% 169.23/25.63 | | Case 1:
% 169.23/25.63 | | |
% 169.23/25.63 | | | (22) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.63 | | |
% 169.23/25.63 | | | ALPHA: (22) implies:
% 169.23/25.63 | | | (23) all_58_6 = e1
% 169.23/25.63 | | |
% 169.23/25.63 | | | REF_CLOSE: (16), (19), (23) are inconsistent by sub-proof #823.
% 169.23/25.63 | | |
% 169.23/25.63 | | Case 2:
% 169.23/25.63 | | |
% 169.23/25.63 | | | (24) all_58_12 = e1 & op(e0, e3) = e1
% 169.23/25.63 | | |
% 169.23/25.63 | | | ALPHA: (24) implies:
% 169.23/25.63 | | | (25) all_58_12 = e1
% 169.23/25.63 | | |
% 169.23/25.63 | | | BETA: splitting (6) gives:
% 169.23/25.63 | | |
% 169.23/25.63 | | | Case 1:
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | (26) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 169.23/25.63 | | | | = e3)
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | BETA: splitting (26) gives:
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | Case 1:
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | (27) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | ALPHA: (27) implies:
% 169.23/25.63 | | | | | (28) all_58_0 = e3
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | REF_CLOSE: (2), (5), (7), (8), (10), (12), (13), (19), (25), (28) are
% 169.23/25.63 | | | | | inconsistent by sub-proof #275.
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | Case 2:
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | (29) all_58_2 = e3 & op(e2, e3) = e3
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | ALPHA: (29) implies:
% 169.23/25.63 | | | | | (30) op(e2, e3) = e3
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | | REF_CLOSE: (7), (8), (12), (18), (30) are inconsistent by sub-proof
% 169.23/25.63 | | | | | #462.
% 169.23/25.63 | | | | |
% 169.23/25.63 | | | | End of split
% 169.23/25.63 | | | |
% 169.23/25.63 | | | Case 2:
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | (31) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 169.23/25.63 | | | | = e3)
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 169.23/25.63 | | | | (13), (14), (15), (16), (18), (19), (31) are inconsistent by
% 169.23/25.63 | | | | sub-proof #274.
% 169.23/25.63 | | | |
% 169.23/25.63 | | | End of split
% 169.23/25.63 | | |
% 169.23/25.63 | | End of split
% 169.23/25.63 | |
% 169.23/25.63 | End of split
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #253 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) all_54_2 = e1 | all_54_2 = e0
% 169.23/25.63 (2) all_54_2 = all_52_8
% 169.23/25.63 (3) ~ (all_52_8 = e1)
% 169.23/25.63 (4) ~ (all_52_8 = e0)
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | BETA: splitting (1) gives:
% 169.23/25.63 |
% 169.23/25.63 | Case 1:
% 169.23/25.63 | |
% 169.23/25.63 | | (5) all_54_2 = e1
% 169.23/25.63 | |
% 169.23/25.63 | | COMBINE_EQS: (2), (5) imply:
% 169.23/25.63 | | (6) all_52_8 = e1
% 169.23/25.63 | |
% 169.23/25.63 | | REDUCE: (3), (6) imply:
% 169.23/25.63 | | (7) $false
% 169.23/25.63 | |
% 169.23/25.63 | | CLOSE: (7) is inconsistent.
% 169.23/25.63 | |
% 169.23/25.63 | Case 2:
% 169.23/25.63 | |
% 169.23/25.63 | | (8) all_54_2 = e0
% 169.23/25.63 | |
% 169.23/25.63 | | COMBINE_EQS: (2), (8) imply:
% 169.23/25.63 | | (9) all_52_8 = e0
% 169.23/25.63 | |
% 169.23/25.63 | | REDUCE: (4), (9) imply:
% 169.23/25.63 | | (10) $false
% 169.23/25.63 | |
% 169.23/25.63 | | CLOSE: (10) is inconsistent.
% 169.23/25.63 | |
% 169.23/25.63 | End of split
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #254 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.63 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.63 (2) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 169.23/25.63 (3) all_58_2 = e2
% 169.23/25.63 (4) ~ (all_52_6 = all_52_7)
% 169.23/25.63 (5) op(e2, e3) = all_52_1
% 169.23/25.63 (6) op(e3, e1) = e3
% 169.23/25.63 (7) ~ (all_52_7 = e3)
% 169.23/25.63 (8) op(e2, e3) = e2
% 169.23/25.63 (9) ~ (e3 = e0)
% 169.23/25.63 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.63 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.63 (11) ( ~ (all_28_0 = e0) & op(all_28_1, e1) = all_28_0 & op(e3, e1) =
% 169.23/25.63 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e3,
% 169.23/25.63 e1) = all_28_1 & $i(all_28_1))
% 169.23/25.63 (12) all_54_9 = e1 | all_54_9 = e0
% 169.23/25.63 (13) ~ (all_52_7 = e0)
% 169.23/25.63 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.63 (15) ~ (all_52_6 = e0)
% 169.23/25.63 (16) all_58_3 = e3
% 169.23/25.63 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.63 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.63 (18) all_54_9 = all_52_6
% 169.23/25.63 (19) ~ (all_52_6 = e3)
% 169.23/25.63 (20) all_54_13 = all_52_7
% 169.23/25.63 (21) op(e3, e1) = all_36_1
% 169.23/25.63 (22) op(e3, e1) = e2
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | BETA: splitting (12) gives:
% 169.23/25.63 |
% 169.23/25.63 | Case 1:
% 169.23/25.63 | |
% 169.23/25.63 | | (23) all_54_9 = e1
% 169.23/25.63 | |
% 169.23/25.63 | | COMBINE_EQS: (18), (23) imply:
% 169.23/25.63 | | (24) all_52_6 = e1
% 169.23/25.63 | |
% 169.23/25.63 | | SIMP: (24) implies:
% 169.23/25.63 | | (25) all_52_6 = e1
% 169.23/25.63 | |
% 169.23/25.63 | | REDUCE: (4), (25) imply:
% 169.23/25.63 | | (26) ~ (all_52_7 = e1)
% 169.23/25.63 | |
% 169.23/25.63 | | SIMP: (26) implies:
% 169.23/25.63 | | (27) ~ (all_52_7 = e1)
% 169.23/25.63 | |
% 169.23/25.63 | | REDUCE: (19), (25) imply:
% 169.23/25.63 | | (28) ~ (e3 = e1)
% 169.23/25.63 | |
% 169.23/25.63 | | SIMP: (28) implies:
% 169.23/25.63 | | (29) ~ (e3 = e1)
% 169.23/25.63 | |
% 169.23/25.63 | | REDUCE: (15), (25) imply:
% 169.23/25.63 | | (30) ~ (e1 = e0)
% 169.23/25.63 | |
% 169.23/25.63 | | BETA: splitting (2) gives:
% 169.23/25.63 | |
% 169.23/25.63 | | Case 1:
% 169.23/25.63 | | |
% 169.23/25.63 | | | (31) all_54_13 = e3
% 169.23/25.63 | | |
% 169.23/25.63 | | | REF_CLOSE: (7), (20), (31) are inconsistent by sub-proof #971.
% 169.23/25.63 | | |
% 169.23/25.63 | | Case 2:
% 169.23/25.63 | | |
% 169.23/25.63 | | | (32) ~ (all_54_13 = e3)
% 169.23/25.63 | | | (33) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 169.23/25.63 | | |
% 169.23/25.63 | | | BETA: splitting (11) gives:
% 169.23/25.63 | | |
% 169.23/25.63 | | | Case 1:
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | (34) ~ (all_28_0 = e0) & op(all_28_1, e1) = all_28_0 & op(e3, e1) =
% 169.23/25.63 | | | | all_28_1 & $i(all_28_0) & $i(all_28_1)
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | ALPHA: (34) implies:
% 169.23/25.63 | | | | (35) op(e3, e1) = all_28_1
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (13), (14), (16),
% 169.23/25.63 | | | | (17), (20), (21), (22), (27), (29), (30), (33), (35) are
% 169.23/25.63 | | | | inconsistent by sub-proof #255.
% 169.23/25.63 | | | |
% 169.23/25.63 | | | Case 2:
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | (36) ~ (all_28_1 = e2) & op(e3, e1) = all_28_1 & $i(all_28_1)
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | ALPHA: (36) implies:
% 169.23/25.63 | | | | (37) op(e3, e1) = all_28_1
% 169.23/25.63 | | | |
% 169.23/25.63 | | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (13), (14), (16),
% 169.23/25.63 | | | | (17), (20), (21), (22), (27), (29), (30), (33), (37) are
% 169.23/25.63 | | | | inconsistent by sub-proof #255.
% 169.23/25.63 | | | |
% 169.23/25.63 | | | End of split
% 169.23/25.63 | | |
% 169.23/25.63 | | End of split
% 169.23/25.63 | |
% 169.23/25.63 | Case 2:
% 169.23/25.63 | |
% 169.23/25.63 | | (38) all_54_9 = e0
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (15), (18), (38) are inconsistent by sub-proof #601.
% 169.23/25.63 | |
% 169.23/25.63 | End of split
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #255 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.63 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.63 (2) all_58_2 = e2
% 169.23/25.63 (3) ~ (e3 = e1)
% 169.23/25.63 (4) ~ (e1 = e0)
% 169.23/25.63 (5) op(e2, e3) = all_52_1
% 169.23/25.63 (6) op(e3, e1) = e3
% 169.23/25.63 (7) ~ (all_52_7 = e3)
% 169.23/25.63 (8) op(e2, e3) = e2
% 169.23/25.63 (9) ~ (e3 = e0)
% 169.23/25.63 (10) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 169.23/25.63 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.63 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.63 (12) op(e3, e1) = all_28_1
% 169.23/25.63 (13) ~ (all_52_7 = e0)
% 169.23/25.63 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.63 (15) all_58_3 = e3
% 169.23/25.63 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.63 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.63 (17) ~ (all_52_7 = e1)
% 169.23/25.63 (18) all_54_13 = all_52_7
% 169.23/25.63 (19) op(e3, e1) = all_36_1
% 169.23/25.63 (20) op(e3, e1) = e2
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | BETA: splitting (10) gives:
% 169.23/25.63 |
% 169.23/25.63 | Case 1:
% 169.23/25.63 | |
% 169.23/25.63 | | (21) all_54_13 = e2
% 169.23/25.63 | |
% 169.23/25.63 | | COMBINE_EQS: (18), (21) imply:
% 169.23/25.63 | | (22) all_52_7 = e2
% 169.23/25.63 | |
% 169.23/25.63 | | SIMP: (22) implies:
% 169.23/25.63 | | (23) all_52_7 = e2
% 169.23/25.63 | |
% 169.23/25.63 | | REDUCE: (7), (23) imply:
% 169.23/25.63 | | (24) ~ (e3 = e2)
% 169.23/25.63 | |
% 169.23/25.63 | | SIMP: (24) implies:
% 169.23/25.63 | | (25) ~ (e3 = e2)
% 169.23/25.63 | |
% 169.23/25.63 | | REDUCE: (17), (23) imply:
% 169.23/25.63 | | (26) ~ (e2 = e1)
% 169.23/25.63 | |
% 169.23/25.63 | | REDUCE: (13), (23) imply:
% 169.23/25.63 | | (27) ~ (e2 = e0)
% 169.23/25.63 | |
% 169.23/25.63 | | GROUND_INST: instantiating (14) with e2, all_28_1, e1, e3, simplifying with
% 169.23/25.63 | | (12), (20) gives:
% 169.23/25.63 | | (28) all_28_1 = e2
% 169.23/25.63 | |
% 169.23/25.63 | | GROUND_INST: instantiating (14) with all_28_1, all_36_1, e1, e3, simplifying
% 169.23/25.63 | | with (12), (19) gives:
% 169.23/25.63 | | (29) all_36_1 = all_28_1
% 169.23/25.63 | |
% 169.23/25.63 | | GROUND_INST: instantiating (14) with e3, all_36_1, e1, e3, simplifying with
% 169.23/25.63 | | (6), (19) gives:
% 169.23/25.63 | | (30) all_36_1 = e3
% 169.23/25.63 | |
% 169.23/25.63 | | COMBINE_EQS: (29), (30) imply:
% 169.23/25.63 | | (31) all_28_1 = e3
% 169.23/25.63 | |
% 169.23/25.63 | | SIMP: (31) implies:
% 169.23/25.63 | | (32) all_28_1 = e3
% 169.23/25.63 | |
% 169.23/25.63 | | COMBINE_EQS: (28), (32) imply:
% 169.23/25.63 | | (33) e3 = e2
% 169.23/25.63 | |
% 169.23/25.63 | | COMBINE_EQS: (15), (33) imply:
% 169.23/25.63 | | (34) all_58_3 = e2
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (14), (16), (25), (26),
% 169.23/25.63 | | (27), (34) are inconsistent by sub-proof #779.
% 169.23/25.63 | |
% 169.23/25.63 | Case 2:
% 169.23/25.63 | |
% 169.23/25.63 | | (35) all_54_13 = e1 | all_54_13 = e0
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (13), (17), (18), (35) are inconsistent by sub-proof #256.
% 169.23/25.63 | |
% 169.23/25.63 | End of split
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #256 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) all_54_13 = e1 | all_54_13 = e0
% 169.23/25.63 (2) all_54_13 = all_52_7
% 169.23/25.63 (3) ~ (all_52_7 = e1)
% 169.23/25.63 (4) ~ (all_52_7 = e0)
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | BETA: splitting (1) gives:
% 169.23/25.63 |
% 169.23/25.63 | Case 1:
% 169.23/25.63 | |
% 169.23/25.63 | | (5) all_54_13 = e1
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #257.
% 169.23/25.63 | |
% 169.23/25.63 | Case 2:
% 169.23/25.63 | |
% 169.23/25.63 | | (6) all_54_13 = e0
% 169.23/25.63 | |
% 169.23/25.63 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #963.
% 169.23/25.63 | |
% 169.23/25.63 | End of split
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #257 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) all_54_13 = all_52_7
% 169.23/25.63 (2) all_54_13 = e1
% 169.23/25.63 (3) ~ (all_52_7 = e1)
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | COMBINE_EQS: (1), (2) imply:
% 169.23/25.63 | (4) all_52_7 = e1
% 169.23/25.63 |
% 169.23/25.63 | SIMP: (4) implies:
% 169.23/25.63 | (5) all_52_7 = e1
% 169.23/25.63 |
% 169.23/25.63 | REDUCE: (3), (5) imply:
% 169.23/25.63 | (6) $false
% 169.23/25.63 |
% 169.23/25.63 | CLOSE: (6) is inconsistent.
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #258 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) all_56_14 = e3
% 169.23/25.63 (2) all_56_14 = e1
% 169.23/25.63 (3) ~ (e3 = e1)
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | COMBINE_EQS: (1), (2) imply:
% 169.23/25.63 | (4) e3 = e1
% 169.23/25.63 |
% 169.23/25.63 | SIMP: (4) implies:
% 169.23/25.63 | (5) e3 = e1
% 169.23/25.63 |
% 169.23/25.63 | REDUCE: (3), (5) imply:
% 169.23/25.63 | (6) $false
% 169.23/25.63 |
% 169.23/25.63 | CLOSE: (6) is inconsistent.
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #259 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.63 (1) all_54_8 = all_52_2
% 169.23/25.63 (2) all_54_8 = e2
% 169.23/25.63 (3) ~ (all_52_2 = e2)
% 169.23/25.63
% 169.23/25.63 Begin of proof
% 169.23/25.63 |
% 169.23/25.63 | COMBINE_EQS: (1), (2) imply:
% 169.23/25.63 | (4) all_52_2 = e2
% 169.23/25.63 |
% 169.23/25.63 | SIMP: (4) implies:
% 169.23/25.63 | (5) all_52_2 = e2
% 169.23/25.63 |
% 169.23/25.63 | REDUCE: (3), (5) imply:
% 169.23/25.63 | (6) $false
% 169.23/25.63 |
% 169.23/25.63 | CLOSE: (6) is inconsistent.
% 169.23/25.63 |
% 169.23/25.63 End of proof
% 169.23/25.63
% 169.23/25.63 Sub-proof #260 shows that the following formulas are inconsistent:
% 169.23/25.63 ----------------------------------------------------------------
% 169.23/25.64 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.64 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.64 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.64 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.64 (3) ~ (all_52_13 = e3)
% 169.23/25.64 (4) all_58_15 = e2
% 169.23/25.64 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.64 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.64 (6) all_58_2 = e2
% 169.23/25.64 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.23/25.64 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.64 (8) op(e3, e3) = all_10_2
% 169.23/25.64 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.64 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.64 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.64 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.23/25.64 e1)
% 169.23/25.64 (11) op(e1, e3) = all_52_2
% 169.23/25.64 (12) ~ (all_10_2 = e0)
% 169.23/25.64 (13) ~ (e1 = e0)
% 169.23/25.64 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.64 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.64 (15) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.64 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.64 (16) op(e2, e3) = all_52_1
% 169.23/25.64 (17) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.64 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.64 (18) op(e2, e3) = e2
% 169.23/25.64 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.64 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.64 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.64 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.64 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.64 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.64 (22) op(e1, e1) = e3
% 169.23/25.64 (23) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.64 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.64 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.64 (24) all_58_14 = e3
% 169.23/25.64 (25) ~ (all_10_2 = e1)
% 169.23/25.64 (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.64 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.64 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.64 (28) ~ (e2 = e0)
% 169.23/25.64 (29) ~ (all_10_2 = e2)
% 169.23/25.64 (30) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.64 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.64 (31) all_58_3 = e3
% 169.23/25.64 (32) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.64 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.64 (33) ~ (e2 = e1)
% 169.23/25.64 (34) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.23/25.64 (35) all_54_0 = all_10_2
% 169.23/25.64 (36) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.23/25.64 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.23/25.64 (37) all_58_4 = e2
% 169.23/25.64 (38) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.64 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.64 (39) op(e1, e3) = e1
% 169.23/25.64 (40) op(e2, e0) = all_52_13
% 169.23/25.64
% 169.23/25.64 Begin of proof
% 169.23/25.64 |
% 169.23/25.64 | BETA: splitting (34) gives:
% 169.23/25.64 |
% 169.23/25.64 | Case 1:
% 169.23/25.64 | |
% 169.23/25.64 | | (41) all_54_0 = e3
% 169.23/25.64 | |
% 169.23/25.64 | | COMBINE_EQS: (35), (41) imply:
% 169.23/25.64 | | (42) all_10_2 = e3
% 169.23/25.64 | |
% 169.23/25.64 | | SIMP: (42) implies:
% 169.23/25.64 | | (43) all_10_2 = e3
% 169.23/25.64 | |
% 169.23/25.64 | | REDUCE: (29), (43) imply:
% 169.23/25.64 | | (44) ~ (e3 = e2)
% 169.23/25.64 | |
% 169.23/25.64 | | REDUCE: (25), (43) imply:
% 169.23/25.64 | | (45) ~ (e3 = e1)
% 169.23/25.64 | |
% 169.23/25.64 | | REDUCE: (12), (43) imply:
% 169.23/25.64 | | (46) ~ (e3 = e0)
% 169.23/25.64 | |
% 169.23/25.64 | | REDUCE: (8), (43) imply:
% 169.23/25.64 | | (47) op(e3, e3) = e3
% 169.23/25.64 | |
% 169.23/25.64 | | BETA: splitting (36) gives:
% 169.23/25.64 | |
% 169.23/25.64 | | Case 1:
% 169.23/25.64 | | |
% 169.23/25.64 | | | (48) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 169.23/25.64 | | | e3)
% 169.23/25.64 | | |
% 169.23/25.64 | | | BETA: splitting (48) gives:
% 169.23/25.64 | | |
% 169.23/25.64 | | | Case 1:
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | (49) all_58_9 = e3 & op(e3, e0) = e3
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | ALPHA: (49) implies:
% 169.23/25.64 | | | | (50) all_58_9 = e3
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | REF_CLOSE: (4), (5), (6), (9), (10), (11), (13), (14), (16), (18), (19),
% 169.23/25.64 | | | | (23), (24), (26), (27), (28), (33), (37), (39), (44), (45),
% 169.23/25.64 | | | | (46), (47), (50) are inconsistent by sub-proof #262.
% 169.23/25.64 | | | |
% 169.23/25.64 | | | Case 2:
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | (51) all_58_10 = e3 & op(e2, e0) = e3
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | ALPHA: (51) implies:
% 169.23/25.64 | | | | (52) op(e2, e0) = e3
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | REF_CLOSE: (3), (27), (40), (52) are inconsistent by sub-proof #562.
% 169.23/25.64 | | | |
% 169.23/25.64 | | | End of split
% 169.23/25.64 | | |
% 169.23/25.64 | | Case 2:
% 169.23/25.64 | | |
% 169.23/25.64 | | | (53) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0)
% 169.23/25.64 | | | = e3)
% 169.23/25.64 | | |
% 169.23/25.64 | | | BETA: splitting (53) gives:
% 169.23/25.64 | | |
% 169.23/25.64 | | | Case 1:
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | (54) all_58_11 = e3 & op(e1, e0) = e3
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | ALPHA: (54) implies:
% 169.23/25.64 | | | | (55) all_58_11 = e3
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | BETA: splitting (14) gives:
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | Case 1:
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | (56) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2,
% 169.23/25.64 | | | | | e3) = e3)
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | BETA: splitting (56) gives:
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | Case 1:
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | (57) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | ALPHA: (57) implies:
% 169.23/25.64 | | | | | | (58) all_58_0 = e3
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | BETA: splitting (38) gives:
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | Case 1:
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | (59) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 &
% 169.23/25.64 | | | | | | | op(e2, e1) = e1)
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | BETA: splitting (59) gives:
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | Case 1:
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | (60) all_58_4 = e1 & op(e3, e1) = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | REF_CLOSE: (33), (37), (60) are inconsistent by sub-proof #943.
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | Case 2:
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | (61) all_58_5 = e1 & op(e2, e1) = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | ALPHA: (61) implies:
% 169.23/25.64 | | | | | | | | (62) all_58_5 = e1
% 169.23/25.64 | | | | | | | | (63) op(e2, e1) = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (13),
% 169.23/25.64 | | | | | | | | (14), (15), (16), (17), (18), (19), (20), (21), (23),
% 169.23/25.64 | | | | | | | | (24), (27), (28), (30), (31), (32), (33), (37), (39),
% 169.23/25.64 | | | | | | | | (44), (45), (46), (47), (55), (58), (62), (63) are
% 169.23/25.64 | | | | | | | | inconsistent by sub-proof #261.
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | End of split
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | Case 2:
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | (64) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 169.23/25.64 | | | | | | | op(e0, e1) = e1)
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | BETA: splitting (64) gives:
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | Case 1:
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | (65) all_58_8 = e1 & op(e1, e1) = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | ALPHA: (65) implies:
% 169.23/25.64 | | | | | | | | (66) all_58_8 = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | BETA: splitting (7) gives:
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | Case 1:
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | (67) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 169.23/25.64 | | | | | | | | | op(e1, e2) = e2)
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | BETA: splitting (67) gives:
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | Case 1:
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | (68) all_58_6 = e2 & op(e1, e3) = e2
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | REF_CLOSE: (2), (5), (6), (11), (13), (14), (16), (18), (19),
% 169.23/25.64 | | | | | | | | | | (20), (27), (28), (31), (32), (33), (39), (44),
% 169.23/25.64 | | | | | | | | | | (45), (46), (47), (68) are inconsistent by
% 169.23/25.64 | | | | | | | | | | sub-proof #278.
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | Case 2:
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | (69) all_58_7 = e2 & op(e1, e2) = e2
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | ALPHA: (69) implies:
% 169.23/25.64 | | | | | | | | | | (70) all_58_7 = e2
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | REF_CLOSE: (11), (13), (21), (27), (28), (39), (46), (55),
% 169.23/25.64 | | | | | | | | | | (66), (70) are inconsistent by sub-proof #325.
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | End of split
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | Case 2:
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | (71) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 169.23/25.64 | | | | | | | | | op(e1, e0) = e2)
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | REF_CLOSE: (2), (5), (6), (11), (13), (14), (16), (18), (19),
% 169.23/25.64 | | | | | | | | | (20), (22), (27), (28), (31), (32), (33), (39),
% 169.23/25.64 | | | | | | | | | (44), (45), (46), (47), (55), (71) are inconsistent
% 169.23/25.64 | | | | | | | | | by sub-proof #268.
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | End of split
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | Case 2:
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | (72) all_58_14 = e1 & op(e0, e1) = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | ALPHA: (72) implies:
% 169.23/25.64 | | | | | | | | (73) all_58_14 = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | REF_CLOSE: (24), (45), (73) are inconsistent by sub-proof #626.
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | End of split
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | End of split
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | Case 2:
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | (74) all_58_2 = e3 & op(e2, e3) = e3
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | ALPHA: (74) implies:
% 169.23/25.64 | | | | | | (75) op(e2, e3) = e3
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | REF_CLOSE: (16), (18), (27), (44), (75) are inconsistent by
% 169.23/25.64 | | | | | | sub-proof #462.
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | End of split
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | Case 2:
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | (76) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0,
% 169.23/25.64 | | | | | e3) = e3)
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | BETA: splitting (76) gives:
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | Case 1:
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | (77) all_58_6 = e3 & op(e1, e3) = e3
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | ALPHA: (77) implies:
% 169.23/25.64 | | | | | | (78) all_58_6 = e3
% 169.23/25.64 | | | | | | (79) op(e1, e3) = e3
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | BETA: splitting (19) gives:
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | Case 1:
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | (80) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 169.23/25.64 | | | | | | | op(e2, e3) = e1)
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | BETA: splitting (80) gives:
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | Case 1:
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | (81) all_58_0 = e1 & op(e3, e3) = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | ALPHA: (81) implies:
% 169.23/25.64 | | | | | | | | (82) all_58_0 = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | BETA: splitting (7) gives:
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | Case 1:
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | (83) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 169.23/25.64 | | | | | | | | | op(e1, e2) = e2)
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | BETA: splitting (83) gives:
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | Case 1:
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | (84) all_58_6 = e2 & op(e1, e3) = e2
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | ALPHA: (84) implies:
% 169.23/25.64 | | | | | | | | | | (85) all_58_6 = e2
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | REF_CLOSE: (2), (5), (6), (13), (14), (16), (18), (20), (27),
% 169.23/25.64 | | | | | | | | | | (28), (31), (32), (33), (44), (45), (46), (82),
% 169.23/25.64 | | | | | | | | | | (85) are inconsistent by sub-proof #400.
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | Case 2:
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | (86) all_58_7 = e2 & op(e1, e2) = e2
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | ALPHA: (86) implies:
% 169.23/25.64 | | | | | | | | | | (87) all_58_7 = e2
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | REF_CLOSE: (5), (6), (11), (13), (14), (16), (18), (21),
% 169.23/25.64 | | | | | | | | | | (27), (28), (30), (33), (39), (44), (45), (46),
% 169.23/25.64 | | | | | | | | | | (55), (78), (82), (87) are inconsistent by
% 169.23/25.64 | | | | | | | | | | sub-proof #265.
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | End of split
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | Case 2:
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | (88) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 169.23/25.64 | | | | | | | | | op(e1, e0) = e2)
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | BETA: splitting (88) gives:
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | | Case 1:
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | (89) all_58_8 = e2 & op(e1, e1) = e2
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | ALPHA: (89) implies:
% 169.23/25.64 | | | | | | | | | | (90) op(e1, e1) = e2
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | REF_CLOSE: (5), (6), (11), (13), (14), (16), (18), (22),
% 169.23/25.64 | | | | | | | | | | (27), (28), (39), (44), (45), (46), (47), (78),
% 169.23/25.64 | | | | | | | | | | (79), (82), (90) are inconsistent by sub-proof
% 169.23/25.64 | | | | | | | | | | #342.
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | Case 2:
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | (91) all_58_11 = e2 & op(e1, e0) = e2
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | | REF_CLOSE: (2), (6), (13), (16), (18), (20), (27), (28),
% 169.23/25.64 | | | | | | | | | | (31), (32), (33), (44), (45), (46), (55), (91) are
% 169.23/25.64 | | | | | | | | | | inconsistent by sub-proof #419.
% 169.23/25.64 | | | | | | | | | |
% 169.23/25.64 | | | | | | | | | End of split
% 169.23/25.64 | | | | | | | | |
% 169.23/25.64 | | | | | | | | End of split
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | Case 2:
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | (92) all_58_2 = e1 & op(e2, e3) = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | ALPHA: (92) implies:
% 169.23/25.64 | | | | | | | | (93) op(e2, e3) = e1
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | | REF_CLOSE: (16), (18), (27), (33), (93) are inconsistent by
% 169.23/25.64 | | | | | | | | sub-proof #784.
% 169.23/25.64 | | | | | | | |
% 169.23/25.64 | | | | | | | End of split
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | Case 2:
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | (94) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 &
% 169.23/25.64 | | | | | | | op(e0, e3) = e1)
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | REF_CLOSE: (5), (11), (13), (16), (18), (27), (28), (39), (45),
% 169.23/25.64 | | | | | | | (46), (47), (78), (94) are inconsistent by sub-proof
% 169.23/25.64 | | | | | | | #280.
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | End of split
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | Case 2:
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | (95) all_58_12 = e3 & op(e0, e3) = e3
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | REF_CLOSE: (5), (11), (13), (16), (18), (27), (28), (39), (46),
% 169.23/25.64 | | | | | | (47), (95) are inconsistent by sub-proof #301.
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | End of split
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | End of split
% 169.23/25.64 | | | |
% 169.23/25.64 | | | Case 2:
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | (96) all_58_15 = e3 & op(e0, e0) = e3
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | REF_CLOSE: (2), (4), (6), (13), (16), (18), (20), (27), (28), (31),
% 169.23/25.64 | | | | (32), (33), (44), (45), (46), (96) are inconsistent by
% 169.23/25.64 | | | | sub-proof #359.
% 169.23/25.64 | | | |
% 169.23/25.64 | | | End of split
% 169.23/25.64 | | |
% 169.23/25.64 | | End of split
% 169.23/25.64 | |
% 169.23/25.64 | Case 2:
% 169.23/25.64 | |
% 169.23/25.64 | | (97) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.23/25.64 | |
% 169.23/25.64 | | REF_CLOSE: (12), (25), (29), (35), (97) are inconsistent by sub-proof #958.
% 169.23/25.64 | |
% 169.23/25.64 | End of split
% 169.23/25.64 |
% 169.23/25.64 End of proof
% 169.23/25.64
% 169.23/25.64 Sub-proof #261 shows that the following formulas are inconsistent:
% 169.23/25.64 ----------------------------------------------------------------
% 169.23/25.64 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.64 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.64 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.64 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.64 (3) all_58_15 = e2
% 169.23/25.64 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.64 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.64 (5) all_58_2 = e2
% 169.23/25.64 (6) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.23/25.64 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.64 (7) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.64 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.64 (8) ~ (e3 = e1)
% 169.23/25.64 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 169.23/25.64 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.64 (10) op(e1, e3) = all_52_2
% 169.23/25.64 (11) ~ (e1 = e0)
% 169.23/25.64 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.64 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.64 (13) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.64 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.64 (14) op(e2, e3) = all_52_1
% 169.23/25.64 (15) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.64 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.64 (16) op(e2, e3) = e2
% 169.23/25.64 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.64 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.64 (18) ~ (e3 = e0)
% 169.23/25.64 (19) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.64 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.64 (20) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.64 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.64 (21) all_58_11 = e3
% 169.23/25.64 (22) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.64 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.64 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.64 (23) all_58_14 = e3
% 169.23/25.64 (24) all_58_0 = e3
% 169.23/25.64 (25) op(e2, e1) = e1
% 169.23/25.64 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.64 (27) ~ (e2 = e0)
% 169.23/25.64 (28) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.64 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.64 (29) all_58_5 = e1
% 169.23/25.64 (30) all_58_3 = e3
% 169.23/25.64 (31) op(e3, e3) = e3
% 169.23/25.64 (32) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.64 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.64 (33) ~ (e2 = e1)
% 169.23/25.64 (34) all_58_4 = e2
% 169.23/25.64 (35) op(e1, e3) = e1
% 169.23/25.64 (36) ~ (e3 = e2)
% 169.23/25.64
% 169.23/25.64 Begin of proof
% 169.23/25.64 |
% 169.23/25.64 | BETA: splitting (6) gives:
% 169.23/25.64 |
% 169.23/25.64 | Case 1:
% 169.23/25.64 | |
% 169.23/25.64 | | (37) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 169.23/25.64 | | e2)
% 169.23/25.64 | |
% 169.23/25.64 | | BETA: splitting (37) gives:
% 169.23/25.64 | |
% 169.23/25.64 | | Case 1:
% 169.23/25.64 | | |
% 169.23/25.64 | | | (38) all_58_6 = e2 & op(e1, e3) = e2
% 169.23/25.64 | | |
% 169.23/25.64 | | | REF_CLOSE: (2), (4), (5), (8), (10), (11), (12), (14), (16), (17), (18),
% 169.23/25.64 | | | (19), (26), (27), (30), (31), (32), (33), (35), (36), (38) are
% 169.23/25.64 | | | inconsistent by sub-proof #278.
% 169.23/25.64 | | |
% 169.23/25.64 | | Case 2:
% 169.23/25.64 | | |
% 169.23/25.64 | | | (39) all_58_7 = e2 & op(e1, e2) = e2
% 169.23/25.64 | | |
% 169.23/25.64 | | | ALPHA: (39) implies:
% 169.23/25.64 | | | (40) all_58_7 = e2
% 169.23/25.64 | | |
% 169.23/25.64 | | | BETA: splitting (19) gives:
% 169.23/25.64 | | |
% 169.23/25.64 | | | Case 1:
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | (41) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2)
% 169.23/25.64 | | | | = e0)
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | BETA: splitting (41) gives:
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | Case 1:
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | (42) all_58_2 = e0 & op(e2, e3) = e0
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | REF_CLOSE: (14), (16), (26), (27), (42) are inconsistent by sub-proof
% 169.23/25.64 | | | | | #782.
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | Case 2:
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | (43) all_58_3 = e0 & op(e2, e2) = e0
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | REF_CLOSE: (18), (30), (43) are inconsistent by sub-proof #427.
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | End of split
% 169.23/25.64 | | | |
% 169.23/25.64 | | | Case 2:
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | (44) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0)
% 169.23/25.64 | | | | = e0)
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | BETA: splitting (44) gives:
% 169.23/25.64 | | | |
% 169.23/25.64 | | | | Case 1:
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | (45) all_58_5 = e0 & op(e2, e1) = e0
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | ALPHA: (45) implies:
% 169.23/25.64 | | | | | (46) op(e2, e1) = e0
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | REF_CLOSE: (11), (25), (26), (46) are inconsistent by sub-proof #911.
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | Case 2:
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | (47) all_58_10 = e0 & op(e2, e0) = e0
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | ALPHA: (47) implies:
% 169.23/25.64 | | | | | (48) op(e2, e0) = e0
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | BETA: splitting (28) gives:
% 169.23/25.64 | | | | |
% 169.23/25.64 | | | | | Case 1:
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | (49) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1,
% 169.23/25.64 | | | | | | e2) = e1)
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | BETA: splitting (49) gives:
% 169.23/25.64 | | | | | |
% 169.23/25.64 | | | | | | Case 1:
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | (50) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.64 | | | | | | |
% 169.23/25.64 | | | | | | | ALPHA: (50) implies:
% 169.23/25.64 | | | | | | | (51) all_58_6 = e1
% 169.23/25.65 | | | | | | |
% 169.23/25.65 | | | | | | | BETA: splitting (4) gives:
% 169.23/25.65 | | | | | | |
% 169.23/25.65 | | | | | | | Case 1:
% 169.23/25.65 | | | | | | | |
% 169.23/25.65 | | | | | | | | (52) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 169.23/25.65 | | | | | | | | op(e2, e3) = e0)
% 169.23/25.65 | | | | | | | |
% 169.23/25.65 | | | | | | | | REF_CLOSE: (14), (16), (18), (26), (27), (31), (52) are
% 169.23/25.65 | | | | | | | | inconsistent by sub-proof #460.
% 169.23/25.65 | | | | | | | |
% 169.23/25.65 | | | | | | | Case 2:
% 169.23/25.65 | | | | | | | |
% 169.23/25.65 | | | | | | | | (53) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 169.23/25.65 | | | | | | | | op(e0, e3) = e0)
% 169.23/25.65 | | | | | | | |
% 169.23/25.65 | | | | | | | | BETA: splitting (53) gives:
% 169.23/25.65 | | | | | | | |
% 169.23/25.65 | | | | | | | | Case 1:
% 169.23/25.65 | | | | | | | | |
% 169.23/25.65 | | | | | | | | | (54) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.65 | | | | | | | | |
% 169.23/25.65 | | | | | | | | | ALPHA: (54) implies:
% 169.23/25.65 | | | | | | | | | (55) op(e1, e3) = e0
% 169.23/25.65 | | | | | | | | |
% 169.23/25.65 | | | | | | | | | REF_CLOSE: (10), (11), (26), (35), (55) are inconsistent by
% 169.23/25.65 | | | | | | | | | sub-proof #749.
% 169.23/25.65 | | | | | | | | |
% 169.23/25.65 | | | | | | | | Case 2:
% 169.23/25.65 | | | | | | | | |
% 169.23/25.65 | | | | | | | | | (56) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.65 | | | | | | | | |
% 169.23/25.65 | | | | | | | | | ALPHA: (56) implies:
% 169.23/25.65 | | | | | | | | | (57) all_58_12 = e0
% 169.23/25.65 | | | | | | | | |
% 169.23/25.65 | | | | | | | | | BETA: splitting (1) gives:
% 169.23/25.65 | | | | | | | | |
% 169.23/25.65 | | | | | | | | | Case 1:
% 169.23/25.65 | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | (58) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1
% 169.23/25.65 | | | | | | | | | | & op(e2, e0) = e1)
% 169.23/25.65 | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | BETA: splitting (58) gives:
% 169.23/25.65 | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | Case 1:
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | (59) all_58_9 = e1 & op(e3, e0) = e1
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | ALPHA: (59) implies:
% 169.23/25.65 | | | | | | | | | | | (60) all_58_9 = e1
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | BETA: splitting (9) gives:
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | Case 1:
% 169.23/25.65 | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | (61) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 169.23/25.65 | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 169.23/25.65 | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | BETA: splitting (61) gives:
% 169.23/25.65 | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | Case 1:
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | (62) all_58_12 = e1 & op(e0, e3) = e1
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | ALPHA: (62) implies:
% 169.23/25.65 | | | | | | | | | | | | | (63) all_58_12 = e1
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | REF_CLOSE: (4), (10), (11), (14), (16), (18), (26), (27),
% 169.23/25.65 | | | | | | | | | | | | | (31), (35), (63) are inconsistent by sub-proof
% 169.23/25.65 | | | | | | | | | | | | | #296.
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | Case 2:
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | (64) all_58_13 = e1 & op(e0, e2) = e1
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | ALPHA: (64) implies:
% 169.23/25.65 | | | | | | | | | | | | | (65) op(e0, e2) = e1
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | BETA: splitting (7) gives:
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | Case 1:
% 169.23/25.65 | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | (66) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 169.23/25.65 | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 169.23/25.65 | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | REF_CLOSE: (18), (22), (26), (31), (65), (66) are
% 169.23/25.65 | | | | | | | | | | | | | | inconsistent by sub-proof #295.
% 169.23/25.65 | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | Case 2:
% 169.23/25.65 | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | (67) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 169.23/25.65 | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 169.23/25.65 | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 169.23/25.65 | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | Case 1:
% 169.23/25.65 | | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | | (68) all_58_4 = e0 & op(e3, e1) = e0
% 169.23/25.65 | | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | | REF_CLOSE: (27), (34), (68) are inconsistent by sub-proof
% 169.23/25.65 | | | | | | | | | | | | | | | #902.
% 169.23/25.65 | | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | Case 2:
% 169.23/25.65 | | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | | (69) all_58_9 = e0 & op(e3, e0) = e0
% 169.23/25.65 | | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | | REF_CLOSE: (11), (60), (69) are inconsistent by sub-proof
% 169.23/25.65 | | | | | | | | | | | | | | | #897.
% 169.23/25.65 | | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | | End of split
% 169.23/25.65 | | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | End of split
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | End of split
% 169.23/25.65 | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | Case 2:
% 169.23/25.65 | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | (70) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 169.23/25.65 | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.23/25.65 | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | BETA: splitting (70) gives:
% 169.23/25.65 | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | Case 1:
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | (71) all_58_14 = e1 & op(e0, e1) = e1
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (18), (23), (24), (36), (51),
% 169.23/25.65 | | | | | | | | | | | | | (57), (71) are inconsistent by sub-proof #266.
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | Case 2:
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | (72) all_58_15 = e1 & op(e0, e0) = e1
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | ALPHA: (72) implies:
% 169.23/25.65 | | | | | | | | | | | | | (73) all_58_15 = e1
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | | REF_CLOSE: (3), (33), (73) are inconsistent by sub-proof
% 169.23/25.65 | | | | | | | | | | | | | #645.
% 169.23/25.65 | | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | | End of split
% 169.23/25.65 | | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | End of split
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | Case 2:
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | (74) all_58_10 = e1 & op(e2, e0) = e1
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | ALPHA: (74) implies:
% 169.23/25.65 | | | | | | | | | | | (75) op(e2, e0) = e1
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | REF_CLOSE: (11), (26), (48), (75) are inconsistent by
% 169.23/25.65 | | | | | | | | | | | sub-proof #849.
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | End of split
% 169.23/25.65 | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | Case 2:
% 169.23/25.65 | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | (76) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1
% 169.23/25.65 | | | | | | | | | | & op(e0, e0) = e1)
% 169.23/25.65 | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | BETA: splitting (76) gives:
% 169.23/25.65 | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | Case 1:
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | (77) all_58_11 = e1 & op(e1, e0) = e1
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | ALPHA: (77) implies:
% 169.23/25.65 | | | | | | | | | | | (78) all_58_11 = e1
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | COMBINE_EQS: (21), (78) imply:
% 169.23/25.65 | | | | | | | | | | | (79) e3 = e1
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | COMBINE_EQS: (24), (79) imply:
% 169.23/25.65 | | | | | | | | | | | (80) all_58_0 = e1
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | REF_CLOSE: (5), (8), (12), (18), (36), (51), (57), (80) are
% 169.23/25.65 | | | | | | | | | | | inconsistent by sub-proof #456.
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | Case 2:
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | (81) all_58_15 = e1 & op(e0, e0) = e1
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | ALPHA: (81) implies:
% 169.23/25.65 | | | | | | | | | | | (82) all_58_15 = e1
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | | REF_CLOSE: (3), (33), (82) are inconsistent by sub-proof
% 169.23/25.65 | | | | | | | | | | | #645.
% 169.23/25.65 | | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | | End of split
% 169.23/25.65 | | | | | | | | | |
% 169.23/25.65 | | | | | | | | | End of split
% 169.23/25.65 | | | | | | | | |
% 169.23/25.65 | | | | | | | | End of split
% 169.23/25.65 | | | | | | | |
% 169.23/25.65 | | | | | | | End of split
% 169.23/25.65 | | | | | | |
% 169.23/25.65 | | | | | | Case 2:
% 169.23/25.65 | | | | | | |
% 169.23/25.65 | | | | | | | (83) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.65 | | | | | | |
% 169.23/25.65 | | | | | | | ALPHA: (83) implies:
% 169.23/25.65 | | | | | | | (84) all_58_7 = e1
% 169.23/25.65 | | | | | | |
% 169.23/25.65 | | | | | | | REF_CLOSE: (33), (40), (84) are inconsistent by sub-proof #494.
% 169.23/25.65 | | | | | | |
% 169.23/25.65 | | | | | | End of split
% 169.23/25.65 | | | | | |
% 169.23/25.65 | | | | | Case 2:
% 169.23/25.65 | | | | | |
% 169.23/25.65 | | | | | | (85) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1,
% 169.23/25.65 | | | | | | e0) = e1)
% 169.23/25.65 | | | | | |
% 169.23/25.65 | | | | | | REF_CLOSE: (8), (10), (11), (18), (20), (21), (26), (27), (35),
% 169.23/25.65 | | | | | | (40), (85) are inconsistent by sub-proof #273.
% 169.23/25.65 | | | | | |
% 169.23/25.65 | | | | | End of split
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | End of split
% 169.23/25.65 | | | |
% 169.23/25.65 | | | End of split
% 169.23/25.65 | | |
% 169.23/25.65 | | End of split
% 169.23/25.65 | |
% 169.23/25.65 | Case 2:
% 169.23/25.65 | |
% 169.23/25.65 | | (86) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 169.23/25.65 | | e2)
% 169.23/25.65 | |
% 169.23/25.65 | | REF_CLOSE: (2), (5), (8), (11), (13), (14), (15), (16), (18), (19), (21),
% 169.23/25.65 | | (26), (27), (29), (30), (32), (33), (34), (36), (86) are
% 169.23/25.65 | | inconsistent by sub-proof #269.
% 169.23/25.65 | |
% 169.23/25.65 | End of split
% 169.23/25.65 |
% 169.23/25.65 End of proof
% 169.23/25.65
% 169.23/25.65 Sub-proof #262 shows that the following formulas are inconsistent:
% 169.23/25.65 ----------------------------------------------------------------
% 169.23/25.65 (1) all_58_15 = e2
% 169.23/25.65 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.65 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.65 (3) all_58_2 = e2
% 169.23/25.65 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.65 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.65 (5) ~ (e3 = e1)
% 169.23/25.65 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 169.23/25.65 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.65 (7) op(e1, e3) = all_52_2
% 169.23/25.65 (8) ~ (e1 = e0)
% 169.23/25.65 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.65 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.65 (10) op(e2, e3) = all_52_1
% 169.23/25.65 (11) op(e2, e3) = e2
% 169.23/25.65 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.65 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.65 (13) ~ (e3 = e0)
% 169.23/25.65 (14) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.65 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.65 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.65 (15) all_58_14 = e3
% 169.23/25.65 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.65 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.65 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.65 (18) ~ (e2 = e0)
% 169.23/25.65 (19) op(e3, e3) = e3
% 169.23/25.65 (20) all_58_9 = e3
% 169.23/25.65 (21) ~ (e2 = e1)
% 169.23/25.65 (22) all_58_4 = e2
% 169.23/25.65 (23) op(e1, e3) = e1
% 169.23/25.65 (24) ~ (e3 = e2)
% 169.23/25.65
% 169.23/25.65 Begin of proof
% 169.23/25.65 |
% 169.23/25.65 | BETA: splitting (9) gives:
% 169.23/25.65 |
% 169.23/25.65 | Case 1:
% 169.23/25.65 | |
% 169.23/25.65 | | (25) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 169.23/25.65 | | e3)
% 169.23/25.65 | |
% 169.23/25.65 | | REF_CLOSE: (4), (5), (8), (10), (11), (13), (16), (17), (18), (20), (21),
% 169.23/25.65 | | (22), (24), (25) are inconsistent by sub-proof #277.
% 169.23/25.65 | |
% 169.23/25.65 | Case 2:
% 169.23/25.65 | |
% 169.23/25.65 | | (26) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 169.23/25.65 | | e3)
% 169.23/25.65 | |
% 169.23/25.65 | | BETA: splitting (26) gives:
% 169.23/25.65 | |
% 169.23/25.65 | | Case 1:
% 169.23/25.65 | | |
% 169.23/25.65 | | | (27) all_58_6 = e3 & op(e1, e3) = e3
% 169.23/25.65 | | |
% 169.23/25.65 | | | ALPHA: (27) implies:
% 169.23/25.65 | | | (28) all_58_6 = e3
% 169.23/25.65 | | |
% 169.23/25.65 | | | BETA: splitting (12) gives:
% 169.23/25.65 | | |
% 169.23/25.65 | | | Case 1:
% 169.23/25.65 | | | |
% 169.23/25.65 | | | | (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 169.23/25.65 | | | | = e1)
% 169.23/25.65 | | | |
% 169.23/25.65 | | | | BETA: splitting (29) gives:
% 169.23/25.65 | | | |
% 169.23/25.65 | | | | Case 1:
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | (30) all_58_0 = e1 & op(e3, e3) = e1
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | ALPHA: (30) implies:
% 169.23/25.65 | | | | | (31) all_58_0 = e1
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13),
% 169.23/25.65 | | | | | (14), (15), (17), (18), (19), (20), (21), (22), (24), (28),
% 169.23/25.65 | | | | | (31) are inconsistent by sub-proof #439.
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | Case 2:
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | (32) all_58_2 = e1 & op(e2, e3) = e1
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | ALPHA: (32) implies:
% 169.23/25.65 | | | | | (33) op(e2, e3) = e1
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | REF_CLOSE: (10), (11), (17), (21), (33) are inconsistent by sub-proof
% 169.23/25.65 | | | | | #784.
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | End of split
% 169.23/25.65 | | | |
% 169.23/25.65 | | | Case 2:
% 169.23/25.65 | | | |
% 169.23/25.65 | | | | (34) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 169.23/25.65 | | | | = e1)
% 169.23/25.65 | | | |
% 169.23/25.65 | | | | REF_CLOSE: (2), (5), (7), (8), (10), (11), (13), (17), (18), (19), (23),
% 169.23/25.65 | | | | (28), (34) are inconsistent by sub-proof #280.
% 169.23/25.65 | | | |
% 169.23/25.65 | | | End of split
% 169.23/25.65 | | |
% 169.23/25.65 | | Case 2:
% 169.23/25.65 | | |
% 169.23/25.65 | | | (35) all_58_12 = e3 & op(e0, e3) = e3
% 169.23/25.65 | | |
% 169.23/25.65 | | | REF_CLOSE: (2), (7), (8), (10), (11), (13), (17), (18), (19), (23), (35)
% 169.23/25.65 | | | are inconsistent by sub-proof #301.
% 169.23/25.65 | | |
% 169.23/25.65 | | End of split
% 169.23/25.65 | |
% 169.23/25.65 | End of split
% 169.23/25.65 |
% 169.23/25.65 End of proof
% 169.23/25.65
% 169.23/25.65 Sub-proof #263 shows that the following formulas are inconsistent:
% 169.23/25.65 ----------------------------------------------------------------
% 169.23/25.65 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.65 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.65 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.65 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.65 (3) all_58_2 = e2
% 169.23/25.65 (4) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.23/25.65 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.65 (5) ~ (e3 = e1)
% 169.23/25.65 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 169.23/25.65 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.65 (7) op(e1, e3) = all_52_2
% 169.23/25.65 (8) ~ (e1 = e0)
% 169.23/25.65 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.65 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.65 (10) op(e1, e2) = all_52_6
% 169.23/25.65 (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.65 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.65 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.23/25.65 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.23/25.65 (13) op(e2, e3) = all_52_1
% 169.23/25.65 (14) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.65 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.65 (15) all_58_11 = e3 & op(e1, e0) = e3
% 169.23/25.65 (16) op(e2, e3) = e2
% 169.23/25.65 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.65 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.65 (18) ~ (e3 = e0)
% 169.23/25.65 (19) all_58_13 = e2
% 169.23/25.65 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.65 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.65 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.65 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.65 (22) op(e1, e1) = e3
% 169.23/25.65 (23) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.65 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.65 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.65 (24) all_58_14 = e3
% 169.23/25.65 (25) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.65 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.23/25.65 (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.65 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.65 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.65 (28) ~ (e2 = e0)
% 169.23/25.65 (29) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.65 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.65 (30) all_58_3 = e3
% 169.23/25.65 (31) op(e3, e3) = e3
% 169.23/25.65 (32) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.65 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.65 (33) ~ (e2 = e1)
% 169.23/25.65 (34) op(e3, e2) = all_52_4
% 169.23/25.65 (35) all_58_4 = e2
% 169.23/25.65 (36) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.65 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.65 (37) op(e1, e3) = e1
% 169.23/25.65 (38) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.23/25.65 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.23/25.65 e2) = all_14_1 & $i(all_14_1))
% 169.23/25.65 (39) ~ (e3 = e2)
% 169.23/25.65
% 169.23/25.65 Begin of proof
% 169.23/25.65 |
% 169.23/25.65 | ALPHA: (15) implies:
% 169.23/25.65 | (40) all_58_11 = e3
% 169.23/25.65 |
% 169.23/25.65 | BETA: splitting (12) gives:
% 169.23/25.65 |
% 169.23/25.65 | Case 1:
% 169.23/25.65 | |
% 169.23/25.65 | | (41) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 169.23/25.65 | | e2)
% 169.23/25.65 | |
% 169.23/25.65 | | BETA: splitting (41) gives:
% 169.23/25.65 | |
% 169.23/25.65 | | Case 1:
% 169.23/25.65 | | |
% 169.23/25.65 | | | (42) all_58_9 = e2 & op(e3, e0) = e2
% 169.23/25.65 | | |
% 169.23/25.65 | | | ALPHA: (42) implies:
% 169.23/25.65 | | | (43) all_58_9 = e2
% 169.23/25.65 | | |
% 169.23/25.65 | | | BETA: splitting (36) gives:
% 169.23/25.65 | | |
% 169.23/25.65 | | | Case 1:
% 169.23/25.65 | | | |
% 169.23/25.65 | | | | (44) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 169.23/25.65 | | | | = e1)
% 169.23/25.65 | | | |
% 169.23/25.65 | | | | BETA: splitting (44) gives:
% 169.23/25.65 | | | |
% 169.23/25.65 | | | | Case 1:
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | (45) all_58_4 = e1 & op(e3, e1) = e1
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | REF_CLOSE: (33), (35), (45) are inconsistent by sub-proof #510.
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | Case 2:
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | (46) all_58_5 = e1 & op(e2, e1) = e1
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | ALPHA: (46) implies:
% 169.23/25.65 | | | | | (47) all_58_5 = e1
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | BETA: splitting (4) gives:
% 169.23/25.65 | | | | |
% 169.23/25.65 | | | | | Case 1:
% 169.23/25.65 | | | | | |
% 169.23/25.65 | | | | | | (48) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 169.23/25.65 | | | | | | e2) = e2)
% 169.23/25.65 | | | | | |
% 169.23/25.65 | | | | | | BETA: splitting (48) gives:
% 169.23/25.65 | | | | | |
% 169.23/25.65 | | | | | | Case 1:
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | (49) all_58_6 = e2 & op(e1, e3) = e2
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | ALPHA: (49) implies:
% 169.23/25.66 | | | | | | | (50) all_58_6 = e2
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | BETA: splitting (9) gives:
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | (51) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 169.23/25.66 | | | | | | | | op(e2, e3) = e3)
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | BETA: splitting (51) gives:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | (52) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | ALPHA: (52) implies:
% 169.23/25.66 | | | | | | | | | (53) all_58_0 = e3
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | BETA: splitting (17) gives:
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | (54) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 169.23/25.66 | | | | | | | | | | op(e2, e3) = e1)
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | REF_CLOSE: (5), (13), (16), (27), (33), (53), (54) are
% 169.23/25.66 | | | | | | | | | | inconsistent by sub-proof #416.
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | (55) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 169.23/25.66 | | | | | | | | | | & op(e0, e3) = e1)
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | BETA: splitting (55) gives:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | (56) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (13), (16),
% 169.23/25.66 | | | | | | | | | | | (18), (19), (23), (25), (26), (27), (28), (30),
% 169.23/25.66 | | | | | | | | | | | (31), (33), (34), (35), (38), (39), (43), (56) are
% 169.23/25.66 | | | | | | | | | | | inconsistent by sub-proof #276.
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | (57) all_58_12 = e1 & op(e0, e3) = e1
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | ALPHA: (57) implies:
% 169.23/25.66 | | | | | | | | | | | (58) all_58_12 = e1
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | REF_CLOSE: (2), (8), (13), (16), (18), (27), (28), (50),
% 169.23/25.66 | | | | | | | | | | | (53), (58) are inconsistent by sub-proof #275.
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | (59) all_58_2 = e3 & op(e2, e3) = e3
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | ALPHA: (59) implies:
% 169.23/25.66 | | | | | | | | | (60) op(e2, e3) = e3
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | REF_CLOSE: (13), (16), (27), (39), (60) are inconsistent by
% 169.23/25.66 | | | | | | | | | sub-proof #462.
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | End of split
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | (61) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 169.23/25.66 | | | | | | | | op(e0, e3) = e3)
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (8), (13), (16), (17), (18),
% 169.23/25.66 | | | | | | | | (20), (27), (28), (30), (32), (33), (39), (50), (61)
% 169.23/25.66 | | | | | | | | are inconsistent by sub-proof #274.
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | End of split
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | Case 2:
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | (62) all_58_7 = e2 & op(e1, e2) = e2
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | ALPHA: (62) implies:
% 169.23/25.66 | | | | | | | (63) all_58_7 = e2
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | BETA: splitting (29) gives:
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | (64) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 169.23/25.66 | | | | | | | | op(e1, e2) = e1)
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | BETA: splitting (64) gives:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | (65) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (13), (16),
% 169.23/25.66 | | | | | | | | | (18), (19), (23), (25), (26), (27), (28), (30),
% 169.23/25.66 | | | | | | | | | (31), (33), (34), (35), (38), (39), (43), (65) are
% 169.23/25.66 | | | | | | | | | inconsistent by sub-proof #276.
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | (66) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | ALPHA: (66) implies:
% 169.23/25.66 | | | | | | | | | (67) all_58_7 = e1
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | REF_CLOSE: (33), (63), (67) are inconsistent by sub-proof
% 169.23/25.66 | | | | | | | | | #494.
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | End of split
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | (68) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 169.23/25.66 | | | | | | | | op(e1, e0) = e1)
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | REF_CLOSE: (5), (7), (8), (18), (21), (27), (28), (37), (40),
% 169.23/25.66 | | | | | | | | (63), (68) are inconsistent by sub-proof #273.
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | End of split
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | End of split
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | Case 2:
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | | (69) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 169.23/25.66 | | | | | | e0) = e2)
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | | REF_CLOSE: (1), (3), (5), (8), (11), (13), (14), (16), (18), (20),
% 169.23/25.66 | | | | | | (27), (28), (30), (32), (33), (35), (39), (40), (47),
% 169.23/25.66 | | | | | | (69) are inconsistent by sub-proof #269.
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | End of split
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | End of split
% 169.23/25.66 | | | |
% 169.23/25.66 | | | Case 2:
% 169.23/25.66 | | | |
% 169.23/25.66 | | | | (70) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 169.23/25.66 | | | | = e1)
% 169.23/25.66 | | | |
% 169.23/25.66 | | | | BETA: splitting (70) gives:
% 169.23/25.66 | | | |
% 169.23/25.66 | | | | Case 1:
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | (71) all_58_8 = e1 & op(e1, e1) = e1
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | ALPHA: (71) implies:
% 169.23/25.66 | | | | | (72) all_58_8 = e1
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | BETA: splitting (4) gives:
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | Case 1:
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | | (73) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 169.23/25.66 | | | | | | e2) = e2)
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | | BETA: splitting (73) gives:
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | | Case 1:
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | (74) all_58_6 = e2 & op(e1, e3) = e2
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | ALPHA: (74) implies:
% 169.23/25.66 | | | | | | | (75) all_58_6 = e2
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | BETA: splitting (2) gives:
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | (76) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 169.23/25.66 | | | | | | | | op(e2, e3) = e0)
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | REF_CLOSE: (13), (16), (18), (27), (28), (31), (76) are
% 169.23/25.66 | | | | | | | | inconsistent by sub-proof #460.
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | (77) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 169.23/25.66 | | | | | | | | op(e0, e3) = e0)
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | BETA: splitting (77) gives:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | (78) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | ALPHA: (78) implies:
% 169.23/25.66 | | | | | | | | | (79) op(e1, e3) = e0
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | REF_CLOSE: (7), (8), (27), (37), (79) are inconsistent by
% 169.23/25.66 | | | | | | | | | sub-proof #749.
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | (80) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | ALPHA: (80) implies:
% 169.23/25.66 | | | | | | | | | (81) all_58_12 = e0
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | BETA: splitting (21) gives:
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | (82) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 169.23/25.66 | | | | | | | | | | op(e1, e2) = e0)
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | BETA: splitting (82) gives:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | (83) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | ALPHA: (83) implies:
% 169.23/25.66 | | | | | | | | | | | (84) op(e1, e3) = e0
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | REF_CLOSE: (7), (8), (27), (37), (84) are inconsistent by
% 169.23/25.66 | | | | | | | | | | | sub-proof #749.
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | (85) all_58_7 = e0 & op(e1, e2) = e0
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | ALPHA: (85) implies:
% 169.23/25.66 | | | | | | | | | | | (86) op(e1, e2) = e0
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | BETA: splitting (26) gives:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | (87) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 169.23/25.66 | | | | | | | | | | | | & op(e3, e2) = e1)
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | BETA: splitting (87) gives:
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | (88) all_58_0 = e1 & op(e3, e3) = e1
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | ALPHA: (88) implies:
% 169.23/25.66 | | | | | | | | | | | | | (89) all_58_0 = e1
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (18), (39), (75), (81), (89) are
% 169.23/25.66 | | | | | | | | | | | | | inconsistent by sub-proof #309.
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | (90) all_58_1 = e1 & op(e3, e2) = e1
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | ALPHA: (90) implies:
% 169.23/25.66 | | | | | | | | | | | | | (91) op(e3, e2) = e1
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | REF_CLOSE: (10), (23), (27), (34), (38), (86), (91) are
% 169.23/25.66 | | | | | | | | | | | | | inconsistent by sub-proof #430.
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | (92) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 169.23/25.66 | | | | | | | | | | | | & op(e3, e0) = e1)
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | BETA: splitting (92) gives:
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | (93) all_58_4 = e1 & op(e3, e1) = e1
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | REF_CLOSE: (33), (35), (93) are inconsistent by sub-proof
% 169.23/25.66 | | | | | | | | | | | | | #943.
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | (94) all_58_9 = e1 & op(e3, e0) = e1
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | REF_CLOSE: (33), (43), (94) are inconsistent by sub-proof
% 169.23/25.66 | | | | | | | | | | | | | #701.
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | (95) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0
% 169.23/25.66 | | | | | | | | | | & op(e1, e0) = e0)
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | BETA: splitting (95) gives:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | (96) all_58_8 = e0 & op(e1, e1) = e0
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | REF_CLOSE: (8), (72), (96) are inconsistent by sub-proof
% 169.23/25.66 | | | | | | | | | | | #718.
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | (97) all_58_11 = e0 & op(e1, e0) = e0
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | REF_CLOSE: (18), (40), (97) are inconsistent by sub-proof
% 169.23/25.66 | | | | | | | | | | | #724.
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | End of split
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | End of split
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | Case 2:
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | (98) all_58_7 = e2 & op(e1, e2) = e2
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | ALPHA: (98) implies:
% 169.23/25.66 | | | | | | | (99) all_58_7 = e2
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | REF_CLOSE: (7), (8), (18), (21), (27), (28), (37), (40), (72),
% 169.23/25.66 | | | | | | | (99) are inconsistent by sub-proof #325.
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | End of split
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | Case 2:
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | | (100) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 169.23/25.66 | | | | | | op(e1, e0) = e2)
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (13), (16), (17),
% 169.23/25.66 | | | | | | (18), (20), (22), (27), (28), (30), (31), (32), (33),
% 169.23/25.66 | | | | | | (37), (39), (40), (100) are inconsistent by sub-proof
% 169.23/25.66 | | | | | | #268.
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | End of split
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | Case 2:
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | (101) all_58_14 = e1 & op(e0, e1) = e1
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | ALPHA: (101) implies:
% 169.23/25.66 | | | | | (102) all_58_14 = e1
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | REF_CLOSE: (5), (24), (102) are inconsistent by sub-proof #626.
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | End of split
% 169.23/25.66 | | | |
% 169.23/25.66 | | | End of split
% 169.23/25.66 | | |
% 169.23/25.66 | | Case 2:
% 169.23/25.66 | | |
% 169.23/25.66 | | | (103) all_58_10 = e2 & op(e2, e0) = e2
% 169.23/25.66 | | |
% 169.23/25.66 | | | REF_CLOSE: (1), (5), (8), (13), (16), (18), (20), (27), (28), (30), (33),
% 169.23/25.66 | | | (103) are inconsistent by sub-proof #447.
% 169.23/25.66 | | |
% 169.23/25.66 | | End of split
% 169.23/25.66 | |
% 169.23/25.66 | Case 2:
% 169.23/25.66 | |
% 169.23/25.66 | | (104) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.23/25.66 | | e2)
% 169.23/25.66 | |
% 169.23/25.66 | | BETA: splitting (104) gives:
% 169.23/25.66 | |
% 169.23/25.66 | | Case 1:
% 169.23/25.66 | | |
% 169.23/25.66 | | | (105) all_58_11 = e2 & op(e1, e0) = e2
% 169.23/25.66 | | |
% 169.23/25.66 | | | REF_CLOSE: (1), (3), (5), (8), (13), (16), (18), (20), (27), (28), (30),
% 169.23/25.66 | | | (32), (33), (39), (40), (105) are inconsistent by sub-proof
% 169.23/25.66 | | | #419.
% 169.23/25.66 | | |
% 169.23/25.66 | | Case 2:
% 169.23/25.66 | | |
% 169.23/25.66 | | | (106) all_58_15 = e2 & op(e0, e0) = e2
% 169.23/25.66 | | |
% 169.23/25.66 | | | ALPHA: (106) implies:
% 169.23/25.66 | | | (107) all_58_15 = e2
% 169.23/25.66 | | |
% 169.23/25.66 | | | BETA: splitting (4) gives:
% 169.23/25.66 | | |
% 169.23/25.66 | | | Case 1:
% 169.23/25.66 | | | |
% 169.23/25.66 | | | | (108) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 169.23/25.66 | | | | = e2)
% 169.23/25.66 | | | |
% 169.23/25.66 | | | | BETA: splitting (108) gives:
% 169.23/25.66 | | | |
% 169.23/25.66 | | | | Case 1:
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | (109) all_58_6 = e2 & op(e1, e3) = e2
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (13), (16), (17), (18),
% 169.23/25.66 | | | | | (20), (27), (28), (30), (31), (32), (33), (37), (39), (109)
% 169.23/25.66 | | | | | are inconsistent by sub-proof #278.
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | Case 2:
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | (110) all_58_7 = e2 & op(e1, e2) = e2
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | ALPHA: (110) implies:
% 169.23/25.66 | | | | | (111) all_58_7 = e2
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | BETA: splitting (25) gives:
% 169.23/25.66 | | | | |
% 169.23/25.66 | | | | | Case 1:
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | | (112) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2,
% 169.23/25.66 | | | | | | e2) = e0)
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | | BETA: splitting (112) gives:
% 169.23/25.66 | | | | | |
% 169.23/25.66 | | | | | | Case 1:
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | (113) all_58_1 = e0 & op(e3, e2) = e0
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | ALPHA: (113) implies:
% 169.23/25.66 | | | | | | | (114) op(e3, e2) = e0
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | BETA: splitting (29) gives:
% 169.23/25.66 | | | | | | |
% 169.23/25.66 | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | (115) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 &
% 169.23/25.66 | | | | | | | | op(e1, e2) = e1)
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | BETA: splitting (115) gives:
% 169.23/25.66 | | | | | | | |
% 169.23/25.66 | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | (116) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | ALPHA: (116) implies:
% 169.23/25.66 | | | | | | | | | (117) all_58_6 = e1
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | BETA: splitting (9) gives:
% 169.23/25.66 | | | | | | | | |
% 169.23/25.66 | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | (118) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 169.23/25.66 | | | | | | | | | | & op(e2, e3) = e3)
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | BETA: splitting (118) gives:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | (119) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | ALPHA: (119) implies:
% 169.23/25.66 | | | | | | | | | | | (120) all_58_0 = e3
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | BETA: splitting (2) gives:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | (121) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 169.23/25.66 | | | | | | | | | | | | & op(e2, e3) = e0)
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | REF_CLOSE: (13), (16), (18), (27), (28), (31), (121) are
% 169.23/25.66 | | | | | | | | | | | | inconsistent by sub-proof #460.
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | (122) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 169.23/25.66 | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | BETA: splitting (122) gives:
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | (123) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | ALPHA: (123) implies:
% 169.23/25.66 | | | | | | | | | | | | | (124) op(e1, e3) = e0
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | REF_CLOSE: (7), (8), (27), (37), (124) are inconsistent by
% 169.23/25.66 | | | | | | | | | | | | | sub-proof #749.
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | (125) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | ALPHA: (125) implies:
% 169.23/25.66 | | | | | | | | | | | | | (126) all_58_12 = e0
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | BETA: splitting (6) gives:
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | (127) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 169.23/25.66 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 169.23/25.66 | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (8), (13), (16), (18), (23), (27), (28),
% 169.23/25.66 | | | | | | | | | | | | | | (31), (37), (114), (127) are inconsistent by
% 169.23/25.66 | | | | | | | | | | | | | | sub-proof #267.
% 169.23/25.66 | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | (128) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 169.23/25.66 | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.23/25.66 | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 169.23/25.66 | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | | (129) all_58_14 = e1 & op(e0, e1) = e1
% 169.23/25.66 | | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | | REF_CLOSE: (3), (5), (9), (18), (24), (39), (117), (120),
% 169.23/25.66 | | | | | | | | | | | | | | | (126), (129) are inconsistent by sub-proof #266.
% 169.23/25.66 | | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | | (130) all_58_15 = e1 & op(e0, e0) = e1
% 169.23/25.66 | | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | | REF_CLOSE: (33), (107), (130) are inconsistent by sub-proof
% 169.23/25.66 | | | | | | | | | | | | | | | #720.
% 169.23/25.66 | | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | (131) all_58_2 = e3 & op(e2, e3) = e3
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | ALPHA: (131) implies:
% 169.23/25.66 | | | | | | | | | | | (132) op(e2, e3) = e3
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | REF_CLOSE: (13), (16), (27), (39), (132) are inconsistent by
% 169.23/25.66 | | | | | | | | | | | sub-proof #462.
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | (133) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3
% 169.23/25.66 | | | | | | | | | | & op(e0, e3) = e3)
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | BETA: splitting (133) gives:
% 169.23/25.66 | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | (134) all_58_6 = e3 & op(e1, e3) = e3
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | ALPHA: (134) implies:
% 169.23/25.66 | | | | | | | | | | | (135) all_58_6 = e3
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | BETA: splitting (17) gives:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | (136) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1
% 169.23/25.66 | | | | | | | | | | | | & op(e2, e3) = e1)
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | BETA: splitting (136) gives:
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | Case 1:
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | (137) all_58_0 = e1 & op(e3, e3) = e1
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | ALPHA: (137) implies:
% 169.23/25.66 | | | | | | | | | | | | | (138) all_58_0 = e1
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (13), (16), (18),
% 169.23/25.66 | | | | | | | | | | | | | (21), (27), (28), (29), (33), (37), (39), (40),
% 169.23/25.66 | | | | | | | | | | | | | (111), (135), (138) are inconsistent by sub-proof
% 169.23/25.66 | | | | | | | | | | | | | #265.
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | (139) all_58_2 = e1 & op(e2, e3) = e1
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | ALPHA: (139) implies:
% 169.23/25.66 | | | | | | | | | | | | | (140) op(e2, e3) = e1
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | | REF_CLOSE: (13), (16), (27), (33), (140) are inconsistent by
% 169.23/25.66 | | | | | | | | | | | | | sub-proof #784.
% 169.23/25.66 | | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | (141) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 =
% 169.23/25.66 | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (13), (16), (18), (27), (28),
% 169.23/25.66 | | | | | | | | | | | | (31), (37), (135), (141) are inconsistent by
% 169.23/25.66 | | | | | | | | | | | | sub-proof #285.
% 169.23/25.66 | | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | | End of split
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.66 | | | | | | | | | | Case 2:
% 169.23/25.66 | | | | | | | | | | |
% 169.23/25.67 | | | | | | | | | | | (142) all_58_12 = e3 & op(e0, e3) = e3
% 169.23/25.67 | | | | | | | | | | |
% 169.23/25.67 | | | | | | | | | | | REF_CLOSE: (2), (7), (8), (13), (16), (18), (27), (28), (31),
% 169.23/25.67 | | | | | | | | | | | (37), (142) are inconsistent by sub-proof #301.
% 169.23/25.67 | | | | | | | | | | |
% 169.23/25.67 | | | | | | | | | | End of split
% 169.23/25.67 | | | | | | | | | |
% 169.23/25.67 | | | | | | | | | End of split
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | Case 2:
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | | (143) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | | REF_CLOSE: (33), (111), (143) are inconsistent by sub-proof
% 169.23/25.67 | | | | | | | | | #503.
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | End of split
% 169.23/25.67 | | | | | | | |
% 169.23/25.67 | | | | | | | Case 2:
% 169.23/25.67 | | | | | | | |
% 169.23/25.67 | | | | | | | | (144) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 &
% 169.23/25.67 | | | | | | | | op(e1, e0) = e1)
% 169.23/25.67 | | | | | | | |
% 169.23/25.67 | | | | | | | | BETA: splitting (144) gives:
% 169.23/25.67 | | | | | | | |
% 169.23/25.67 | | | | | | | | Case 1:
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | | (145) all_58_8 = e1 & op(e1, e1) = e1
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | | ALPHA: (145) implies:
% 169.23/25.67 | | | | | | | | | (146) all_58_8 = e1
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | | REF_CLOSE: (7), (8), (18), (21), (27), (28), (37), (40),
% 169.23/25.67 | | | | | | | | | (111), (146) are inconsistent by sub-proof #325.
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | Case 2:
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | | (147) all_58_11 = e1 & op(e1, e0) = e1
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | | ALPHA: (147) implies:
% 169.23/25.67 | | | | | | | | | (148) all_58_11 = e1
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | | REF_CLOSE: (5), (40), (148) are inconsistent by sub-proof
% 169.23/25.67 | | | | | | | | | #755.
% 169.23/25.67 | | | | | | | | |
% 169.23/25.67 | | | | | | | | End of split
% 169.23/25.67 | | | | | | | |
% 169.23/25.67 | | | | | | | End of split
% 169.23/25.67 | | | | | | |
% 169.23/25.67 | | | | | | Case 2:
% 169.23/25.67 | | | | | | |
% 169.23/25.67 | | | | | | | (149) all_58_3 = e0 & op(e2, e2) = e0
% 169.23/25.67 | | | | | | |
% 169.23/25.67 | | | | | | | REF_CLOSE: (18), (30), (149) are inconsistent by sub-proof #869.
% 169.23/25.67 | | | | | | |
% 169.23/25.67 | | | | | | End of split
% 169.23/25.67 | | | | | |
% 169.23/25.67 | | | | | Case 2:
% 169.23/25.67 | | | | | |
% 169.23/25.67 | | | | | | (150) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 &
% 169.23/25.67 | | | | | | op(e0, e2) = e0)
% 169.23/25.67 | | | | | |
% 169.23/25.67 | | | | | | REF_CLOSE: (19), (28), (111), (150) are inconsistent by sub-proof
% 169.23/25.67 | | | | | | #264.
% 169.23/25.67 | | | | | |
% 169.23/25.67 | | | | | End of split
% 169.23/25.67 | | | | |
% 169.23/25.67 | | | | End of split
% 169.23/25.67 | | | |
% 169.23/25.67 | | | Case 2:
% 169.23/25.67 | | | |
% 169.23/25.67 | | | | (151) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 169.23/25.67 | | | | e0) = e2)
% 169.23/25.67 | | | |
% 169.23/25.67 | | | | BETA: splitting (151) gives:
% 169.23/25.67 | | | |
% 169.23/25.67 | | | | Case 1:
% 169.23/25.67 | | | | |
% 169.23/25.67 | | | | | (152) all_58_8 = e2 & op(e1, e1) = e2
% 169.23/25.67 | | | | |
% 169.23/25.67 | | | | | ALPHA: (152) implies:
% 169.23/25.67 | | | | | (153) op(e1, e1) = e2
% 169.23/25.67 | | | | |
% 169.23/25.67 | | | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (13), (16), (17), (18),
% 169.23/25.67 | | | | | (20), (22), (27), (28), (30), (31), (32), (33), (37), (39),
% 169.23/25.67 | | | | | (153) are inconsistent by sub-proof #339.
% 169.23/25.67 | | | | |
% 169.23/25.67 | | | | Case 2:
% 169.23/25.67 | | | | |
% 169.23/25.67 | | | | | (154) all_58_11 = e2 & op(e1, e0) = e2
% 169.23/25.67 | | | | |
% 169.23/25.67 | | | | | REF_CLOSE: (1), (3), (5), (8), (13), (16), (18), (20), (27), (28),
% 169.23/25.67 | | | | | (30), (32), (33), (39), (40), (154) are inconsistent by
% 169.23/25.67 | | | | | sub-proof #419.
% 169.23/25.67 | | | | |
% 169.23/25.67 | | | | End of split
% 169.23/25.67 | | | |
% 169.23/25.67 | | | End of split
% 169.23/25.67 | | |
% 169.23/25.67 | | End of split
% 169.23/25.67 | |
% 169.23/25.67 | End of split
% 169.23/25.67 |
% 169.23/25.67 End of proof
% 169.23/25.67
% 169.23/25.67 Sub-proof #264 shows that the following formulas are inconsistent:
% 169.23/25.67 ----------------------------------------------------------------
% 169.23/25.67 (1) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.23/25.67 (2) all_58_7 = e2
% 169.23/25.67 (3) ~ (e2 = e0)
% 169.23/25.67 (4) all_58_13 = e2
% 169.23/25.67
% 169.23/25.67 Begin of proof
% 169.23/25.67 |
% 169.23/25.67 | BETA: splitting (1) gives:
% 169.23/25.67 |
% 169.23/25.67 | Case 1:
% 169.23/25.67 | |
% 169.23/25.67 | | (5) all_58_7 = e0 & op(e1, e2) = e0
% 169.23/25.67 | |
% 169.23/25.67 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #363.
% 169.23/25.67 | |
% 169.23/25.67 | Case 2:
% 169.23/25.67 | |
% 169.23/25.67 | | (6) all_58_13 = e0 & op(e0, e2) = e0
% 169.23/25.67 | |
% 169.23/25.67 | | ALPHA: (6) implies:
% 169.23/25.67 | | (7) all_58_13 = e0
% 169.23/25.67 | |
% 169.23/25.67 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #865.
% 169.23/25.67 | |
% 169.23/25.67 | End of split
% 169.23/25.67 |
% 169.23/25.67 End of proof
% 169.23/25.67
% 169.23/25.67 Sub-proof #265 shows that the following formulas are inconsistent:
% 169.23/25.67 ----------------------------------------------------------------
% 169.23/25.67 (1) all_58_7 = e2
% 169.23/25.67 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.67 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.67 (3) all_58_2 = e2
% 169.23/25.67 (4) all_58_0 = e1
% 169.23/25.67 (5) ~ (e3 = e1)
% 169.23/25.67 (6) all_58_6 = e3
% 169.23/25.67 (7) op(e1, e3) = all_52_2
% 169.23/25.67 (8) ~ (e1 = e0)
% 169.23/25.67 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.67 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.67 (10) op(e2, e3) = all_52_1
% 169.23/25.67 (11) op(e2, e3) = e2
% 169.23/25.67 (12) ~ (e3 = e0)
% 169.23/25.67 (13) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.67 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.67 (14) all_58_11 = e3
% 169.23/25.67 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.67 (16) ~ (e2 = e0)
% 169.23/25.67 (17) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.67 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.67 (18) ~ (e2 = e1)
% 169.23/25.67 (19) op(e1, e3) = e1
% 169.23/25.67 (20) ~ (e3 = e2)
% 169.23/25.67
% 169.23/25.67 Begin of proof
% 169.23/25.67 |
% 169.23/25.67 | BETA: splitting (17) gives:
% 169.23/25.67 |
% 169.23/25.67 | Case 1:
% 169.23/25.67 | |
% 169.23/25.67 | | (21) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 169.23/25.67 | | e1)
% 169.23/25.67 | |
% 169.23/25.67 | | BETA: splitting (21) gives:
% 169.23/25.67 | |
% 169.23/25.67 | | Case 1:
% 169.23/25.67 | | |
% 169.23/25.67 | | | (22) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.67 | | |
% 169.23/25.67 | | | ALPHA: (22) implies:
% 169.23/25.67 | | | (23) all_58_6 = e1
% 169.23/25.67 | | |
% 169.23/25.67 | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (11), (12), (15), (16),
% 169.23/25.67 | | | (20), (23) are inconsistent by sub-proof #455.
% 169.23/25.67 | | |
% 169.23/25.67 | | Case 2:
% 169.23/25.67 | | |
% 169.23/25.67 | | | (24) all_58_7 = e1 & op(e1, e2) = e1
% 169.23/25.67 | | |
% 169.23/25.67 | | | REF_CLOSE: (1), (18), (24) are inconsistent by sub-proof #503.
% 169.23/25.67 | | |
% 169.23/25.67 | | End of split
% 169.23/25.67 | |
% 169.23/25.67 | Case 2:
% 169.23/25.67 | |
% 169.23/25.67 | | (25) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 169.23/25.67 | | e1)
% 169.23/25.67 | |
% 169.23/25.67 | | BETA: splitting (25) gives:
% 169.23/25.67 | |
% 169.23/25.67 | | Case 1:
% 169.23/25.67 | | |
% 169.23/25.67 | | | (26) all_58_8 = e1 & op(e1, e1) = e1
% 169.23/25.67 | | |
% 169.23/25.67 | | | ALPHA: (26) implies:
% 169.23/25.67 | | | (27) all_58_8 = e1
% 169.23/25.67 | | |
% 169.23/25.67 | | | REF_CLOSE: (1), (7), (8), (12), (13), (14), (15), (16), (19), (27) are
% 169.23/25.67 | | | inconsistent by sub-proof #325.
% 169.23/25.67 | | |
% 169.23/25.67 | | Case 2:
% 169.23/25.67 | | |
% 169.23/25.67 | | | (28) all_58_11 = e1 & op(e1, e0) = e1
% 169.23/25.67 | | |
% 169.23/25.67 | | | ALPHA: (28) implies:
% 169.23/25.67 | | | (29) all_58_11 = e1
% 169.23/25.67 | | |
% 169.23/25.67 | | | COMBINE_EQS: (14), (29) imply:
% 169.23/25.67 | | | (30) e3 = e1
% 169.23/25.67 | | |
% 169.23/25.67 | | | SIMP: (30) implies:
% 169.23/25.67 | | | (31) e3 = e1
% 169.23/25.67 | | |
% 169.23/25.67 | | | COMBINE_EQS: (6), (31) imply:
% 169.23/25.67 | | | (32) all_58_6 = e1
% 169.23/25.67 | | |
% 169.23/25.67 | | | REF_CLOSE: (2), (3), (4), (5), (8), (9), (10), (11), (12), (15), (16),
% 169.23/25.67 | | | (20), (32) are inconsistent by sub-proof #455.
% 169.23/25.67 | | |
% 169.23/25.67 | | End of split
% 169.23/25.67 | |
% 169.23/25.67 | End of split
% 169.23/25.67 |
% 169.23/25.67 End of proof
% 169.23/25.67
% 169.23/25.67 Sub-proof #266 shows that the following formulas are inconsistent:
% 169.23/25.67 ----------------------------------------------------------------
% 169.23/25.67 (1) all_58_2 = e2
% 169.23/25.67 (2) all_58_6 = e1
% 169.23/25.67 (3) all_58_14 = e1 & op(e0, e1) = e1
% 169.23/25.67 (4) ~ (e3 = e1)
% 169.23/25.67 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.67 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.67 (6) ~ (e3 = e0)
% 169.23/25.67 (7) all_58_12 = e0
% 169.23/25.67 (8) all_58_14 = e3
% 169.23/25.67 (9) all_58_0 = e3
% 169.23/25.67 (10) ~ (e3 = e2)
% 169.23/25.67
% 169.23/25.67 Begin of proof
% 169.23/25.67 |
% 169.23/25.67 | ALPHA: (3) implies:
% 169.23/25.67 | (11) all_58_14 = e1
% 169.23/25.67 |
% 169.23/25.67 | COMBINE_EQS: (8), (11) imply:
% 169.23/25.67 | (12) e3 = e1
% 169.23/25.67 |
% 169.23/25.67 | SIMP: (12) implies:
% 169.23/25.67 | (13) e3 = e1
% 169.23/25.67 |
% 169.23/25.67 | COMBINE_EQS: (9), (13) imply:
% 169.23/25.67 | (14) all_58_0 = e1
% 169.23/25.67 |
% 169.23/25.67 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10), (14) are inconsistent by
% 169.23/25.67 | sub-proof #456.
% 169.23/25.67 |
% 169.23/25.67 End of proof
% 169.23/25.67
% 169.23/25.67 Sub-proof #267 shows that the following formulas are inconsistent:
% 169.23/25.67 ----------------------------------------------------------------
% 169.23/25.67 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.67 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.67 (2) op(e1, e3) = all_52_2
% 169.23/25.67 (3) ~ (e1 = e0)
% 169.23/25.67 (4) op(e2, e3) = all_52_1
% 169.23/25.67 (5) op(e2, e3) = e2
% 169.23/25.67 (6) ~ (e3 = e0)
% 169.23/25.67 (7) op(e3, e2) = e0
% 169.23/25.67 (8) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) = all_22_1
% 169.23/25.67 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2) =
% 169.23/25.67 all_22_1 & $i(all_22_1))
% 169.23/25.67 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.67 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.67 (11) ~ (e2 = e0)
% 169.23/25.67 (12) op(e3, e3) = e3
% 169.23/25.67 (13) op(e1, e3) = e1
% 169.23/25.67
% 169.23/25.67 Begin of proof
% 169.23/25.67 |
% 169.23/25.67 | BETA: splitting (9) gives:
% 169.23/25.67 |
% 169.23/25.67 | Case 1:
% 169.23/25.67 | |
% 169.23/25.67 | | (14) all_58_12 = e1 & op(e0, e3) = e1
% 169.23/25.67 | |
% 169.23/25.67 | | ALPHA: (14) implies:
% 169.23/25.67 | | (15) all_58_12 = e1
% 169.23/25.67 | |
% 169.23/25.67 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (11), (12), (13), (15) are
% 169.23/25.67 | | inconsistent by sub-proof #296.
% 169.23/25.67 | |
% 169.23/25.67 | Case 2:
% 169.23/25.67 | |
% 169.23/25.67 | | (16) all_58_13 = e1 & op(e0, e2) = e1
% 169.23/25.67 | |
% 169.23/25.67 | | ALPHA: (16) implies:
% 169.23/25.67 | | (17) op(e0, e2) = e1
% 169.23/25.67 | |
% 169.23/25.67 | | REF_CLOSE: (7), (8), (10), (17) are inconsistent by sub-proof #443.
% 169.23/25.67 | |
% 169.23/25.67 | End of split
% 169.23/25.67 |
% 169.23/25.67 End of proof
% 169.23/25.67
% 169.23/25.67 Sub-proof #268 shows that the following formulas are inconsistent:
% 169.23/25.67 ----------------------------------------------------------------
% 169.23/25.67 (1) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.67 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.67 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.67 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.67 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.67 (4) all_58_2 = e2
% 169.23/25.67 (5) ~ (e3 = e1)
% 169.23/25.67 (6) op(e1, e3) = all_52_2
% 169.23/25.67 (7) ~ (e1 = e0)
% 169.23/25.67 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.67 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.67 (9) op(e2, e3) = all_52_1
% 169.23/25.67 (10) op(e2, e3) = e2
% 169.23/25.67 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.67 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.67 (12) ~ (e3 = e0)
% 169.23/25.67 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.67 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.67 (14) op(e1, e1) = e3
% 169.23/25.67 (15) all_58_11 = e3
% 169.23/25.67 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.67 (17) ~ (e2 = e0)
% 169.23/25.67 (18) all_58_3 = e3
% 169.23/25.67 (19) op(e3, e3) = e3
% 169.23/25.67 (20) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.67 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.67 (21) ~ (e2 = e1)
% 169.23/25.67 (22) op(e1, e3) = e1
% 169.23/25.67 (23) ~ (e3 = e2)
% 169.23/25.67
% 169.23/25.67 Begin of proof
% 169.23/25.67 |
% 169.23/25.67 | BETA: splitting (1) gives:
% 169.23/25.67 |
% 169.23/25.67 | Case 1:
% 169.23/25.67 | |
% 169.23/25.67 | | (24) all_58_8 = e2 & op(e1, e1) = e2
% 169.23/25.67 | |
% 169.23/25.67 | | ALPHA: (24) implies:
% 169.23/25.67 | | (25) op(e1, e1) = e2
% 169.23/25.67 | |
% 169.23/25.67 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.23/25.67 | | (14), (16), (17), (18), (19), (20), (21), (22), (23), (25) are
% 169.23/25.67 | | inconsistent by sub-proof #339.
% 169.23/25.67 | |
% 169.23/25.67 | Case 2:
% 169.23/25.67 | |
% 169.23/25.67 | | (26) all_58_11 = e2 & op(e1, e0) = e2
% 169.23/25.67 | |
% 169.23/25.67 | | ALPHA: (26) implies:
% 169.23/25.67 | | (27) all_58_11 = e2
% 169.23/25.67 | |
% 169.23/25.67 | | REF_CLOSE: (2), (4), (5), (7), (9), (10), (12), (13), (15), (16), (17),
% 169.23/25.67 | | (18), (20), (21), (23), (27) are inconsistent by sub-proof #421.
% 169.23/25.67 | |
% 169.23/25.67 | End of split
% 169.23/25.67 |
% 169.23/25.67 End of proof
% 169.23/25.67
% 169.23/25.67 Sub-proof #269 shows that the following formulas are inconsistent:
% 169.23/25.67 ----------------------------------------------------------------
% 169.23/25.67 (1) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.67 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.67 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.67 (3) all_58_2 = e2
% 169.23/25.67 (4) ~ (e3 = e1)
% 169.23/25.67 (5) ~ (e1 = e0)
% 169.23/25.67 (6) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.67 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.67 (7) op(e2, e3) = all_52_1
% 169.23/25.67 (8) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.67 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.67 (9) op(e2, e3) = e2
% 169.23/25.67 (10) ~ (e3 = e0)
% 169.23/25.67 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.67 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.67 (12) all_58_11 = e3
% 169.23/25.67 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.67 (14) ~ (e2 = e0)
% 169.23/25.67 (15) all_58_5 = e1
% 169.23/25.67 (16) all_58_3 = e3
% 169.23/25.67 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.67 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.67 (18) ~ (e2 = e1)
% 169.23/25.67 (19) all_58_4 = e2
% 169.23/25.67 (20) ~ (e3 = e2)
% 169.23/25.67
% 169.23/25.67 Begin of proof
% 169.23/25.67 |
% 169.23/25.67 | BETA: splitting (1) gives:
% 169.23/25.67 |
% 169.23/25.67 | Case 1:
% 169.23/25.67 | |
% 169.23/25.67 | | (21) all_58_8 = e2 & op(e1, e1) = e2
% 169.23/25.67 | |
% 169.23/25.67 | | ALPHA: (21) implies:
% 169.23/25.67 | | (22) all_58_8 = e2
% 169.23/25.67 | |
% 169.23/25.67 | | REF_CLOSE: (4), (5), (6), (8), (10), (14), (15), (19), (20), (22) are
% 169.23/25.67 | | inconsistent by sub-proof #270.
% 169.23/25.67 | |
% 169.23/25.67 | Case 2:
% 169.23/25.67 | |
% 169.23/25.67 | | (23) all_58_11 = e2 & op(e1, e0) = e2
% 169.23/25.67 | |
% 169.23/25.67 | | ALPHA: (23) implies:
% 169.23/25.67 | | (24) all_58_11 = e2
% 169.23/25.67 | |
% 169.23/25.67 | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14), (16),
% 169.23/25.67 | | (17), (18), (20), (24) are inconsistent by sub-proof #421.
% 169.23/25.67 | |
% 169.23/25.67 | End of split
% 169.23/25.67 |
% 169.23/25.67 End of proof
% 169.23/25.67
% 169.23/25.67 Sub-proof #270 shows that the following formulas are inconsistent:
% 169.23/25.67 ----------------------------------------------------------------
% 169.23/25.67 (1) ~ (e3 = e1)
% 169.23/25.67 (2) ~ (e1 = e0)
% 169.23/25.67 (3) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.67 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.67 (4) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.67 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.67 (5) ~ (e3 = e0)
% 169.23/25.67 (6) all_58_8 = e2
% 169.23/25.67 (7) ~ (e2 = e0)
% 169.23/25.67 (8) all_58_5 = e1
% 169.23/25.67 (9) all_58_4 = e2
% 169.23/25.67 (10) ~ (e3 = e2)
% 169.23/25.67
% 169.23/25.67 Begin of proof
% 169.23/25.67 |
% 169.23/25.67 | BETA: splitting (3) gives:
% 169.23/25.67 |
% 169.23/25.67 | Case 1:
% 169.23/25.67 | |
% 169.23/25.67 | | (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 169.23/25.67 | | e3)
% 169.23/25.67 | |
% 169.23/25.67 | | REF_CLOSE: (1), (8), (9), (10), (11) are inconsistent by sub-proof #323.
% 169.23/25.67 | |
% 169.23/25.67 | Case 2:
% 169.23/25.67 | |
% 169.23/25.67 | | (12) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 169.23/25.67 | | e3)
% 169.23/25.67 | |
% 169.23/25.67 | | BETA: splitting (12) gives:
% 169.23/25.67 | |
% 169.23/25.67 | | Case 1:
% 169.23/25.67 | | |
% 169.23/25.67 | | | (13) all_58_8 = e3 & op(e1, e1) = e3
% 169.23/25.67 | | |
% 169.23/25.67 | | | REF_CLOSE: (6), (10), (13) are inconsistent by sub-proof #272.
% 169.23/25.67 | | |
% 169.23/25.67 | | Case 2:
% 169.23/25.67 | | |
% 169.23/25.67 | | | (14) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.67 | | |
% 169.23/25.67 | | | ALPHA: (14) implies:
% 169.23/25.67 | | | (15) all_58_14 = e3
% 169.23/25.67 | | |
% 169.23/25.67 | | | BETA: splitting (4) gives:
% 169.23/25.67 | | |
% 169.23/25.67 | | | Case 1:
% 169.23/25.67 | | | |
% 169.23/25.68 | | | | (16) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 169.23/25.68 | | | | = e0)
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | BETA: splitting (16) gives:
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | Case 1:
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | (17) all_58_4 = e0 & op(e3, e1) = e0
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | REF_CLOSE: (7), (9), (17) are inconsistent by sub-proof #902.
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | Case 2:
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | (18) all_58_5 = e0 & op(e2, e1) = e0
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | REF_CLOSE: (2), (8), (18) are inconsistent by sub-proof #781.
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | End of split
% 169.23/25.68 | | | |
% 169.23/25.68 | | | Case 2:
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | (19) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1)
% 169.23/25.68 | | | | = e0)
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | BETA: splitting (19) gives:
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | Case 1:
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | (20) all_58_8 = e0 & op(e1, e1) = e0
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | REF_CLOSE: (6), (7), (20) are inconsistent by sub-proof #271.
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | Case 2:
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | (21) all_58_14 = e0 & op(e0, e1) = e0
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | REF_CLOSE: (5), (15), (21) are inconsistent by sub-proof #871.
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | End of split
% 169.23/25.68 | | | |
% 169.23/25.68 | | | End of split
% 169.23/25.68 | | |
% 169.23/25.68 | | End of split
% 169.23/25.68 | |
% 169.23/25.68 | End of split
% 169.23/25.68 |
% 169.23/25.68 End of proof
% 169.23/25.68
% 169.23/25.68 Sub-proof #271 shows that the following formulas are inconsistent:
% 169.23/25.68 ----------------------------------------------------------------
% 169.23/25.68 (1) all_58_8 = e0 & op(e1, e1) = e0
% 169.23/25.68 (2) all_58_8 = e2
% 169.23/25.68 (3) ~ (e2 = e0)
% 169.23/25.68
% 169.23/25.68 Begin of proof
% 169.23/25.68 |
% 169.23/25.68 | ALPHA: (1) implies:
% 169.23/25.68 | (4) all_58_8 = e0
% 169.23/25.68 |
% 169.23/25.68 | COMBINE_EQS: (2), (4) imply:
% 169.23/25.68 | (5) e2 = e0
% 169.23/25.68 |
% 169.23/25.68 | SIMP: (5) implies:
% 169.23/25.68 | (6) e2 = e0
% 169.23/25.68 |
% 169.23/25.68 | REDUCE: (3), (6) imply:
% 169.23/25.68 | (7) $false
% 169.23/25.68 |
% 169.23/25.68 | CLOSE: (7) is inconsistent.
% 169.23/25.68 |
% 169.23/25.68 End of proof
% 169.23/25.68
% 169.23/25.68 Sub-proof #272 shows that the following formulas are inconsistent:
% 169.23/25.68 ----------------------------------------------------------------
% 169.23/25.68 (1) all_58_8 = e3 & op(e1, e1) = e3
% 169.23/25.68 (2) all_58_8 = e2
% 169.23/25.68 (3) ~ (e3 = e2)
% 169.23/25.68
% 169.23/25.68 Begin of proof
% 169.23/25.68 |
% 169.23/25.68 | ALPHA: (1) implies:
% 169.23/25.68 | (4) all_58_8 = e3
% 169.23/25.68 |
% 169.23/25.68 | COMBINE_EQS: (2), (4) imply:
% 169.23/25.68 | (5) e3 = e2
% 169.23/25.68 |
% 169.23/25.68 | REDUCE: (3), (5) imply:
% 169.23/25.68 | (6) $false
% 169.23/25.68 |
% 169.23/25.68 | CLOSE: (6) is inconsistent.
% 169.23/25.68 |
% 169.23/25.68 End of proof
% 169.23/25.68
% 169.23/25.68 Sub-proof #273 shows that the following formulas are inconsistent:
% 169.23/25.68 ----------------------------------------------------------------
% 169.23/25.68 (1) all_58_7 = e2
% 169.23/25.68 (2) ~ (e3 = e1)
% 169.23/25.68 (3) op(e1, e3) = all_52_2
% 169.23/25.68 (4) ~ (e1 = e0)
% 169.23/25.68 (5) ~ (e3 = e0)
% 169.23/25.68 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.68 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.68 (7) all_58_11 = e3
% 169.23/25.68 (8) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.68 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.68 (10) ~ (e2 = e0)
% 169.23/25.68 (11) op(e1, e3) = e1
% 169.23/25.68
% 169.23/25.68 Begin of proof
% 169.23/25.68 |
% 169.23/25.68 | BETA: splitting (8) gives:
% 169.23/25.68 |
% 169.23/25.68 | Case 1:
% 169.23/25.68 | |
% 169.23/25.68 | | (12) all_58_8 = e1 & op(e1, e1) = e1
% 169.23/25.68 | |
% 169.23/25.68 | | ALPHA: (12) implies:
% 169.23/25.68 | | (13) all_58_8 = e1
% 169.23/25.68 | |
% 169.23/25.68 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (13) are
% 169.23/25.68 | | inconsistent by sub-proof #325.
% 169.23/25.68 | |
% 169.23/25.68 | Case 2:
% 169.23/25.68 | |
% 169.23/25.68 | | (14) all_58_11 = e1 & op(e1, e0) = e1
% 169.23/25.68 | |
% 169.23/25.68 | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #721.
% 169.23/25.68 | |
% 169.23/25.68 | End of split
% 169.23/25.68 |
% 169.23/25.68 End of proof
% 169.23/25.68
% 169.23/25.68 Sub-proof #274 shows that the following formulas are inconsistent:
% 169.23/25.68 ----------------------------------------------------------------
% 169.23/25.68 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.68 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.68 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.68 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.68 (3) all_58_2 = e2
% 169.23/25.68 (4) ~ (e3 = e1)
% 169.23/25.68 (5) ~ (e1 = e0)
% 169.23/25.68 (6) op(e2, e3) = all_52_1
% 169.23/25.68 (7) all_58_6 = e2
% 169.23/25.68 (8) op(e2, e3) = e2
% 169.23/25.68 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.68 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.68 (10) ~ (e3 = e0)
% 169.23/25.68 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.68 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.68 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.68 (13) ~ (e2 = e0)
% 169.23/25.68 (14) all_58_3 = e3
% 169.23/25.68 (15) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.68 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.68 (16) ~ (e2 = e1)
% 169.23/25.68 (17) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.68 (18) ~ (e3 = e2)
% 169.23/25.68
% 169.23/25.68 Begin of proof
% 169.23/25.68 |
% 169.23/25.68 | BETA: splitting (17) gives:
% 169.23/25.68 |
% 169.23/25.68 | Case 1:
% 169.23/25.68 | |
% 169.23/25.68 | | (19) all_58_6 = e3 & op(e1, e3) = e3
% 169.23/25.68 | |
% 169.23/25.68 | | ALPHA: (19) implies:
% 169.23/25.68 | | (20) all_58_6 = e3
% 169.23/25.68 | |
% 169.23/25.68 | | COMBINE_EQS: (7), (20) imply:
% 169.23/25.68 | | (21) e3 = e2
% 169.23/25.68 | |
% 169.23/25.68 | | SIMP: (21) implies:
% 169.23/25.68 | | (22) e3 = e2
% 169.23/25.68 | |
% 169.23/25.68 | | COMBINE_EQS: (14), (22) imply:
% 169.23/25.68 | | (23) all_58_3 = e2
% 169.23/25.68 | |
% 169.23/25.68 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (11), (12), (13), (15), (16),
% 169.23/25.68 | | (18), (23) are inconsistent by sub-proof #779.
% 169.23/25.68 | |
% 169.23/25.68 | Case 2:
% 169.23/25.68 | |
% 169.23/25.68 | | (24) all_58_12 = e3 & op(e0, e3) = e3
% 169.23/25.68 | |
% 169.23/25.68 | | ALPHA: (24) implies:
% 169.23/25.68 | | (25) all_58_12 = e3
% 169.23/25.68 | |
% 169.23/25.68 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (12), (13), (16), (25)
% 169.23/25.68 | | are inconsistent by sub-proof #329.
% 169.23/25.68 | |
% 169.23/25.68 | End of split
% 169.23/25.68 |
% 169.23/25.68 End of proof
% 169.23/25.68
% 169.23/25.68 Sub-proof #275 shows that the following formulas are inconsistent:
% 169.23/25.68 ----------------------------------------------------------------
% 169.23/25.68 (1) all_58_12 = e1
% 169.23/25.68 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.68 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.68 (3) ~ (e1 = e0)
% 169.23/25.68 (4) op(e2, e3) = all_52_1
% 169.23/25.68 (5) all_58_6 = e2
% 169.23/25.68 (6) op(e2, e3) = e2
% 169.23/25.68 (7) ~ (e3 = e0)
% 169.23/25.68 (8) all_58_0 = e3
% 169.23/25.68 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.68 (10) ~ (e2 = e0)
% 169.23/25.68
% 169.23/25.68 Begin of proof
% 169.23/25.68 |
% 169.23/25.68 | BETA: splitting (2) gives:
% 169.23/25.68 |
% 169.23/25.68 | Case 1:
% 169.23/25.68 | |
% 169.23/25.68 | | (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.23/25.68 | | e0)
% 169.23/25.68 | |
% 169.23/25.68 | | BETA: splitting (11) gives:
% 169.23/25.68 | |
% 169.23/25.68 | | Case 1:
% 169.23/25.68 | | |
% 169.23/25.68 | | | (12) all_58_0 = e0 & op(e3, e3) = e0
% 169.23/25.68 | | |
% 169.23/25.68 | | | REF_CLOSE: (7), (8), (12) are inconsistent by sub-proof #898.
% 169.23/25.68 | | |
% 169.23/25.68 | | Case 2:
% 169.23/25.68 | | |
% 169.23/25.68 | | | (13) all_58_2 = e0 & op(e2, e3) = e0
% 169.23/25.68 | | |
% 169.23/25.68 | | | REF_CLOSE: (4), (6), (9), (10), (13) are inconsistent by sub-proof #782.
% 169.23/25.68 | | |
% 169.23/25.68 | | End of split
% 169.23/25.68 | |
% 169.23/25.68 | Case 2:
% 169.23/25.68 | |
% 169.23/25.68 | | (14) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.23/25.68 | | e0)
% 169.23/25.68 | |
% 169.23/25.68 | | BETA: splitting (14) gives:
% 169.23/25.68 | |
% 169.23/25.68 | | Case 1:
% 169.23/25.68 | | |
% 169.23/25.68 | | | (15) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.68 | | |
% 169.23/25.68 | | | REF_CLOSE: (5), (10), (15) are inconsistent by sub-proof #769.
% 169.23/25.68 | | |
% 169.23/25.68 | | Case 2:
% 169.23/25.68 | | |
% 169.23/25.68 | | | (16) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.68 | | |
% 169.23/25.68 | | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #859.
% 169.23/25.68 | | |
% 169.23/25.68 | | End of split
% 169.23/25.68 | |
% 169.23/25.68 | End of split
% 169.23/25.68 |
% 169.23/25.68 End of proof
% 169.23/25.68
% 169.23/25.68 Sub-proof #276 shows that the following formulas are inconsistent:
% 169.23/25.68 ----------------------------------------------------------------
% 169.23/25.68 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.68 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.68 (2) all_58_9 = e2
% 169.23/25.68 (3) all_58_2 = e2
% 169.23/25.68 (4) ~ (e3 = e1)
% 169.23/25.68 (5) op(e1, e3) = all_52_2
% 169.23/25.68 (6) ~ (e1 = e0)
% 169.23/25.68 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.68 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.68 (8) op(e1, e2) = all_52_6
% 169.23/25.68 (9) op(e2, e3) = all_52_1
% 169.23/25.68 (10) op(e2, e3) = e2
% 169.23/25.68 (11) ~ (e3 = e0)
% 169.23/25.68 (12) all_58_13 = e2
% 169.23/25.68 (13) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.68 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.68 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.68 (14) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.68 (15) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.68 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.23/25.68 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.68 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.68 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.68 (18) ~ (e2 = e0)
% 169.23/25.68 (19) all_58_3 = e3
% 169.23/25.68 (20) op(e3, e3) = e3
% 169.23/25.68 (21) ~ (e2 = e1)
% 169.23/25.68 (22) op(e3, e2) = all_52_4
% 169.23/25.68 (23) all_58_4 = e2
% 169.23/25.68 (24) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.23/25.68 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.23/25.68 e2) = all_14_1 & $i(all_14_1))
% 169.23/25.68 (25) ~ (e3 = e2)
% 169.23/25.68
% 169.23/25.68 Begin of proof
% 169.23/25.68 |
% 169.23/25.68 | ALPHA: (14) implies:
% 169.23/25.68 | (26) all_58_6 = e1
% 169.23/25.68 | (27) op(e1, e3) = e1
% 169.23/25.68 |
% 169.23/25.68 | BETA: splitting (1) gives:
% 169.23/25.68 |
% 169.23/25.68 | Case 1:
% 169.23/25.68 | |
% 169.23/25.68 | | (28) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.23/25.68 | | e0)
% 169.23/25.68 | |
% 169.23/25.68 | | REF_CLOSE: (9), (10), (11), (17), (18), (20), (28) are inconsistent by
% 169.23/25.68 | | sub-proof #460.
% 169.23/25.68 | |
% 169.23/25.68 | Case 2:
% 169.23/25.68 | |
% 169.23/25.68 | | (29) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.23/25.68 | | e0)
% 169.23/25.68 | |
% 169.23/25.68 | | BETA: splitting (29) gives:
% 169.23/25.68 | |
% 169.23/25.68 | | Case 1:
% 169.23/25.68 | | |
% 169.23/25.68 | | | (30) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.68 | | |
% 169.23/25.68 | | | ALPHA: (30) implies:
% 169.23/25.68 | | | (31) op(e1, e3) = e0
% 169.23/25.68 | | |
% 169.23/25.68 | | | REF_CLOSE: (5), (6), (17), (27), (31) are inconsistent by sub-proof #749.
% 169.23/25.68 | | |
% 169.23/25.68 | | Case 2:
% 169.23/25.68 | | |
% 169.23/25.68 | | | (32) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.68 | | |
% 169.23/25.68 | | | ALPHA: (32) implies:
% 169.23/25.68 | | | (33) all_58_12 = e0
% 169.23/25.68 | | |
% 169.23/25.68 | | | BETA: splitting (16) gives:
% 169.23/25.68 | | |
% 169.23/25.68 | | | Case 1:
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | (34) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 169.23/25.68 | | | | = e1)
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | BETA: splitting (34) gives:
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | Case 1:
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | (35) all_58_0 = e1 & op(e3, e3) = e1
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | ALPHA: (35) implies:
% 169.23/25.68 | | | | | (36) all_58_0 = e1
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | REF_CLOSE: (3), (4), (7), (11), (25), (26), (33), (36) are
% 169.23/25.68 | | | | | inconsistent by sub-proof #456.
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | Case 2:
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | (37) all_58_1 = e1 & op(e3, e2) = e1
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | ALPHA: (37) implies:
% 169.23/25.68 | | | | | (38) all_58_1 = e1
% 169.23/25.68 | | | | | (39) op(e3, e2) = e1
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | REF_CLOSE: (6), (8), (11), (12), (13), (15), (17), (18), (19), (22),
% 169.23/25.68 | | | | | (24), (38), (39) are inconsistent by sub-proof #429.
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | End of split
% 169.23/25.68 | | | |
% 169.23/25.68 | | | Case 2:
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | (40) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 169.23/25.68 | | | | = e1)
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | BETA: splitting (40) gives:
% 169.23/25.68 | | | |
% 169.23/25.68 | | | | Case 1:
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | (41) all_58_4 = e1 & op(e3, e1) = e1
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | REF_CLOSE: (21), (23), (41) are inconsistent by sub-proof #943.
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | Case 2:
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | (42) all_58_9 = e1 & op(e3, e0) = e1
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | | REF_CLOSE: (2), (21), (42) are inconsistent by sub-proof #701.
% 169.23/25.68 | | | | |
% 169.23/25.68 | | | | End of split
% 169.23/25.68 | | | |
% 169.23/25.68 | | | End of split
% 169.23/25.68 | | |
% 169.23/25.68 | | End of split
% 169.23/25.68 | |
% 169.23/25.68 | End of split
% 169.23/25.68 |
% 169.23/25.68 End of proof
% 169.23/25.68
% 169.23/25.68 Sub-proof #277 shows that the following formulas are inconsistent:
% 169.23/25.68 ----------------------------------------------------------------
% 169.23/25.68 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.68 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.68 (2) ~ (e3 = e1)
% 169.23/25.68 (3) ~ (e1 = e0)
% 169.23/25.68 (4) op(e2, e3) = all_52_1
% 169.23/25.68 (5) op(e2, e3) = e2
% 169.23/25.68 (6) ~ (e3 = e0)
% 169.23/25.68 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.68 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.68 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.68 (9) ~ (e2 = e0)
% 169.23/25.68 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 169.23/25.68 (11) all_58_9 = e3
% 169.23/25.68 (12) ~ (e2 = e1)
% 169.23/25.68 (13) all_58_4 = e2
% 169.23/25.68 (14) ~ (e3 = e2)
% 169.23/25.68
% 169.23/25.68 Begin of proof
% 169.23/25.68 |
% 169.23/25.68 | BETA: splitting (10) gives:
% 169.23/25.68 |
% 169.23/25.68 | Case 1:
% 169.23/25.68 | |
% 169.23/25.68 | | (15) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.68 | |
% 169.23/25.68 | | ALPHA: (15) implies:
% 169.23/25.68 | | (16) all_58_0 = e3
% 169.23/25.68 | |
% 169.23/25.68 | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (11), (12), (13), (16) are
% 169.23/25.68 | | inconsistent by sub-proof #509.
% 169.23/25.68 | |
% 169.23/25.68 | Case 2:
% 169.23/25.68 | |
% 169.23/25.68 | | (17) all_58_2 = e3 & op(e2, e3) = e3
% 169.23/25.68 | |
% 169.23/25.68 | | ALPHA: (17) implies:
% 169.23/25.68 | | (18) op(e2, e3) = e3
% 169.23/25.68 | |
% 169.23/25.68 | | REF_CLOSE: (4), (5), (8), (14), (18) are inconsistent by sub-proof #462.
% 169.23/25.68 | |
% 169.23/25.68 | End of split
% 169.23/25.68 |
% 169.23/25.68 End of proof
% 169.23/25.68
% 169.23/25.68 Sub-proof #278 shows that the following formulas are inconsistent:
% 169.23/25.68 ----------------------------------------------------------------
% 169.23/25.68 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.68 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.68 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.68 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.68 (3) all_58_2 = e2
% 169.23/25.68 (4) ~ (e3 = e1)
% 169.23/25.68 (5) op(e1, e3) = all_52_2
% 169.23/25.68 (6) ~ (e1 = e0)
% 169.23/25.68 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.68 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.68 (8) op(e2, e3) = all_52_1
% 169.23/25.68 (9) op(e2, e3) = e2
% 169.23/25.68 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.68 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.68 (11) ~ (e3 = e0)
% 169.23/25.68 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.68 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.68 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.68 (14) ~ (e2 = e0)
% 169.23/25.68 (15) all_58_3 = e3
% 169.23/25.68 (16) op(e3, e3) = e3
% 169.23/25.68 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.68 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.69 (18) ~ (e2 = e1)
% 169.23/25.69 (19) op(e1, e3) = e1
% 169.23/25.69 (20) all_58_6 = e2 & op(e1, e3) = e2
% 169.23/25.69 (21) ~ (e3 = e2)
% 169.23/25.69
% 169.23/25.69 Begin of proof
% 169.23/25.69 |
% 169.23/25.69 | ALPHA: (20) implies:
% 169.23/25.69 | (22) all_58_6 = e2
% 169.23/25.69 |
% 169.23/25.69 | BETA: splitting (10) gives:
% 169.23/25.69 |
% 169.23/25.69 | Case 1:
% 169.23/25.69 | |
% 169.23/25.69 | | (23) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 169.23/25.69 | | e1)
% 169.23/25.69 | |
% 169.23/25.69 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14),
% 169.23/25.69 | | (15), (17), (18), (21), (22), (23) are inconsistent by sub-proof
% 169.23/25.69 | | #279.
% 169.23/25.69 | |
% 169.23/25.69 | Case 2:
% 169.23/25.69 | |
% 169.23/25.69 | | (24) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 169.23/25.69 | | e1)
% 169.23/25.69 | |
% 169.23/25.69 | | BETA: splitting (24) gives:
% 169.23/25.69 | |
% 169.23/25.69 | | Case 1:
% 169.23/25.69 | | |
% 169.23/25.69 | | | (25) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.69 | | |
% 169.23/25.69 | | | REF_CLOSE: (18), (22), (25) are inconsistent by sub-proof #774.
% 169.23/25.69 | | |
% 169.23/25.69 | | Case 2:
% 169.23/25.69 | | |
% 169.23/25.69 | | | (26) all_58_12 = e1 & op(e0, e3) = e1
% 169.23/25.69 | | |
% 169.23/25.69 | | | ALPHA: (26) implies:
% 169.23/25.69 | | | (27) all_58_12 = e1
% 169.23/25.69 | | |
% 169.23/25.69 | | | REF_CLOSE: (2), (5), (6), (8), (9), (11), (13), (14), (16), (19), (27) are
% 169.23/25.69 | | | inconsistent by sub-proof #296.
% 169.23/25.69 | | |
% 169.23/25.69 | | End of split
% 169.23/25.69 | |
% 169.23/25.69 | End of split
% 169.23/25.69 |
% 169.23/25.69 End of proof
% 169.23/25.69
% 169.23/25.69 Sub-proof #279 shows that the following formulas are inconsistent:
% 169.23/25.69 ----------------------------------------------------------------
% 169.23/25.69 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.69 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.69 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.69 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.69 (3) all_58_2 = e2
% 169.23/25.69 (4) ~ (e3 = e1)
% 169.23/25.69 (5) ~ (e1 = e0)
% 169.23/25.69 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.69 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.69 (7) op(e2, e3) = all_52_1
% 169.23/25.69 (8) all_58_6 = e2
% 169.23/25.69 (9) op(e2, e3) = e2
% 169.23/25.69 (10) ~ (e3 = e0)
% 169.23/25.69 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.69 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.69 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 169.23/25.69 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.69 (14) ~ (e2 = e0)
% 169.23/25.69 (15) all_58_3 = e3
% 169.23/25.69 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.69 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.69 (17) ~ (e2 = e1)
% 169.23/25.69 (18) ~ (e3 = e2)
% 169.23/25.69
% 169.23/25.69 Begin of proof
% 169.23/25.69 |
% 169.23/25.69 | BETA: splitting (12) gives:
% 169.23/25.69 |
% 169.23/25.69 | Case 1:
% 169.23/25.69 | |
% 169.23/25.69 | | (19) all_58_0 = e1 & op(e3, e3) = e1
% 169.23/25.69 | |
% 169.23/25.69 | | ALPHA: (19) implies:
% 169.23/25.69 | | (20) all_58_0 = e1
% 169.23/25.69 | |
% 169.23/25.69 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 169.23/25.69 | | (14), (15), (16), (17), (18), (20) are inconsistent by sub-proof
% 169.23/25.69 | | #400.
% 169.23/25.69 | |
% 169.23/25.69 | Case 2:
% 169.23/25.69 | |
% 169.23/25.69 | | (21) all_58_2 = e1 & op(e2, e3) = e1
% 169.23/25.69 | |
% 169.23/25.69 | | ALPHA: (21) implies:
% 169.23/25.69 | | (22) op(e2, e3) = e1
% 169.23/25.69 | |
% 169.23/25.69 | | REF_CLOSE: (7), (9), (13), (17), (22) are inconsistent by sub-proof #784.
% 169.23/25.69 | |
% 169.23/25.69 | End of split
% 169.23/25.69 |
% 169.23/25.69 End of proof
% 169.23/25.69
% 169.23/25.69 Sub-proof #280 shows that the following formulas are inconsistent:
% 169.23/25.69 ----------------------------------------------------------------
% 169.23/25.69 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.69 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.69 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.69 (3) ~ (e3 = e1)
% 169.23/25.69 (4) all_58_6 = e3
% 169.23/25.69 (5) op(e1, e3) = all_52_2
% 169.23/25.69 (6) ~ (e1 = e0)
% 169.23/25.69 (7) op(e2, e3) = all_52_1
% 169.23/25.69 (8) op(e2, e3) = e2
% 169.23/25.69 (9) ~ (e3 = e0)
% 169.23/25.69 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.69 (11) ~ (e2 = e0)
% 169.23/25.69 (12) op(e3, e3) = e3
% 169.23/25.69 (13) op(e1, e3) = e1
% 169.23/25.69
% 169.23/25.69 Begin of proof
% 169.23/25.69 |
% 169.23/25.69 | BETA: splitting (1) gives:
% 169.23/25.69 |
% 169.23/25.69 | Case 1:
% 169.23/25.69 | |
% 169.23/25.69 | | (14) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.69 | |
% 169.23/25.69 | | REF_CLOSE: (3), (4), (14) are inconsistent by sub-proof #487.
% 169.23/25.69 | |
% 169.23/25.69 | Case 2:
% 169.23/25.69 | |
% 169.23/25.69 | | (15) all_58_12 = e1 & op(e0, e3) = e1
% 169.23/25.69 | |
% 169.23/25.69 | | ALPHA: (15) implies:
% 169.23/25.69 | | (16) all_58_12 = e1
% 169.23/25.69 | |
% 169.23/25.69 | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (16) are
% 169.23/25.69 | | inconsistent by sub-proof #296.
% 169.23/25.69 | |
% 169.23/25.69 | End of split
% 169.23/25.69 |
% 169.23/25.69 End of proof
% 169.23/25.69
% 169.23/25.69 Sub-proof #281 shows that the following formulas are inconsistent:
% 169.23/25.69 ----------------------------------------------------------------
% 169.23/25.69 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.69 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.69 (2) all_58_2 = e2
% 169.23/25.69 (3) all_58_0 = e1
% 169.23/25.69 (4) ~ (e3 = e1)
% 169.23/25.69 (5) all_58_6 = e3
% 169.23/25.69 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 169.23/25.69 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.69 (7) ~ (e1 = e0)
% 169.23/25.69 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.69 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.69 (9) op(e2, e3) = all_52_1
% 169.23/25.69 (10) op(e2, e3) = e2
% 169.23/25.69 (11) ~ (e3 = e0)
% 169.23/25.69 (12) op(e3, e2) = e0
% 169.23/25.69 (13) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.69 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.69 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.69 (14) all_58_14 = e3
% 169.23/25.69 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.69 (16) ~ (e2 = e0)
% 169.23/25.69 (17) all_58_15 = e0
% 169.23/25.69 (18) ~ (e3 = e2)
% 169.23/25.69
% 169.23/25.69 Begin of proof
% 169.23/25.69 |
% 169.23/25.69 | BETA: splitting (6) gives:
% 169.23/25.69 |
% 169.23/25.69 | Case 1:
% 169.23/25.69 | |
% 169.23/25.69 | | (19) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.23/25.69 | | e1)
% 169.23/25.69 | |
% 169.23/25.69 | | REF_CLOSE: (1), (3), (5), (7), (9), (10), (11), (12), (13), (15), (16), (19)
% 169.23/25.69 | | are inconsistent by sub-proof #442.
% 169.23/25.69 | |
% 169.23/25.69 | Case 2:
% 169.23/25.69 | |
% 169.23/25.69 | | (20) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.23/25.69 | | e1)
% 169.23/25.69 | |
% 169.23/25.69 | | BETA: splitting (20) gives:
% 169.23/25.69 | |
% 169.23/25.69 | | Case 1:
% 169.23/25.69 | | |
% 169.23/25.69 | | | (21) all_58_14 = e1 & op(e0, e1) = e1
% 169.23/25.69 | | |
% 169.23/25.69 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (14), (15),
% 169.23/25.69 | | | (16), (18), (21) are inconsistent by sub-proof #441.
% 169.23/25.69 | | |
% 169.23/25.69 | | Case 2:
% 169.23/25.69 | | |
% 169.23/25.69 | | | (22) all_58_15 = e1 & op(e0, e0) = e1
% 169.23/25.69 | | |
% 169.23/25.69 | | | ALPHA: (22) implies:
% 169.23/25.69 | | | (23) all_58_15 = e1
% 169.23/25.69 | | |
% 169.23/25.69 | | | REF_CLOSE: (7), (17), (23) are inconsistent by sub-proof #881.
% 169.23/25.69 | | |
% 169.23/25.69 | | End of split
% 169.23/25.69 | |
% 169.23/25.69 | End of split
% 169.23/25.69 |
% 169.23/25.69 End of proof
% 169.23/25.69
% 169.23/25.69 Sub-proof #282 shows that the following formulas are inconsistent:
% 169.23/25.69 ----------------------------------------------------------------
% 169.23/25.69 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.23/25.69 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.23/25.69 (2) op(e2, e1) = all_52_9
% 169.23/25.69 (3) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.23/25.69 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.23/25.69 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.69 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.69 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.23/25.69 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.69 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.69 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.69 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.69 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 169.23/25.69 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.69 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.69 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.69 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.69 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.23/25.69 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.69 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.69 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.69 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.69 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.23/25.69 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.69 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.69 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.69 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.69 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 169.23/25.69 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 169.23/25.69 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.23/25.69 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.69 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.69 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.23/25.69 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.69 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.69 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.69 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.69 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 169.23/25.69 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 169.23/25.69 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.23/25.69 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.69 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.69 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.23/25.69 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.69 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.69 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.69 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.69 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 169.23/25.69 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.23/25.69 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.23/25.69 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 169.23/25.69 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.23/25.69 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 169.23/25.69 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.23/25.69 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.69 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.69 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.69 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.69 (6) op(e0, e1) = all_52_11
% 169.23/25.69 (7) ~ (all_52_14 = all_4_2)
% 169.23/25.69 (8) ~ (all_52_9 = e3)
% 169.23/25.69 (9) ~ (all_52_13 = e3)
% 169.23/25.69 (10) ~ (all_4_2 = e2)
% 169.23/25.69 (11) all_56_2 = e1
% 169.23/25.69 (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.69 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.69 (13) all_54_12 = all_52_3
% 169.23/25.69 (14) all_58_2 = e2
% 169.23/25.69 (15) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.69 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.69 (16) ~ (all_52_11 = all_4_2)
% 169.23/25.69 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.23/25.69 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.69 (18) ~ (all_56_15 = e3) | (all_56_6 = e0 & op(e0, e3) = e0)
% 169.23/25.69 (19) all_56_14 = e3
% 169.23/25.69 (20) ~ (all_4_2 = e1)
% 169.23/25.69 (21) op(e3, e3) = all_10_2
% 169.23/25.69 (22) ~ (all_52_3 = e2)
% 169.23/25.69 (23) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.69 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.69 (24) ~ (e3 = e1)
% 169.23/25.69 (25) op(e3, e0) = all_52_12
% 169.23/25.69 (26) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.69 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.23/25.69 e1)
% 169.23/25.69 (27) op(e1, e3) = all_52_2
% 169.23/25.69 (28) ~ (all_10_2 = e0)
% 169.23/25.69 (29) op(e3, e1) = all_52_8
% 169.23/25.69 (30) ~ (all_52_9 = all_52_11)
% 169.23/25.69 (31) ~ (e1 = e0)
% 169.23/25.69 (32) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.23/25.69 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.23/25.69 e3)
% 169.23/25.69 (33) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.69 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.69 (34) op(e1, e2) = all_52_6
% 169.23/25.69 (35) ~ (all_52_3 = all_4_2)
% 169.23/25.69 (36) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.69 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.69 (37) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.23/25.69 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.23/25.69 (38) op(e2, e3) = all_52_1
% 169.23/25.69 (39) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.69 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.69 (40) ~ (all_52_7 = all_4_2)
% 169.23/25.69 (41) ~ (all_52_12 = all_4_2)
% 169.23/25.69 (42) ~ (all_52_3 = all_52_7)
% 169.23/25.69 (43) ~ (all_36_2 = e3) | ( ~ (all_36_0 = e2) & op(all_36_1, e1) = all_36_0 &
% 169.23/25.69 op(e3, e1) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 169.23/25.69 e0) & op(e3, e1) = all_36_1 & $i(all_36_1))
% 169.23/25.69 (44) ~ (all_52_7 = e3)
% 169.23/25.69 (45) ~ (all_52_12 = all_52_14)
% 169.23/25.69 (46) op(e2, e3) = e2
% 169.23/25.69 (47) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.69 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.69 (48) all_56_15 = all_4_2
% 169.23/25.69 (49) ~ (e3 = e0)
% 169.23/25.69 (50) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.69 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.69 (51) ~ (all_52_13 = all_52_14)
% 169.23/25.69 (52) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.69 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.69 (53) op(e1, e1) = e3
% 169.23/25.69 (54) ( ~ (all_28_0 = e0) & op(all_28_1, e1) = all_28_0 & op(e3, e1) =
% 169.23/25.69 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e3,
% 169.23/25.69 e1) = all_28_1 & $i(all_28_1))
% 169.23/25.69 (55) op(e0, e0) = all_4_2
% 169.23/25.70 (56) ~ (all_52_13 = e2)
% 169.23/25.70 (57) ~ (all_52_2 = e2)
% 169.23/25.70 (58) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.70 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.70 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.70 (59) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 169.23/25.70 (60) all_36_2 = e3
% 169.23/25.70 (61) ~ (all_52_4 = e3)
% 169.23/25.70 (62) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.23/25.70 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.23/25.70 (63) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.70 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.23/25.70 (64) ~ (all_52_3 = all_52_11)
% 169.23/25.70 (65) ~ (all_10_2 = e1)
% 169.23/25.70 (66) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.70 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.70 (67) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.23/25.70 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.23/25.70 (68) ~ (all_52_7 = all_52_11)
% 169.23/25.70 (69) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.70 (70) ~ (e2 = e0)
% 169.23/25.70 (71) all_58_8 = e3
% 169.23/25.70 (72) op(e1, e0) = all_52_14
% 169.23/25.70 (73) ~ (all_52_13 = all_4_2)
% 169.23/25.70 (74) ~ (all_10_2 = e2)
% 169.23/25.70 (75) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.70 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.70 (76) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.23/25.70 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.23/25.70 (77) ~ (all_52_12 = all_52_13)
% 169.23/25.70 (78) all_58_3 = e3
% 169.23/25.70 (79) op(e3, e3) = e3
% 169.23/25.70 (80) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.70 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.70 (81) ~ (e2 = e1)
% 169.23/25.70 (82) op(e3, e2) = all_52_4
% 169.23/25.70 (83) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.23/25.70 (84) all_54_0 = all_10_2
% 169.23/25.70 (85) op(e0, e2) = all_52_7
% 169.23/25.70 (86) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.23/25.70 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.23/25.70 (87) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.23/25.70 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.23/25.70 (88) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.70 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.70 (89) op(e1, e3) = e1
% 169.23/25.70 (90) ~ (all_52_9 = all_52_13)
% 169.23/25.70 (91) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.70 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.23/25.70 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.23/25.70 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.23/25.70 (92) ~ (all_52_2 = all_52_3)
% 169.23/25.70 (93) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.23/25.70 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.23/25.70 (94) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.23/25.70 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.23/25.70 e2) = all_14_1 & $i(all_14_1))
% 169.23/25.70 (95) op(e2, e0) = all_52_13
% 169.23/25.70 (96) ~ (e3 = e2)
% 169.23/25.70
% 169.23/25.70 Begin of proof
% 169.23/25.70 |
% 169.23/25.70 | BETA: splitting (32) gives:
% 169.23/25.70 |
% 169.23/25.70 | Case 1:
% 169.23/25.70 | |
% 169.23/25.70 | | (97) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 169.23/25.70 | | e3)
% 169.23/25.70 | |
% 169.23/25.70 | | BETA: splitting (97) gives:
% 169.23/25.70 | |
% 169.23/25.70 | | Case 1:
% 169.23/25.70 | | |
% 169.23/25.70 | | | (98) all_58_12 = e3 & op(e0, e3) = e3
% 169.23/25.70 | | |
% 169.23/25.70 | | | REF_CLOSE: (12), (27), (31), (38), (46), (49), (69), (70), (79), (89),
% 169.23/25.70 | | | (98) are inconsistent by sub-proof #301.
% 169.23/25.70 | | |
% 169.23/25.70 | | Case 2:
% 169.23/25.70 | | |
% 169.23/25.70 | | | (99) all_58_13 = e3 & op(e0, e2) = e3
% 169.23/25.70 | | |
% 169.23/25.70 | | | REF_CLOSE: (44), (69), (85), (99) are inconsistent by sub-proof #962.
% 169.23/25.70 | | |
% 169.23/25.70 | | End of split
% 169.23/25.70 | |
% 169.23/25.70 | Case 2:
% 169.23/25.70 | |
% 169.23/25.70 | | (100) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.23/25.70 | | e3)
% 169.23/25.70 | |
% 169.23/25.70 | | BETA: splitting (100) gives:
% 169.23/25.70 | |
% 169.23/25.70 | | Case 1:
% 169.23/25.70 | | |
% 169.23/25.70 | | | (101) all_58_14 = e3 & op(e0, e1) = e3
% 169.23/25.70 | | |
% 169.23/25.70 | | | ALPHA: (101) implies:
% 169.23/25.70 | | | (102) all_58_14 = e3
% 169.23/25.70 | | |
% 169.23/25.70 | | | BETA: splitting (93) gives:
% 169.23/25.70 | | |
% 169.23/25.70 | | | Case 1:
% 169.23/25.70 | | | |
% 169.23/25.70 | | | | (103) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 169.23/25.70 | | | | = e2)
% 169.23/25.70 | | | |
% 169.23/25.70 | | | | BETA: splitting (103) gives:
% 169.23/25.70 | | | |
% 169.23/25.70 | | | | Case 1:
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | | (104) all_58_4 = e2 & op(e3, e1) = e2
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | | ALPHA: (104) implies:
% 169.23/25.70 | | | | | (105) all_58_4 = e2
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | | REF_CLOSE: (24), (31), (39), (49), (70), (71), (81), (88), (102),
% 169.23/25.70 | | | | | (105) are inconsistent by sub-proof #422.
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | Case 2:
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | | (106) all_58_5 = e2 & op(e2, e1) = e2
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | | REF_CLOSE: (5), (24), (31), (38), (46), (49), (50), (69), (70), (78),
% 169.23/25.70 | | | | | (81), (106) are inconsistent by sub-proof #412.
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | End of split
% 169.23/25.70 | | | |
% 169.23/25.70 | | | Case 2:
% 169.23/25.70 | | | |
% 169.23/25.70 | | | | (107) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0,
% 169.23/25.70 | | | | e1) = e2)
% 169.23/25.70 | | | |
% 169.23/25.70 | | | | BETA: splitting (107) gives:
% 169.23/25.70 | | | |
% 169.23/25.70 | | | | Case 1:
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | | (108) all_58_8 = e2 & op(e1, e1) = e2
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | | ALPHA: (108) implies:
% 169.23/25.70 | | | | | (109) op(e1, e1) = e2
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | | REF_CLOSE: (5), (12), (14), (24), (27), (31), (33), (38), (46), (47),
% 169.23/25.70 | | | | | (49), (50), (53), (69), (70), (78), (79), (80), (81), (89),
% 169.23/25.70 | | | | | (96), (109) are inconsistent by sub-proof #339.
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | Case 2:
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | | (110) all_58_14 = e2 & op(e0, e1) = e2
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | | REF_CLOSE: (5), (14), (24), (31), (38), (46), (49), (50), (69), (70),
% 169.23/25.70 | | | | | (78), (80), (81), (96), (102), (110) are inconsistent by
% 169.23/25.70 | | | | | sub-proof #411.
% 169.23/25.70 | | | | |
% 169.23/25.70 | | | | End of split
% 169.23/25.70 | | | |
% 169.23/25.70 | | | End of split
% 169.23/25.70 | | |
% 169.23/25.70 | | Case 2:
% 169.23/25.70 | | |
% 169.23/25.70 | | | (111) all_58_15 = e3 & op(e0, e0) = e3
% 169.23/25.70 | | |
% 169.23/25.70 | | | ALPHA: (111) implies:
% 169.23/25.70 | | | (112) all_58_15 = e3
% 169.23/25.70 | | | (113) op(e0, e0) = e3
% 169.23/25.70 | | |
% 169.23/25.70 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.23/25.70 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 169.23/25.70 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 169.23/25.70 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 169.23/25.70 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 169.23/25.70 | | | (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 169.23/25.70 | | | (63), (64), (65), (66), (67), (68), (69), (70), (71), (72),
% 169.23/25.70 | | | (73), (74), (75), (76), (77), (78), (79), (80), (81), (82),
% 169.23/25.70 | | | (83), (84), (85), (86), (87), (88), (89), (90), (91), (92),
% 169.23/25.70 | | | (93), (94), (95), (96), (112), (113) are inconsistent by
% 169.23/25.70 | | | sub-proof #283.
% 169.23/25.70 | | |
% 169.23/25.70 | | End of split
% 169.23/25.70 | |
% 169.23/25.70 | End of split
% 169.23/25.70 |
% 169.23/25.70 End of proof
% 169.23/25.70
% 169.23/25.70 Sub-proof #283 shows that the following formulas are inconsistent:
% 169.23/25.70 ----------------------------------------------------------------
% 169.23/25.70 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.23/25.70 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.23/25.70 (2) op(e2, e1) = all_52_9
% 169.23/25.70 (3) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.23/25.70 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.23/25.70 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.70 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.70 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.23/25.70 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.70 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.70 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.70 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.70 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 169.23/25.70 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.70 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.70 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.70 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.70 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.23/25.70 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.70 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.70 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.70 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.70 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.23/25.70 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.70 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.70 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.70 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.70 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 169.23/25.70 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 169.23/25.70 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.23/25.70 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.70 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.70 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.23/25.70 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.23/25.70 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.23/25.70 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.23/25.70 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.23/25.70 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 169.23/25.70 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 169.23/25.70 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.23/25.70 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.23/25.70 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.23/25.70 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.23/25.70 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 169.23/25.70 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.23/25.70 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.23/25.70 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.23/25.70 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 169.23/25.70 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.23/25.70 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.23/25.70 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 169.23/25.70 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.23/25.70 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 169.23/25.70 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.23/25.70 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.23/25.70 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.23/25.70 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.70 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.23/25.70 (6) op(e0, e1) = all_52_11
% 169.23/25.70 (7) ~ (all_52_14 = all_4_2)
% 169.23/25.70 (8) ~ (all_52_9 = e3)
% 169.23/25.70 (9) ~ (all_52_13 = e3)
% 169.23/25.70 (10) ~ (all_4_2 = e2)
% 169.23/25.70 (11) all_56_2 = e1
% 169.23/25.70 (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.23/25.70 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.23/25.70 (13) all_54_12 = all_52_3
% 169.23/25.70 (14) all_58_2 = e2
% 169.23/25.70 (15) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.23/25.70 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.70 (16) ~ (all_52_11 = all_4_2)
% 169.23/25.70 (17) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.23/25.70 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.23/25.70 (18) ~ (all_56_15 = e3) | (all_56_6 = e0 & op(e0, e3) = e0)
% 169.23/25.70 (19) all_56_14 = e3
% 169.23/25.70 (20) ~ (all_4_2 = e1)
% 169.23/25.70 (21) op(e3, e3) = all_10_2
% 169.23/25.70 (22) ~ (all_52_3 = e2)
% 169.23/25.70 (23) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.23/25.70 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.70 (24) ~ (e3 = e1)
% 169.23/25.70 (25) op(e3, e0) = all_52_12
% 169.23/25.70 (26) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.23/25.70 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.23/25.70 e1)
% 169.23/25.70 (27) op(e1, e3) = all_52_2
% 169.23/25.70 (28) ~ (all_10_2 = e0)
% 169.23/25.70 (29) op(e3, e1) = all_52_8
% 169.23/25.70 (30) ~ (all_52_9 = all_52_11)
% 169.23/25.70 (31) ~ (e1 = e0)
% 169.23/25.70 (32) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.23/25.70 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.23/25.70 e3)
% 169.23/25.70 (33) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.23/25.70 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.23/25.70 (34) op(e1, e2) = all_52_6
% 169.23/25.70 (35) ~ (all_52_3 = all_4_2)
% 169.23/25.70 (36) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.23/25.70 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.23/25.70 (37) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.23/25.70 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.23/25.70 (38) op(e2, e3) = all_52_1
% 169.23/25.70 (39) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.23/25.70 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.23/25.70 (40) ~ (all_52_7 = all_4_2)
% 169.23/25.70 (41) ~ (all_52_12 = all_4_2)
% 169.23/25.70 (42) ~ (all_52_3 = all_52_7)
% 169.23/25.70 (43) ~ (all_36_2 = e3) | ( ~ (all_36_0 = e2) & op(all_36_1, e1) = all_36_0 &
% 169.23/25.70 op(e3, e1) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 =
% 169.23/25.70 e0) & op(e3, e1) = all_36_1 & $i(all_36_1))
% 169.23/25.70 (44) ~ (all_52_7 = e3)
% 169.23/25.70 (45) op(e0, e0) = e3
% 169.23/25.70 (46) ~ (all_52_12 = all_52_14)
% 169.23/25.70 (47) op(e2, e3) = e2
% 169.23/25.70 (48) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.23/25.70 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.23/25.70 (49) all_56_15 = all_4_2
% 169.23/25.70 (50) ~ (e3 = e0)
% 169.23/25.70 (51) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.70 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.23/25.70 (52) ~ (all_52_13 = all_52_14)
% 169.23/25.70 (53) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.23/25.70 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.23/25.70 (54) op(e1, e1) = e3
% 169.23/25.70 (55) ( ~ (all_28_0 = e0) & op(all_28_1, e1) = all_28_0 & op(e3, e1) =
% 169.23/25.70 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e3,
% 169.23/25.70 e1) = all_28_1 & $i(all_28_1))
% 169.23/25.71 (56) op(e0, e0) = all_4_2
% 169.23/25.71 (57) ~ (all_52_13 = e2)
% 169.23/25.71 (58) ~ (all_52_2 = e2)
% 169.23/25.71 (59) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.23/25.71 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.23/25.71 e2) = all_22_1 & $i(all_22_1))
% 169.23/25.71 (60) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 169.23/25.71 (61) all_36_2 = e3
% 169.23/25.71 (62) ~ (all_52_4 = e3)
% 169.23/25.71 (63) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.23/25.71 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.23/25.71 (64) all_58_15 = e3
% 169.23/25.71 (65) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.23/25.71 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.23/25.71 (66) ~ (all_52_3 = all_52_11)
% 169.23/25.71 (67) ~ (all_10_2 = e1)
% 169.23/25.71 (68) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.23/25.71 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.23/25.71 (69) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.23/25.71 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.23/25.71 (70) ~ (all_52_7 = all_52_11)
% 169.23/25.71 (71) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.23/25.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.23/25.71 (72) ~ (e2 = e0)
% 169.23/25.71 (73) all_58_8 = e3
% 169.23/25.71 (74) op(e1, e0) = all_52_14
% 169.23/25.71 (75) ~ (all_52_13 = all_4_2)
% 169.23/25.71 (76) ~ (all_10_2 = e2)
% 169.23/25.71 (77) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.23/25.71 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.23/25.71 (78) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.23/25.71 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.23/25.71 (79) ~ (all_52_12 = all_52_13)
% 169.23/25.71 (80) all_58_3 = e3
% 169.23/25.71 (81) op(e3, e3) = e3
% 169.23/25.71 (82) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.23/25.71 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.23/25.71 (83) ~ (e2 = e1)
% 169.23/25.71 (84) op(e3, e2) = all_52_4
% 169.23/25.71 (85) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.23/25.71 (86) all_54_0 = all_10_2
% 169.23/25.71 (87) op(e0, e2) = all_52_7
% 169.23/25.71 (88) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.23/25.71 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.23/25.71 (89) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.23/25.71 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.23/25.71 (90) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.23/25.71 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.23/25.71 (91) op(e1, e3) = e1
% 169.23/25.71 (92) ~ (all_52_9 = all_52_13)
% 169.23/25.71 (93) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.23/25.71 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.23/25.71 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.23/25.71 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.23/25.71 (94) ~ (all_52_2 = all_52_3)
% 169.23/25.71 (95) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.23/25.71 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.23/25.71 (96) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.23/25.71 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.23/25.71 e2) = all_14_1 & $i(all_14_1))
% 169.23/25.71 (97) op(e2, e0) = all_52_13
% 169.23/25.71 (98) ~ (e3 = e2)
% 169.23/25.71
% 169.23/25.71 Begin of proof
% 169.23/25.71 |
% 169.23/25.71 | BETA: splitting (33) gives:
% 169.23/25.71 |
% 169.23/25.71 | Case 1:
% 169.23/25.71 | |
% 169.23/25.71 | | (99) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 169.23/25.71 | | e3)
% 169.23/25.71 | |
% 169.23/25.71 | | BETA: splitting (99) gives:
% 169.23/25.71 | |
% 169.23/25.71 | | Case 1:
% 169.23/25.71 | | |
% 169.23/25.71 | | | (100) all_58_0 = e3 & op(e3, e3) = e3
% 169.23/25.71 | | |
% 169.23/25.71 | | | ALPHA: (100) implies:
% 169.23/25.71 | | | (101) all_58_0 = e3
% 169.23/25.71 | | |
% 169.23/25.71 | | | GROUND_INST: instantiating (71) with all_4_2, e3, e0, e0, simplifying with
% 169.23/25.71 | | | (45), (56) gives:
% 169.23/25.71 | | | (102) all_4_2 = e3
% 169.23/25.71 | | |
% 169.23/25.71 | | | GROUND_INST: instantiating (71) with all_52_2, e1, e3, e1, simplifying
% 169.23/25.71 | | | with (27), (91) gives:
% 169.23/25.71 | | | (103) all_52_2 = e1
% 169.23/25.71 | | |
% 169.23/25.71 | | | COMBINE_EQS: (49), (102) imply:
% 169.23/25.71 | | | (104) all_56_15 = e3
% 169.23/25.71 | | |
% 169.23/25.71 | | | REDUCE: (94), (103) imply:
% 169.23/25.71 | | | (105) ~ (all_52_3 = e1)
% 169.23/25.71 | | |
% 169.23/25.71 | | | SIMP: (105) implies:
% 169.23/25.71 | | | (106) ~ (all_52_3 = e1)
% 169.23/25.71 | | |
% 169.23/25.71 | | | REDUCE: (58), (103) imply:
% 169.23/25.71 | | | (107) ~ (e2 = e1)
% 169.23/25.71 | | |
% 169.23/25.71 | | | REDUCE: (35), (102) imply:
% 169.23/25.71 | | | (108) ~ (all_52_3 = e3)
% 169.23/25.71 | | |
% 169.23/25.71 | | | REDUCE: (16), (102) imply:
% 169.23/25.71 | | | (109) ~ (all_52_11 = e3)
% 169.23/25.71 | | |
% 169.23/25.71 | | | REDUCE: (41), (102) imply:
% 169.23/25.71 | | | (110) ~ (all_52_12 = e3)
% 169.23/25.71 | | |
% 169.23/25.71 | | | REDUCE: (7), (102) imply:
% 169.23/25.71 | | | (111) ~ (all_52_14 = e3)
% 169.23/25.71 | | |
% 169.23/25.71 | | | BETA: splitting (18) gives:
% 169.23/25.71 | | |
% 169.23/25.71 | | | Case 1:
% 169.23/25.71 | | | |
% 169.23/25.71 | | | | (112) ~ (all_56_15 = e3)
% 169.23/25.71 | | | |
% 169.23/25.71 | | | | REDUCE: (104), (112) imply:
% 169.23/25.71 | | | | (113) $false
% 169.23/25.71 | | | |
% 169.23/25.71 | | | | CLOSE: (113) is inconsistent.
% 169.23/25.71 | | | |
% 169.23/25.71 | | | Case 2:
% 169.23/25.71 | | | |
% 169.23/25.71 | | | | (114) all_56_6 = e0 & op(e0, e3) = e0
% 169.23/25.71 | | | |
% 169.23/25.71 | | | | ALPHA: (114) implies:
% 169.23/25.71 | | | | (115) all_56_6 = e0
% 169.23/25.71 | | | |
% 169.23/25.71 | | | | BETA: splitting (48) gives:
% 169.23/25.71 | | | |
% 169.23/25.71 | | | | Case 1:
% 169.23/25.71 | | | | |
% 169.23/25.71 | | | | | (116) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 169.23/25.71 | | | | | e3) = e1)
% 169.23/25.71 | | | | |
% 169.23/25.71 | | | | | REF_CLOSE: (24), (38), (47), (71), (83), (101), (116) are inconsistent
% 169.23/25.71 | | | | | by sub-proof #416.
% 169.23/25.71 | | | | |
% 169.23/25.71 | | | | Case 2:
% 169.23/25.71 | | | | |
% 169.23/25.71 | | | | | (117) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 169.23/25.71 | | | | | e3) = e1)
% 169.23/25.71 | | | | |
% 169.23/25.71 | | | | | BETA: splitting (117) gives:
% 169.23/25.71 | | | | |
% 169.23/25.71 | | | | | Case 1:
% 169.23/25.71 | | | | | |
% 169.23/25.71 | | | | | | (118) all_58_6 = e1 & op(e1, e3) = e1
% 169.23/25.71 | | | | | |
% 169.23/25.71 | | | | | | ALPHA: (118) implies:
% 169.23/25.71 | | | | | | (119) all_58_6 = e1
% 169.23/25.71 | | | | | |
% 169.23/25.71 | | | | | | BETA: splitting (12) gives:
% 169.23/25.71 | | | | | |
% 169.23/25.71 | | | | | | Case 1:
% 169.23/25.71 | | | | | | |
% 169.23/25.71 | | | | | | | (120) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 169.23/25.71 | | | | | | | op(e2, e3) = e0)
% 169.23/25.71 | | | | | | |
% 169.23/25.71 | | | | | | | REF_CLOSE: (38), (47), (50), (71), (72), (81), (120) are
% 169.23/25.71 | | | | | | | inconsistent by sub-proof #460.
% 169.23/25.71 | | | | | | |
% 169.23/25.71 | | | | | | Case 2:
% 169.23/25.71 | | | | | | |
% 169.23/25.71 | | | | | | | (121) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 169.23/25.71 | | | | | | | op(e0, e3) = e0)
% 169.23/25.71 | | | | | | |
% 169.23/25.71 | | | | | | | BETA: splitting (121) gives:
% 169.23/25.71 | | | | | | |
% 169.23/25.71 | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | |
% 169.23/25.71 | | | | | | | | (122) all_58_6 = e0 & op(e1, e3) = e0
% 169.23/25.71 | | | | | | | |
% 169.23/25.71 | | | | | | | | ALPHA: (122) implies:
% 169.23/25.71 | | | | | | | | (123) op(e1, e3) = e0
% 169.23/25.71 | | | | | | | |
% 169.23/25.71 | | | | | | | | REF_CLOSE: (27), (31), (71), (91), (123) are inconsistent by
% 169.23/25.71 | | | | | | | | sub-proof #749.
% 169.23/25.71 | | | | | | | |
% 169.23/25.71 | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | |
% 169.23/25.71 | | | | | | | | (124) all_58_12 = e0 & op(e0, e3) = e0
% 169.23/25.71 | | | | | | | |
% 169.23/25.71 | | | | | | | | ALPHA: (124) implies:
% 169.23/25.71 | | | | | | | | (125) all_58_12 = e0
% 169.23/25.71 | | | | | | | |
% 169.23/25.71 | | | | | | | | BETA: splitting (60) gives:
% 169.23/25.71 | | | | | | | |
% 169.23/25.71 | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | |
% 169.23/25.71 | | | | | | | | | (126) all_54_12 = e3
% 169.23/25.71 | | | | | | | | |
% 169.23/25.71 | | | | | | | | | REF_CLOSE: (13), (108), (126) are inconsistent by sub-proof
% 169.23/25.71 | | | | | | | | | #738.
% 169.23/25.71 | | | | | | | | |
% 169.23/25.71 | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | |
% 169.23/25.71 | | | | | | | | | (127) ~ (all_54_12 = e3)
% 169.23/25.71 | | | | | | | | | (128) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 169.23/25.71 | | | | | | | | |
% 169.23/25.71 | | | | | | | | | BETA: splitting (128) gives:
% 169.23/25.71 | | | | | | | | |
% 169.23/25.71 | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | (129) all_54_12 = e2
% 169.23/25.71 | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | REF_CLOSE: (13), (22), (129) are inconsistent by sub-proof
% 169.23/25.71 | | | | | | | | | | #676.
% 169.23/25.71 | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | (130) ~ (all_54_12 = e2)
% 169.23/25.71 | | | | | | | | | | (131) all_54_12 = e1 | all_54_12 = e0
% 169.23/25.71 | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | BETA: splitting (131) gives:
% 169.23/25.71 | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | (132) all_54_12 = e1
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | COMBINE_EQS: (13), (132) imply:
% 169.23/25.71 | | | | | | | | | | | (133) all_52_3 = e1
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | SIMP: (133) implies:
% 169.23/25.71 | | | | | | | | | | | (134) all_52_3 = e1
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | REDUCE: (106), (134) imply:
% 169.23/25.71 | | | | | | | | | | | (135) $false
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | CLOSE: (135) is inconsistent.
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | (136) all_54_12 = e0
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | COMBINE_EQS: (13), (136) imply:
% 169.23/25.71 | | | | | | | | | | | (137) all_52_3 = e0
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | SIMP: (137) implies:
% 169.23/25.71 | | | | | | | | | | | (138) all_52_3 = e0
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | REDUCE: (42), (138) imply:
% 169.23/25.71 | | | | | | | | | | | (139) ~ (all_52_7 = e0)
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | SIMP: (139) implies:
% 169.23/25.71 | | | | | | | | | | | (140) ~ (all_52_7 = e0)
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | REDUCE: (66), (138) imply:
% 169.23/25.71 | | | | | | | | | | | (141) ~ (all_52_11 = e0)
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | SIMP: (141) implies:
% 169.23/25.71 | | | | | | | | | | | (142) ~ (all_52_11 = e0)
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | REDUCE: (108), (138) imply:
% 169.23/25.71 | | | | | | | | | | | (143) ~ (e3 = e0)
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | REDUCE: (22), (138) imply:
% 169.23/25.71 | | | | | | | | | | | (144) ~ (e2 = e0)
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | REDUCE: (106), (138) imply:
% 169.23/25.71 | | | | | | | | | | | (145) ~ (e1 = e0)
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | BETA: splitting (43) gives:
% 169.23/25.71 | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | (146) ~ (all_36_2 = e3)
% 169.23/25.71 | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | REDUCE: (61), (146) imply:
% 169.23/25.71 | | | | | | | | | | | | (147) $false
% 169.23/25.71 | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | CLOSE: (147) is inconsistent.
% 169.23/25.71 | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | (148) ( ~ (all_36_0 = e2) & op(all_36_1, e1) = all_36_0
% 169.23/25.71 | | | | | | | | | | | | & op(e3, e1) = all_36_1 & $i(all_36_0) &
% 169.23/25.71 | | | | | | | | | | | | $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e3, e1)
% 169.23/25.71 | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 169.23/25.71 | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | BETA: splitting (95) gives:
% 169.23/25.71 | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | (149) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2
% 169.23/25.71 | | | | | | | | | | | | | & op(e2, e1) = e2)
% 169.23/25.71 | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | BETA: splitting (149) gives:
% 169.23/25.71 | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | (150) all_58_4 = e2 & op(e3, e1) = e2
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | ALPHA: (150) implies:
% 169.23/25.71 | | | | | | | | | | | | | | (151) all_58_4 = e2
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | (152) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 169.23/25.71 | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | (153) all_58_4 = e0 & op(e3, e1) = e0
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | REF_CLOSE: (72), (151), (153) are inconsistent by sub-proof
% 169.23/25.71 | | | | | | | | | | | | | | | | #902.
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | (154) all_58_5 = e0 & op(e2, e1) = e0
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | (155) all_58_5 = e0
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | (156) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (157) all_58_4 = e1 & op(e3, e1) = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (83), (151), (157) are inconsistent by sub-proof
% 169.23/25.71 | | | | | | | | | | | | | | | | | | #943.
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (158) all_58_5 = e1 & op(e2, e1) = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (159) all_58_5 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (155), (159) are inconsistent by sub-proof
% 169.23/25.71 | | | | | | | | | | | | | | | | | | #449.
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | End of split
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | (160) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 169.23/25.71 | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (161) all_58_8 = e1 & op(e1, e1) = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (162) all_58_8 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (162) imply:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (163) e3 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | SIMP: (163) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (164) e3 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (164) imply:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (165) all_58_0 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (33), (50), (98), (119), (125), (165)
% 169.23/25.71 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #456.
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (166) all_58_14 = e1 & op(e0, e1) = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (167) all_58_14 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (12), (14), (15), (17), (24), (27),
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (31), (33), (34), (38), (47), (48), (50), (51),
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (53), (54), (59), (64), (65), (71), (72), (73),
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (91), (96), (98),
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (101), (119), (125), (167) are inconsistent by
% 169.23/25.71 | | | | | | | | | | | | | | | | | | sub-proof #299.
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | End of split
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | End of split
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | End of split
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | (168) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 169.23/25.71 | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | (169) all_58_8 = e0 & op(e1, e1) = e0
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | REF_CLOSE: (50), (73), (169) are inconsistent by sub-proof
% 169.23/25.71 | | | | | | | | | | | | | | | | #496.
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | (170) all_58_14 = e0 & op(e0, e1) = e0
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | (171) all_58_14 = e0
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (12), (14), (15), (17), (24), (27),
% 169.23/25.71 | | | | | | | | | | | | | | | | (31), (32), (33), (34), (38), (44), (47), (48),
% 169.23/25.71 | | | | | | | | | | | | | | | | (50), (51), (53), (54), (59), (65), (71), (72),
% 169.23/25.71 | | | | | | | | | | | | | | | | (73), (80), (81), (82), (83), (84), (87), (91),
% 169.23/25.71 | | | | | | | | | | | | | | | | (96), (98), (101), (119), (125), (171) are
% 169.23/25.71 | | | | | | | | | | | | | | | | inconsistent by sub-proof #297.
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | End of split
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | End of split
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | (172) all_58_5 = e2 & op(e2, e1) = e2
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | REF_CLOSE: (5), (24), (31), (38), (47), (50), (51), (71),
% 169.23/25.71 | | | | | | | | | | | | | | (72), (80), (83), (172) are inconsistent by
% 169.23/25.71 | | | | | | | | | | | | | | sub-proof #412.
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | End of split
% 169.23/25.71 | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | (173) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 =
% 169.23/25.71 | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 169.23/25.71 | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | BETA: splitting (173) gives:
% 169.23/25.71 | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | (174) all_58_8 = e2 & op(e1, e1) = e2
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | ALPHA: (174) implies:
% 169.23/25.71 | | | | | | | | | | | | | | (175) op(e1, e1) = e2
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (14), (24), (27), (31), (33), (38),
% 169.23/25.71 | | | | | | | | | | | | | | (47), (48), (50), (51), (54), (71), (72), (80),
% 169.23/25.71 | | | | | | | | | | | | | | (81), (82), (83), (91), (98), (175) are
% 169.23/25.71 | | | | | | | | | | | | | | inconsistent by sub-proof #339.
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | (176) all_58_14 = e2 & op(e0, e1) = e2
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | ALPHA: (176) implies:
% 169.23/25.71 | | | | | | | | | | | | | | (177) all_58_14 = e2
% 169.23/25.71 | | | | | | | | | | | | | | (178) op(e0, e1) = e2
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 169.23/25.71 | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | (179) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 169.23/25.71 | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 169.23/25.71 | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | (180) all_58_12 = e1 & op(e0, e3) = e1
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | (181) all_58_12 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (31), (38), (47), (50), (71), (72),
% 169.23/25.71 | | | | | | | | | | | | | | | | (81), (91), (181) are inconsistent by sub-proof
% 169.23/25.71 | | | | | | | | | | | | | | | | #296.
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | (182) all_58_13 = e1 & op(e0, e2) = e1
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | (183) all_58_13 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | (184) op(e0, e2) = e1
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_52_11, e2, e1, e0,
% 169.23/25.71 | | | | | | | | | | | | | | | | simplifying with (6), (178) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | | (185) all_52_11 = e2
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_52_7, e1, e2, e0,
% 169.23/25.71 | | | | | | | | | | | | | | | | simplifying with (87), (184) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | | (186) all_52_7 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | REDUCE: (44), (186) imply:
% 169.23/25.71 | | | | | | | | | | | | | | | | (187) ~ (e3 = e1)
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | REDUCE: (30), (185) imply:
% 169.23/25.71 | | | | | | | | | | | | | | | | (188) ~ (all_52_9 = e2)
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | REDUCE: (109), (185) imply:
% 169.23/25.71 | | | | | | | | | | | | | | | | (189) ~ (e3 = e2)
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | (190) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 169.23/25.71 | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (191) all_58_9 = e1 & op(e3, e0) = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | (192) all_58_9 = e1
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | (193) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 169.23/25.71 | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (59), (71), (81), (184), (193) are
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #295.
% 169.23/25.71 | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | (194) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 169.23/25.71 | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | (195) all_58_4 = e0 & op(e3, e1) = e0
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | (196) op(e3, e1) = e0
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | (197) ~ (all_36_0 = e2) & op(all_36_1, e1) = all_36_0 &
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_36_1 & $i(all_36_0) &
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | (198) ~ (all_36_0 = e2)
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | (199) op(e3, e1) = all_36_1
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | (200) op(all_36_1, e1) = all_36_0
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e0, all_36_1, e1, e3,
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | simplifying with (196), (199) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | (201) all_36_1 = e0
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (200), (201) imply:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | (202) op(e0, e1) = all_36_0
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e2, all_36_0, e1, e0,
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | simplifying with (178), (202) gives:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | (203) all_36_0 = e2
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | REDUCE: (198), (203) imply:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | (204) $false
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.71 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | (205) ~ (all_36_1 = e0) & op(e3, e1) = all_36_1 &
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | (206) ~ (all_36_1 = e0)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | (207) op(e3, e1) = all_36_1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e0, all_36_1, e1, e3,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | simplifying with (196), (207) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | (208) all_36_1 = e0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | REDUCE: (206), (208) imply:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | (209) $false
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | CLOSE: (209) is inconsistent.
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | (210) all_58_9 = e0 & op(e3, e0) = e0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (192), (210) are inconsistent by sub-proof
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | #897.
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.72 | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.72 | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.72 | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | (211) all_58_10 = e1 & op(e2, e0) = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | (212) all_58_10 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | (213) op(e2, e0) = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | (214) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | (215) all_58_2 = e0 & op(e2, e3) = e0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (47), (71), (72), (215) are inconsistent by
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | sub-proof #782.
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | (216) all_58_3 = e0 & op(e2, e2) = e0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (24), (31), (32), (38), (44), (47),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | (50), (51), (64), (71), (72), (80), (82), (83),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | (87), (98), (125), (177), (216) are inconsistent
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | by sub-proof #294.
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.72 | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | (217) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | (218) all_58_5 = e0 & op(e2, e1) = e0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | (219) op(e2, e1) = e0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | (220) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | (221) all_58_4 = e1 & op(e3, e1) = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | (222) all_58_4 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | (223) op(e3, e1) = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_52_13, e1, e0, e2,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | simplifying with (97), (213) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | (224) all_52_13 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_52_9, e0, e1, e2,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | simplifying with (2), (219) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | (225) all_52_9 = e0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_52_8, e1, e1, e3,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | simplifying with (29), (223) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | (226) all_52_8 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (79), (224) imply:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | (227) ~ (all_52_12 = e1)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (224) imply:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | (228) ~ (all_52_14 = e1)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | SIMP: (228) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | (229) ~ (all_52_14 = e1)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | (230) ~ (all_28_0 = e0) & op(all_28_1, e1) = all_28_0 &
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_28_1 & $i(all_28_0) &
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_1)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | (231) ~ (all_28_0 = e0)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | (232) op(e3, e1) = all_28_1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | (233) op(all_28_1, e1) = all_28_0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (234) ~ (all_36_0 = e2) & op(all_36_1, e1) = all_36_0 &
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_36_1 & $i(all_36_0) &
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (234) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (235) ~ (all_36_0 = e2)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (236) op(e3, e1) = all_36_1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (237) op(all_36_1, e1) = all_36_0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e1, all_36_1, e1, e3,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (223), (236) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (238) all_36_1 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_28_1, all_36_1, e1,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (232), (236) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (239) all_36_1 = all_28_1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (239) imply:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (240) all_28_1 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (240) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (241) all_28_1 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (237), (238) imply:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (242) op(e1, e1) = all_36_0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (233), (241) imply:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (243) op(e1, e1) = all_28_0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e3, all_36_0, e1, e1,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (54), (242) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (244) all_36_0 = e3
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_28_0, all_36_0, e1,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | e1, simplifying with (242), (243) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (245) all_36_0 = all_28_0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (244), (245) imply:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (246) all_28_0 = e3
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | (247) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (248) all_58_1 = e2 & op(e3, e2) = e2
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (249) all_58_1 = e2
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (11), (12), (14), (15), (17), (19),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (23), (24), (25), (27), (31), (32), (33), (34),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (44), (46), (47), (48), (50), (51), (53),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (54), (59), (64), (65), (71), (72), (73), (74),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (87), (91), (96),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (98), (101), (104), (110), (111), (115), (119),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (177), (178), (183), (184), (213), (219),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (222), (227), (229), (249) are inconsistent by
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #290.
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (250) all_58_3 = e2 & op(e2, e2) = e2
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_58_3 = e2
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (24), (31), (38), (47), (50), (51),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (71), (72), (82), (83), (98), (251) are
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | (252) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 =
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (252) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (253) all_58_7 = e2 & op(e1, e2) = e2
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (254) all_58_7 = e2
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (12), (14), (15), (17), (24), (27),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (38), (44), (47), (48),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (50), (51), (53), (54), (59), (64), (65), (71),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (72), (73), (80), (81), (82), (83), (84), (87),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (91), (96), (98), (101), (119), (125), (177),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (183), (184), (254) are inconsistent by sub-proof
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | #289.
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_58_13 = e2 & op(e0, e2) = e2
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_58_13 = e2
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (14), (15), (17), (24), (27), (31),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (33), (34), (38), (47), (48), (50), (51), (53),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (54), (59), (65), (71), (72), (73), (80), (81),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (82), (83), (84), (91), (96), (98), (101), (119),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (125), (256) are inconsistent by sub-proof #300.
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (257) ~ (all_36_1 = e0) & op(e3, e1) = all_36_1 &
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (257) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (258) ~ (all_36_1 = e0)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (259) op(e3, e1) = all_36_1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e1, all_36_1, e1, e3,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (223), (259) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (260) all_36_1 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_28_1, all_36_1, e1,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (232), (259) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (261) all_36_1 = all_28_1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (261) imply:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (262) all_28_1 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (262) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (263) all_28_1 = e1
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (233), (263) imply:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (264) op(e1, e1) = all_28_0
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e3, all_28_0, e1, e1,
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (54), (264) gives:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (265) all_28_0 = e3
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (11), (12), (14), (15), (17), (19),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (23), (24), (25), (27), (31), (32), (33), (34),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (38), (44), (46), (47), (48), (50), (51), (53),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (54), (59), (63), (64), (65), (71), (72), (73),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (74), (80), (81), (82), (83), (84), (87), (91),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (96), (98), (101), (104), (110), (111), (115),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (119), (125), (177), (178), (183), (184), (213),
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (219), (222), (227), (229) are inconsistent by
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #288.
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | (266) ~ (all_28_1 = e2) & op(e3, e1) = all_28_1 &
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_1)
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 169.23/25.72 | | | | | | | | | | | | | | | | | | | | | | | (267) ~ (all_28_1 = e2)
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | (268) op(e3, e1) = all_28_1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (269) ~ (all_36_0 = e2) & op(all_36_1, e1) = all_36_0 &
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_36_1 & $i(all_36_0) &
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (269) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (270) ~ (all_36_0 = e2)
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (271) op(e3, e1) = all_36_1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (272) op(all_36_1, e1) = all_36_0
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e1, all_36_1, e1, e3,
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (223), (271) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (273) all_36_1 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_28_1, all_36_1, e1,
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (268), (271) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (274) all_36_1 = all_28_1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (273), (274) imply:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (275) all_28_1 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (275) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (276) all_28_1 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (272), (273) imply:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (277) op(e1, e1) = all_36_0
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e3, all_36_0, e1, e1,
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (54), (277) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (278) all_36_0 = e3
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (11), (12), (14), (15), (17), (19),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (23), (24), (25), (27), (31), (32), (33), (34),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (38), (44), (46), (47), (48), (50), (51), (53),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (54), (59), (63), (64), (65), (71), (72), (73),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (74), (80), (81), (82), (83), (84), (87), (91),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (96), (98), (101), (104), (110), (111), (115),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (119), (125), (177), (178), (183), (184), (213),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (219), (222), (227), (229) are inconsistent by
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #288.
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (279) ~ (all_36_1 = e0) & op(e3, e1) = all_36_1 &
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (280) ~ (all_36_1 = e0)
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (281) op(e3, e1) = all_36_1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with e1, all_36_1, e1, e3,
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (223), (281) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (282) all_36_1 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (71) with all_28_1, all_36_1, e1,
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | e3, simplifying with (268), (281) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (283) all_36_1 = all_28_1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (282), (283) imply:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (284) all_28_1 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (284) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (285) all_28_1 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (11), (12), (14), (15), (17), (19),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (23), (24), (25), (27), (31), (32), (33), (34),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (38), (44), (46), (47), (48), (50), (51), (53),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (54), (59), (63), (64), (65), (71), (72), (73),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (74), (80), (81), (82), (83), (84), (87), (91),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (96), (98), (101), (104), (110), (111), (115),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (119), (125), (177), (178), (183), (184), (213),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | (219), (222), (227), (229) are inconsistent by
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #288.
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (286) all_58_5 = e1 & op(e2, e1) = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (287) op(e2, e1) = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (71), (219), (287) are inconsistent by
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | sub-proof #911.
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | (288) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (288) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (289) all_58_8 = e1 & op(e1, e1) = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (290) all_58_8 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (73), (290) imply:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (291) e3 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (101), (291) imply:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (292) all_58_0 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (33), (50), (98), (119), (125), (292)
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #456.
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (293) all_58_14 = e1 & op(e0, e1) = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (294) all_58_14 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (12), (14), (15), (17), (24), (27),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (31), (33), (34), (38), (47), (48), (50), (51),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (53), (54), (59), (64), (65), (71), (72), (73),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (91), (96), (98),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | (101), (119), (125), (294) are inconsistent by
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | | sub-proof #299.
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (295) all_58_10 = e0 & op(e2, e0) = e0
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (212), (295) are inconsistent by sub-proof
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | #925.
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | (296) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 169.30/25.72 | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.30/25.72 | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | Case 1:
% 169.30/25.72 | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | (297) all_58_11 = e1 & op(e1, e0) = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | (298) all_58_11 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | Case 1:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | (299) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 169.30/25.72 | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (299) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (300) all_58_6 = e2 & op(e1, e3) = e2
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | ALPHA: (300) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (301) all_58_6 = e2
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (301) imply:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (302) e2 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (12), (14), (15), (17), (24), (27),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (31), (33), (34), (38), (47), (48), (50), (51),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (53), (54), (59), (64), (65), (71), (72), (73),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (91), (96), (98),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (101), (119), (125), (177), (302) are inconsistent
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | by sub-proof #292.
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (303) all_58_7 = e2 & op(e1, e2) = e2
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (304) all_58_7 = e2
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (12), (14), (15), (17), (24), (27),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (31), (32), (33), (34), (38), (44), (47), (48),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (50), (51), (53), (54), (59), (64), (65), (71),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (72), (73), (80), (81), (82), (83), (84), (87),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (91), (96), (98), (101), (119), (125), (177),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (183), (184), (304) are inconsistent by sub-proof
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | #289.
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | (305) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 169.30/25.72 | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (305) gives:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (306) all_58_8 = e2 & op(e1, e1) = e2
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | ALPHA: (306) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (307) op(e1, e1) = e2
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (14), (24), (27), (31), (33), (38),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (47), (48), (50), (51), (54), (71), (72), (80),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (81), (82), (83), (91), (98), (307) are
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #339.
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (308) all_58_11 = e2 & op(e1, e0) = e2
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | ALPHA: (308) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (309) all_58_11 = e2
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (309) imply:
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (310) e2 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (12), (14), (15), (17), (24), (27),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (31), (33), (34), (38), (47), (48), (50), (51),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (53), (54), (59), (64), (65), (71), (72), (73),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (91), (96), (98),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | (101), (119), (125), (177), (310) are inconsistent
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | | by sub-proof #292.
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | (311) all_58_15 = e1 & op(e0, e0) = e1
% 169.30/25.72 | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (33), (50), (64), (98), (101), (119),
% 169.30/25.72 | | | | | | | | | | | | | | | | | | (125), (311) are inconsistent by sub-proof #287.
% 169.30/25.72 | | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | End of split
% 169.30/25.72 | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | Case 2:
% 169.30/25.72 | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | (312) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 169.30/25.72 | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.30/25.72 | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | BETA: splitting (312) gives:
% 169.30/25.72 | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | Case 1:
% 169.30/25.72 | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | (313) all_58_14 = e1 & op(e0, e1) = e1
% 169.30/25.72 | | | | | | | | | | | | | | | |
% 169.30/25.72 | | | | | | | | | | | | | | | | ALPHA: (313) implies:
% 169.30/25.72 | | | | | | | | | | | | | | | | (314) all_58_14 = e1
% 169.30/25.72 | | | | | | | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (12), (14), (15), (17), (24), (27),
% 169.30/25.73 | | | | | | | | | | | | | | | | (31), (33), (34), (38), (47), (48), (50), (51),
% 169.30/25.73 | | | | | | | | | | | | | | | | (53), (54), (59), (64), (65), (71), (72), (73),
% 169.30/25.73 | | | | | | | | | | | | | | | | (80), (81), (82), (83), (84), (91), (96), (98),
% 169.30/25.73 | | | | | | | | | | | | | | | | (101), (119), (125), (314) are inconsistent by
% 169.30/25.73 | | | | | | | | | | | | | | | | sub-proof #299.
% 169.30/25.73 | | | | | | | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | | | | | | | Case 2:
% 169.30/25.73 | | | | | | | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | | | | | | | | (315) all_58_15 = e1 & op(e0, e0) = e1
% 169.30/25.73 | | | | | | | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (24), (33), (50), (64), (98), (101), (119),
% 169.30/25.73 | | | | | | | | | | | | | | | | (125), (315) are inconsistent by sub-proof #287.
% 169.30/25.73 | | | | | | | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | | | | | | | End of split
% 169.30/25.73 | | | | | | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | | | | | | End of split
% 169.30/25.73 | | | | | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | | | | | End of split
% 169.30/25.73 | | | | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | | | | End of split
% 169.30/25.73 | | | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | | | End of split
% 169.30/25.73 | | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | | End of split
% 169.30/25.73 | | | | | | | | | |
% 169.30/25.73 | | | | | | | | | End of split
% 169.30/25.73 | | | | | | | | |
% 169.30/25.73 | | | | | | | | End of split
% 169.30/25.73 | | | | | | | |
% 169.30/25.73 | | | | | | | End of split
% 169.30/25.73 | | | | | | |
% 169.30/25.73 | | | | | | End of split
% 169.30/25.73 | | | | | |
% 169.30/25.73 | | | | | Case 2:
% 169.30/25.73 | | | | | |
% 169.30/25.73 | | | | | | (316) all_58_12 = e1 & op(e0, e3) = e1
% 169.30/25.73 | | | | | |
% 169.30/25.73 | | | | | | ALPHA: (316) implies:
% 169.30/25.73 | | | | | | (317) all_58_12 = e1
% 169.30/25.73 | | | | | |
% 169.30/25.73 | | | | | | REF_CLOSE: (12), (27), (31), (38), (47), (50), (71), (72), (81),
% 169.30/25.73 | | | | | | (91), (317) are inconsistent by sub-proof #296.
% 169.30/25.73 | | | | | |
% 169.30/25.73 | | | | | End of split
% 169.30/25.73 | | | | |
% 169.30/25.73 | | | | End of split
% 169.30/25.73 | | | |
% 169.30/25.73 | | | End of split
% 169.30/25.73 | | |
% 169.30/25.73 | | Case 2:
% 169.30/25.73 | | |
% 169.30/25.73 | | | (318) all_58_2 = e3 & op(e2, e3) = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | ALPHA: (318) implies:
% 169.30/25.73 | | | (319) op(e2, e3) = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | REF_CLOSE: (38), (47), (71), (98), (319) are inconsistent by sub-proof
% 169.30/25.73 | | | #462.
% 169.30/25.73 | | |
% 169.30/25.73 | | End of split
% 169.30/25.73 | |
% 169.30/25.73 | Case 2:
% 169.30/25.73 | |
% 169.30/25.73 | | (320) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 169.30/25.73 | | e3)
% 169.30/25.73 | |
% 169.30/25.73 | | BETA: splitting (320) gives:
% 169.30/25.73 | |
% 169.30/25.73 | | Case 1:
% 169.30/25.73 | | |
% 169.30/25.73 | | | (321) all_58_6 = e3 & op(e1, e3) = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | ALPHA: (321) implies:
% 169.30/25.73 | | | (322) all_58_6 = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | REF_CLOSE: (4), (5), (9), (12), (14), (15), (17), (21), (23), (24), (26),
% 169.30/25.73 | | | (27), (28), (31), (32), (33), (36), (37), (38), (39), (44),
% 169.30/25.73 | | | (47), (48), (50), (51), (53), (54), (62), (63), (64), (65),
% 169.30/25.73 | | | (67), (68), (69), (71), (72), (76), (77), (78), (80), (81),
% 169.30/25.73 | | | (82), (83), (84), (85), (86), (87), (88), (89), (90), (91),
% 169.30/25.73 | | | (93), (95), (97), (98), (322) are inconsistent by sub-proof
% 169.30/25.73 | | | #284.
% 169.30/25.73 | | |
% 169.30/25.73 | | Case 2:
% 169.30/25.73 | | |
% 169.30/25.73 | | | (323) all_58_12 = e3 & op(e0, e3) = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | REF_CLOSE: (12), (27), (31), (38), (47), (50), (71), (72), (81), (91),
% 169.30/25.73 | | | (323) are inconsistent by sub-proof #301.
% 169.30/25.73 | | |
% 169.30/25.73 | | End of split
% 169.30/25.73 | |
% 169.30/25.73 | End of split
% 169.30/25.73 |
% 169.30/25.73 End of proof
% 169.30/25.73
% 169.30/25.73 Sub-proof #284 shows that the following formulas are inconsistent:
% 169.30/25.73 ----------------------------------------------------------------
% 169.30/25.73 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.30/25.73 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.30/25.73 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.73 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.73 (3) ~ (all_52_13 = e3)
% 169.30/25.73 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.73 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.73 (5) all_58_2 = e2
% 169.30/25.73 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.73 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.73 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.73 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.73 (8) op(e3, e3) = all_10_2
% 169.30/25.73 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.30/25.73 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.30/25.73 (10) ~ (e3 = e1)
% 169.30/25.73 (11) all_58_6 = e3
% 169.30/25.73 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.73 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.30/25.73 e1)
% 169.30/25.73 (13) op(e1, e3) = all_52_2
% 169.30/25.73 (14) ~ (all_10_2 = e0)
% 169.30/25.73 (15) ~ (e1 = e0)
% 169.30/25.73 (16) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.30/25.73 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.30/25.73 e3)
% 169.30/25.73 (17) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.73 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.73 (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.30/25.73 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.30/25.73 (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.30/25.73 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.30/25.73 (20) op(e2, e3) = all_52_1
% 169.30/25.73 (21) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.30/25.73 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.30/25.73 (22) ~ (all_52_7 = e3)
% 169.30/25.73 (23) op(e2, e3) = e2
% 169.30/25.73 (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.73 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.73 (25) ~ (e3 = e0)
% 169.30/25.73 (26) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.73 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.73 (27) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.73 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.73 (28) op(e1, e1) = e3
% 169.30/25.73 (29) ~ (all_52_4 = e3)
% 169.30/25.73 (30) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.30/25.73 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.30/25.73 (31) all_58_15 = e3
% 169.30/25.73 (32) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.73 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.73 (33) ~ (all_10_2 = e1)
% 169.30/25.73 (34) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.30/25.73 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.30/25.73 (35) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.30/25.73 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.30/25.73 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.73 (37) ~ (e2 = e0)
% 169.30/25.73 (38) ~ (all_10_2 = e2)
% 169.30/25.73 (39) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.30/25.73 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.30/25.73 (40) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.30/25.73 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.30/25.73 (41) all_58_3 = e3
% 169.30/25.73 (42) op(e3, e3) = e3
% 169.30/25.73 (43) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.73 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.73 (44) ~ (e2 = e1)
% 169.30/25.73 (45) op(e3, e2) = all_52_4
% 169.30/25.73 (46) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.30/25.73 (47) all_54_0 = all_10_2
% 169.30/25.73 (48) op(e0, e2) = all_52_7
% 169.30/25.73 (49) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.30/25.73 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.30/25.73 (50) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.30/25.73 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.30/25.73 (51) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.30/25.73 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.30/25.73 (52) op(e1, e3) = e1
% 169.30/25.73 (53) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.30/25.73 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.30/25.73 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.30/25.73 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.30/25.73 (54) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.30/25.73 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.30/25.73 (55) op(e2, e0) = all_52_13
% 169.30/25.73 (56) ~ (e3 = e2)
% 169.30/25.73
% 169.30/25.73 Begin of proof
% 169.30/25.73 |
% 169.30/25.73 | BETA: splitting (24) gives:
% 169.30/25.73 |
% 169.30/25.73 | Case 1:
% 169.30/25.73 | |
% 169.30/25.73 | | (57) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 169.30/25.73 | | e1)
% 169.30/25.73 | |
% 169.30/25.73 | | BETA: splitting (57) gives:
% 169.30/25.73 | |
% 169.30/25.73 | | Case 1:
% 169.30/25.73 | | |
% 169.30/25.73 | | | (58) all_58_0 = e1 & op(e3, e3) = e1
% 169.30/25.73 | | |
% 169.30/25.73 | | | ALPHA: (58) implies:
% 169.30/25.73 | | | (59) all_58_0 = e1
% 169.30/25.73 | | |
% 169.30/25.73 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.30/25.73 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 169.30/25.73 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 169.30/25.73 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (43),
% 169.30/25.73 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 169.30/25.73 | | | (54), (55), (56), (59) are inconsistent by sub-proof #286.
% 169.30/25.73 | | |
% 169.30/25.73 | | Case 2:
% 169.30/25.73 | | |
% 169.30/25.73 | | | (60) all_58_2 = e1 & op(e2, e3) = e1
% 169.30/25.73 | | |
% 169.30/25.73 | | | ALPHA: (60) implies:
% 169.30/25.73 | | | (61) op(e2, e3) = e1
% 169.30/25.73 | | |
% 169.30/25.73 | | | REF_CLOSE: (20), (23), (36), (44), (61) are inconsistent by sub-proof
% 169.30/25.73 | | | #784.
% 169.30/25.73 | | |
% 169.30/25.73 | | End of split
% 169.30/25.73 | |
% 169.30/25.73 | Case 2:
% 169.30/25.73 | |
% 169.30/25.73 | | (62) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 169.30/25.73 | | e1)
% 169.30/25.73 | |
% 169.30/25.73 | | REF_CLOSE: (4), (10), (11), (13), (15), (20), (23), (25), (36), (37), (42),
% 169.30/25.73 | | (52), (62) are inconsistent by sub-proof #285.
% 169.30/25.73 | |
% 169.30/25.73 | End of split
% 169.30/25.73 |
% 169.30/25.73 End of proof
% 169.30/25.73
% 169.30/25.73 Sub-proof #285 shows that the following formulas are inconsistent:
% 169.30/25.73 ----------------------------------------------------------------
% 169.30/25.73 (1) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.73 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.73 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.73 (3) ~ (e3 = e1)
% 169.30/25.73 (4) all_58_6 = e3
% 169.30/25.73 (5) op(e1, e3) = all_52_2
% 169.30/25.73 (6) ~ (e1 = e0)
% 169.30/25.73 (7) op(e2, e3) = all_52_1
% 169.30/25.73 (8) op(e2, e3) = e2
% 169.30/25.73 (9) ~ (e3 = e0)
% 169.30/25.73 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.73 (11) ~ (e2 = e0)
% 169.30/25.73 (12) op(e3, e3) = e3
% 169.30/25.73 (13) op(e1, e3) = e1
% 169.30/25.73
% 169.30/25.73 Begin of proof
% 169.30/25.73 |
% 169.30/25.73 | BETA: splitting (1) gives:
% 169.30/25.73 |
% 169.30/25.73 | Case 1:
% 169.30/25.73 | |
% 169.30/25.73 | | (14) all_58_6 = e1 & op(e1, e3) = e1
% 169.30/25.73 | |
% 169.30/25.73 | | ALPHA: (14) implies:
% 169.30/25.73 | | (15) all_58_6 = e1
% 169.30/25.73 | |
% 169.30/25.73 | | REF_CLOSE: (3), (4), (15) are inconsistent by sub-proof #476.
% 169.30/25.73 | |
% 169.30/25.73 | Case 2:
% 169.30/25.73 | |
% 169.30/25.73 | | (16) all_58_12 = e1 & op(e0, e3) = e1
% 169.30/25.73 | |
% 169.30/25.73 | | ALPHA: (16) implies:
% 169.30/25.73 | | (17) all_58_12 = e1
% 169.30/25.73 | |
% 169.30/25.73 | | REF_CLOSE: (2), (5), (6), (7), (8), (9), (10), (11), (12), (13), (17) are
% 169.30/25.73 | | inconsistent by sub-proof #296.
% 169.30/25.73 | |
% 169.30/25.73 | End of split
% 169.30/25.73 |
% 169.30/25.73 End of proof
% 169.30/25.73
% 169.30/25.73 Sub-proof #286 shows that the following formulas are inconsistent:
% 169.30/25.73 ----------------------------------------------------------------
% 169.30/25.73 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.30/25.73 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.30/25.73 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.73 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.73 (3) ~ (all_52_13 = e3)
% 169.30/25.73 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.73 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.73 (5) all_58_2 = e2
% 169.30/25.73 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.73 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.73 (7) all_58_0 = e1
% 169.30/25.73 (8) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.73 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.73 (9) op(e3, e3) = all_10_2
% 169.30/25.73 (10) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.30/25.73 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.30/25.73 (11) ~ (e3 = e1)
% 169.30/25.73 (12) all_58_6 = e3
% 169.30/25.73 (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.73 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.30/25.73 e1)
% 169.30/25.73 (14) op(e1, e3) = all_52_2
% 169.30/25.73 (15) ~ (all_10_2 = e0)
% 169.30/25.73 (16) ~ (e1 = e0)
% 169.30/25.73 (17) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.30/25.73 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.30/25.73 e3)
% 169.30/25.73 (18) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.73 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.73 (19) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.30/25.73 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.30/25.73 (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.30/25.73 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.30/25.73 (21) op(e2, e3) = all_52_1
% 169.30/25.73 (22) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.30/25.73 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.30/25.73 (23) ~ (all_52_7 = e3)
% 169.30/25.73 (24) op(e2, e3) = e2
% 169.30/25.73 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.73 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.73 (26) ~ (e3 = e0)
% 169.30/25.73 (27) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.73 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.73 (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.73 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.73 (29) op(e1, e1) = e3
% 169.30/25.73 (30) ~ (all_52_4 = e3)
% 169.30/25.73 (31) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.30/25.73 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.30/25.73 (32) all_58_15 = e3
% 169.30/25.73 (33) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.73 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.73 (34) ~ (all_10_2 = e1)
% 169.30/25.73 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.30/25.73 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.30/25.73 (36) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.30/25.73 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.30/25.73 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.73 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.73 (38) ~ (e2 = e0)
% 169.30/25.73 (39) ~ (all_10_2 = e2)
% 169.30/25.73 (40) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.30/25.73 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.30/25.73 (41) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.30/25.73 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.30/25.73 (42) all_58_3 = e3
% 169.30/25.73 (43) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.73 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.73 (44) ~ (e2 = e1)
% 169.30/25.73 (45) op(e3, e2) = all_52_4
% 169.30/25.73 (46) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.30/25.73 (47) all_54_0 = all_10_2
% 169.30/25.73 (48) op(e0, e2) = all_52_7
% 169.30/25.73 (49) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.30/25.73 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.30/25.73 (50) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.30/25.73 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.30/25.73 (51) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.30/25.73 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.30/25.73 (52) op(e1, e3) = e1
% 169.30/25.73 (53) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.30/25.73 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.30/25.73 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.30/25.73 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.30/25.73 (54) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.30/25.73 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.30/25.73 (55) op(e2, e0) = all_52_13
% 169.30/25.73 (56) ~ (e3 = e2)
% 169.30/25.73
% 169.30/25.73 Begin of proof
% 169.30/25.73 |
% 169.30/25.73 | BETA: splitting (36) gives:
% 169.30/25.73 |
% 169.30/25.73 | Case 1:
% 169.30/25.73 | |
% 169.30/25.73 | | (57) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 169.30/25.73 | | e3)
% 169.30/25.73 | |
% 169.30/25.73 | | BETA: splitting (57) gives:
% 169.30/25.73 | |
% 169.30/25.73 | | Case 1:
% 169.30/25.73 | | |
% 169.30/25.73 | | | (58) all_58_0 = e3 & op(e3, e3) = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | ALPHA: (58) implies:
% 169.30/25.73 | | | (59) all_58_0 = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | COMBINE_EQS: (7), (59) imply:
% 169.30/25.73 | | | (60) e3 = e1
% 169.30/25.73 | | |
% 169.30/25.73 | | | SIMP: (60) implies:
% 169.30/25.73 | | | (61) e3 = e1
% 169.30/25.73 | | |
% 169.30/25.73 | | | COMBINE_EQS: (12), (61) imply:
% 169.30/25.73 | | | (62) all_58_6 = e1
% 169.30/25.73 | | |
% 169.30/25.73 | | | REF_CLOSE: (4), (5), (7), (11), (16), (18), (21), (24), (26), (37), (38),
% 169.30/25.73 | | | (56), (62) are inconsistent by sub-proof #455.
% 169.30/25.73 | | |
% 169.30/25.73 | | Case 2:
% 169.30/25.73 | | |
% 169.30/25.73 | | | (63) all_58_1 = e3 & op(e3, e2) = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | ALPHA: (63) implies:
% 169.30/25.73 | | | (64) op(e3, e2) = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | REF_CLOSE: (30), (37), (45), (64) are inconsistent by sub-proof #974.
% 169.30/25.73 | | |
% 169.30/25.73 | | End of split
% 169.30/25.73 | |
% 169.30/25.73 | Case 2:
% 169.30/25.73 | |
% 169.30/25.73 | | (65) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 169.30/25.73 | | e3)
% 169.30/25.73 | |
% 169.30/25.73 | | BETA: splitting (65) gives:
% 169.30/25.73 | |
% 169.30/25.73 | | Case 1:
% 169.30/25.73 | | |
% 169.30/25.73 | | | (66) all_58_4 = e3 & op(e3, e1) = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | ALPHA: (66) implies:
% 169.30/25.73 | | | (67) all_58_4 = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 169.30/25.73 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 169.30/25.73 | | | (25), (26), (27), (28), (29), (31), (33), (34), (35), (37),
% 169.30/25.73 | | | (38), (39), (40), (41), (42), (43), (44), (46), (47), (48),
% 169.30/25.73 | | | (49), (50), (51), (52), (53), (54), (55), (56), (67) are
% 169.30/25.73 | | | inconsistent by sub-proof #302.
% 169.30/25.73 | | |
% 169.30/25.73 | | Case 2:
% 169.30/25.73 | | |
% 169.30/25.73 | | | (68) all_58_9 = e3 & op(e3, e0) = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | ALPHA: (68) implies:
% 169.30/25.73 | | | (69) all_58_9 = e3
% 169.30/25.73 | | |
% 169.30/25.73 | | | BETA: splitting (20) gives:
% 169.30/25.73 | | |
% 169.30/25.73 | | | Case 1:
% 169.30/25.73 | | | |
% 169.30/25.73 | | | | (70) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 169.30/25.73 | | | | = e2)
% 169.30/25.73 | | | |
% 169.30/25.73 | | | | REF_CLOSE: (2), (5), (11), (16), (21), (24), (26), (27), (37), (38),
% 169.30/25.73 | | | | (42), (43), (44), (56), (69), (70) are inconsistent by
% 169.30/25.73 | | | | sub-proof #446.
% 169.30/25.73 | | | |
% 169.30/25.73 | | | Case 2:
% 169.30/25.73 | | | |
% 169.30/25.73 | | | | (71) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 169.30/25.73 | | | | e0) = e2)
% 169.30/25.73 | | | |
% 169.30/25.73 | | | | BETA: splitting (71) gives:
% 169.30/25.73 | | | |
% 169.30/25.73 | | | | Case 1:
% 169.30/25.73 | | | | |
% 169.30/25.73 | | | | | (72) all_58_11 = e2 & op(e1, e0) = e2
% 169.30/25.73 | | | | |
% 169.30/25.73 | | | | | ALPHA: (72) implies:
% 169.30/25.73 | | | | | (73) all_58_11 = e2
% 169.30/25.73 | | | | |
% 169.30/25.73 | | | | | BETA: splitting (53) gives:
% 169.30/25.73 | | | | |
% 169.30/25.73 | | | | | Case 1:
% 169.30/25.73 | | | | | |
% 169.30/25.73 | | | | | | (74) all_58_15 = e0 & op(e0, e0) = e0
% 169.30/25.73 | | | | | |
% 169.30/25.73 | | | | | | REF_CLOSE: (26), (32), (74) are inconsistent by sub-proof #887.
% 169.30/25.73 | | | | | |
% 169.30/25.73 | | | | | Case 2:
% 169.30/25.73 | | | | | |
% 169.30/25.74 | | | | | | (75) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 169.30/25.74 | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 169.30/25.74 | | | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.30/25.74 | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.30/25.74 | | | | | |
% 169.30/25.74 | | | | | | ALPHA: (75) implies:
% 169.30/25.74 | | | | | | (76) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 169.30/25.74 | | | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.74 | | | | | |
% 169.30/25.74 | | | | | | BETA: splitting (1) gives:
% 169.30/25.74 | | | | | |
% 169.30/25.74 | | | | | | Case 1:
% 169.30/25.74 | | | | | | |
% 169.30/25.74 | | | | | | | (77) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 &
% 169.30/25.74 | | | | | | | op(e2, e0) = e1)
% 169.30/25.74 | | | | | | |
% 169.30/25.74 | | | | | | | BETA: splitting (77) gives:
% 169.30/25.74 | | | | | | |
% 169.30/25.74 | | | | | | | Case 1:
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | (78) all_58_9 = e1 & op(e3, e0) = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | ALPHA: (78) implies:
% 169.30/25.74 | | | | | | | | (79) all_58_9 = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | COMBINE_EQS: (69), (79) imply:
% 169.30/25.74 | | | | | | | | (80) e3 = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | SIMP: (80) implies:
% 169.30/25.74 | | | | | | | | (81) e3 = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | COMBINE_EQS: (12), (81) imply:
% 169.30/25.74 | | | | | | | | (82) all_58_6 = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | REF_CLOSE: (4), (5), (7), (11), (16), (18), (21), (24), (26),
% 169.30/25.74 | | | | | | | | (37), (38), (56), (82) are inconsistent by sub-proof
% 169.30/25.74 | | | | | | | | #455.
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | Case 2:
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | (83) all_58_10 = e1 & op(e2, e0) = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | ALPHA: (83) implies:
% 169.30/25.74 | | | | | | | | (84) all_58_10 = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | REF_CLOSE: (16), (26), (38), (69), (73), (76), (84) are
% 169.30/25.74 | | | | | | | | inconsistent by sub-proof #833.
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | End of split
% 169.30/25.74 | | | | | | |
% 169.30/25.74 | | | | | | Case 2:
% 169.30/25.74 | | | | | | |
% 169.30/25.74 | | | | | | | (85) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 169.30/25.74 | | | | | | | op(e0, e0) = e1)
% 169.30/25.74 | | | | | | |
% 169.30/25.74 | | | | | | | BETA: splitting (85) gives:
% 169.30/25.74 | | | | | | |
% 169.30/25.74 | | | | | | | Case 1:
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | (86) all_58_11 = e1 & op(e1, e0) = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | REF_CLOSE: (44), (73), (86) are inconsistent by sub-proof #547.
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | Case 2:
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | (87) all_58_15 = e1 & op(e0, e0) = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | ALPHA: (87) implies:
% 169.30/25.74 | | | | | | | | (88) all_58_15 = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | COMBINE_EQS: (32), (88) imply:
% 169.30/25.74 | | | | | | | | (89) e3 = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | SIMP: (89) implies:
% 169.30/25.74 | | | | | | | | (90) e3 = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | COMBINE_EQS: (12), (90) imply:
% 169.30/25.74 | | | | | | | | (91) all_58_6 = e1
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | | REF_CLOSE: (4), (5), (7), (11), (16), (18), (21), (24), (26),
% 169.30/25.74 | | | | | | | | (37), (38), (56), (91) are inconsistent by sub-proof
% 169.30/25.74 | | | | | | | | #455.
% 169.30/25.74 | | | | | | | |
% 169.30/25.74 | | | | | | | End of split
% 169.30/25.74 | | | | | | |
% 169.30/25.74 | | | | | | End of split
% 169.30/25.74 | | | | | |
% 169.30/25.74 | | | | | End of split
% 169.30/25.74 | | | | |
% 169.30/25.74 | | | | Case 2:
% 169.30/25.74 | | | | |
% 169.30/25.74 | | | | | (92) all_58_15 = e2 & op(e0, e0) = e2
% 169.30/25.74 | | | | |
% 169.30/25.74 | | | | | REF_CLOSE: (2), (5), (11), (16), (21), (24), (26), (27), (32), (37),
% 169.30/25.74 | | | | | (38), (42), (43), (44), (56), (92) are inconsistent by
% 169.30/25.74 | | | | | sub-proof #310.
% 169.30/25.74 | | | | |
% 169.30/25.74 | | | | End of split
% 169.30/25.74 | | | |
% 169.30/25.74 | | | End of split
% 169.30/25.74 | | |
% 169.30/25.74 | | End of split
% 169.30/25.74 | |
% 169.30/25.74 | End of split
% 169.30/25.74 |
% 169.30/25.74 End of proof
% 169.30/25.74
% 169.30/25.74 Sub-proof #287 shows that the following formulas are inconsistent:
% 169.30/25.74 ----------------------------------------------------------------
% 169.30/25.74 (1) all_58_2 = e2
% 169.30/25.74 (2) all_58_6 = e1
% 169.30/25.74 (3) ~ (e3 = e1)
% 169.30/25.74 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.74 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.74 (5) ~ (e3 = e0)
% 169.30/25.74 (6) all_58_12 = e0
% 169.30/25.74 (7) all_58_15 = e1 & op(e0, e0) = e1
% 169.30/25.74 (8) all_58_15 = e3
% 169.30/25.74 (9) all_58_0 = e3
% 169.30/25.74 (10) ~ (e3 = e2)
% 169.30/25.74
% 169.30/25.74 Begin of proof
% 169.30/25.74 |
% 169.30/25.74 | ALPHA: (7) implies:
% 169.30/25.74 | (11) all_58_15 = e1
% 169.30/25.74 |
% 169.30/25.74 | COMBINE_EQS: (8), (11) imply:
% 169.30/25.74 | (12) e3 = e1
% 169.30/25.74 |
% 169.30/25.74 | COMBINE_EQS: (9), (12) imply:
% 169.30/25.74 | (13) all_58_0 = e1
% 169.30/25.74 |
% 169.30/25.74 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (13) are inconsistent by
% 169.30/25.74 | sub-proof #456.
% 169.30/25.74 |
% 169.30/25.74 End of proof
% 169.30/25.74
% 169.30/25.74 Sub-proof #288 shows that the following formulas are inconsistent:
% 169.30/25.74 ----------------------------------------------------------------
% 169.30/25.74 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.30/25.74 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.30/25.74 (2) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.30/25.74 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.30/25.74 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.30/25.74 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.30/25.74 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.30/25.74 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.30/25.74 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.74 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.74 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.30/25.74 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 169.30/25.74 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 169.30/25.74 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.74 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.30/25.74 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.30/25.74 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.30/25.74 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 169.30/25.74 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.74 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.30/25.74 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.30/25.74 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.30/25.74 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.30/25.74 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.74 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.74 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.30/25.74 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 169.30/25.74 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 169.30/25.74 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.74 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.30/25.74 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.30/25.74 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.30/25.74 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.30/25.74 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.74 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.74 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.30/25.74 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 169.30/25.74 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 169.30/25.74 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.74 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.30/25.74 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.30/25.74 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.30/25.74 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 169.30/25.74 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.74 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.30/25.74 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.30/25.74 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 169.30/25.74 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.30/25.74 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.30/25.74 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 169.30/25.74 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.30/25.74 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 169.30/25.74 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.30/25.74 (3) ~ (all_52_14 = e1)
% 169.30/25.74 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.74 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.74 (5) all_58_14 = e2
% 169.30/25.74 (6) all_56_2 = e1
% 169.30/25.74 (7) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.74 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.74 (8) all_58_2 = e2
% 169.30/25.74 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.74 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.74 (10) all_58_6 = e1
% 169.30/25.74 (11) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.74 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.74 (12) all_56_6 = e0
% 169.30/25.74 (13) ~ (all_52_12 = e1)
% 169.30/25.74 (14) all_56_14 = e3
% 169.30/25.74 (15) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.30/25.74 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.30/25.74 (16) ~ (e3 = e1)
% 169.30/25.74 (17) op(e3, e0) = all_52_12
% 169.30/25.74 (18) op(e1, e3) = all_52_2
% 169.30/25.74 (19) ~ (all_52_12 = e3)
% 169.30/25.74 (20) ~ (e1 = e0)
% 169.30/25.74 (21) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.30/25.74 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.30/25.74 e3)
% 169.30/25.74 (22) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.74 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.74 (23) ~ (all_52_14 = e3)
% 169.30/25.74 (24) op(e1, e2) = all_52_6
% 169.30/25.74 (25) op(e0, e2) = e1
% 169.30/25.74 (26) op(e2, e3) = all_52_1
% 169.30/25.74 (27) ~ (all_52_7 = e3)
% 169.30/25.74 (28) ~ (all_52_12 = all_52_14)
% 169.30/25.74 (29) op(e2, e3) = e2
% 169.30/25.74 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.74 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.74 (31) ~ (e3 = e0)
% 169.30/25.74 (32) all_58_12 = e0
% 169.30/25.74 (33) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.74 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.74 (34) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.74 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.74 (35) op(e1, e1) = e3
% 169.30/25.74 (36) all_58_4 = e1
% 169.30/25.74 (37) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.30/25.74 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.30/25.74 e2) = all_22_1 & $i(all_22_1))
% 169.30/25.74 (38) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.30/25.74 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.30/25.74 (39) all_58_15 = e3
% 169.30/25.74 (40) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.74 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.74 (41) all_58_0 = e3
% 169.30/25.74 (42) op(e2, e0) = e1
% 169.30/25.74 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.74 (44) ~ (e2 = e0)
% 169.30/25.74 (45) all_58_8 = e3
% 169.30/25.74 (46) op(e1, e0) = all_52_14
% 169.30/25.74 (47) all_58_13 = e1
% 169.30/25.74 (48) all_58_3 = e3
% 169.30/25.74 (49) op(e3, e3) = e3
% 169.30/25.74 (50) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.74 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.74 (51) ~ (e2 = e1)
% 169.30/25.74 (52) op(e2, e1) = e0
% 169.30/25.74 (53) op(e3, e2) = all_52_4
% 169.30/25.74 (54) op(e0, e1) = e2
% 169.30/25.74 (55) op(e0, e2) = all_52_7
% 169.30/25.74 (56) all_56_15 = e3
% 169.30/25.74 (57) op(e1, e3) = e1
% 169.30/25.74 (58) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.30/25.74 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.30/25.74 e2) = all_14_1 & $i(all_14_1))
% 169.30/25.74 (59) ~ (e3 = e2)
% 169.30/25.74
% 169.30/25.74 Begin of proof
% 169.30/25.74 |
% 169.30/25.74 | BETA: splitting (38) gives:
% 169.30/25.74 |
% 169.30/25.74 | Case 1:
% 169.30/25.74 | |
% 169.30/25.74 | | (60) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 169.30/25.74 | | e2)
% 169.30/25.74 | |
% 169.30/25.74 | | BETA: splitting (60) gives:
% 169.30/25.74 | |
% 169.30/25.74 | | Case 1:
% 169.30/25.74 | | |
% 169.30/25.74 | | | (61) all_58_1 = e2 & op(e3, e2) = e2
% 169.30/25.74 | | |
% 169.30/25.74 | | | ALPHA: (61) implies:
% 169.30/25.74 | | | (62) all_58_1 = e2
% 169.30/25.74 | | |
% 169.30/25.74 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.30/25.74 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 169.30/25.74 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 169.30/25.74 | | | (33), (34), (35), (36), (37), (39), (40), (41), (42), (43),
% 169.30/25.74 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 169.30/25.74 | | | (54), (55), (56), (57), (58), (59), (62) are inconsistent by
% 169.30/25.74 | | | sub-proof #290.
% 169.30/25.74 | | |
% 169.30/25.74 | | Case 2:
% 169.30/25.74 | | |
% 169.30/25.74 | | | (63) all_58_3 = e2 & op(e2, e2) = e2
% 169.30/25.74 | | |
% 169.30/25.74 | | | ALPHA: (63) implies:
% 169.30/25.74 | | | (64) all_58_3 = e2
% 169.30/25.74 | | |
% 169.30/25.74 | | | REF_CLOSE: (4), (8), (16), (20), (26), (29), (31), (33), (43), (44), (50),
% 169.30/25.74 | | | (51), (59), (64) are inconsistent by sub-proof #779.
% 169.30/25.74 | | |
% 169.30/25.74 | | End of split
% 169.30/25.74 | |
% 169.30/25.74 | Case 2:
% 169.30/25.74 | |
% 169.30/25.74 | | (65) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 169.30/25.74 | | e2)
% 169.30/25.74 | |
% 169.30/25.74 | | BETA: splitting (65) gives:
% 169.30/25.74 | |
% 169.30/25.74 | | Case 1:
% 169.30/25.74 | | |
% 169.30/25.74 | | | (66) all_58_7 = e2 & op(e1, e2) = e2
% 169.30/25.74 | | |
% 169.30/25.74 | | | ALPHA: (66) implies:
% 169.30/25.74 | | | (67) all_58_7 = e2
% 169.30/25.74 | | |
% 169.30/25.74 | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (16), (18), (20),
% 169.30/25.74 | | | (21), (22), (24), (25), (26), (27), (29), (30), (31), (32),
% 169.30/25.74 | | | (33), (34), (35), (37), (39), (40), (41), (43), (44), (45),
% 169.30/25.74 | | | (47), (48), (49), (50), (51), (53), (55), (57), (58), (59),
% 169.30/25.74 | | | (67) are inconsistent by sub-proof #289.
% 169.30/25.74 | | |
% 169.30/25.74 | | Case 2:
% 169.30/25.74 | | |
% 169.30/25.74 | | | (68) all_58_13 = e2 & op(e0, e2) = e2
% 169.30/25.74 | | |
% 169.30/25.74 | | | ALPHA: (68) implies:
% 169.30/25.74 | | | (69) all_58_13 = e2
% 169.30/25.74 | | |
% 169.30/25.74 | | | REF_CLOSE: (4), (7), (8), (9), (10), (11), (16), (18), (20), (22), (24),
% 169.30/25.74 | | | (26), (29), (30), (31), (32), (33), (34), (35), (37), (40),
% 169.30/25.74 | | | (41), (43), (44), (45), (48), (49), (50), (51), (53), (57),
% 169.30/25.74 | | | (58), (59), (69) are inconsistent by sub-proof #300.
% 169.30/25.74 | | |
% 169.30/25.74 | | End of split
% 169.30/25.74 | |
% 169.30/25.74 | End of split
% 169.30/25.74 |
% 169.30/25.74 End of proof
% 169.30/25.74
% 169.30/25.74 Sub-proof #289 shows that the following formulas are inconsistent:
% 169.30/25.74 ----------------------------------------------------------------
% 169.30/25.74 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.30/25.74 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.30/25.74 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.74 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.74 (3) all_58_14 = e2
% 169.30/25.74 (4) all_58_7 = e2
% 169.30/25.74 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.74 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.74 (6) all_58_2 = e2
% 169.30/25.74 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.74 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.74 (8) all_58_6 = e1
% 169.30/25.74 (9) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.74 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.74 (10) ~ (e3 = e1)
% 169.30/25.74 (11) op(e1, e3) = all_52_2
% 169.30/25.74 (12) ~ (e1 = e0)
% 169.30/25.74 (13) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.30/25.74 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.30/25.74 e3)
% 169.30/25.74 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.74 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.74 (15) op(e1, e2) = all_52_6
% 169.30/25.74 (16) op(e0, e2) = e1
% 169.30/25.74 (17) op(e2, e3) = all_52_1
% 169.30/25.74 (18) ~ (all_52_7 = e3)
% 169.30/25.74 (19) op(e2, e3) = e2
% 169.30/25.74 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.74 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.74 (21) ~ (e3 = e0)
% 169.30/25.74 (22) all_58_12 = e0
% 169.30/25.74 (23) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.74 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.74 (24) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.74 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.74 (25) op(e1, e1) = e3
% 169.30/25.74 (26) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.30/25.74 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.30/25.74 e2) = all_22_1 & $i(all_22_1))
% 169.30/25.74 (27) all_58_15 = e3
% 169.30/25.74 (28) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.74 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.74 (29) all_58_0 = e3
% 169.30/25.74 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.74 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.74 (31) ~ (e2 = e0)
% 169.30/25.74 (32) all_58_8 = e3
% 169.30/25.74 (33) all_58_13 = e1
% 169.30/25.74 (34) all_58_3 = e3
% 169.30/25.74 (35) op(e3, e3) = e3
% 169.30/25.74 (36) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.74 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.74 (37) ~ (e2 = e1)
% 169.30/25.74 (38) op(e3, e2) = all_52_4
% 169.30/25.74 (39) op(e0, e2) = all_52_7
% 169.30/25.74 (40) op(e1, e3) = e1
% 169.30/25.74 (41) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.30/25.74 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.30/25.74 e2) = all_14_1 & $i(all_14_1))
% 169.30/25.74 (42) ~ (e3 = e2)
% 169.30/25.74
% 169.30/25.74 Begin of proof
% 169.30/25.74 |
% 169.30/25.74 | BETA: splitting (28) gives:
% 169.30/25.74 |
% 169.30/25.74 | Case 1:
% 169.30/25.74 | |
% 169.30/25.74 | | (43) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 169.30/25.74 | | e0)
% 169.30/25.74 | |
% 169.30/25.74 | | BETA: splitting (43) gives:
% 169.30/25.74 | |
% 169.30/25.74 | | Case 1:
% 169.30/25.74 | | |
% 169.30/25.74 | | | (44) all_58_1 = e0 & op(e3, e2) = e0
% 169.30/25.74 | | |
% 169.30/25.74 | | | ALPHA: (44) implies:
% 169.30/25.74 | | | (45) op(e3, e2) = e0
% 169.30/25.74 | | |
% 169.30/25.74 | | | REF_CLOSE: (16), (26), (30), (45) are inconsistent by sub-proof #443.
% 169.30/25.74 | | |
% 169.30/25.74 | | Case 2:
% 169.30/25.74 | | |
% 169.30/25.74 | | | (46) all_58_3 = e0 & op(e2, e2) = e0
% 169.30/25.74 | | |
% 169.30/25.74 | | | REF_CLOSE: (2), (3), (6), (10), (12), (13), (17), (18), (19), (21), (22),
% 169.30/25.74 | | | (23), (27), (30), (31), (34), (36), (37), (39), (42), (46) are
% 169.30/25.74 | | | inconsistent by sub-proof #294.
% 169.30/25.74 | | |
% 169.30/25.74 | | End of split
% 169.30/25.74 | |
% 169.30/25.74 | Case 2:
% 169.30/25.74 | |
% 169.30/25.74 | | (47) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.30/25.74 | | e0)
% 169.30/25.74 | |
% 169.30/25.74 | | BETA: splitting (47) gives:
% 169.30/25.74 | |
% 169.30/25.74 | | Case 1:
% 169.30/25.74 | | |
% 169.30/25.74 | | | (48) all_58_7 = e0 & op(e1, e2) = e0
% 169.30/25.74 | | |
% 169.30/25.74 | | | ALPHA: (48) implies:
% 169.30/25.74 | | | (49) all_58_7 = e0
% 169.30/25.74 | | |
% 169.30/25.74 | | | COMBINE_EQS: (4), (49) imply:
% 169.30/25.74 | | | (50) e2 = e0
% 169.30/25.74 | | |
% 169.30/25.74 | | | COMBINE_EQS: (3), (50) imply:
% 169.30/25.74 | | | (51) all_58_14 = e0
% 169.30/25.74 | | |
% 169.30/25.74 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.30/25.74 | | | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 169.30/25.74 | | | (25), (26), (28), (29), (30), (31), (32), (34), (35), (36),
% 169.30/25.74 | | | (37), (38), (39), (40), (41), (42), (51) are inconsistent by
% 169.30/25.74 | | | sub-proof #297.
% 169.30/25.74 | | |
% 169.30/25.74 | | Case 2:
% 169.30/25.74 | | |
% 169.30/25.74 | | | (52) all_58_13 = e0 & op(e0, e2) = e0
% 169.30/25.74 | | |
% 169.30/25.74 | | | REF_CLOSE: (12), (33), (52) are inconsistent by sub-proof #582.
% 169.30/25.74 | | |
% 169.30/25.74 | | End of split
% 169.30/25.74 | |
% 169.30/25.74 | End of split
% 169.30/25.74 |
% 169.30/25.74 End of proof
% 169.30/25.74
% 169.30/25.74 Sub-proof #290 shows that the following formulas are inconsistent:
% 169.30/25.74 ----------------------------------------------------------------
% 169.30/25.74 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.30/25.74 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.30/25.75 (2) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.30/25.75 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.30/25.75 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.30/25.75 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.30/25.75 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.30/25.75 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.30/25.75 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.75 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.75 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.30/25.75 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 169.30/25.75 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 169.30/25.75 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.75 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.30/25.75 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.30/25.75 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.30/25.75 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 169.30/25.75 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.75 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.30/25.75 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.30/25.75 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.30/25.75 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.30/25.75 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.75 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.75 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.30/25.75 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 169.30/25.75 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 169.30/25.75 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.75 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.30/25.75 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.30/25.75 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.30/25.75 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.30/25.75 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.75 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.75 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.30/25.75 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 169.30/25.75 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 169.30/25.75 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.75 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.30/25.75 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.30/25.75 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.30/25.75 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 169.30/25.75 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.75 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.30/25.75 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.30/25.75 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 169.30/25.75 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.30/25.75 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.30/25.75 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 169.30/25.75 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.30/25.75 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 169.30/25.75 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.30/25.75 (3) ~ (all_52_14 = e1)
% 169.30/25.75 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.75 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.75 (5) all_58_14 = e2
% 169.30/25.75 (6) all_56_2 = e1
% 169.30/25.75 (7) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.75 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.75 (8) all_58_2 = e2
% 169.30/25.75 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.75 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.75 (10) all_58_6 = e1
% 169.30/25.75 (11) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.75 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.75 (12) all_56_6 = e0
% 169.30/25.75 (13) ~ (all_52_12 = e1)
% 169.30/25.75 (14) all_56_14 = e3
% 169.30/25.75 (15) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.30/25.75 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.30/25.75 (16) ~ (e3 = e1)
% 169.30/25.75 (17) op(e3, e0) = all_52_12
% 169.30/25.75 (18) op(e1, e3) = all_52_2
% 169.30/25.75 (19) ~ (all_52_12 = e3)
% 169.30/25.75 (20) ~ (e1 = e0)
% 169.30/25.75 (21) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.30/25.75 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.30/25.75 e3)
% 169.30/25.75 (22) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.75 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.75 (23) ~ (all_52_14 = e3)
% 169.30/25.75 (24) op(e1, e2) = all_52_6
% 169.30/25.75 (25) op(e0, e2) = e1
% 169.30/25.75 (26) op(e2, e3) = all_52_1
% 169.30/25.75 (27) all_58_1 = e2
% 169.30/25.75 (28) ~ (all_52_7 = e3)
% 169.30/25.75 (29) ~ (all_52_12 = all_52_14)
% 169.30/25.75 (30) op(e2, e3) = e2
% 169.30/25.75 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.75 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.75 (32) ~ (e3 = e0)
% 169.30/25.75 (33) all_58_12 = e0
% 169.30/25.75 (34) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.75 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.75 (35) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.75 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.75 (36) op(e1, e1) = e3
% 169.30/25.75 (37) all_58_4 = e1
% 169.30/25.75 (38) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.30/25.75 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.30/25.75 e2) = all_22_1 & $i(all_22_1))
% 169.30/25.75 (39) all_58_15 = e3
% 169.30/25.75 (40) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.75 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.75 (41) all_58_0 = e3
% 169.30/25.75 (42) op(e2, e0) = e1
% 169.30/25.75 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.75 (44) ~ (e2 = e0)
% 169.30/25.75 (45) all_58_8 = e3
% 169.30/25.75 (46) op(e1, e0) = all_52_14
% 169.30/25.75 (47) all_58_13 = e1
% 169.30/25.75 (48) all_58_3 = e3
% 169.30/25.75 (49) op(e3, e3) = e3
% 169.30/25.75 (50) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.75 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.75 (51) ~ (e2 = e1)
% 169.30/25.75 (52) op(e2, e1) = e0
% 169.30/25.75 (53) op(e3, e2) = all_52_4
% 169.30/25.75 (54) op(e0, e1) = e2
% 169.30/25.75 (55) op(e0, e2) = all_52_7
% 169.30/25.75 (56) all_56_15 = e3
% 169.30/25.75 (57) op(e1, e3) = e1
% 169.30/25.75 (58) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.30/25.75 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.30/25.75 e2) = all_14_1 & $i(all_14_1))
% 169.30/25.75 (59) ~ (e3 = e2)
% 169.30/25.75
% 169.30/25.75 Begin of proof
% 169.30/25.75 |
% 169.30/25.75 | BETA: splitting (40) gives:
% 169.30/25.75 |
% 169.30/25.75 | Case 1:
% 169.30/25.75 | |
% 169.30/25.75 | | (60) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 169.30/25.75 | | e0)
% 169.30/25.75 | |
% 169.30/25.75 | | BETA: splitting (60) gives:
% 169.30/25.75 | |
% 169.30/25.75 | | Case 1:
% 169.30/25.75 | | |
% 169.30/25.75 | | | (61) all_58_1 = e0 & op(e3, e2) = e0
% 169.30/25.75 | | |
% 169.30/25.75 | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (16), (18), (20),
% 169.30/25.75 | | | (21), (22), (24), (26), (27), (28), (30), (31), (32), (33),
% 169.30/25.75 | | | (34), (35), (36), (38), (40), (41), (43), (44), (45), (48),
% 169.30/25.75 | | | (49), (50), (51), (53), (55), (57), (58), (59), (61) are
% 169.30/25.75 | | | inconsistent by sub-proof #293.
% 169.30/25.75 | | |
% 169.30/25.75 | | Case 2:
% 169.30/25.75 | | |
% 169.30/25.75 | | | (62) all_58_3 = e0 & op(e2, e2) = e0
% 169.30/25.75 | | |
% 169.30/25.75 | | | ALPHA: (62) implies:
% 169.30/25.75 | | | (63) all_58_3 = e0
% 169.30/25.75 | | |
% 169.30/25.75 | | | COMBINE_EQS: (48), (63) imply:
% 169.30/25.75 | | | (64) e3 = e0
% 169.30/25.75 | | |
% 169.30/25.75 | | | SIMP: (64) implies:
% 169.30/25.75 | | | (65) e3 = e0
% 169.30/25.75 | | |
% 169.30/25.75 | | | COMBINE_EQS: (39), (65) imply:
% 169.30/25.75 | | | (66) all_58_15 = e0
% 169.30/25.75 | | |
% 169.30/25.75 | | | REF_CLOSE: (4), (5), (8), (16), (20), (21), (26), (28), (30), (32), (33),
% 169.30/25.75 | | | (34), (43), (44), (48), (50), (51), (55), (59), (66) are
% 169.30/25.75 | | | inconsistent by sub-proof #404.
% 169.30/25.75 | | |
% 169.30/25.75 | | End of split
% 169.30/25.75 | |
% 169.30/25.75 | Case 2:
% 169.30/25.75 | |
% 169.30/25.75 | | (67) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.30/25.75 | | e0)
% 169.30/25.75 | |
% 169.30/25.75 | | BETA: splitting (67) gives:
% 169.30/25.75 | |
% 169.30/25.75 | | Case 1:
% 169.30/25.75 | | |
% 169.30/25.75 | | | (68) all_58_7 = e0 & op(e1, e2) = e0
% 169.30/25.75 | | |
% 169.30/25.75 | | | ALPHA: (68) implies:
% 169.30/25.75 | | | (69) all_58_7 = e0
% 169.30/25.75 | | | (70) op(e1, e2) = e0
% 169.30/25.75 | | |
% 169.30/25.75 | | | BETA: splitting (11) gives:
% 169.30/25.75 | | |
% 169.30/25.75 | | | Case 1:
% 169.30/25.75 | | | |
% 169.30/25.75 | | | | (71) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 169.30/25.75 | | | | = e2)
% 169.30/25.75 | | | |
% 169.30/25.75 | | | | BETA: splitting (71) gives:
% 169.30/25.75 | | | |
% 169.30/25.75 | | | | Case 1:
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | (72) all_58_6 = e2 & op(e1, e3) = e2
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | ALPHA: (72) implies:
% 169.30/25.75 | | | | | (73) all_58_6 = e2
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | COMBINE_EQS: (10), (73) imply:
% 169.30/25.75 | | | | | (74) e2 = e1
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (16), (18), (20),
% 169.30/25.75 | | | | | (22), (24), (26), (30), (31), (32), (33), (34), (35), (36),
% 169.30/25.75 | | | | | (38), (39), (40), (41), (43), (44), (45), (48), (49), (50),
% 169.30/25.75 | | | | | (51), (53), (57), (58), (59), (74) are inconsistent by
% 169.30/25.75 | | | | | sub-proof #292.
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | Case 2:
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | (75) all_58_7 = e2 & op(e1, e2) = e2
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | ALPHA: (75) implies:
% 169.30/25.75 | | | | | (76) all_58_7 = e2
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | COMBINE_EQS: (69), (76) imply:
% 169.30/25.75 | | | | | (77) e2 = e0
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | SIMP: (77) implies:
% 169.30/25.75 | | | | | (78) e2 = e0
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | COMBINE_EQS: (5), (78) imply:
% 169.30/25.75 | | | | | (79) all_58_14 = e0
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (11), (16), (18), (20),
% 169.30/25.75 | | | | | (21), (22), (24), (26), (28), (30), (31), (32), (33), (34),
% 169.30/25.75 | | | | | (35), (36), (38), (40), (41), (43), (44), (45), (48), (49),
% 169.30/25.75 | | | | | (50), (51), (53), (55), (57), (58), (59), (79) are
% 169.30/25.75 | | | | | inconsistent by sub-proof #297.
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | End of split
% 169.30/25.75 | | | |
% 169.30/25.75 | | | Case 2:
% 169.30/25.75 | | | |
% 169.30/25.75 | | | | (80) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 169.30/25.75 | | | | = e2)
% 169.30/25.75 | | | |
% 169.30/25.75 | | | | BETA: splitting (80) gives:
% 169.30/25.75 | | | |
% 169.30/25.75 | | | | Case 1:
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | (81) all_58_8 = e2 & op(e1, e1) = e2
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | ALPHA: (81) implies:
% 169.30/25.75 | | | | | (82) op(e1, e1) = e2
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | REF_CLOSE: (4), (7), (8), (16), (18), (20), (22), (26), (30), (31),
% 169.30/25.75 | | | | | (32), (34), (36), (43), (44), (48), (49), (50), (51), (57),
% 169.30/25.75 | | | | | (59), (82) are inconsistent by sub-proof #339.
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | Case 2:
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | (83) all_58_11 = e2 & op(e1, e0) = e2
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | ALPHA: (83) implies:
% 169.30/25.75 | | | | | (84) op(e1, e0) = e2
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | BETA: splitting (15) gives:
% 169.30/25.75 | | | | |
% 169.30/25.75 | | | | | Case 1:
% 169.30/25.75 | | | | | |
% 169.30/25.75 | | | | | | (85) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 169.30/25.75 | | | | | | e2) = e0)
% 169.30/25.75 | | | | | |
% 169.30/25.75 | | | | | | BETA: splitting (85) gives:
% 169.30/25.75 | | | | | |
% 169.30/25.75 | | | | | | Case 1:
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | (86) all_58_0 = e0 & op(e3, e3) = e0
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | ALPHA: (86) implies:
% 169.30/25.75 | | | | | | | (87) op(e3, e3) = e0
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | REF_CLOSE: (32), (43), (49), (87) are inconsistent by sub-proof
% 169.30/25.75 | | | | | | | #949.
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | Case 2:
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | (88) all_58_1 = e0 & op(e3, e2) = e0
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (11), (16), (18),
% 169.30/25.75 | | | | | | | (20), (21), (22), (24), (26), (27), (28), (30), (31),
% 169.30/25.75 | | | | | | | (32), (33), (34), (35), (36), (38), (40), (41), (43),
% 169.30/25.75 | | | | | | | (44), (45), (48), (49), (50), (51), (53), (55), (57),
% 169.30/25.75 | | | | | | | (58), (59), (88) are inconsistent by sub-proof #293.
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | End of split
% 169.30/25.75 | | | | | |
% 169.30/25.75 | | | | | Case 2:
% 169.30/25.75 | | | | | |
% 169.30/25.75 | | | | | | (89) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 169.30/25.75 | | | | | | e0) = e0)
% 169.30/25.75 | | | | | |
% 169.30/25.75 | | | | | | BETA: splitting (89) gives:
% 169.30/25.75 | | | | | |
% 169.30/25.75 | | | | | | Case 1:
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | (90) all_58_4 = e0 & op(e3, e1) = e0
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | REF_CLOSE: (20), (37), (90) are inconsistent by sub-proof #793.
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | Case 2:
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | (91) all_58_9 = e0 & op(e3, e0) = e0
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | ALPHA: (91) implies:
% 169.30/25.75 | | | | | | | (92) op(e3, e0) = e0
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | GROUND_INST: instantiating (43) with all_52_14, e2, e0, e1,
% 169.30/25.75 | | | | | | | simplifying with (46), (84) gives:
% 169.30/25.75 | | | | | | | (93) all_52_14 = e2
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | GROUND_INST: instantiating (43) with all_52_6, e0, e2, e1,
% 169.30/25.75 | | | | | | | simplifying with (24), (70) gives:
% 169.30/25.75 | | | | | | | (94) all_52_6 = e0
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | GROUND_INST: instantiating (43) with all_52_12, e0, e0, e3,
% 169.30/25.75 | | | | | | | simplifying with (17), (92) gives:
% 169.30/25.75 | | | | | | | (95) all_52_12 = e0
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | REDUCE: (29), (93), (95) imply:
% 169.30/25.75 | | | | | | | (96) ~ (e2 = e0)
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | REDUCE: (19), (95) imply:
% 169.30/25.75 | | | | | | | (97) ~ (e3 = e0)
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | REDUCE: (13), (95) imply:
% 169.30/25.75 | | | | | | | (98) ~ (e1 = e0)
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | REDUCE: (23), (93) imply:
% 169.30/25.75 | | | | | | | (99) ~ (e3 = e2)
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | BETA: splitting (2) gives:
% 169.30/25.75 | | | | | | |
% 169.30/25.75 | | | | | | | Case 1:
% 169.30/25.75 | | | | | | | |
% 169.30/25.75 | | | | | | | | (100) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3
% 169.30/25.75 | | | | | | | | & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 169.30/25.75 | | | | | | | | e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.75 | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2)
% 169.30/25.75 | | | | | | | | = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 =
% 169.30/25.75 | | | | | | | | e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 169.30/25.75 | | | | | | | | & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.30/25.75 | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 =
% 169.30/25.75 | | | | | | | | e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0
% 169.30/25.75 | | | | | | | | & $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 169.30/25.75 | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.75 | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 169.30/25.75 | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 169.30/25.75 | | | | | | | | $i(all_56_6)))) | (all_56_2 = e3 & ~ (all_56_14
% 169.30/25.75 | | | | | | | | = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | (
% 169.30/25.75 | | | | | | | | ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.30/25.75 | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.30/25.75 | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.30/25.75 | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.30/25.75 | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.30/25.75 | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~ (all_56_14
% 169.30/25.75 | | | | | | | | = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | (
% 169.30/25.75 | | | | | | | | ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.30/25.75 | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.30/25.75 | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.30/25.75 | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.30/25.75 | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.30/25.75 | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~ (all_56_10
% 169.30/25.75 | | | | | | | | = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | (
% 169.30/25.75 | | | | | | | | ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.30/25.75 | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 169.30/25.75 | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.75 | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 169.30/25.75 | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 169.30/25.75 | | | | | | | | $i(all_56_6))))
% 169.30/25.75 | | | | | | | |
% 169.30/25.75 | | | | | | | | BETA: splitting (100) gives:
% 169.30/25.75 | | | | | | | |
% 169.30/25.75 | | | | | | | | Case 1:
% 169.30/25.75 | | | | | | | | |
% 169.30/25.75 | | | | | | | | | (101) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 169.30/25.75 | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 169.30/25.75 | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.75 | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 169.30/25.75 | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 169.30/25.75 | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.30/25.75 | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))) | (all_56_1
% 169.30/25.75 | | | | | | | | | = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.30/25.75 | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2,
% 169.30/25.75 | | | | | | | | | e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.75 | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.30/25.75 | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.30/25.75 | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.30/25.75 | | | | | | | | | e3) = all_56_6 & $i(all_56_6))))
% 169.30/25.75 | | | | | | | | |
% 169.30/25.75 | | | | | | | | | BETA: splitting (101) gives:
% 169.30/25.75 | | | | | | | | |
% 169.30/25.75 | | | | | | | | | Case 1:
% 169.30/25.75 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | (102) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) =
% 169.30/25.76 | | | | | | | | | | e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 169.30/25.76 | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | ALPHA: (102) implies:
% 169.30/25.76 | | | | | | | | | | (103) op(e2, e3) = e3
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | REF_CLOSE: (26), (30), (43), (59), (103) are inconsistent by
% 169.30/25.76 | | | | | | | | | | sub-proof #462.
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | Case 2:
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | (104) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) =
% 169.30/25.76 | | | | | | | | | | e2 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.30/25.76 | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | ALPHA: (104) implies:
% 169.30/25.76 | | | | | | | | | | (105) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | REF_CLOSE: (6), (14), (105) are inconsistent by sub-proof
% 169.30/25.76 | | | | | | | | | | #485.
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | End of split
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | Case 2:
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | | (106) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 169.30/25.76 | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.30/25.76 | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.30/25.76 | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) | (all_56_3
% 169.30/25.76 | | | | | | | | | = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 169.30/25.76 | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.30/25.76 | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) | (all_56_4
% 169.30/25.76 | | | | | | | | | = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2,
% 169.30/25.76 | | | | | | | | | e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | e3) = all_56_6 & $i(all_56_6))))
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | | BETA: splitting (106) gives:
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | | Case 1:
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | (107) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 169.30/25.76 | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.30/25.76 | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.30/25.76 | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | ALPHA: (107) implies:
% 169.30/25.76 | | | | | | | | | | (108) all_56_2 = e3
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | COMBINE_EQS: (6), (108) imply:
% 169.30/25.76 | | | | | | | | | | (109) e3 = e1
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | COMBINE_EQS: (41), (109) imply:
% 169.30/25.76 | | | | | | | | | | (110) all_58_0 = e1
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | REF_CLOSE: (8), (10), (16), (22), (32), (33), (59), (110) are
% 169.30/25.76 | | | | | | | | | | inconsistent by sub-proof #456.
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | Case 2:
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | (111) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 169.30/25.76 | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.30/25.76 | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.30/25.76 | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) |
% 169.30/25.76 | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 169.30/25.76 | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.30/25.76 | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | | e3) = all_56_6 & $i(all_56_6))))
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | BETA: splitting (111) gives:
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | Case 1:
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | (112) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 169.30/25.76 | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.30/25.76 | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.76 | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.30/25.76 | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.30/25.76 | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | ALPHA: (112) implies:
% 169.30/25.76 | | | | | | | | | | | (113) ~ (all_56_14 = e1)
% 169.30/25.76 | | | | | | | | | | | (114) op(e1, e2) = e2
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | GROUND_INST: instantiating (43) with e0, e2, e2, e1,
% 169.30/25.76 | | | | | | | | | | | simplifying with (70), (114) gives:
% 169.30/25.76 | | | | | | | | | | | (115) e2 = e0
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | COMBINE_EQS: (5), (115) imply:
% 169.30/25.76 | | | | | | | | | | | (116) all_58_14 = e0
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (11), (16), (18),
% 169.30/25.76 | | | | | | | | | | | (20), (21), (22), (24), (26), (28), (30), (31),
% 169.30/25.76 | | | | | | | | | | | (32), (33), (34), (35), (36), (38), (40), (41),
% 169.30/25.76 | | | | | | | | | | | (43), (44), (45), (48), (49), (50), (51), (53),
% 169.30/25.76 | | | | | | | | | | | (55), (57), (58), (59), (116) are inconsistent by
% 169.30/25.76 | | | | | | | | | | | sub-proof #297.
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | Case 2:
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | (117) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 169.30/25.76 | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.30/25.76 | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.76 | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.30/25.76 | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | ALPHA: (117) implies:
% 169.30/25.76 | | | | | | | | | | | (118) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | REF_CLOSE: (6), (14), (118) are inconsistent by sub-proof
% 169.30/25.76 | | | | | | | | | | | #485.
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | End of split
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | End of split
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | End of split
% 169.30/25.76 | | | | | | | |
% 169.30/25.76 | | | | | | | Case 2:
% 169.30/25.76 | | | | | | | |
% 169.30/25.76 | | | | | | | | (119) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1
% 169.30/25.76 | | | | | | | | & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 169.30/25.76 | | | | | | | | e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.76 | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2)
% 169.30/25.76 | | | | | | | | = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 =
% 169.30/25.76 | | | | | | | | e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 169.30/25.76 | | | | | | | | & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.30/25.76 | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 =
% 169.30/25.76 | | | | | | | | e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0
% 169.30/25.76 | | | | | | | | & $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 169.30/25.76 | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.76 | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 169.30/25.76 | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 169.30/25.76 | | | | | | | | $i(all_56_6)))) | (all_56_11 = e0 & ~ (all_56_12
% 169.30/25.76 | | | | | | | | = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | (
% 169.30/25.76 | | | | | | | | ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 169.30/25.76 | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.30/25.76 | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.30/25.76 | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.30/25.76 | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.30/25.76 | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~ (all_56_14
% 169.30/25.76 | | | | | | | | = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | (
% 169.30/25.76 | | | | | | | | ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.30/25.76 | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.30/25.76 | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.30/25.76 | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.30/25.76 | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.30/25.76 | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 169.30/25.76 | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0)
% 169.30/25.76 | | | | | | | | = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 =
% 169.30/25.76 | | | | | | | | e0) | ( ~ (all_56_11 = e2) & op(e2, e0) =
% 169.30/25.76 | | | | | | | | all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 =
% 169.30/25.76 | | | | | | | | e0) | ( ~ (all_56_13 = e1) & op(e1, e0) =
% 169.30/25.76 | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_6 = e3 &
% 169.30/25.76 | | | | | | | | op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 169.30/25.76 | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.30/25.76 | | | | | | | |
% 169.30/25.76 | | | | | | | | BETA: splitting (119) gives:
% 169.30/25.76 | | | | | | | |
% 169.30/25.76 | | | | | | | | Case 1:
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | | (120) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 169.30/25.76 | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 169.30/25.76 | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))) | (all_56_9
% 169.30/25.76 | | | | | | | | | = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2,
% 169.30/25.76 | | | | | | | | | e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | e3) = all_56_6 & $i(all_56_6))))
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | | REF_CLOSE: (6), (14), (20), (43), (52), (120) are inconsistent
% 169.30/25.76 | | | | | | | | | by sub-proof #291.
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | Case 2:
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | | (121) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) =
% 169.30/25.76 | | | | | | | | | e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 169.30/25.76 | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))) | (all_56_13
% 169.30/25.76 | | | | | | | | | = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 169.30/25.76 | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.30/25.76 | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.30/25.76 | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) | ( ~
% 169.30/25.76 | | | | | | | | | (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.30/25.76 | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.30/25.76 | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.30/25.76 | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.30/25.76 | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.30/25.76 | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.30/25.76 | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 169.30/25.76 | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 169.30/25.76 | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | | BETA: splitting (121) gives:
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | | Case 1:
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | (122) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) =
% 169.30/25.76 | | | | | | | | | | e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 169.30/25.76 | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 169.30/25.76 | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | ALPHA: (122) implies:
% 169.30/25.76 | | | | | | | | | | (123) op(e2, e0) = e0
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | REF_CLOSE: (20), (42), (43), (123) are inconsistent by
% 169.30/25.76 | | | | | | | | | | sub-proof #849.
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | Case 2:
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | (124) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 169.30/25.76 | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 169.30/25.76 | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & (
% 169.30/25.76 | | | | | | | | | | ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.30/25.76 | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) | ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.30/25.76 | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.30/25.76 | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.30/25.76 | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.30/25.76 | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 169.30/25.76 | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 169.30/25.76 | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | BETA: splitting (124) gives:
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | Case 1:
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | (125) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 169.30/25.76 | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 169.30/25.76 | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.30/25.76 | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.30/25.76 | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.30/25.76 | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.30/25.76 | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | ALPHA: (125) implies:
% 169.30/25.76 | | | | | | | | | | | (126) ~ (all_56_14 = e1)
% 169.30/25.76 | | | | | | | | | | | (127) op(e1, e0) = e0
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | GROUND_INST: instantiating (43) with e2, e0, e0, e1,
% 169.30/25.76 | | | | | | | | | | | simplifying with (84), (127) gives:
% 169.30/25.76 | | | | | | | | | | | (128) e2 = e0
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | COMBINE_EQS: (5), (128) imply:
% 169.30/25.76 | | | | | | | | | | | (129) all_58_14 = e0
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (11), (16), (18),
% 169.30/25.76 | | | | | | | | | | | (20), (21), (22), (24), (26), (28), (30), (31),
% 169.30/25.76 | | | | | | | | | | | (32), (33), (34), (35), (36), (38), (40), (41),
% 169.30/25.76 | | | | | | | | | | | (43), (44), (45), (48), (49), (50), (51), (53),
% 169.30/25.76 | | | | | | | | | | | (55), (57), (58), (59), (129) are inconsistent by
% 169.30/25.76 | | | | | | | | | | | sub-proof #297.
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | Case 2:
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | (130) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.30/25.76 | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.30/25.76 | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.30/25.76 | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.30/25.76 | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.30/25.76 | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.30/25.76 | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 169.30/25.76 | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 169.30/25.76 | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | ALPHA: (130) implies:
% 169.30/25.76 | | | | | | | | | | | (131) ~ (all_56_15 = e0)
% 169.30/25.76 | | | | | | | | | | | (132) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 169.30/25.76 | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 169.30/25.76 | | | | | | | | | | | = e1)
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | BETA: splitting (132) gives:
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | Case 1:
% 169.30/25.76 | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | (133) all_56_6 = e3 & op(e0, e3) = e3
% 169.30/25.76 | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | ALPHA: (133) implies:
% 169.30/25.76 | | | | | | | | | | | | (134) all_56_6 = e3
% 169.30/25.76 | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | COMBINE_EQS: (12), (134) imply:
% 169.30/25.76 | | | | | | | | | | | | (135) e3 = e0
% 169.30/25.76 | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | COMBINE_EQS: (39), (135) imply:
% 169.30/25.76 | | | | | | | | | | | | (136) all_58_15 = e0
% 169.30/25.76 | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (16), (20), (21), (26), (28), (30),
% 169.30/25.76 | | | | | | | | | | | | (32), (33), (34), (43), (44), (48), (50), (51),
% 169.30/25.76 | | | | | | | | | | | | (55), (59), (136) are inconsistent by sub-proof
% 169.30/25.76 | | | | | | | | | | | | #404.
% 169.30/25.76 | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | Case 2:
% 169.30/25.76 | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | (137) (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1
% 169.30/25.76 | | | | | | | | | | | | & op(e0, e1) = e1)
% 169.30/25.76 | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | BETA: splitting (137) gives:
% 169.30/25.76 | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | Case 1:
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | | (138) all_56_7 = e2 & op(e0, e2) = e2
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | | ALPHA: (138) implies:
% 169.30/25.76 | | | | | | | | | | | | | (139) op(e0, e2) = e2
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | | GROUND_INST: instantiating (43) with e1, e2, e2, e0,
% 169.30/25.76 | | | | | | | | | | | | | simplifying with (25), (139) gives:
% 169.30/25.76 | | | | | | | | | | | | | (140) e2 = e1
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | | COMBINE_EQS: (5), (140) imply:
% 169.30/25.76 | | | | | | | | | | | | | (141) all_58_14 = e1
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (11), (16), (18),
% 169.30/25.76 | | | | | | | | | | | | | (20), (22), (24), (26), (30), (31), (32), (33),
% 169.30/25.76 | | | | | | | | | | | | | (34), (35), (36), (38), (39), (40), (41), (43),
% 169.30/25.76 | | | | | | | | | | | | | (44), (45), (48), (49), (50), (51), (53), (57),
% 169.30/25.76 | | | | | | | | | | | | | (58), (59), (141) are inconsistent by sub-proof
% 169.30/25.76 | | | | | | | | | | | | | #299.
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | Case 2:
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | | (142) all_56_8 = e1 & op(e0, e1) = e1
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | | ALPHA: (142) implies:
% 169.30/25.76 | | | | | | | | | | | | | (143) op(e0, e1) = e1
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | | GROUND_INST: instantiating (43) with e2, e1, e1, e0,
% 169.30/25.76 | | | | | | | | | | | | | simplifying with (54), (143) gives:
% 169.30/25.76 | | | | | | | | | | | | | (144) e2 = e1
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | | COMBINE_EQS: (5), (144) imply:
% 169.30/25.76 | | | | | | | | | | | | | (145) all_58_14 = e1
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | | REF_CLOSE: (1), (4), (7), (8), (9), (10), (11), (16), (18),
% 169.30/25.76 | | | | | | | | | | | | | (20), (22), (24), (26), (30), (31), (32), (33),
% 169.30/25.76 | | | | | | | | | | | | | (34), (35), (36), (38), (39), (40), (41), (43),
% 169.30/25.76 | | | | | | | | | | | | | (44), (45), (48), (49), (50), (51), (53), (57),
% 169.30/25.76 | | | | | | | | | | | | | (58), (59), (145) are inconsistent by sub-proof
% 169.30/25.76 | | | | | | | | | | | | | #299.
% 169.30/25.76 | | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | | End of split
% 169.30/25.76 | | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | | End of split
% 169.30/25.76 | | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | | End of split
% 169.30/25.76 | | | | | | | | | |
% 169.30/25.76 | | | | | | | | | End of split
% 169.30/25.76 | | | | | | | | |
% 169.30/25.76 | | | | | | | | End of split
% 169.30/25.76 | | | | | | | |
% 169.30/25.76 | | | | | | | End of split
% 169.30/25.76 | | | | | | |
% 169.30/25.76 | | | | | | End of split
% 169.30/25.76 | | | | | |
% 169.30/25.76 | | | | | End of split
% 169.30/25.76 | | | | |
% 169.30/25.76 | | | | End of split
% 169.30/25.76 | | | |
% 169.30/25.76 | | | End of split
% 169.30/25.76 | | |
% 169.30/25.76 | | Case 2:
% 169.30/25.76 | | |
% 169.30/25.76 | | | (146) all_58_13 = e0 & op(e0, e2) = e0
% 169.30/25.76 | | |
% 169.30/25.76 | | | REF_CLOSE: (20), (47), (146) are inconsistent by sub-proof #582.
% 169.30/25.76 | | |
% 169.30/25.76 | | End of split
% 169.30/25.76 | |
% 169.30/25.76 | End of split
% 169.30/25.76 |
% 169.30/25.76 End of proof
% 169.30/25.76
% 169.30/25.76 Sub-proof #291 shows that the following formulas are inconsistent:
% 169.30/25.76 ----------------------------------------------------------------
% 169.30/25.76 (1) all_56_2 = e1
% 169.30/25.76 (2) all_56_14 = e3
% 169.30/25.76 (3) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 =
% 169.30/25.76 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.30/25.76 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.30/25.76 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.30/25.77 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.30/25.77 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.30/25.77 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.30/25.77 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.77 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.30/25.77 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.30/25.77 (4) ~ (e1 = e0)
% 169.30/25.77 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.77 (6) op(e2, e1) = e0
% 169.30/25.77
% 169.30/25.77 Begin of proof
% 169.30/25.77 |
% 169.30/25.77 | BETA: splitting (3) gives:
% 169.30/25.77 |
% 169.30/25.77 | Case 1:
% 169.30/25.77 | |
% 169.30/25.77 | | (7) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~
% 169.30/25.77 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 169.30/25.77 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 169.30/25.77 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 169.30/25.77 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 169.30/25.77 | |
% 169.30/25.77 | | ALPHA: (7) implies:
% 169.30/25.77 | | (8) op(e2, e1) = e1
% 169.30/25.77 | |
% 169.30/25.77 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #911.
% 169.30/25.77 | |
% 169.30/25.77 | Case 2:
% 169.30/25.77 | |
% 169.30/25.77 | | (9) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.30/25.77 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.30/25.77 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.30/25.77 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 169.30/25.77 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 169.30/25.77 | |
% 169.30/25.77 | | ALPHA: (9) implies:
% 169.30/25.77 | | (10) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.30/25.77 | | $i(all_56_2))
% 169.30/25.77 | |
% 169.30/25.77 | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #485.
% 169.30/25.77 | |
% 169.30/25.77 | End of split
% 169.30/25.77 |
% 169.30/25.77 End of proof
% 169.30/25.77
% 169.30/25.77 Sub-proof #292 shows that the following formulas are inconsistent:
% 169.30/25.77 ----------------------------------------------------------------
% 169.30/25.77 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.30/25.77 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.30/25.77 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.77 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.77 (3) all_58_14 = e2
% 169.30/25.77 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.77 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.77 (5) all_58_2 = e2
% 169.30/25.77 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.77 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.77 (7) all_58_6 = e1
% 169.30/25.77 (8) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.77 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.77 (9) ~ (e3 = e1)
% 169.30/25.77 (10) op(e1, e3) = all_52_2
% 169.30/25.77 (11) ~ (e1 = e0)
% 169.30/25.77 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.77 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.77 (13) op(e1, e2) = all_52_6
% 169.30/25.77 (14) op(e2, e3) = all_52_1
% 169.30/25.77 (15) op(e2, e3) = e2
% 169.30/25.77 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.77 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.77 (17) ~ (e3 = e0)
% 169.30/25.77 (18) all_58_12 = e0
% 169.30/25.77 (19) e2 = e1
% 169.30/25.77 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.77 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.77 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.77 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.77 (22) op(e1, e1) = e3
% 169.30/25.77 (23) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.30/25.77 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.30/25.77 e2) = all_22_1 & $i(all_22_1))
% 169.30/25.77 (24) all_58_15 = e3
% 169.30/25.77 (25) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.77 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.77 (26) all_58_0 = e3
% 169.30/25.77 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.77 (28) ~ (e2 = e0)
% 169.30/25.77 (29) all_58_8 = e3
% 169.30/25.77 (30) all_58_3 = e3
% 169.30/25.77 (31) op(e3, e3) = e3
% 169.30/25.77 (32) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.77 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.77 (33) ~ (e2 = e1)
% 169.30/25.77 (34) op(e3, e2) = all_52_4
% 169.30/25.77 (35) op(e1, e3) = e1
% 169.30/25.77 (36) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.30/25.77 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.30/25.77 e2) = all_14_1 & $i(all_14_1))
% 169.30/25.77 (37) ~ (e3 = e2)
% 169.30/25.77
% 169.30/25.77 Begin of proof
% 169.30/25.77 |
% 169.30/25.77 | SIMP: (19) implies:
% 169.30/25.77 | (38) e2 = e1
% 169.30/25.77 |
% 169.30/25.77 | COMBINE_EQS: (3), (38) imply:
% 169.30/25.77 | (39) all_58_14 = e1
% 169.30/25.77 |
% 169.30/25.77 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.30/25.77 | (14), (15), (16), (17), (18), (20), (21), (22), (23), (24), (25),
% 169.30/25.77 | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 169.30/25.77 | (37), (39) are inconsistent by sub-proof #299.
% 169.30/25.77 |
% 169.30/25.77 End of proof
% 169.30/25.77
% 169.30/25.77 Sub-proof #293 shows that the following formulas are inconsistent:
% 169.30/25.77 ----------------------------------------------------------------
% 169.30/25.77 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.30/25.77 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.30/25.77 (2) all_58_1 = e0 & op(e3, e2) = e0
% 169.30/25.77 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.77 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.77 (4) all_58_14 = e2
% 169.30/25.77 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.77 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.77 (6) all_58_2 = e2
% 169.30/25.77 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.77 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.77 (8) all_58_6 = e1
% 169.30/25.77 (9) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.77 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.77 (10) ~ (e3 = e1)
% 169.30/25.77 (11) op(e1, e3) = all_52_2
% 169.30/25.77 (12) ~ (e1 = e0)
% 169.30/25.77 (13) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.30/25.77 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.30/25.77 e3)
% 169.30/25.77 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.77 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.77 (15) op(e1, e2) = all_52_6
% 169.30/25.77 (16) op(e2, e3) = all_52_1
% 169.30/25.77 (17) all_58_1 = e2
% 169.30/25.77 (18) ~ (all_52_7 = e3)
% 169.30/25.77 (19) op(e2, e3) = e2
% 169.30/25.77 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.77 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.77 (21) ~ (e3 = e0)
% 169.30/25.77 (22) all_58_12 = e0
% 169.30/25.77 (23) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.77 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.77 (24) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.77 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.77 (25) op(e1, e1) = e3
% 169.30/25.77 (26) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.30/25.77 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.30/25.77 e2) = all_22_1 & $i(all_22_1))
% 169.30/25.77 (27) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.77 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.77 (28) all_58_0 = e3
% 169.30/25.77 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.77 (30) ~ (e2 = e0)
% 169.30/25.77 (31) all_58_8 = e3
% 169.30/25.77 (32) all_58_3 = e3
% 169.30/25.77 (33) op(e3, e3) = e3
% 169.30/25.77 (34) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.77 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.77 (35) ~ (e2 = e1)
% 169.30/25.77 (36) op(e3, e2) = all_52_4
% 169.30/25.77 (37) op(e0, e2) = all_52_7
% 169.30/25.77 (38) op(e1, e3) = e1
% 169.30/25.77 (39) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.30/25.77 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.30/25.77 e2) = all_14_1 & $i(all_14_1))
% 169.30/25.77 (40) ~ (e3 = e2)
% 169.30/25.77
% 169.30/25.77 Begin of proof
% 169.30/25.77 |
% 169.30/25.77 | ALPHA: (2) implies:
% 169.30/25.77 | (41) all_58_1 = e0
% 169.30/25.77 |
% 169.30/25.77 | COMBINE_EQS: (17), (41) imply:
% 169.30/25.77 | (42) e2 = e0
% 169.30/25.77 |
% 169.30/25.77 | COMBINE_EQS: (4), (42) imply:
% 169.30/25.77 | (43) all_58_14 = e0
% 169.30/25.77 |
% 169.30/25.77 | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 169.30/25.77 | (15), (16), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 169.30/25.77 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 169.30/25.77 | (38), (39), (40), (43) are inconsistent by sub-proof #297.
% 169.30/25.77 |
% 169.30/25.77 End of proof
% 169.30/25.77
% 169.30/25.77 Sub-proof #294 shows that the following formulas are inconsistent:
% 169.30/25.77 ----------------------------------------------------------------
% 169.30/25.77 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.77 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.77 (2) all_58_14 = e2
% 169.30/25.77 (3) all_58_2 = e2
% 169.30/25.77 (4) ~ (e3 = e1)
% 169.30/25.77 (5) ~ (e1 = e0)
% 169.30/25.77 (6) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.30/25.77 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.30/25.77 (7) all_58_3 = e0 & op(e2, e2) = e0
% 169.30/25.77 (8) op(e2, e3) = all_52_1
% 169.30/25.77 (9) ~ (all_52_7 = e3)
% 169.30/25.77 (10) op(e2, e3) = e2
% 169.30/25.77 (11) ~ (e3 = e0)
% 169.30/25.77 (12) all_58_12 = e0
% 169.30/25.77 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.77 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.77 (14) all_58_15 = e3
% 169.30/25.77 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.77 (16) ~ (e2 = e0)
% 169.30/25.77 (17) all_58_3 = e3
% 169.30/25.77 (18) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.77 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.77 (19) ~ (e2 = e1)
% 169.30/25.77 (20) op(e0, e2) = all_52_7
% 169.30/25.77 (21) ~ (e3 = e2)
% 169.30/25.77
% 169.30/25.77 Begin of proof
% 169.30/25.77 |
% 169.30/25.77 | ALPHA: (7) implies:
% 169.30/25.77 | (22) all_58_3 = e0
% 169.30/25.77 |
% 169.30/25.77 | COMBINE_EQS: (17), (22) imply:
% 169.30/25.77 | (23) e3 = e0
% 169.30/25.77 |
% 169.30/25.77 | COMBINE_EQS: (14), (23) imply:
% 169.30/25.77 | (24) all_58_15 = e0
% 169.30/25.77 |
% 169.30/25.77 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 169.30/25.77 | (15), (16), (17), (18), (19), (20), (21), (24) are inconsistent by
% 169.30/25.77 | sub-proof #404.
% 169.30/25.77 |
% 169.30/25.77 End of proof
% 169.30/25.77
% 169.30/25.77 Sub-proof #295 shows that the following formulas are inconsistent:
% 169.30/25.77 ----------------------------------------------------------------
% 169.30/25.77 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 169.30/25.77 (2) op(e0, e2) = e1
% 169.30/25.77 (3) ~ (e3 = e0)
% 169.30/25.77 (4) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) = all_22_1
% 169.30/25.77 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2) =
% 169.30/25.77 all_22_1 & $i(all_22_1))
% 169.30/25.77 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.77 (6) op(e3, e3) = e3
% 169.30/25.77
% 169.30/25.77 Begin of proof
% 169.30/25.77 |
% 169.30/25.77 | BETA: splitting (1) gives:
% 169.30/25.77 |
% 169.30/25.77 | Case 1:
% 169.30/25.77 | |
% 169.30/25.77 | | (7) all_58_0 = e0 & op(e3, e3) = e0
% 169.30/25.77 | |
% 169.30/25.77 | | ALPHA: (7) implies:
% 169.30/25.77 | | (8) op(e3, e3) = e0
% 169.30/25.77 | |
% 169.30/25.77 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #949.
% 169.30/25.77 | |
% 169.30/25.77 | Case 2:
% 169.30/25.77 | |
% 169.30/25.77 | | (9) all_58_1 = e0 & op(e3, e2) = e0
% 169.30/25.77 | |
% 169.30/25.77 | | ALPHA: (9) implies:
% 169.30/25.77 | | (10) op(e3, e2) = e0
% 169.30/25.77 | |
% 169.30/25.77 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #443.
% 169.30/25.77 | |
% 169.30/25.77 | End of split
% 169.30/25.77 |
% 169.30/25.77 End of proof
% 169.30/25.77
% 169.30/25.77 Sub-proof #296 shows that the following formulas are inconsistent:
% 169.30/25.77 ----------------------------------------------------------------
% 169.30/25.77 (1) all_58_12 = e1
% 169.30/25.77 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.77 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.77 (3) op(e1, e3) = all_52_2
% 169.30/25.77 (4) ~ (e1 = e0)
% 169.30/25.77 (5) op(e2, e3) = all_52_1
% 169.30/25.77 (6) op(e2, e3) = e2
% 169.30/25.77 (7) ~ (e3 = e0)
% 169.30/25.77 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.77 (9) ~ (e2 = e0)
% 169.30/25.77 (10) op(e3, e3) = e3
% 169.30/25.77 (11) op(e1, e3) = e1
% 169.30/25.77
% 169.30/25.77 Begin of proof
% 169.30/25.77 |
% 169.30/25.77 | BETA: splitting (2) gives:
% 169.30/25.77 |
% 169.30/25.77 | Case 1:
% 169.30/25.77 | |
% 169.30/25.77 | | (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.30/25.77 | | e0)
% 169.30/25.77 | |
% 169.30/25.77 | | REF_CLOSE: (5), (6), (7), (8), (9), (10), (12) are inconsistent by sub-proof
% 169.30/25.77 | | #460.
% 169.30/25.77 | |
% 169.30/25.77 | Case 2:
% 169.30/25.77 | |
% 169.30/25.77 | | (13) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.30/25.77 | | e0)
% 169.30/25.77 | |
% 169.30/25.77 | | REF_CLOSE: (1), (3), (4), (8), (11), (13) are inconsistent by sub-proof
% 169.30/25.77 | | #341.
% 169.30/25.77 | |
% 169.30/25.77 | End of split
% 169.30/25.77 |
% 169.30/25.77 End of proof
% 169.30/25.77
% 169.30/25.77 Sub-proof #297 shows that the following formulas are inconsistent:
% 169.30/25.77 ----------------------------------------------------------------
% 169.30/25.77 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.30/25.77 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.30/25.77 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.77 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.77 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.77 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.77 (4) all_58_2 = e2
% 169.30/25.77 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.77 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.77 (6) all_58_6 = e1
% 169.30/25.77 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.77 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.77 (8) ~ (e3 = e1)
% 169.30/25.77 (9) op(e1, e3) = all_52_2
% 169.30/25.77 (10) ~ (e1 = e0)
% 169.30/25.77 (11) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.30/25.77 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.30/25.77 e3)
% 169.30/25.77 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.77 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.78 (13) op(e1, e2) = all_52_6
% 169.30/25.78 (14) op(e2, e3) = all_52_1
% 169.30/25.78 (15) ~ (all_52_7 = e3)
% 169.30/25.78 (16) op(e2, e3) = e2
% 169.30/25.78 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.78 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.78 (18) ~ (e3 = e0)
% 169.30/25.78 (19) all_58_12 = e0
% 169.30/25.78 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.78 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.78 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.78 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.78 (22) op(e1, e1) = e3
% 169.30/25.78 (23) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.30/25.78 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.30/25.78 e2) = all_22_1 & $i(all_22_1))
% 169.30/25.78 (24) all_58_14 = e0
% 169.30/25.78 (25) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.78 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.78 (26) all_58_0 = e3
% 169.30/25.78 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.78 (28) ~ (e2 = e0)
% 169.30/25.78 (29) all_58_8 = e3
% 169.30/25.78 (30) all_58_3 = e3
% 169.30/25.78 (31) op(e3, e3) = e3
% 169.30/25.78 (32) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.78 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.78 (33) ~ (e2 = e1)
% 169.30/25.78 (34) op(e3, e2) = all_52_4
% 169.30/25.78 (35) op(e0, e2) = all_52_7
% 169.30/25.78 (36) op(e1, e3) = e1
% 169.30/25.78 (37) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.30/25.78 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.30/25.78 e2) = all_14_1 & $i(all_14_1))
% 169.30/25.78 (38) ~ (e3 = e2)
% 169.30/25.78
% 169.30/25.78 Begin of proof
% 169.30/25.78 |
% 169.30/25.78 | BETA: splitting (1) gives:
% 169.30/25.78 |
% 169.30/25.78 | Case 1:
% 169.30/25.78 | |
% 169.30/25.78 | | (39) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 169.30/25.78 | | e2)
% 169.30/25.78 | |
% 169.30/25.78 | | BETA: splitting (39) gives:
% 169.30/25.78 | |
% 169.30/25.78 | | Case 1:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (40) all_58_12 = e2 & op(e0, e3) = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | ALPHA: (40) implies:
% 169.30/25.78 | | | (41) all_58_12 = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (3), (4), (6), (10), (18), (26), (28), (41) are inconsistent by
% 169.30/25.78 | | | sub-proof #434.
% 169.30/25.78 | | |
% 169.30/25.78 | | Case 2:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (42) all_58_13 = e2 & op(e0, e2) = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | ALPHA: (42) implies:
% 169.30/25.78 | | | (43) all_58_13 = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 169.30/25.78 | | | (16), (17), (18), (19), (20), (21), (22), (23), (25), (26),
% 169.30/25.78 | | | (27), (28), (29), (30), (31), (32), (33), (34), (36), (37),
% 169.30/25.78 | | | (38), (43) are inconsistent by sub-proof #300.
% 169.30/25.78 | | |
% 169.30/25.78 | | End of split
% 169.30/25.78 | |
% 169.30/25.78 | Case 2:
% 169.30/25.78 | |
% 169.30/25.78 | | (44) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.30/25.78 | | e2)
% 169.30/25.78 | |
% 169.30/25.78 | | BETA: splitting (44) gives:
% 169.30/25.78 | |
% 169.30/25.78 | | Case 1:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (45) all_58_14 = e2 & op(e0, e1) = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | ALPHA: (45) implies:
% 169.30/25.78 | | | (46) all_58_14 = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (24), (28), (46) are inconsistent by sub-proof #806.
% 169.30/25.78 | | |
% 169.30/25.78 | | Case 2:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (47) all_58_15 = e2 & op(e0, e0) = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | ALPHA: (47) implies:
% 169.30/25.78 | | | (48) all_58_15 = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (2), (4), (8), (10), (11), (14), (15), (16), (18), (19), (20),
% 169.30/25.78 | | | (24), (27), (28), (30), (32), (33), (35), (38), (48) are
% 169.30/25.78 | | | inconsistent by sub-proof #298.
% 169.30/25.78 | | |
% 169.30/25.78 | | End of split
% 169.30/25.78 | |
% 169.30/25.78 | End of split
% 169.30/25.78 |
% 169.30/25.78 End of proof
% 169.30/25.78
% 169.30/25.78 Sub-proof #298 shows that the following formulas are inconsistent:
% 169.30/25.78 ----------------------------------------------------------------
% 169.30/25.78 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.78 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.78 (2) all_58_15 = e2
% 169.30/25.78 (3) all_58_2 = e2
% 169.30/25.78 (4) ~ (e3 = e1)
% 169.30/25.78 (5) ~ (e1 = e0)
% 169.30/25.78 (6) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.30/25.78 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.30/25.78 (7) op(e2, e3) = all_52_1
% 169.30/25.78 (8) ~ (all_52_7 = e3)
% 169.30/25.78 (9) op(e2, e3) = e2
% 169.30/25.78 (10) ~ (e3 = e0)
% 169.30/25.78 (11) all_58_12 = e0
% 169.30/25.78 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.78 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.78 (13) all_58_14 = e0
% 169.30/25.78 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.78 (15) ~ (e2 = e0)
% 169.30/25.78 (16) all_58_3 = e3
% 169.30/25.78 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.78 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.78 (18) ~ (e2 = e1)
% 169.30/25.78 (19) op(e0, e2) = all_52_7
% 169.30/25.78 (20) ~ (e3 = e2)
% 169.30/25.78
% 169.30/25.78 Begin of proof
% 169.30/25.78 |
% 169.30/25.78 | BETA: splitting (6) gives:
% 169.30/25.78 |
% 169.30/25.78 | Case 1:
% 169.30/25.78 | |
% 169.30/25.78 | | (21) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 169.30/25.78 | | e3)
% 169.30/25.78 | |
% 169.30/25.78 | | REF_CLOSE: (8), (10), (11), (14), (19), (21) are inconsistent by sub-proof
% 169.30/25.78 | | #557.
% 169.30/25.78 | |
% 169.30/25.78 | Case 2:
% 169.30/25.78 | |
% 169.30/25.78 | | (22) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.30/25.78 | | e3)
% 169.30/25.78 | |
% 169.30/25.78 | | BETA: splitting (22) gives:
% 169.30/25.78 | |
% 169.30/25.78 | | Case 1:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (23) all_58_14 = e3 & op(e0, e1) = e3
% 169.30/25.78 | | |
% 169.30/25.78 | | | ALPHA: (23) implies:
% 169.30/25.78 | | | (24) all_58_14 = e3
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (10), (13), (24) are inconsistent by sub-proof #423.
% 169.30/25.78 | | |
% 169.30/25.78 | | Case 2:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (25) all_58_15 = e3 & op(e0, e0) = e3
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (12), (14), (15),
% 169.30/25.78 | | | (16), (17), (18), (20), (25) are inconsistent by sub-proof
% 169.30/25.78 | | | #359.
% 169.30/25.78 | | |
% 169.30/25.78 | | End of split
% 169.30/25.78 | |
% 169.30/25.78 | End of split
% 169.30/25.78 |
% 169.30/25.78 End of proof
% 169.30/25.78
% 169.30/25.78 Sub-proof #299 shows that the following formulas are inconsistent:
% 169.30/25.78 ----------------------------------------------------------------
% 169.30/25.78 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.30/25.78 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.30/25.78 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.78 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.78 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.78 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.78 (4) all_58_2 = e2
% 169.30/25.78 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.78 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.78 (6) all_58_6 = e1
% 169.30/25.78 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.78 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.78 (8) ~ (e3 = e1)
% 169.30/25.78 (9) op(e1, e3) = all_52_2
% 169.30/25.78 (10) ~ (e1 = e0)
% 169.30/25.78 (11) all_58_14 = e1
% 169.30/25.78 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.78 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.78 (13) op(e1, e2) = all_52_6
% 169.30/25.78 (14) op(e2, e3) = all_52_1
% 169.30/25.78 (15) op(e2, e3) = e2
% 169.30/25.78 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.78 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.78 (17) ~ (e3 = e0)
% 169.30/25.78 (18) all_58_12 = e0
% 169.30/25.78 (19) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.78 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.78 (20) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.78 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.78 (21) op(e1, e1) = e3
% 169.30/25.78 (22) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.30/25.78 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.30/25.78 e2) = all_22_1 & $i(all_22_1))
% 169.30/25.78 (23) all_58_15 = e3
% 169.30/25.78 (24) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.78 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.78 (25) all_58_0 = e3
% 169.30/25.78 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.78 (27) ~ (e2 = e0)
% 169.30/25.78 (28) all_58_8 = e3
% 169.30/25.78 (29) all_58_3 = e3
% 169.30/25.78 (30) op(e3, e3) = e3
% 169.30/25.78 (31) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.78 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.78 (32) ~ (e2 = e1)
% 169.30/25.78 (33) op(e3, e2) = all_52_4
% 169.30/25.78 (34) op(e1, e3) = e1
% 169.30/25.78 (35) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.30/25.78 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.30/25.78 e2) = all_14_1 & $i(all_14_1))
% 169.30/25.78 (36) ~ (e3 = e2)
% 169.30/25.78
% 169.30/25.78 Begin of proof
% 169.30/25.78 |
% 169.30/25.78 | BETA: splitting (1) gives:
% 169.30/25.78 |
% 169.30/25.78 | Case 1:
% 169.30/25.78 | |
% 169.30/25.78 | | (37) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 169.30/25.78 | | e2)
% 169.30/25.78 | |
% 169.30/25.78 | | BETA: splitting (37) gives:
% 169.30/25.78 | |
% 169.30/25.78 | | Case 1:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (38) all_58_12 = e2 & op(e0, e3) = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | ALPHA: (38) implies:
% 169.30/25.78 | | | (39) all_58_12 = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (3), (4), (6), (10), (17), (25), (27), (39) are inconsistent by
% 169.30/25.78 | | | sub-proof #434.
% 169.30/25.78 | | |
% 169.30/25.78 | | Case 2:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (40) all_58_13 = e2 & op(e0, e2) = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | ALPHA: (40) implies:
% 169.30/25.78 | | | (41) all_58_13 = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 169.30/25.78 | | | (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 169.30/25.78 | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 169.30/25.78 | | | (36), (41) are inconsistent by sub-proof #300.
% 169.30/25.78 | | |
% 169.30/25.78 | | End of split
% 169.30/25.78 | |
% 169.30/25.78 | Case 2:
% 169.30/25.78 | |
% 169.30/25.78 | | (42) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.30/25.78 | | e2)
% 169.30/25.78 | |
% 169.30/25.78 | | BETA: splitting (42) gives:
% 169.30/25.78 | |
% 169.30/25.78 | | Case 1:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (43) all_58_14 = e2 & op(e0, e1) = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | ALPHA: (43) implies:
% 169.30/25.78 | | | (44) all_58_14 = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (11), (32), (44) are inconsistent by sub-proof #649.
% 169.30/25.78 | | |
% 169.30/25.78 | | Case 2:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (45) all_58_15 = e2 & op(e0, e0) = e2
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (2), (4), (8), (10), (14), (15), (17), (19), (23), (26), (27),
% 169.30/25.78 | | | (29), (31), (32), (36), (45) are inconsistent by sub-proof
% 169.30/25.78 | | | #310.
% 169.30/25.78 | | |
% 169.30/25.78 | | End of split
% 169.30/25.78 | |
% 169.30/25.78 | End of split
% 169.30/25.78 |
% 169.30/25.78 End of proof
% 169.30/25.78
% 169.30/25.78 Sub-proof #300 shows that the following formulas are inconsistent:
% 169.30/25.78 ----------------------------------------------------------------
% 169.30/25.78 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.78 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.78 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.78 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.78 (3) all_58_2 = e2
% 169.30/25.78 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.78 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.78 (5) all_58_6 = e1
% 169.30/25.78 (6) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.78 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.78 (7) ~ (e3 = e1)
% 169.30/25.78 (8) op(e1, e3) = all_52_2
% 169.30/25.78 (9) ~ (e1 = e0)
% 169.30/25.78 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.78 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.78 (11) op(e1, e2) = all_52_6
% 169.30/25.78 (12) op(e2, e3) = all_52_1
% 169.30/25.78 (13) op(e2, e3) = e2
% 169.30/25.78 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.78 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.78 (15) ~ (e3 = e0)
% 169.30/25.78 (16) all_58_12 = e0
% 169.30/25.78 (17) all_58_13 = e2
% 169.30/25.78 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.78 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.78 (19) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.78 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.78 (20) op(e1, e1) = e3
% 169.30/25.78 (21) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.30/25.78 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.30/25.78 e2) = all_22_1 & $i(all_22_1))
% 169.30/25.78 (22) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.78 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.78 (23) all_58_0 = e3
% 169.30/25.78 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.78 (25) ~ (e2 = e0)
% 169.30/25.78 (26) all_58_8 = e3
% 169.30/25.78 (27) all_58_3 = e3
% 169.30/25.78 (28) op(e3, e3) = e3
% 169.30/25.78 (29) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.78 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.78 (30) ~ (e2 = e1)
% 169.30/25.78 (31) op(e3, e2) = all_52_4
% 169.30/25.78 (32) op(e1, e3) = e1
% 169.30/25.78 (33) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.30/25.78 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.30/25.78 e2) = all_14_1 & $i(all_14_1))
% 169.30/25.78 (34) ~ (e3 = e2)
% 169.30/25.78
% 169.30/25.78 Begin of proof
% 169.30/25.78 |
% 169.30/25.78 | BETA: splitting (4) gives:
% 169.30/25.78 |
% 169.30/25.78 | Case 1:
% 169.30/25.78 | |
% 169.30/25.78 | | (35) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.30/25.78 | | e1)
% 169.30/25.78 | |
% 169.30/25.78 | | BETA: splitting (35) gives:
% 169.30/25.78 | |
% 169.30/25.78 | | Case 1:
% 169.30/25.78 | | |
% 169.30/25.78 | | | (36) all_58_1 = e1 & op(e3, e2) = e1
% 169.30/25.78 | | |
% 169.30/25.78 | | | ALPHA: (36) implies:
% 169.30/25.78 | | | (37) all_58_1 = e1
% 169.30/25.78 | | | (38) op(e3, e2) = e1
% 169.30/25.78 | | |
% 169.30/25.78 | | | REF_CLOSE: (9), (11), (15), (17), (21), (22), (24), (25), (27), (31),
% 169.30/25.78 | | | (33), (37), (38) are inconsistent by sub-proof #429.
% 169.30/25.78 | | |
% 169.30/25.79 | | Case 2:
% 169.30/25.79 | | |
% 169.30/25.79 | | | (39) all_58_3 = e1 & op(e2, e2) = e1
% 169.30/25.79 | | |
% 169.30/25.79 | | | ALPHA: (39) implies:
% 169.30/25.79 | | | (40) all_58_3 = e1
% 169.30/25.79 | | |
% 169.30/25.79 | | | COMBINE_EQS: (27), (40) imply:
% 169.30/25.79 | | | (41) e3 = e1
% 169.30/25.79 | | |
% 169.30/25.79 | | | COMBINE_EQS: (23), (41) imply:
% 169.30/25.79 | | | (42) all_58_0 = e1
% 169.30/25.79 | | |
% 169.30/25.79 | | | REF_CLOSE: (3), (5), (7), (10), (15), (16), (34), (42) are inconsistent by
% 169.30/25.79 | | | sub-proof #456.
% 169.30/25.79 | | |
% 169.30/25.79 | | End of split
% 169.30/25.79 | |
% 169.30/25.79 | Case 2:
% 169.30/25.79 | |
% 169.30/25.79 | | (43) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.30/25.79 | | e1)
% 169.30/25.79 | |
% 169.30/25.79 | | BETA: splitting (43) gives:
% 169.30/25.79 | |
% 169.30/25.79 | | Case 1:
% 169.30/25.79 | | |
% 169.30/25.79 | | | (44) all_58_7 = e1 & op(e1, e2) = e1
% 169.30/25.79 | | |
% 169.30/25.79 | | | ALPHA: (44) implies:
% 169.30/25.79 | | | (45) all_58_7 = e1
% 169.30/25.79 | | |
% 169.30/25.79 | | | BETA: splitting (6) gives:
% 169.30/25.79 | | |
% 169.30/25.79 | | | Case 1:
% 169.30/25.79 | | | |
% 169.30/25.79 | | | | (46) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 169.30/25.79 | | | | = e2)
% 169.30/25.79 | | | |
% 169.30/25.79 | | | | BETA: splitting (46) gives:
% 169.30/25.79 | | | |
% 169.30/25.79 | | | | Case 1:
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | (47) all_58_6 = e2 & op(e1, e3) = e2
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | ALPHA: (47) implies:
% 169.30/25.79 | | | | | (48) all_58_6 = e2
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | REF_CLOSE: (5), (30), (48) are inconsistent by sub-proof #823.
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | Case 2:
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | (49) all_58_7 = e2 & op(e1, e2) = e2
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | ALPHA: (49) implies:
% 169.30/25.79 | | | | | (50) all_58_7 = e2
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | REF_CLOSE: (30), (45), (50) are inconsistent by sub-proof #494.
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | End of split
% 169.30/25.79 | | | |
% 169.30/25.79 | | | Case 2:
% 169.30/25.79 | | | |
% 169.30/25.79 | | | | (51) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 169.30/25.79 | | | | = e2)
% 169.30/25.79 | | | |
% 169.30/25.79 | | | | BETA: splitting (51) gives:
% 169.30/25.79 | | | |
% 169.30/25.79 | | | | Case 1:
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | (52) all_58_8 = e2 & op(e1, e1) = e2
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | ALPHA: (52) implies:
% 169.30/25.79 | | | | | (53) op(e1, e1) = e2
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (12), (13), (14), (15),
% 169.30/25.79 | | | | | (18), (20), (24), (25), (27), (28), (29), (30), (32), (34),
% 169.30/25.79 | | | | | (53) are inconsistent by sub-proof #339.
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | Case 2:
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | (54) all_58_11 = e2 & op(e1, e0) = e2
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | | REF_CLOSE: (8), (9), (15), (19), (24), (25), (26), (32), (45), (54)
% 169.30/25.79 | | | | | are inconsistent by sub-proof #495.
% 169.30/25.79 | | | | |
% 169.30/25.79 | | | | End of split
% 169.30/25.79 | | | |
% 169.30/25.79 | | | End of split
% 169.30/25.79 | | |
% 169.30/25.79 | | Case 2:
% 169.30/25.79 | | |
% 169.30/25.79 | | | (55) all_58_13 = e1 & op(e0, e2) = e1
% 169.30/25.79 | | |
% 169.30/25.79 | | | REF_CLOSE: (17), (30), (55) are inconsistent by sub-proof #866.
% 169.30/25.79 | | |
% 169.30/25.79 | | End of split
% 169.30/25.79 | |
% 169.30/25.79 | End of split
% 169.30/25.79 |
% 169.30/25.79 End of proof
% 169.30/25.79
% 169.30/25.79 Sub-proof #301 shows that the following formulas are inconsistent:
% 169.30/25.79 ----------------------------------------------------------------
% 169.30/25.79 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.79 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.79 (2) op(e1, e3) = all_52_2
% 169.30/25.79 (3) ~ (e1 = e0)
% 169.30/25.79 (4) op(e2, e3) = all_52_1
% 169.30/25.79 (5) op(e2, e3) = e2
% 169.30/25.79 (6) ~ (e3 = e0)
% 169.30/25.79 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.79 (8) ~ (e2 = e0)
% 169.30/25.79 (9) all_58_12 = e3 & op(e0, e3) = e3
% 169.30/25.79 (10) op(e3, e3) = e3
% 169.30/25.79 (11) op(e1, e3) = e1
% 169.30/25.79
% 169.30/25.79 Begin of proof
% 169.30/25.79 |
% 169.30/25.79 | ALPHA: (9) implies:
% 169.30/25.79 | (12) all_58_12 = e3
% 169.30/25.79 |
% 169.30/25.79 | BETA: splitting (1) gives:
% 169.30/25.79 |
% 169.30/25.79 | Case 1:
% 169.30/25.79 | |
% 169.30/25.79 | | (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.30/25.79 | | e0)
% 169.30/25.79 | |
% 169.30/25.79 | | REF_CLOSE: (4), (5), (6), (7), (8), (10), (13) are inconsistent by sub-proof
% 169.30/25.79 | | #460.
% 169.30/25.79 | |
% 169.30/25.79 | Case 2:
% 169.30/25.79 | |
% 169.30/25.79 | | (14) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.30/25.79 | | e0)
% 169.30/25.79 | |
% 169.30/25.79 | | REF_CLOSE: (2), (3), (6), (7), (11), (12), (14) are inconsistent by
% 169.30/25.79 | | sub-proof #340.
% 169.30/25.79 | |
% 169.30/25.79 | End of split
% 169.30/25.79 |
% 169.30/25.79 End of proof
% 169.30/25.79
% 169.30/25.79 Sub-proof #302 shows that the following formulas are inconsistent:
% 169.30/25.79 ----------------------------------------------------------------
% 169.30/25.79 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.30/25.79 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.30/25.79 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.79 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.30/25.79 (3) ~ (all_52_13 = e3)
% 169.30/25.79 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.30/25.79 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.30/25.79 (5) all_58_2 = e2
% 169.30/25.79 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.30/25.79 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.79 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.30/25.79 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.30/25.79 (8) op(e3, e3) = all_10_2
% 169.30/25.79 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.30/25.79 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.30/25.79 (10) ~ (e3 = e1)
% 169.30/25.79 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.30/25.79 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.30/25.79 e1)
% 169.30/25.79 (12) op(e1, e3) = all_52_2
% 169.30/25.79 (13) ~ (all_10_2 = e0)
% 169.30/25.79 (14) ~ (e1 = e0)
% 169.30/25.79 (15) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.30/25.79 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.30/25.79 e3)
% 169.30/25.79 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.30/25.79 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.30/25.79 (17) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.30/25.79 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.30/25.79 (18) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.30/25.79 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.30/25.79 (19) op(e2, e3) = all_52_1
% 169.30/25.79 (20) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.30/25.79 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.30/25.79 (21) ~ (all_52_7 = e3)
% 169.30/25.79 (22) op(e2, e3) = e2
% 169.30/25.79 (23) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.30/25.79 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.30/25.79 (24) ~ (e3 = e0)
% 169.30/25.79 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.79 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.30/25.79 (26) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.30/25.79 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.30/25.79 (27) op(e1, e1) = e3
% 169.30/25.79 (28) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.30/25.79 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.30/25.79 (29) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.30/25.79 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.30/25.79 (30) ~ (all_10_2 = e1)
% 169.30/25.79 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.30/25.79 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.30/25.79 (32) all_58_4 = e3
% 169.30/25.79 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.30/25.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.30/25.79 (34) ~ (e2 = e0)
% 169.30/25.79 (35) ~ (all_10_2 = e2)
% 169.30/25.79 (36) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.30/25.79 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.30/25.79 (37) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.30/25.79 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.30/25.79 (38) all_58_3 = e3
% 169.30/25.79 (39) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.30/25.79 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.30/25.79 (40) ~ (e2 = e1)
% 169.30/25.79 (41) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.30/25.79 (42) all_54_0 = all_10_2
% 169.30/25.79 (43) op(e0, e2) = all_52_7
% 169.30/25.79 (44) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.30/25.79 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.30/25.79 (45) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.30/25.79 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.52/25.79 (46) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.52/25.79 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.52/25.79 (47) op(e1, e3) = e1
% 169.52/25.79 (48) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.52/25.79 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.52/25.79 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.52/25.79 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.52/25.79 (49) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.52/25.79 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.52/25.79 (50) op(e2, e0) = all_52_13
% 169.52/25.79 (51) ~ (e3 = e2)
% 169.52/25.79
% 169.52/25.79 Begin of proof
% 169.52/25.79 |
% 169.52/25.79 | BETA: splitting (49) gives:
% 169.52/25.79 |
% 169.52/25.79 | Case 1:
% 169.52/25.79 | |
% 169.52/25.79 | | (52) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 169.52/25.79 | | e2)
% 169.52/25.79 | |
% 169.52/25.79 | | BETA: splitting (52) gives:
% 169.52/25.79 | |
% 169.52/25.79 | | Case 1:
% 169.52/25.79 | | |
% 169.52/25.79 | | | (53) all_58_4 = e2 & op(e3, e1) = e2
% 169.52/25.79 | | |
% 169.52/25.79 | | | ALPHA: (53) implies:
% 169.52/25.79 | | | (54) all_58_4 = e2
% 169.52/25.79 | | |
% 169.52/25.79 | | | REF_CLOSE: (2), (5), (10), (14), (19), (22), (24), (25), (32), (33), (34),
% 169.52/25.79 | | | (38), (39), (40), (51), (54) are inconsistent by sub-proof
% 169.52/25.79 | | | #452.
% 169.52/25.79 | | |
% 169.52/25.79 | | Case 2:
% 169.52/25.79 | | |
% 169.52/25.79 | | | (55) all_58_5 = e2 & op(e2, e1) = e2
% 169.52/25.79 | | |
% 169.52/25.79 | | | REF_CLOSE: (2), (10), (14), (19), (22), (24), (25), (33), (34), (38),
% 169.52/25.79 | | | (40), (55) are inconsistent by sub-proof #412.
% 169.52/25.79 | | |
% 169.52/25.79 | | End of split
% 169.52/25.79 | |
% 169.52/25.79 | Case 2:
% 169.52/25.79 | |
% 169.52/25.79 | | (56) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 169.52/25.79 | | e2)
% 169.52/25.79 | |
% 169.52/25.79 | | BETA: splitting (56) gives:
% 169.52/25.79 | |
% 169.52/25.79 | | Case 1:
% 169.52/25.79 | | |
% 169.52/25.79 | | | (57) all_58_8 = e2 & op(e1, e1) = e2
% 169.52/25.79 | | |
% 169.52/25.79 | | | REF_CLOSE: (2), (4), (5), (8), (12), (13), (14), (16), (19), (22), (23),
% 169.52/25.79 | | | (25), (27), (30), (33), (34), (35), (38), (39), (40), (41),
% 169.52/25.79 | | | (42), (47), (57) are inconsistent by sub-proof #338.
% 169.52/25.79 | | |
% 169.52/25.79 | | Case 2:
% 169.52/25.79 | | |
% 169.52/25.79 | | | (58) all_58_14 = e2 & op(e0, e1) = e2
% 169.52/25.79 | | |
% 169.52/25.79 | | | ALPHA: (58) implies:
% 169.52/25.79 | | | (59) all_58_14 = e2
% 169.52/25.79 | | |
% 169.52/25.79 | | | BETA: splitting (37) gives:
% 169.52/25.79 | | |
% 169.52/25.79 | | | Case 1:
% 169.52/25.79 | | | |
% 169.52/25.79 | | | | (60) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 169.52/25.79 | | | | = e3)
% 169.52/25.79 | | | |
% 169.52/25.79 | | | | BETA: splitting (60) gives:
% 169.52/25.79 | | | |
% 169.52/25.79 | | | | Case 1:
% 169.52/25.79 | | | | |
% 169.52/25.79 | | | | | (61) all_58_6 = e3 & op(e1, e3) = e3
% 169.52/25.79 | | | | |
% 169.52/25.79 | | | | | ALPHA: (61) implies:
% 169.52/25.79 | | | | | (62) all_58_6 = e3
% 169.52/25.79 | | | | | (63) op(e1, e3) = e3
% 169.52/25.79 | | | | |
% 169.52/25.79 | | | | | BETA: splitting (41) gives:
% 169.52/25.79 | | | | |
% 169.52/25.79 | | | | | Case 1:
% 169.52/25.79 | | | | | |
% 169.52/25.79 | | | | | | (64) all_54_0 = e3
% 169.52/25.79 | | | | | |
% 169.52/25.79 | | | | | | COMBINE_EQS: (42), (64) imply:
% 169.52/25.79 | | | | | | (65) all_10_2 = e3
% 169.52/25.79 | | | | | |
% 169.52/25.79 | | | | | | SIMP: (65) implies:
% 169.52/25.79 | | | | | | (66) all_10_2 = e3
% 169.52/25.79 | | | | | |
% 169.52/25.79 | | | | | | REDUCE: (8), (66) imply:
% 169.52/25.79 | | | | | | (67) op(e3, e3) = e3
% 169.52/25.79 | | | | | |
% 169.52/25.79 | | | | | | BETA: splitting (44) gives:
% 169.52/25.79 | | | | | |
% 169.52/25.79 | | | | | | Case 1:
% 169.52/25.79 | | | | | | |
% 169.52/25.79 | | | | | | | (68) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 169.52/25.79 | | | | | | | op(e2, e0) = e3)
% 169.52/25.79 | | | | | | |
% 169.52/25.79 | | | | | | | BETA: splitting (68) gives:
% 169.52/25.79 | | | | | | |
% 169.52/25.79 | | | | | | | Case 1:
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | | (69) all_58_9 = e3 & op(e3, e0) = e3
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | | ALPHA: (69) implies:
% 169.52/25.79 | | | | | | | | (70) all_58_9 = e3
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | | BETA: splitting (15) gives:
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | | Case 1:
% 169.52/25.79 | | | | | | | | |
% 169.52/25.79 | | | | | | | | | (71) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 169.52/25.79 | | | | | | | | | op(e0, e2) = e3)
% 169.52/25.79 | | | | | | | | |
% 169.52/25.79 | | | | | | | | | REF_CLOSE: (2), (4), (5), (9), (10), (14), (16), (19), (21),
% 169.52/25.79 | | | | | | | | | (22), (23), (24), (25), (31), (32), (33), (34),
% 169.52/25.79 | | | | | | | | | (38), (39), (40), (43), (45), (51), (70), (71) are
% 169.52/25.79 | | | | | | | | | inconsistent by sub-proof #337.
% 169.52/25.79 | | | | | | | | |
% 169.52/25.79 | | | | | | | | Case 2:
% 169.52/25.79 | | | | | | | | |
% 169.52/25.79 | | | | | | | | | (72) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 169.52/25.79 | | | | | | | | | op(e0, e0) = e3)
% 169.52/25.79 | | | | | | | | |
% 169.52/25.79 | | | | | | | | | BETA: splitting (72) gives:
% 169.52/25.79 | | | | | | | | |
% 169.52/25.79 | | | | | | | | | Case 1:
% 169.52/25.79 | | | | | | | | | |
% 169.52/25.79 | | | | | | | | | | (73) all_58_14 = e3 & op(e0, e1) = e3
% 169.52/25.79 | | | | | | | | | |
% 169.52/25.79 | | | | | | | | | | REF_CLOSE: (2), (5), (10), (14), (19), (22), (24), (25),
% 169.52/25.79 | | | | | | | | | | (33), (34), (38), (39), (40), (51), (59), (73) are
% 169.52/25.79 | | | | | | | | | | inconsistent by sub-proof #405.
% 169.52/25.79 | | | | | | | | | |
% 169.52/25.79 | | | | | | | | | Case 2:
% 169.52/25.79 | | | | | | | | | |
% 169.52/25.79 | | | | | | | | | | (74) all_58_15 = e3 & op(e0, e0) = e3
% 169.52/25.79 | | | | | | | | | |
% 169.52/25.79 | | | | | | | | | | REF_CLOSE: (2), (4), (5), (10), (12), (14), (15), (16), (19),
% 169.52/25.79 | | | | | | | | | | (20), (21), (22), (23), (24), (25), (32), (33),
% 169.52/25.79 | | | | | | | | | | (34), (38), (39), (40), (43), (46), (47), (48),
% 169.52/25.79 | | | | | | | | | | (51), (59), (62), (63), (67), (74) are
% 169.52/25.79 | | | | | | | | | | inconsistent by sub-proof #330.
% 169.52/25.79 | | | | | | | | | |
% 169.52/25.79 | | | | | | | | | End of split
% 169.52/25.79 | | | | | | | | |
% 169.52/25.79 | | | | | | | | End of split
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | Case 2:
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | | (75) all_58_10 = e3 & op(e2, e0) = e3
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | | ALPHA: (75) implies:
% 169.52/25.79 | | | | | | | | (76) op(e2, e0) = e3
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | | REF_CLOSE: (3), (33), (50), (76) are inconsistent by sub-proof
% 169.52/25.79 | | | | | | | | #562.
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | End of split
% 169.52/25.79 | | | | | | |
% 169.52/25.79 | | | | | | Case 2:
% 169.52/25.79 | | | | | | |
% 169.52/25.79 | | | | | | | (77) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 169.52/25.79 | | | | | | | op(e0, e0) = e3)
% 169.52/25.79 | | | | | | |
% 169.52/25.79 | | | | | | | BETA: splitting (77) gives:
% 169.52/25.79 | | | | | | |
% 169.52/25.79 | | | | | | | Case 1:
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | | (78) all_58_11 = e3 & op(e1, e0) = e3
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | | ALPHA: (78) implies:
% 169.52/25.79 | | | | | | | | (79) all_58_11 = e3
% 169.52/25.79 | | | | | | | |
% 169.52/25.79 | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12),
% 169.52/25.79 | | | | | | | | (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 169.52/25.79 | | | | | | | | (24), (25), (26), (29), (31), (32), (33), (34), (38),
% 169.52/25.79 | | | | | | | | (39), (40), (43), (45), (46), (47), (48), (51), (59),
% 169.52/25.80 | | | | | | | | (67), (79) are inconsistent by sub-proof #318.
% 169.52/25.80 | | | | | | | |
% 169.52/25.80 | | | | | | | Case 2:
% 169.52/25.80 | | | | | | | |
% 169.52/25.80 | | | | | | | | (80) all_58_15 = e3 & op(e0, e0) = e3
% 169.52/25.80 | | | | | | | |
% 169.52/25.81 | | | | | | | | REF_CLOSE: (2), (4), (5), (10), (12), (14), (15), (16), (19),
% 169.52/25.81 | | | | | | | | (20), (21), (22), (23), (24), (25), (32), (33), (34),
% 169.52/25.81 | | | | | | | | (38), (39), (40), (43), (46), (47), (48), (51), (59),
% 169.52/25.81 | | | | | | | | (62), (63), (67), (80) are inconsistent by sub-proof
% 169.52/25.81 | | | | | | | | #330.
% 169.52/25.81 | | | | | | | |
% 169.52/25.81 | | | | | | | End of split
% 169.52/25.81 | | | | | | |
% 169.52/25.81 | | | | | | End of split
% 169.52/25.81 | | | | | |
% 169.52/25.81 | | | | | Case 2:
% 169.52/25.81 | | | | | |
% 169.52/25.81 | | | | | | (81) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.52/25.81 | | | | | |
% 169.52/25.81 | | | | | | REF_CLOSE: (13), (30), (35), (42), (81) are inconsistent by
% 169.52/25.81 | | | | | | sub-proof #958.
% 169.52/25.81 | | | | | |
% 169.52/25.81 | | | | | End of split
% 169.52/25.81 | | | | |
% 169.52/25.81 | | | | Case 2:
% 169.52/25.81 | | | | |
% 169.52/25.81 | | | | | (82) all_58_7 = e3 & op(e1, e2) = e3
% 169.52/25.81 | | | | |
% 169.52/25.81 | | | | | ALPHA: (82) implies:
% 169.52/25.81 | | | | | (83) all_58_7 = e3
% 169.52/25.81 | | | | |
% 169.52/25.81 | | | | | BETA: splitting (41) gives:
% 169.52/25.81 | | | | |
% 169.52/25.81 | | | | | Case 1:
% 169.52/25.81 | | | | | |
% 169.52/25.81 | | | | | | (84) all_54_0 = e3
% 169.52/25.81 | | | | | |
% 169.52/25.81 | | | | | | COMBINE_EQS: (42), (84) imply:
% 169.52/25.81 | | | | | | (85) all_10_2 = e3
% 169.52/25.81 | | | | | |
% 169.52/25.81 | | | | | | SIMP: (85) implies:
% 169.52/25.81 | | | | | | (86) all_10_2 = e3
% 169.52/25.81 | | | | | |
% 169.52/25.81 | | | | | | REDUCE: (8), (86) imply:
% 169.52/25.81 | | | | | | (87) op(e3, e3) = e3
% 169.52/25.81 | | | | | |
% 169.52/25.81 | | | | | | BETA: splitting (44) gives:
% 169.52/25.81 | | | | | |
% 169.52/25.81 | | | | | | Case 1:
% 169.52/25.81 | | | | | | |
% 169.52/25.81 | | | | | | | (88) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 169.52/25.81 | | | | | | | op(e2, e0) = e3)
% 169.52/25.81 | | | | | | |
% 169.52/25.81 | | | | | | | BETA: splitting (88) gives:
% 169.52/25.81 | | | | | | |
% 169.52/25.81 | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | |
% 169.52/25.81 | | | | | | | | (89) all_58_9 = e3 & op(e3, e0) = e3
% 169.52/25.81 | | | | | | | |
% 169.52/25.81 | | | | | | | | ALPHA: (89) implies:
% 169.52/25.81 | | | | | | | | (90) all_58_9 = e3
% 169.52/25.81 | | | | | | | |
% 169.52/25.81 | | | | | | | | BETA: splitting (15) gives:
% 169.52/25.81 | | | | | | | |
% 169.52/25.81 | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | |
% 169.52/25.81 | | | | | | | | | (91) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 169.52/25.81 | | | | | | | | | op(e0, e2) = e3)
% 169.52/25.81 | | | | | | | | |
% 169.52/25.81 | | | | | | | | | REF_CLOSE: (2), (4), (5), (9), (10), (14), (16), (19), (21),
% 169.52/25.81 | | | | | | | | | (22), (23), (24), (25), (31), (32), (33), (34),
% 169.52/25.81 | | | | | | | | | (38), (39), (40), (43), (45), (51), (90), (91) are
% 169.52/25.81 | | | | | | | | | inconsistent by sub-proof #337.
% 169.52/25.81 | | | | | | | | |
% 169.52/25.81 | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | |
% 169.52/25.81 | | | | | | | | | (92) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 169.52/25.81 | | | | | | | | | op(e0, e0) = e3)
% 169.52/25.81 | | | | | | | | |
% 169.52/25.81 | | | | | | | | | BETA: splitting (92) gives:
% 169.52/25.81 | | | | | | | | |
% 169.52/25.81 | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | (93) all_58_14 = e3 & op(e0, e1) = e3
% 169.52/25.81 | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | REF_CLOSE: (2), (5), (10), (14), (19), (22), (24), (25),
% 169.52/25.81 | | | | | | | | | | (33), (34), (38), (39), (40), (51), (59), (93) are
% 169.52/25.81 | | | | | | | | | | inconsistent by sub-proof #405.
% 169.52/25.81 | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | (94) all_58_15 = e3 & op(e0, e0) = e3
% 169.52/25.81 | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | ALPHA: (94) implies:
% 169.52/25.81 | | | | | | | | | | (95) all_58_15 = e3
% 169.52/25.81 | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | BETA: splitting (18) gives:
% 169.52/25.81 | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | (96) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 169.52/25.81 | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 169.52/25.81 | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (14), (19), (22), (24), (25),
% 169.52/25.81 | | | | | | | | | | | (33), (34), (38), (39), (40), (51), (90), (96) are
% 169.52/25.81 | | | | | | | | | | | inconsistent by sub-proof #446.
% 169.52/25.81 | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | (97) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 169.52/25.81 | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 169.52/25.81 | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | BETA: splitting (97) gives:
% 169.52/25.81 | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | (98) all_58_11 = e2 & op(e1, e0) = e2
% 169.52/25.81 | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | ALPHA: (98) implies:
% 169.52/25.81 | | | | | | | | | | | | (99) all_58_11 = e2
% 169.52/25.81 | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | BETA: splitting (46) gives:
% 169.52/25.81 | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | (100) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 169.52/25.81 | | | | | | | | | | | | | & op(e2, e1) = e1)
% 169.52/25.81 | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | BETA: splitting (100) gives:
% 169.52/25.81 | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | (101) all_58_4 = e1 & op(e3, e1) = e1
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | REF_CLOSE: (10), (32), (101) are inconsistent by sub-proof
% 169.52/25.81 | | | | | | | | | | | | | | #702.
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | (102) all_58_5 = e1 & op(e2, e1) = e1
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | ALPHA: (102) implies:
% 169.52/25.81 | | | | | | | | | | | | | | (103) all_58_5 = e1
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | (104) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1
% 169.52/25.81 | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 169.52/25.81 | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 169.52/25.81 | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | (105) all_58_6 = e1 & op(e1, e3) = e1
% 169.52/25.81 | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 169.52/25.81 | | | | | | | | | | | | | | | | (106) all_58_6 = e1
% 169.52/25.81 | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 169.52/25.81 | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | (107) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 169.52/25.81 | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 169.52/25.81 | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | BETA: splitting (107) gives:
% 169.52/25.81 | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (108) all_58_0 = e3 & op(e3, e3) = e3
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (109) all_58_0 = e3
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | (110) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 169.52/25.81 | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (111) all_58_0 = e2 & op(e3, e3) = e2
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (14), (19), (22), (24), (25),
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (33), (34), (38), (39), (40), (51), (109), (111)
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #317.
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (112) all_58_1 = e2 & op(e3, e2) = e2
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (9), (10), (14), (19), (22), (24),
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (25), (29), (32), (33), (34), (38), (39), (40),
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (45), (51), (83), (109), (112) are inconsistent by
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | sub-proof #313.
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | (113) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 169.52/25.81 | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (114) all_58_4 = e2 & op(e3, e1) = e2
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (115) all_58_4 = e2
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (14), (17), (20), (24), (34), (51), (59),
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (103), (115) are inconsistent by sub-proof #321.
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (116) all_58_9 = e2 & op(e3, e0) = e2
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (117) all_58_9 = e2
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (117) imply:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (118) e3 = e2
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (118) imply:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (119) all_58_0 = e2
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (14), (24), (31), (32), (34), (40),
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | | (117), (119) are inconsistent by sub-proof #700.
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (120) all_58_2 = e3 & op(e2, e3) = e3
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (121) op(e2, e3) = e3
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (22), (33), (51), (121) are inconsistent by
% 169.52/25.81 | | | | | | | | | | | | | | | | | | sub-proof #462.
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | (122) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 169.52/25.81 | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 169.52/25.81 | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 169.52/25.81 | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (123) all_58_6 = e3 & op(e1, e3) = e3
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (124) all_58_6 = e3
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (125) op(e1, e3) = e3
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (10), (12), (14), (15), (16), (19),
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (21), (22), (23), (24), (25), (33), (34), (38),
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (39), (40), (43), (47), (48), (51), (59), (87),
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (95), (103), (124), (125) are inconsistent by
% 169.52/25.81 | | | | | | | | | | | | | | | | | | sub-proof #332.
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (126) all_58_12 = e3 & op(e0, e3) = e3
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (127) all_58_12 = e3
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (10), (14), (16), (19), (22), (24),
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (25), (31), (32), (33), (34), (38), (39), (40),
% 169.52/25.81 | | | | | | | | | | | | | | | | | | (45), (51), (90), (106), (127) are inconsistent by
% 169.52/25.81 | | | | | | | | | | | | | | | | | | sub-proof #389.
% 169.52/25.81 | | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | (128) all_58_7 = e1 & op(e1, e2) = e1
% 169.52/25.81 | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 169.52/25.81 | | | | | | | | | | | | | | | | (129) all_58_7 = e1
% 169.52/25.81 | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | | REF_CLOSE: (10), (83), (129) are inconsistent by sub-proof
% 169.52/25.81 | | | | | | | | | | | | | | | | #821.
% 169.52/25.81 | | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | (130) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 =
% 169.52/25.81 | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 169.52/25.81 | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (24), (26), (33), (34), (40), (47),
% 169.52/25.81 | | | | | | | | | | | | | | | (83), (99), (130) are inconsistent by sub-proof
% 169.52/25.81 | | | | | | | | | | | | | | | #311.
% 169.52/25.81 | | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | (131) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 169.52/25.81 | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 169.52/25.81 | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | BETA: splitting (131) gives:
% 169.52/25.81 | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | Case 1:
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | (132) all_58_8 = e1 & op(e1, e1) = e1
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | ALPHA: (132) implies:
% 169.52/25.81 | | | | | | | | | | | | | | (133) all_58_8 = e1
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (24), (26), (33), (34), (47), (83),
% 169.52/25.81 | | | | | | | | | | | | | | (99), (133) are inconsistent by sub-proof #312.
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | (134) all_58_14 = e1 & op(e0, e1) = e1
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | | REF_CLOSE: (40), (59), (134) are inconsistent by sub-proof
% 169.52/25.81 | | | | | | | | | | | | | | #396.
% 169.52/25.81 | | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | | End of split
% 169.52/25.81 | | | | | | | | | | | |
% 169.52/25.81 | | | | | | | | | | | Case 2:
% 169.52/25.81 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | (135) all_58_15 = e2 & op(e0, e0) = e2
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (14), (19), (22), (24), (25),
% 169.52/25.82 | | | | | | | | | | | | (33), (34), (38), (39), (40), (51), (95), (135)
% 169.52/25.82 | | | | | | | | | | | | are inconsistent by sub-proof #310.
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | |
% 169.52/25.82 | | | | | | | | End of split
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | | (136) all_58_10 = e3 & op(e2, e0) = e3
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | | ALPHA: (136) implies:
% 169.52/25.82 | | | | | | | | (137) op(e2, e0) = e3
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | | REF_CLOSE: (3), (33), (50), (137) are inconsistent by sub-proof
% 169.52/25.82 | | | | | | | | #562.
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | End of split
% 169.52/25.82 | | | | | | |
% 169.52/25.82 | | | | | | Case 2:
% 169.52/25.82 | | | | | | |
% 169.52/25.82 | | | | | | | (138) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 169.52/25.82 | | | | | | | op(e0, e0) = e3)
% 169.52/25.82 | | | | | | |
% 169.52/25.82 | | | | | | | BETA: splitting (138) gives:
% 169.52/25.82 | | | | | | |
% 169.52/25.82 | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | | (139) all_58_11 = e3 & op(e1, e0) = e3
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | | ALPHA: (139) implies:
% 169.52/25.82 | | | | | | | | (140) all_58_11 = e3
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12),
% 169.52/25.82 | | | | | | | | (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 169.52/25.82 | | | | | | | | (24), (25), (26), (29), (31), (32), (33), (34), (38),
% 169.52/25.82 | | | | | | | | (39), (40), (43), (45), (46), (47), (48), (51), (59),
% 169.52/25.82 | | | | | | | | (87), (140) are inconsistent by sub-proof #318.
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | | (141) all_58_15 = e3 & op(e0, e0) = e3
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | | ALPHA: (141) implies:
% 169.52/25.82 | | | | | | | | (142) all_58_15 = e3
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | | BETA: splitting (7) gives:
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | |
% 169.52/25.82 | | | | | | | | | (143) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 169.52/25.82 | | | | | | | | | op(e1, e2) = e2)
% 169.52/25.82 | | | | | | | | |
% 169.52/25.82 | | | | | | | | | BETA: splitting (143) gives:
% 169.52/25.82 | | | | | | | | |
% 169.52/25.82 | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | (144) all_58_6 = e2 & op(e1, e3) = e2
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | ALPHA: (144) implies:
% 169.52/25.82 | | | | | | | | | | (145) all_58_6 = e2
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | BETA: splitting (46) gives:
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | (146) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 169.52/25.82 | | | | | | | | | | | & op(e2, e1) = e1)
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | BETA: splitting (146) gives:
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | (147) all_58_4 = e1 & op(e3, e1) = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | ALPHA: (147) implies:
% 169.52/25.82 | | | | | | | | | | | | (148) all_58_4 = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | REF_CLOSE: (10), (32), (148) are inconsistent by sub-proof
% 169.52/25.82 | | | | | | | | | | | | #767.
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | (149) all_58_5 = e1 & op(e2, e1) = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | ALPHA: (149) implies:
% 169.52/25.82 | | | | | | | | | | | | (150) all_58_5 = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | BETA: splitting (16) gives:
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | (151) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 169.52/25.82 | | | | | | | | | | | | | & op(e2, e3) = e3)
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | BETA: splitting (151) gives:
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | (152) all_58_0 = e3 & op(e3, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | ALPHA: (152) implies:
% 169.52/25.82 | | | | | | | | | | | | | | (153) all_58_0 = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | (154) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 169.52/25.82 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | (155) all_58_9 = e2 & op(e3, e0) = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (9), (10), (12), (14), (16),
% 169.52/25.82 | | | | | | | | | | | | | | | | (19), (22), (24), (25), (29), (31), (32), (33),
% 169.52/25.82 | | | | | | | | | | | | | | | | (34), (38), (39), (40), (45), (47), (51), (83),
% 169.52/25.82 | | | | | | | | | | | | | | | | (87), (145), (153), (155) are inconsistent by
% 169.52/25.82 | | | | | | | | | | | | | | | | sub-proof #308.
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | (156) all_58_10 = e2 & op(e2, e0) = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 169.52/25.82 | | | | | | | | | | | | | | | | (157) all_58_10 = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (22), (24), (25), (33), (34), (38),
% 169.52/25.82 | | | | | | | | | | | | | | | | (150), (157) are inconsistent by sub-proof #448.
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | (158) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 169.52/25.82 | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | (159) all_58_11 = e2 & op(e1, e0) = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 169.52/25.82 | | | | | | | | | | | | | | | | (160) all_58_11 = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (11), (12),
% 169.52/25.82 | | | | | | | | | | | | | | | | (14), (15), (16), (19), (21), (22), (23), (24),
% 169.52/25.82 | | | | | | | | | | | | | | | | (25), (26), (28), (29), (32), (33), (34), (36),
% 169.52/25.82 | | | | | | | | | | | | | | | | (38), (39), (40), (43), (45), (46), (47), (48),
% 169.52/25.82 | | | | | | | | | | | | | | | | (51), (59), (83), (87), (142), (150), (160) are
% 169.52/25.82 | | | | | | | | | | | | | | | | inconsistent by sub-proof #304.
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | (161) all_58_15 = e2 & op(e0, e0) = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 169.52/25.82 | | | | | | | | | | | | | | | | (162) all_58_15 = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (14), (19), (22), (24), (25),
% 169.52/25.82 | | | | | | | | | | | | | | | | (33), (34), (38), (39), (40), (51), (142), (162)
% 169.52/25.82 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #320.
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | (163) all_58_2 = e3 & op(e2, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | ALPHA: (163) implies:
% 169.52/25.82 | | | | | | | | | | | | | | (164) op(e2, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | REF_CLOSE: (19), (22), (33), (51), (164) are inconsistent by
% 169.52/25.82 | | | | | | | | | | | | | | sub-proof #462.
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | (165) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 169.52/25.82 | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | BETA: splitting (165) gives:
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | (166) all_58_6 = e3 & op(e1, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | ALPHA: (166) implies:
% 169.52/25.82 | | | | | | | | | | | | | | (167) all_58_6 = e3
% 169.52/25.82 | | | | | | | | | | | | | | (168) op(e1, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (10), (12), (14), (15), (16), (19),
% 169.52/25.82 | | | | | | | | | | | | | | (21), (22), (23), (24), (25), (33), (34), (38),
% 169.52/25.82 | | | | | | | | | | | | | | (39), (40), (43), (47), (48), (51), (59), (87),
% 169.52/25.82 | | | | | | | | | | | | | | (142), (150), (167), (168) are inconsistent by
% 169.52/25.82 | | | | | | | | | | | | | | sub-proof #332.
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | (169) all_58_12 = e3 & op(e0, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | ALPHA: (169) implies:
% 169.52/25.82 | | | | | | | | | | | | | | (170) all_58_12 = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (14), (19), (22), (23), (24), (33),
% 169.52/25.82 | | | | | | | | | | | | | | (34), (40), (145), (170) are inconsistent by
% 169.52/25.82 | | | | | | | | | | | | | | sub-proof #329.
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | (171) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 169.52/25.82 | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | BETA: splitting (171) gives:
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | (172) all_58_8 = e1 & op(e1, e1) = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | ALPHA: (172) implies:
% 169.52/25.82 | | | | | | | | | | | | (173) all_58_8 = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | BETA: splitting (16) gives:
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | (174) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 169.52/25.82 | | | | | | | | | | | | | & op(e2, e3) = e3)
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | BETA: splitting (174) gives:
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | (175) all_58_0 = e3 & op(e3, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | ALPHA: (175) implies:
% 169.52/25.82 | | | | | | | | | | | | | | (176) all_58_0 = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | (177) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 169.52/25.82 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | (178) all_58_9 = e2 & op(e3, e0) = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (9), (10), (12), (14), (16),
% 169.52/25.82 | | | | | | | | | | | | | | | | (19), (22), (24), (25), (29), (31), (32), (33),
% 169.52/25.82 | | | | | | | | | | | | | | | | (34), (38), (39), (40), (45), (47), (51), (83),
% 169.52/25.82 | | | | | | | | | | | | | | | | (87), (145), (176), (178) are inconsistent by
% 169.52/25.82 | | | | | | | | | | | | | | | | sub-proof #308.
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | (179) all_58_10 = e2 & op(e2, e0) = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (10), (14), (19), (22), (24), (25), (33),
% 169.52/25.82 | | | | | | | | | | | | | | | | (34), (38), (40), (179) are inconsistent by
% 169.52/25.82 | | | | | | | | | | | | | | | | sub-proof #447.
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | (180) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 169.52/25.82 | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | (181) all_58_11 = e2 & op(e1, e0) = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 169.52/25.82 | | | | | | | | | | | | | | | | (182) all_58_11 = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (24), (26), (33), (34), (47), (83),
% 169.52/25.82 | | | | | | | | | | | | | | | | (173), (182) are inconsistent by sub-proof #312.
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | (183) all_58_15 = e2 & op(e0, e0) = e2
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (14), (19), (22), (24), (25),
% 169.52/25.82 | | | | | | | | | | | | | | | | (33), (34), (38), (39), (40), (51), (142), (183)
% 169.52/25.82 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #310.
% 169.52/25.82 | | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | (184) all_58_2 = e3 & op(e2, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | ALPHA: (184) implies:
% 169.52/25.82 | | | | | | | | | | | | | | (185) op(e2, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | REF_CLOSE: (19), (22), (33), (51), (185) are inconsistent by
% 169.52/25.82 | | | | | | | | | | | | | | sub-proof #462.
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | (186) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 169.52/25.82 | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | BETA: splitting (186) gives:
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | (187) all_58_6 = e3 & op(e1, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | ALPHA: (187) implies:
% 169.52/25.82 | | | | | | | | | | | | | | (188) all_58_6 = e3
% 169.52/25.82 | | | | | | | | | | | | | | (189) op(e1, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (10), (12), (14), (15), (16), (19),
% 169.52/25.82 | | | | | | | | | | | | | | (20), (21), (22), (23), (24), (25), (32), (33),
% 169.52/25.82 | | | | | | | | | | | | | | (34), (38), (39), (40), (43), (47), (48), (51),
% 169.52/25.82 | | | | | | | | | | | | | | (59), (87), (142), (173), (188), (189) are
% 169.52/25.82 | | | | | | | | | | | | | | inconsistent by sub-proof #331.
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | (190) all_58_12 = e3 & op(e0, e3) = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | ALPHA: (190) implies:
% 169.52/25.82 | | | | | | | | | | | | | | (191) all_58_12 = e3
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (14), (19), (22), (23), (24), (33),
% 169.52/25.82 | | | | | | | | | | | | | | (34), (40), (145), (191) are inconsistent by
% 169.52/25.82 | | | | | | | | | | | | | | sub-proof #329.
% 169.52/25.82 | | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | (192) all_58_14 = e1 & op(e0, e1) = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | ALPHA: (192) implies:
% 169.52/25.82 | | | | | | | | | | | | (193) all_58_14 = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | REF_CLOSE: (40), (59), (193) are inconsistent by sub-proof
% 169.52/25.82 | | | | | | | | | | | | #649.
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | (194) all_58_7 = e2 & op(e1, e2) = e2
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | REF_CLOSE: (2), (5), (10), (14), (19), (22), (24), (25),
% 169.52/25.82 | | | | | | | | | | (33), (34), (38), (39), (40), (51), (83), (194)
% 169.52/25.82 | | | | | | | | | | are inconsistent by sub-proof #303.
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | |
% 169.52/25.82 | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | |
% 169.52/25.82 | | | | | | | | | (195) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 169.52/25.82 | | | | | | | | | op(e1, e0) = e2)
% 169.52/25.82 | | | | | | | | |
% 169.52/25.82 | | | | | | | | | BETA: splitting (195) gives:
% 169.52/25.82 | | | | | | | | |
% 169.52/25.82 | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | (196) all_58_8 = e2 & op(e1, e1) = e2
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | ALPHA: (196) implies:
% 169.52/25.82 | | | | | | | | | | (197) all_58_8 = e2
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | REF_CLOSE: (10), (14), (20), (24), (32), (34), (40), (46),
% 169.52/25.82 | | | | | | | | | | (59), (197) are inconsistent by sub-proof #395.
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | (198) all_58_11 = e2 & op(e1, e0) = e2
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | ALPHA: (198) implies:
% 169.52/25.82 | | | | | | | | | | (199) all_58_11 = e2
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | BETA: splitting (46) gives:
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | (200) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 169.52/25.82 | | | | | | | | | | | & op(e2, e1) = e1)
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | BETA: splitting (200) gives:
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | (201) all_58_4 = e1 & op(e3, e1) = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | ALPHA: (201) implies:
% 169.52/25.82 | | | | | | | | | | | | (202) all_58_4 = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | REF_CLOSE: (10), (32), (202) are inconsistent by sub-proof
% 169.52/25.82 | | | | | | | | | | | | #767.
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | (203) all_58_5 = e1 & op(e2, e1) = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | ALPHA: (203) implies:
% 169.52/25.82 | | | | | | | | | | | | (204) all_58_5 = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (11), (12),
% 169.52/25.82 | | | | | | | | | | | | (14), (15), (16), (19), (21), (22), (23), (24),
% 169.52/25.82 | | | | | | | | | | | | (25), (26), (28), (29), (32), (33), (34), (36),
% 169.52/25.82 | | | | | | | | | | | | (38), (39), (40), (43), (45), (46), (47), (48),
% 169.52/25.82 | | | | | | | | | | | | (51), (59), (83), (87), (142), (199), (204) are
% 169.52/25.82 | | | | | | | | | | | | inconsistent by sub-proof #304.
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | (205) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 169.52/25.82 | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | BETA: splitting (205) gives:
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | Case 1:
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | (206) all_58_8 = e1 & op(e1, e1) = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | ALPHA: (206) implies:
% 169.52/25.82 | | | | | | | | | | | | (207) all_58_8 = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | REF_CLOSE: (12), (14), (24), (26), (33), (34), (47), (83),
% 169.52/25.82 | | | | | | | | | | | | (199), (207) are inconsistent by sub-proof #312.
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | Case 2:
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | (208) all_58_14 = e1 & op(e0, e1) = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | ALPHA: (208) implies:
% 169.52/25.82 | | | | | | | | | | | | (209) all_58_14 = e1
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | | REF_CLOSE: (40), (59), (209) are inconsistent by sub-proof
% 169.52/25.82 | | | | | | | | | | | | #649.
% 169.52/25.82 | | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | | |
% 169.52/25.82 | | | | | | | | | End of split
% 169.52/25.82 | | | | | | | | |
% 169.52/25.82 | | | | | | | | End of split
% 169.52/25.82 | | | | | | | |
% 169.52/25.82 | | | | | | | End of split
% 169.52/25.82 | | | | | | |
% 169.52/25.82 | | | | | | End of split
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | Case 2:
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | | (210) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | | REF_CLOSE: (13), (30), (35), (42), (210) are inconsistent by
% 169.52/25.82 | | | | | | sub-proof #958.
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | End of split
% 169.52/25.82 | | | | |
% 169.52/25.82 | | | | End of split
% 169.52/25.82 | | | |
% 169.52/25.82 | | | Case 2:
% 169.52/25.82 | | | |
% 169.52/25.82 | | | | (211) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 169.52/25.82 | | | | e0) = e3)
% 169.52/25.82 | | | |
% 169.52/25.82 | | | | BETA: splitting (211) gives:
% 169.52/25.82 | | | |
% 169.52/25.82 | | | | Case 1:
% 169.52/25.82 | | | | |
% 169.52/25.82 | | | | | (212) all_58_8 = e3 & op(e1, e1) = e3
% 169.52/25.82 | | | | |
% 169.52/25.82 | | | | | REF_CLOSE: (10), (14), (20), (24), (32), (34), (40), (46), (59), (212)
% 169.52/25.82 | | | | | are inconsistent by sub-proof #383.
% 169.52/25.82 | | | | |
% 169.52/25.82 | | | | Case 2:
% 169.52/25.82 | | | | |
% 169.52/25.82 | | | | | (213) all_58_11 = e3 & op(e1, e0) = e3
% 169.52/25.82 | | | | |
% 169.52/25.82 | | | | | ALPHA: (213) implies:
% 169.52/25.82 | | | | | (214) all_58_11 = e3
% 169.52/25.82 | | | | |
% 169.52/25.82 | | | | | BETA: splitting (41) gives:
% 169.52/25.82 | | | | |
% 169.52/25.82 | | | | | Case 1:
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | | (215) all_54_0 = e3
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | | COMBINE_EQS: (42), (215) imply:
% 169.52/25.82 | | | | | | (216) all_10_2 = e3
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | | SIMP: (216) implies:
% 169.52/25.82 | | | | | | (217) all_10_2 = e3
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | | REDUCE: (8), (217) imply:
% 169.52/25.82 | | | | | | (218) op(e3, e3) = e3
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12),
% 169.52/25.82 | | | | | | (14), (15), (17), (18), (19), (20), (21), (22), (23),
% 169.52/25.82 | | | | | | (24), (25), (26), (29), (31), (32), (33), (34), (38),
% 169.52/25.82 | | | | | | (39), (40), (43), (45), (46), (47), (48), (51), (59),
% 169.52/25.82 | | | | | | (214), (218) are inconsistent by sub-proof #318.
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | Case 2:
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | | (219) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | | REF_CLOSE: (13), (30), (35), (42), (219) are inconsistent by
% 169.52/25.82 | | | | | | sub-proof #958.
% 169.52/25.82 | | | | | |
% 169.52/25.82 | | | | | End of split
% 169.52/25.82 | | | | |
% 169.52/25.82 | | | | End of split
% 169.52/25.82 | | | |
% 169.52/25.82 | | | End of split
% 169.52/25.82 | | |
% 169.52/25.82 | | End of split
% 169.52/25.82 | |
% 169.52/25.82 | End of split
% 169.52/25.82 |
% 169.52/25.82 End of proof
% 169.52/25.82
% 169.52/25.82 Sub-proof #303 shows that the following formulas are inconsistent:
% 169.52/25.82 ----------------------------------------------------------------
% 169.52/25.82 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.52/25.82 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.52/25.82 (2) all_58_2 = e2
% 169.52/25.82 (3) ~ (e3 = e1)
% 169.52/25.82 (4) ~ (e1 = e0)
% 169.52/25.82 (5) op(e2, e3) = all_52_1
% 169.52/25.82 (6) all_58_7 = e2 & op(e1, e2) = e2
% 169.52/25.82 (7) op(e2, e3) = e2
% 169.52/25.82 (8) ~ (e3 = e0)
% 169.52/25.82 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.52/25.82 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.52/25.82 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.52/25.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.52/25.82 (11) ~ (e2 = e0)
% 169.52/25.82 (12) all_58_3 = e3
% 169.52/25.82 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.52/25.82 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.52/25.82 (14) ~ (e2 = e1)
% 169.52/25.82 (15) all_58_7 = e3
% 169.52/25.82 (16) ~ (e3 = e2)
% 169.52/25.83
% 169.52/25.83 Begin of proof
% 169.52/25.83 |
% 169.52/25.83 | ALPHA: (6) implies:
% 169.52/25.83 | (17) all_58_7 = e2
% 169.52/25.83 |
% 169.52/25.83 | COMBINE_EQS: (15), (17) imply:
% 169.52/25.83 | (18) e3 = e2
% 169.52/25.83 |
% 169.52/25.83 | COMBINE_EQS: (12), (18) imply:
% 169.52/25.83 | (19) all_58_3 = e2
% 169.52/25.83 |
% 169.52/25.83 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 169.52/25.83 | (16), (19) are inconsistent by sub-proof #779.
% 169.52/25.83 |
% 169.52/25.83 End of proof
% 169.52/25.83
% 169.52/25.83 Sub-proof #304 shows that the following formulas are inconsistent:
% 169.52/25.83 ----------------------------------------------------------------
% 169.61/25.83 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.61/25.83 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.61/25.83 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.61/25.83 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.61/25.83 (3) all_58_14 = e2
% 169.61/25.83 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.61/25.83 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.61/25.83 (5) all_58_2 = e2
% 169.61/25.83 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.61/25.83 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.61/25.83 (7) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.61/25.83 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.61/25.83 (8) ~ (e3 = e1)
% 169.61/25.83 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 169.61/25.83 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.61/25.83 (10) op(e1, e3) = all_52_2
% 169.61/25.83 (11) ~ (e1 = e0)
% 169.61/25.83 (12) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.61/25.83 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.61/25.83 e3)
% 169.61/25.83 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.61/25.83 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.61/25.83 (14) all_58_11 = e2
% 169.61/25.83 (15) op(e2, e3) = all_52_1
% 169.61/25.83 (16) ~ (all_52_7 = e3)
% 169.61/25.83 (17) op(e2, e3) = e2
% 169.61/25.83 (18) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.61/25.83 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.61/25.83 (19) ~ (e3 = e0)
% 169.61/25.83 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.61/25.83 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.61/25.83 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.61/25.83 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.61/25.83 (22) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 169.61/25.83 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 169.61/25.83 (23) all_58_15 = e3
% 169.61/25.83 (24) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.61/25.83 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.61/25.83 (25) all_58_4 = e3
% 169.61/25.83 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.61/25.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.61/25.83 (27) ~ (e2 = e0)
% 169.61/25.83 (28) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 169.61/25.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.61/25.83 (29) all_58_5 = e1
% 169.61/25.83 (30) all_58_3 = e3
% 169.61/25.83 (31) op(e3, e3) = e3
% 169.61/25.83 (32) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.61/25.83 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.61/25.83 (33) ~ (e2 = e1)
% 169.61/25.83 (34) op(e0, e2) = all_52_7
% 169.61/25.83 (35) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.61/25.83 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.61/25.83 (36) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.61/25.83 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.61/25.83 (37) op(e1, e3) = e1
% 169.61/25.83 (38) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.61/25.83 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.61/25.83 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.61/25.83 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.61/25.83 (39) all_58_7 = e3
% 169.61/25.83 (40) ~ (e3 = e2)
% 169.61/25.83
% 169.61/25.83 Begin of proof
% 169.61/25.83 |
% 169.61/25.83 | BETA: splitting (28) gives:
% 169.61/25.83 |
% 169.61/25.83 | Case 1:
% 169.61/25.83 | |
% 169.61/25.83 | | (41) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 169.61/25.83 | | e1)
% 169.61/25.83 | |
% 169.61/25.83 | | BETA: splitting (41) gives:
% 169.61/25.83 | |
% 169.61/25.83 | | Case 1:
% 169.61/25.83 | | |
% 169.61/25.83 | | | (42) all_58_6 = e1 & op(e1, e3) = e1
% 169.61/25.83 | | |
% 169.61/25.83 | | | ALPHA: (42) implies:
% 169.61/25.83 | | | (43) all_58_6 = e1
% 169.61/25.83 | | |
% 169.61/25.83 | | | BETA: splitting (13) gives:
% 169.61/25.83 | | |
% 169.61/25.83 | | | Case 1:
% 169.61/25.83 | | | |
% 169.61/25.83 | | | | (44) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 169.61/25.83 | | | | = e3)
% 169.61/25.83 | | | |
% 169.61/25.83 | | | | BETA: splitting (44) gives:
% 169.61/25.83 | | | |
% 169.61/25.83 | | | | Case 1:
% 169.61/25.83 | | | | |
% 169.61/25.83 | | | | | (45) all_58_0 = e3 & op(e3, e3) = e3
% 169.61/25.83 | | | | |
% 169.61/25.83 | | | | | ALPHA: (45) implies:
% 169.61/25.83 | | | | | (46) all_58_0 = e3
% 169.61/25.83 | | | | |
% 169.61/25.83 | | | | | BETA: splitting (4) gives:
% 169.61/25.83 | | | | |
% 169.61/25.83 | | | | | Case 1:
% 169.61/25.83 | | | | | |
% 169.61/25.83 | | | | | | (47) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 169.61/25.83 | | | | | | e3) = e0)
% 169.61/25.83 | | | | | |
% 169.61/25.83 | | | | | | REF_CLOSE: (15), (17), (19), (26), (27), (31), (47) are inconsistent
% 169.61/25.83 | | | | | | by sub-proof #460.
% 169.61/25.83 | | | | | |
% 169.61/25.83 | | | | | Case 2:
% 169.61/25.83 | | | | | |
% 169.61/25.83 | | | | | | (48) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 169.61/25.83 | | | | | | e3) = e0)
% 169.61/25.83 | | | | | |
% 169.61/25.83 | | | | | | BETA: splitting (48) gives:
% 169.61/25.83 | | | | | |
% 169.61/25.83 | | | | | | Case 1:
% 169.61/25.83 | | | | | | |
% 169.61/25.83 | | | | | | | (49) all_58_6 = e0 & op(e1, e3) = e0
% 169.61/25.83 | | | | | | |
% 169.61/25.83 | | | | | | | ALPHA: (49) implies:
% 169.61/25.83 | | | | | | | (50) op(e1, e3) = e0
% 169.61/25.83 | | | | | | |
% 169.61/25.83 | | | | | | | REF_CLOSE: (10), (11), (26), (37), (50) are inconsistent by
% 169.61/25.83 | | | | | | | sub-proof #749.
% 169.61/25.83 | | | | | | |
% 169.61/25.83 | | | | | | Case 2:
% 169.61/25.83 | | | | | | |
% 169.61/25.83 | | | | | | | (51) all_58_12 = e0 & op(e0, e3) = e0
% 169.61/25.83 | | | | | | |
% 169.61/25.83 | | | | | | | ALPHA: (51) implies:
% 169.61/25.83 | | | | | | | (52) all_58_12 = e0
% 169.61/25.83 | | | | | | |
% 169.61/25.83 | | | | | | | BETA: splitting (9) gives:
% 169.61/25.83 | | | | | | |
% 169.61/25.83 | | | | | | | Case 1:
% 169.61/25.83 | | | | | | | |
% 169.61/25.83 | | | | | | | | (53) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 169.61/25.83 | | | | | | | | op(e0, e2) = e1)
% 169.61/25.83 | | | | | | | |
% 169.61/25.83 | | | | | | | | BETA: splitting (53) gives:
% 169.61/25.83 | | | | | | | |
% 169.61/25.83 | | | | | | | | Case 1:
% 169.61/25.83 | | | | | | | | |
% 169.61/25.83 | | | | | | | | | (54) all_58_12 = e1 & op(e0, e3) = e1
% 169.61/25.83 | | | | | | | | |
% 169.61/25.83 | | | | | | | | | ALPHA: (54) implies:
% 169.61/25.83 | | | | | | | | | (55) all_58_12 = e1
% 169.61/25.83 | | | | | | | | |
% 169.61/25.83 | | | | | | | | | BETA: splitting (38) gives:
% 169.61/25.83 | | | | | | | | |
% 169.61/25.83 | | | | | | | | | Case 1:
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | (56) all_58_15 = e0 & op(e0, e0) = e0
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | ALPHA: (56) implies:
% 169.61/25.83 | | | | | | | | | | (57) all_58_15 = e0
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (11), (12), (15), (16), (17),
% 169.61/25.83 | | | | | | | | | | (19), (20), (26), (27), (30), (32), (33), (34),
% 169.61/25.83 | | | | | | | | | | (40), (55), (57) are inconsistent by sub-proof
% 169.61/25.83 | | | | | | | | | | #380.
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | Case 2:
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | (58) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 169.61/25.83 | | | | | | | | | | & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 169.61/25.83 | | | | | | | | | | e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) =
% 169.61/25.83 | | | | | | | | | | e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 169.61/25.83 | | | | | | | | | | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | ALPHA: (58) implies:
% 169.61/25.83 | | | | | | | | | | (59) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0
% 169.61/25.83 | | | | | | | | | | & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1)
% 169.61/25.83 | | | | | | | | | | = e0)
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | BETA: splitting (6) gives:
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | Case 1:
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | (60) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 169.61/25.83 | | | | | | | | | | | & op(e2, e2) = e1)
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | BETA: splitting (60) gives:
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | Case 1:
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | (61) all_58_1 = e1 & op(e3, e2) = e1
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (11), (15), (17), (19), (20),
% 169.61/25.83 | | | | | | | | | | | | (25), (26), (27), (30), (32), (33), (35), (40),
% 169.61/25.83 | | | | | | | | | | | | (46), (61) are inconsistent by sub-proof #314.
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | Case 2:
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | (62) all_58_3 = e1 & op(e2, e2) = e1
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (11), (12), (15), (17), (19),
% 169.61/25.83 | | | | | | | | | | | | (20), (23), (26), (27), (30), (32), (33), (38),
% 169.61/25.83 | | | | | | | | | | | | (40), (55), (62) are inconsistent by sub-proof
% 169.61/25.83 | | | | | | | | | | | | #335.
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | End of split
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | Case 2:
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | (63) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 169.61/25.83 | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | BETA: splitting (63) gives:
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | Case 1:
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | (64) all_58_7 = e1 & op(e1, e2) = e1
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | ALPHA: (64) implies:
% 169.61/25.83 | | | | | | | | | | | | (65) all_58_7 = e1
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | COMBINE_EQS: (39), (65) imply:
% 169.61/25.83 | | | | | | | | | | | | (66) e3 = e1
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | SIMP: (66) implies:
% 169.61/25.83 | | | | | | | | | | | | (67) e3 = e1
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | COMBINE_EQS: (23), (67) imply:
% 169.61/25.83 | | | | | | | | | | | | (68) all_58_15 = e1
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (11), (12), (15), (17), (19),
% 169.61/25.83 | | | | | | | | | | | | (20), (26), (27), (30), (32), (33), (38), (40),
% 169.61/25.83 | | | | | | | | | | | | (55), (68) are inconsistent by sub-proof #362.
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | Case 2:
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | (69) all_58_13 = e1 & op(e0, e2) = e1
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | ALPHA: (69) implies:
% 169.61/25.83 | | | | | | | | | | | | (70) all_58_13 = e1
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | | REF_CLOSE: (3), (11), (27), (55), (59), (70) are inconsistent
% 169.61/25.83 | | | | | | | | | | | | by sub-proof #530.
% 169.61/25.83 | | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | End of split
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | End of split
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | End of split
% 169.61/25.83 | | | | | | | | |
% 169.61/25.83 | | | | | | | | Case 2:
% 169.61/25.83 | | | | | | | | |
% 169.61/25.83 | | | | | | | | | (71) all_58_13 = e1 & op(e0, e2) = e1
% 169.61/25.83 | | | | | | | | |
% 169.61/25.83 | | | | | | | | | ALPHA: (71) implies:
% 169.61/25.83 | | | | | | | | | (72) all_58_13 = e1
% 169.61/25.83 | | | | | | | | |
% 169.61/25.83 | | | | | | | | | BETA: splitting (22) gives:
% 169.61/25.83 | | | | | | | | |
% 169.61/25.83 | | | | | | | | | Case 1:
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | (73) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 &
% 169.61/25.83 | | | | | | | | | | op(e2, e2) = e2)
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | BETA: splitting (73) gives:
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | Case 1:
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | (74) all_58_1 = e2 & op(e3, e2) = e2
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (7), (8), (11), (15), (17), (19),
% 169.61/25.83 | | | | | | | | | | | (20), (24), (25), (26), (27), (30), (32), (33),
% 169.61/25.83 | | | | | | | | | | | (35), (39), (40), (46), (74) are inconsistent by
% 169.61/25.83 | | | | | | | | | | | sub-proof #313.
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | Case 2:
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | (75) all_58_3 = e2 & op(e2, e2) = e2
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | ALPHA: (75) implies:
% 169.61/25.83 | | | | | | | | | | | (76) all_58_3 = e2
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (11), (15), (17), (19), (20), (26),
% 169.61/25.83 | | | | | | | | | | | (27), (32), (33), (40), (76) are inconsistent by
% 169.61/25.83 | | | | | | | | | | | sub-proof #779.
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | End of split
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | Case 2:
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | (77) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2
% 169.61/25.83 | | | | | | | | | | & op(e0, e2) = e2)
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | BETA: splitting (77) gives:
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | Case 1:
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | (78) all_58_7 = e2 & op(e1, e2) = e2
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | ALPHA: (78) implies:
% 169.61/25.83 | | | | | | | | | | | (79) all_58_7 = e2
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (11), (15), (17), (19), (20), (26),
% 169.61/25.83 | | | | | | | | | | | (27), (30), (32), (33), (39), (40), (79) are
% 169.61/25.83 | | | | | | | | | | | inconsistent by sub-proof #399.
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | Case 2:
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | (80) all_58_13 = e2 & op(e0, e2) = e2
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | ALPHA: (80) implies:
% 169.61/25.83 | | | | | | | | | | | (81) all_58_13 = e2
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | | REF_CLOSE: (33), (72), (81) are inconsistent by sub-proof
% 169.61/25.83 | | | | | | | | | | | #458.
% 169.61/25.83 | | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | | End of split
% 169.61/25.83 | | | | | | | | | |
% 169.61/25.83 | | | | | | | | | End of split
% 169.61/25.83 | | | | | | | | |
% 169.61/25.83 | | | | | | | | End of split
% 169.61/25.83 | | | | | | | |
% 169.61/25.83 | | | | | | | Case 2:
% 169.61/25.83 | | | | | | | |
% 169.61/25.83 | | | | | | | | (82) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 169.61/25.83 | | | | | | | | op(e0, e0) = e1)
% 169.61/25.83 | | | | | | | |
% 169.61/25.83 | | | | | | | | BETA: splitting (82) gives:
% 169.61/25.83 | | | | | | | |
% 169.61/25.83 | | | | | | | | Case 1:
% 169.61/25.83 | | | | | | | | |
% 169.62/25.83 | | | | | | | | | (83) all_58_14 = e1 & op(e0, e1) = e1
% 169.62/25.83 | | | | | | | | |
% 169.62/25.83 | | | | | | | | | ALPHA: (83) implies:
% 169.62/25.83 | | | | | | | | | (84) all_58_14 = e1
% 169.62/25.83 | | | | | | | | |
% 169.62/25.83 | | | | | | | | | REF_CLOSE: (3), (33), (84) are inconsistent by sub-proof #649.
% 169.62/25.83 | | | | | | | | |
% 169.62/25.83 | | | | | | | | Case 2:
% 169.62/25.83 | | | | | | | | |
% 169.62/25.83 | | | | | | | | | (85) all_58_15 = e1 & op(e0, e0) = e1
% 169.62/25.83 | | | | | | | | |
% 169.62/25.83 | | | | | | | | | REF_CLOSE: (5), (8), (13), (19), (23), (40), (43), (46), (52),
% 169.62/25.83 | | | | | | | | | (85) are inconsistent by sub-proof #307.
% 169.62/25.83 | | | | | | | | |
% 169.62/25.83 | | | | | | | | End of split
% 169.62/25.83 | | | | | | | |
% 169.62/25.83 | | | | | | | End of split
% 169.62/25.83 | | | | | | |
% 169.62/25.83 | | | | | | End of split
% 169.62/25.83 | | | | | |
% 169.62/25.83 | | | | | End of split
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | Case 2:
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | | (86) all_58_2 = e3 & op(e2, e3) = e3
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | | ALPHA: (86) implies:
% 169.62/25.83 | | | | | (87) op(e2, e3) = e3
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | | REF_CLOSE: (15), (17), (26), (40), (87) are inconsistent by sub-proof
% 169.62/25.83 | | | | | #462.
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | End of split
% 169.62/25.83 | | | |
% 169.62/25.83 | | | Case 2:
% 169.62/25.83 | | | |
% 169.62/25.83 | | | | (88) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 169.62/25.83 | | | | = e3)
% 169.62/25.83 | | | |
% 169.62/25.83 | | | | BETA: splitting (88) gives:
% 169.62/25.83 | | | |
% 169.62/25.83 | | | | Case 1:
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | | (89) all_58_6 = e3 & op(e1, e3) = e3
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | | ALPHA: (89) implies:
% 169.62/25.83 | | | | | (90) all_58_6 = e3
% 169.62/25.83 | | | | | (91) op(e1, e3) = e3
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | | REF_CLOSE: (2), (3), (4), (5), (8), (10), (11), (12), (13), (15),
% 169.62/25.83 | | | | | (16), (17), (18), (19), (20), (23), (26), (27), (29), (30),
% 169.62/25.83 | | | | | (31), (32), (33), (34), (37), (38), (40), (90), (91) are
% 169.62/25.83 | | | | | inconsistent by sub-proof #332.
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | Case 2:
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | | (92) all_58_12 = e3 & op(e0, e3) = e3
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | | ALPHA: (92) implies:
% 169.62/25.83 | | | | | (93) all_58_12 = e3
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | | BETA: splitting (38) gives:
% 169.62/25.83 | | | | |
% 169.62/25.83 | | | | | Case 1:
% 169.62/25.83 | | | | | |
% 169.62/25.83 | | | | | | (94) all_58_15 = e0 & op(e0, e0) = e0
% 169.62/25.83 | | | | | |
% 169.62/25.83 | | | | | | ALPHA: (94) implies:
% 169.62/25.83 | | | | | | (95) all_58_15 = e0
% 169.62/25.83 | | | | | |
% 169.62/25.83 | | | | | | REF_CLOSE: (2), (3), (5), (8), (11), (12), (15), (16), (17), (19),
% 169.62/25.83 | | | | | | (20), (23), (26), (27), (30), (32), (33), (34), (40),
% 169.62/25.83 | | | | | | (93), (95) are inconsistent by sub-proof #306.
% 169.62/25.83 | | | | | |
% 169.62/25.83 | | | | | Case 2:
% 169.62/25.83 | | | | | |
% 169.62/25.83 | | | | | | (96) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 169.62/25.83 | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 169.62/25.83 | | | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.83 | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.62/25.83 | | | | | |
% 169.62/25.83 | | | | | | ALPHA: (96) implies:
% 169.62/25.83 | | | | | | (97) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.83 | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.62/25.83 | | | | | |
% 169.62/25.83 | | | | | | BETA: splitting (97) gives:
% 169.62/25.83 | | | | | |
% 169.62/25.83 | | | | | | Case 1:
% 169.62/25.83 | | | | | | |
% 169.62/25.83 | | | | | | | (98) all_58_12 = e0 & op(e0, e3) = e0
% 169.62/25.83 | | | | | | |
% 169.62/25.83 | | | | | | | ALPHA: (98) implies:
% 169.62/25.83 | | | | | | | (99) all_58_12 = e0
% 169.62/25.83 | | | | | | |
% 169.62/25.83 | | | | | | | COMBINE_EQS: (93), (99) imply:
% 169.62/25.83 | | | | | | | (100) e3 = e0
% 169.62/25.83 | | | | | | |
% 169.62/25.83 | | | | | | | COMBINE_EQS: (23), (100) imply:
% 169.62/25.83 | | | | | | | (101) all_58_15 = e0
% 169.62/25.83 | | | | | | |
% 169.62/25.83 | | | | | | | REF_CLOSE: (2), (3), (5), (8), (11), (12), (15), (16), (17), (19),
% 169.62/25.83 | | | | | | | (20), (26), (27), (30), (32), (33), (34), (40), (99),
% 169.62/25.83 | | | | | | | (101) are inconsistent by sub-proof #404.
% 169.62/25.83 | | | | | | |
% 169.62/25.83 | | | | | | Case 2:
% 169.62/25.83 | | | | | | |
% 169.62/25.83 | | | | | | | (102) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 169.62/25.83 | | | | | | | op(e0, e1) = e0)
% 169.62/25.83 | | | | | | |
% 169.62/25.83 | | | | | | | BETA: splitting (102) gives:
% 169.62/25.83 | | | | | | |
% 169.62/25.83 | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | |
% 169.62/25.83 | | | | | | | | (103) all_58_13 = e0 & op(e0, e2) = e0
% 169.62/25.83 | | | | | | | |
% 169.62/25.83 | | | | | | | | ALPHA: (103) implies:
% 169.62/25.83 | | | | | | | | (104) all_58_13 = e0
% 169.62/25.83 | | | | | | | |
% 169.62/25.83 | | | | | | | | BETA: splitting (22) gives:
% 169.62/25.83 | | | | | | | |
% 169.62/25.83 | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | |
% 169.62/25.83 | | | | | | | | | (105) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 &
% 169.62/25.83 | | | | | | | | | op(e2, e2) = e2)
% 169.62/25.83 | | | | | | | | |
% 169.62/25.83 | | | | | | | | | BETA: splitting (105) gives:
% 169.62/25.83 | | | | | | | | |
% 169.62/25.83 | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | (106) all_58_1 = e2 & op(e3, e2) = e2
% 169.62/25.83 | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | ALPHA: (106) implies:
% 169.62/25.83 | | | | | | | | | | (107) all_58_1 = e2
% 169.62/25.83 | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | BETA: splitting (7) gives:
% 169.62/25.83 | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | (108) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 169.62/25.83 | | | | | | | | | | | & op(e3, e2) = e0)
% 169.62/25.83 | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | BETA: splitting (108) gives:
% 169.62/25.83 | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | (109) all_58_0 = e0 & op(e3, e3) = e0
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | ALPHA: (109) implies:
% 169.62/25.83 | | | | | | | | | | | | (110) op(e3, e3) = e0
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | REF_CLOSE: (19), (26), (31), (110) are inconsistent by
% 169.62/25.83 | | | | | | | | | | | | sub-proof #949.
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | Case 2:
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | (111) all_58_1 = e0 & op(e3, e2) = e0
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | REF_CLOSE: (27), (107), (111) are inconsistent by sub-proof
% 169.62/25.83 | | | | | | | | | | | | #906.
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | End of split
% 169.62/25.83 | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | Case 2:
% 169.62/25.83 | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | (112) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 169.62/25.83 | | | | | | | | | | | & op(e3, e0) = e0)
% 169.62/25.83 | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | BETA: splitting (112) gives:
% 169.62/25.83 | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | (113) all_58_4 = e0 & op(e3, e1) = e0
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | ALPHA: (113) implies:
% 169.62/25.83 | | | | | | | | | | | | (114) all_58_4 = e0
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | COMBINE_EQS: (25), (114) imply:
% 169.62/25.83 | | | | | | | | | | | | (115) e3 = e0
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | COMBINE_EQS: (23), (115) imply:
% 169.62/25.83 | | | | | | | | | | | | (116) all_58_15 = e0
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | COMBINE_EQS: (93), (115) imply:
% 169.62/25.83 | | | | | | | | | | | | (117) all_58_12 = e0
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (11), (12), (15), (16), (17),
% 169.62/25.83 | | | | | | | | | | | | (19), (20), (26), (27), (30), (32), (33), (34),
% 169.62/25.83 | | | | | | | | | | | | (40), (116), (117) are inconsistent by sub-proof
% 169.62/25.83 | | | | | | | | | | | | #404.
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | Case 2:
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | (118) all_58_9 = e0 & op(e3, e0) = e0
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | ALPHA: (118) implies:
% 169.62/25.83 | | | | | | | | | | | | (119) all_58_9 = e0
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | BETA: splitting (1) gives:
% 169.62/25.83 | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | (120) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 169.62/25.83 | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 169.62/25.83 | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | BETA: splitting (120) gives:
% 169.62/25.83 | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | (121) all_58_9 = e1 & op(e3, e0) = e1
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | ALPHA: (121) implies:
% 169.62/25.83 | | | | | | | | | | | | | | (122) all_58_9 = e1
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | COMBINE_EQS: (119), (122) imply:
% 169.62/25.83 | | | | | | | | | | | | | | (123) e1 = e0
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | SIMP: (123) implies:
% 169.62/25.83 | | | | | | | | | | | | | | (124) e1 = e0
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | COMBINE_EQS: (29), (124) imply:
% 169.62/25.83 | | | | | | | | | | | | | | (125) all_58_5 = e0
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | (126) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 169.62/25.83 | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (25), (125), (126) are inconsistent by
% 169.62/25.83 | | | | | | | | | | | | | | | sub-proof #385.
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | Case 2:
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | (127) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 169.62/25.83 | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | (128) all_58_8 = e1 & op(e1, e1) = e1
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 169.62/25.83 | | | | | | | | | | | | | | | | (129) all_58_8 = e1
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | REF_CLOSE: (10), (11), (14), (19), (21), (26), (27), (37),
% 169.62/25.83 | | | | | | | | | | | | | | | | (39), (129) are inconsistent by sub-proof #312.
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | Case 2:
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | (130) all_58_14 = e1 & op(e0, e1) = e1
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (33), (130) are inconsistent by sub-proof
% 169.62/25.83 | | | | | | | | | | | | | | | | #396.
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | End of split
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | End of split
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | Case 2:
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | (131) all_58_10 = e1 & op(e2, e0) = e1
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | ALPHA: (131) implies:
% 169.62/25.83 | | | | | | | | | | | | | | (132) all_58_10 = e1
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 169.62/25.83 | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | (133) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 169.62/25.83 | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | (134) all_58_1 = e1 & op(e3, e2) = e1
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | REF_CLOSE: (33), (107), (134) are inconsistent by sub-proof
% 169.62/25.83 | | | | | | | | | | | | | | | | #899.
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | Case 2:
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | (135) all_58_3 = e1 & op(e2, e2) = e1
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 169.62/25.83 | | | | | | | | | | | | | | | | (136) all_58_3 = e1
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (136) imply:
% 169.62/25.83 | | | | | | | | | | | | | | | | (137) e3 = e1
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (11), (12), (15), (17), (19),
% 169.62/25.83 | | | | | | | | | | | | | | | | (20), (23), (26), (27), (30), (32), (33), (38),
% 169.62/25.83 | | | | | | | | | | | | | | | | (40), (93), (137) are inconsistent by sub-proof
% 169.62/25.83 | | | | | | | | | | | | | | | | #305.
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | End of split
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | Case 2:
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | (138) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 169.62/25.83 | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 169.62/25.83 | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | Case 1:
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | (139) all_58_7 = e1 & op(e1, e2) = e1
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 169.62/25.83 | | | | | | | | | | | | | | | | (140) all_58_7 = e1
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (39), (140) imply:
% 169.62/25.83 | | | | | | | | | | | | | | | | (141) e3 = e1
% 169.62/25.83 | | | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (11), (12), (15), (17), (19),
% 169.62/25.84 | | | | | | | | | | | | | | | | (20), (23), (26), (27), (30), (32), (33), (38),
% 169.62/25.84 | | | | | | | | | | | | | | | | (40), (93), (141) are inconsistent by sub-proof
% 169.62/25.84 | | | | | | | | | | | | | | | | #305.
% 169.62/25.84 | | | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | | Case 2:
% 169.62/25.84 | | | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | | | (142) all_58_13 = e1 & op(e0, e2) = e1
% 169.62/25.84 | | | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (11), (12), (15), (16), (17),
% 169.62/25.84 | | | | | | | | | | | | | | | | (19), (20), (26), (27), (29), (30), (32), (33),
% 169.62/25.84 | | | | | | | | | | | | | | | | (34), (38), (40), (93), (132), (142) are
% 169.62/25.84 | | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 169.62/25.84 | | | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | | End of split
% 169.62/25.84 | | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | End of split
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | End of split
% 169.62/25.84 | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | Case 2:
% 169.62/25.84 | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | (143) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 169.62/25.84 | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.62/25.84 | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | BETA: splitting (143) gives:
% 169.62/25.84 | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | Case 1:
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | (144) all_58_11 = e1 & op(e1, e0) = e1
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | REF_CLOSE: (14), (33), (144) are inconsistent by sub-proof
% 169.62/25.84 | | | | | | | | | | | | | | #547.
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | Case 2:
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | (145) all_58_15 = e1 & op(e0, e0) = e1
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | ALPHA: (145) implies:
% 169.62/25.84 | | | | | | | | | | | | | | (146) all_58_15 = e1
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | COMBINE_EQS: (23), (146) imply:
% 169.62/25.84 | | | | | | | | | | | | | | (147) e3 = e1
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | SIMP: (147) implies:
% 169.62/25.84 | | | | | | | | | | | | | | (148) e3 = e1
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | COMBINE_EQS: (93), (148) imply:
% 169.62/25.84 | | | | | | | | | | | | | | (149) all_58_12 = e1
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (11), (12), (15), (17), (19),
% 169.62/25.84 | | | | | | | | | | | | | | (20), (26), (27), (30), (32), (33), (38), (40),
% 169.62/25.84 | | | | | | | | | | | | | | (146), (149) are inconsistent by sub-proof #362.
% 169.62/25.84 | | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | | End of split
% 169.62/25.84 | | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | | End of split
% 169.62/25.84 | | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | | End of split
% 169.62/25.84 | | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | End of split
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | Case 2:
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | (150) all_58_3 = e2 & op(e2, e2) = e2
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | ALPHA: (150) implies:
% 169.62/25.84 | | | | | | | | | | (151) all_58_3 = e2
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | REF_CLOSE: (2), (5), (8), (11), (15), (17), (19), (20), (26),
% 169.62/25.84 | | | | | | | | | | (27), (32), (33), (40), (151) are inconsistent by
% 169.62/25.84 | | | | | | | | | | sub-proof #779.
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | End of split
% 169.62/25.84 | | | | | | | | |
% 169.62/25.84 | | | | | | | | Case 2:
% 169.62/25.84 | | | | | | | | |
% 169.62/25.84 | | | | | | | | | (152) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 &
% 169.62/25.84 | | | | | | | | | op(e0, e2) = e2)
% 169.62/25.84 | | | | | | | | |
% 169.62/25.84 | | | | | | | | | BETA: splitting (152) gives:
% 169.62/25.84 | | | | | | | | |
% 169.62/25.84 | | | | | | | | | Case 1:
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | (153) all_58_7 = e2 & op(e1, e2) = e2
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | ALPHA: (153) implies:
% 169.62/25.84 | | | | | | | | | | (154) all_58_7 = e2
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | REF_CLOSE: (2), (5), (8), (11), (15), (17), (19), (20), (26),
% 169.62/25.84 | | | | | | | | | | (27), (30), (32), (33), (39), (40), (154) are
% 169.62/25.84 | | | | | | | | | | inconsistent by sub-proof #399.
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | Case 2:
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | (155) all_58_13 = e2 & op(e0, e2) = e2
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | ALPHA: (155) implies:
% 169.62/25.84 | | | | | | | | | | (156) all_58_13 = e2
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | | REF_CLOSE: (27), (104), (156) are inconsistent by sub-proof
% 169.62/25.84 | | | | | | | | | | #865.
% 169.62/25.84 | | | | | | | | | |
% 169.62/25.84 | | | | | | | | | End of split
% 169.62/25.84 | | | | | | | | |
% 169.62/25.84 | | | | | | | | End of split
% 169.62/25.84 | | | | | | | |
% 169.62/25.84 | | | | | | | Case 2:
% 169.62/25.84 | | | | | | | |
% 169.62/25.84 | | | | | | | | (157) all_58_14 = e0 & op(e0, e1) = e0
% 169.62/25.84 | | | | | | | |
% 169.62/25.84 | | | | | | | | REF_CLOSE: (3), (27), (157) are inconsistent by sub-proof #858.
% 169.62/25.84 | | | | | | | |
% 169.62/25.84 | | | | | | | End of split
% 169.62/25.84 | | | | | | |
% 169.62/25.84 | | | | | | End of split
% 169.62/25.84 | | | | | |
% 169.62/25.84 | | | | | End of split
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | End of split
% 169.62/25.84 | | | |
% 169.62/25.84 | | | End of split
% 169.62/25.84 | | |
% 169.62/25.84 | | Case 2:
% 169.62/25.84 | | |
% 169.62/25.84 | | | (158) all_58_7 = e1 & op(e1, e2) = e1
% 169.62/25.84 | | |
% 169.62/25.84 | | | REF_CLOSE: (8), (39), (158) are inconsistent by sub-proof #757.
% 169.62/25.84 | | |
% 169.62/25.84 | | End of split
% 169.62/25.84 | |
% 169.62/25.84 | Case 2:
% 169.62/25.84 | |
% 169.62/25.84 | | (159) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 169.62/25.84 | | e1)
% 169.62/25.84 | |
% 169.62/25.84 | | BETA: splitting (159) gives:
% 169.62/25.84 | |
% 169.62/25.84 | | Case 1:
% 169.62/25.84 | | |
% 169.62/25.84 | | | (160) all_58_8 = e1 & op(e1, e1) = e1
% 169.62/25.84 | | |
% 169.62/25.84 | | | ALPHA: (160) implies:
% 169.62/25.84 | | | (161) all_58_8 = e1
% 169.62/25.84 | | |
% 169.62/25.84 | | | REF_CLOSE: (10), (11), (14), (19), (21), (26), (27), (37), (39), (161) are
% 169.62/25.84 | | | inconsistent by sub-proof #312.
% 169.62/25.84 | | |
% 169.62/25.84 | | Case 2:
% 169.62/25.84 | | |
% 169.62/25.84 | | | (162) all_58_11 = e1 & op(e1, e0) = e1
% 169.62/25.84 | | |
% 169.62/25.84 | | | ALPHA: (162) implies:
% 169.62/25.84 | | | (163) all_58_11 = e1
% 169.62/25.84 | | |
% 169.62/25.84 | | | REF_CLOSE: (14), (33), (163) are inconsistent by sub-proof #832.
% 169.62/25.84 | | |
% 169.62/25.84 | | End of split
% 169.62/25.84 | |
% 169.62/25.84 | End of split
% 169.62/25.84 |
% 169.62/25.84 End of proof
% 169.62/25.84
% 169.62/25.84 Sub-proof #305 shows that the following formulas are inconsistent:
% 169.62/25.84 ----------------------------------------------------------------
% 169.62/25.84 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.84 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.84 (2) all_58_14 = e2
% 169.62/25.84 (3) all_58_2 = e2
% 169.62/25.84 (4) ~ (e3 = e1)
% 169.62/25.84 (5) ~ (e1 = e0)
% 169.62/25.84 (6) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.62/25.84 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.62/25.84 (7) op(e2, e3) = all_52_1
% 169.62/25.84 (8) op(e2, e3) = e2
% 169.62/25.84 (9) ~ (e3 = e0)
% 169.62/25.84 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.84 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.84 (11) all_58_15 = e3
% 169.62/25.84 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.84 (13) ~ (e2 = e0)
% 169.62/25.84 (14) all_58_12 = e3
% 169.62/25.84 (15) all_58_3 = e3
% 169.62/25.84 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.84 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.84 (17) ~ (e2 = e1)
% 169.62/25.84 (18) e3 = e1
% 169.62/25.84 (19) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.84 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.84 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.84 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.84 (20) ~ (e3 = e2)
% 169.62/25.84
% 169.62/25.84 Begin of proof
% 169.62/25.84 |
% 169.62/25.84 | SIMP: (18) implies:
% 169.62/25.84 | (21) e3 = e1
% 169.62/25.84 |
% 169.62/25.84 | COMBINE_EQS: (11), (21) imply:
% 169.62/25.84 | (22) all_58_15 = e1
% 169.62/25.84 |
% 169.62/25.84 | COMBINE_EQS: (14), (21) imply:
% 169.62/25.84 | (23) all_58_12 = e1
% 169.62/25.84 |
% 169.62/25.84 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 169.62/25.84 | (15), (16), (17), (19), (20), (22), (23) are inconsistent by
% 169.62/25.84 | sub-proof #362.
% 169.62/25.84 |
% 169.62/25.84 End of proof
% 169.62/25.84
% 169.62/25.84 Sub-proof #306 shows that the following formulas are inconsistent:
% 169.62/25.84 ----------------------------------------------------------------
% 169.62/25.84 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.84 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.84 (2) all_58_14 = e2
% 169.62/25.84 (3) all_58_2 = e2
% 169.62/25.84 (4) ~ (e3 = e1)
% 169.62/25.84 (5) ~ (e1 = e0)
% 169.62/25.84 (6) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.62/25.84 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.62/25.84 (7) op(e2, e3) = all_52_1
% 169.62/25.84 (8) ~ (all_52_7 = e3)
% 169.62/25.84 (9) op(e2, e3) = e2
% 169.62/25.84 (10) ~ (e3 = e0)
% 169.62/25.84 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.84 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.84 (12) all_58_15 = e3
% 169.62/25.84 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.84 (14) ~ (e2 = e0)
% 169.62/25.84 (15) all_58_12 = e3
% 169.62/25.84 (16) all_58_3 = e3
% 169.62/25.84 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.84 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.84 (18) ~ (e2 = e1)
% 169.62/25.84 (19) all_58_15 = e0
% 169.62/25.84 (20) op(e0, e2) = all_52_7
% 169.62/25.84 (21) ~ (e3 = e2)
% 169.62/25.84
% 169.62/25.84 Begin of proof
% 169.62/25.84 |
% 169.62/25.84 | COMBINE_EQS: (12), (19) imply:
% 169.62/25.84 | (22) e3 = e0
% 169.62/25.84 |
% 169.62/25.84 | SIMP: (22) implies:
% 169.62/25.84 | (23) e3 = e0
% 169.62/25.84 |
% 169.62/25.84 | COMBINE_EQS: (15), (23) imply:
% 169.62/25.84 | (24) all_58_12 = e0
% 169.62/25.84 |
% 169.62/25.84 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 169.62/25.84 | (14), (16), (17), (18), (19), (20), (21), (24) are inconsistent by
% 169.62/25.84 | sub-proof #404.
% 169.62/25.84 |
% 169.62/25.84 End of proof
% 169.62/25.84
% 169.62/25.84 Sub-proof #307 shows that the following formulas are inconsistent:
% 169.62/25.84 ----------------------------------------------------------------
% 169.62/25.84 (1) all_58_2 = e2
% 169.62/25.84 (2) all_58_6 = e1
% 169.62/25.84 (3) ~ (e3 = e1)
% 169.62/25.84 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.62/25.84 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.62/25.84 (5) ~ (e3 = e0)
% 169.62/25.84 (6) all_58_12 = e0
% 169.62/25.84 (7) all_58_15 = e1 & op(e0, e0) = e1
% 169.62/25.84 (8) all_58_15 = e3
% 169.62/25.84 (9) all_58_0 = e3
% 169.62/25.84 (10) ~ (e3 = e2)
% 169.62/25.84
% 169.62/25.84 Begin of proof
% 169.62/25.84 |
% 169.62/25.84 | ALPHA: (7) implies:
% 169.62/25.84 | (11) all_58_15 = e1
% 169.62/25.84 |
% 169.62/25.84 | COMBINE_EQS: (8), (11) imply:
% 169.62/25.84 | (12) e3 = e1
% 169.62/25.84 |
% 169.62/25.84 | SIMP: (12) implies:
% 169.62/25.84 | (13) e3 = e1
% 169.62/25.84 |
% 169.62/25.84 | COMBINE_EQS: (9), (13) imply:
% 169.62/25.84 | (14) all_58_0 = e1
% 169.62/25.84 |
% 169.62/25.84 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (14) are inconsistent by
% 169.62/25.84 | sub-proof #456.
% 169.62/25.84 |
% 169.62/25.84 End of proof
% 169.62/25.84
% 169.62/25.84 Sub-proof #308 shows that the following formulas are inconsistent:
% 169.62/25.84 ----------------------------------------------------------------
% 169.62/25.84 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.84 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.84 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.62/25.84 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.62/25.84 (3) all_58_2 = e2
% 169.62/25.84 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.84 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.62/25.84 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.62/25.84 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.84 (6) ~ (e3 = e1)
% 169.62/25.84 (7) op(e1, e3) = all_52_2
% 169.62/25.84 (8) ~ (e1 = e0)
% 169.62/25.84 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.62/25.84 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.62/25.84 (10) op(e2, e3) = all_52_1
% 169.62/25.84 (11) all_58_6 = e2
% 169.62/25.84 (12) op(e2, e3) = e2
% 169.62/25.84 (13) ~ (e3 = e0)
% 169.62/25.84 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.84 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.84 (15) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.84 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.62/25.84 (16) all_58_0 = e3
% 169.62/25.84 (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.62/25.84 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.62/25.84 (18) all_58_4 = e3
% 169.62/25.84 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.84 (20) ~ (e2 = e0)
% 169.62/25.84 (21) all_58_3 = e3
% 169.62/25.84 (22) op(e3, e3) = e3
% 169.62/25.84 (23) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.84 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.84 (24) ~ (e2 = e1)
% 169.62/25.84 (25) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.62/25.84 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.62/25.84 (26) all_58_9 = e2 & op(e3, e0) = e2
% 169.62/25.84 (27) op(e1, e3) = e1
% 169.62/25.84 (28) all_58_7 = e3
% 169.62/25.84 (29) ~ (e3 = e2)
% 169.62/25.84
% 169.62/25.84 Begin of proof
% 169.62/25.84 |
% 169.62/25.84 | ALPHA: (26) implies:
% 169.62/25.84 | (30) all_58_9 = e2
% 169.62/25.84 |
% 169.62/25.84 | BETA: splitting (2) gives:
% 169.62/25.84 |
% 169.62/25.84 | Case 1:
% 169.62/25.84 | |
% 169.62/25.84 | | (31) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.62/25.84 | | e0)
% 169.62/25.84 | |
% 169.62/25.84 | | REF_CLOSE: (10), (12), (13), (19), (20), (22), (31) are inconsistent by
% 169.62/25.84 | | sub-proof #460.
% 169.62/25.84 | |
% 169.62/25.84 | Case 2:
% 169.62/25.84 | |
% 169.62/25.84 | | (32) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.62/25.84 | | e0)
% 169.62/25.84 | |
% 169.62/25.84 | | BETA: splitting (32) gives:
% 169.62/25.84 | |
% 169.62/25.84 | | Case 1:
% 169.62/25.84 | | |
% 169.62/25.84 | | | (33) all_58_6 = e0 & op(e1, e3) = e0
% 169.62/25.84 | | |
% 169.62/25.84 | | | ALPHA: (33) implies:
% 169.62/25.84 | | | (34) op(e1, e3) = e0
% 169.62/25.84 | | |
% 169.62/25.84 | | | REF_CLOSE: (7), (8), (19), (27), (34) are inconsistent by sub-proof #749.
% 169.62/25.84 | | |
% 169.62/25.84 | | Case 2:
% 169.62/25.84 | | |
% 169.62/25.84 | | | (35) all_58_12 = e0 & op(e0, e3) = e0
% 169.62/25.84 | | |
% 169.62/25.84 | | | ALPHA: (35) implies:
% 169.62/25.84 | | | (36) all_58_12 = e0
% 169.62/25.84 | | |
% 169.62/25.84 | | | BETA: splitting (17) gives:
% 169.62/25.84 | | |
% 169.62/25.84 | | | Case 1:
% 169.62/25.84 | | | |
% 169.62/25.84 | | | | (37) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 169.62/25.84 | | | | = e1)
% 169.62/25.84 | | | |
% 169.62/25.84 | | | | BETA: splitting (37) gives:
% 169.62/25.84 | | | |
% 169.62/25.84 | | | | Case 1:
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | (38) all_58_0 = e1 & op(e3, e3) = e1
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | ALPHA: (38) implies:
% 169.62/25.84 | | | | | (39) all_58_0 = e1
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | REF_CLOSE: (3), (6), (9), (11), (13), (29), (36), (39) are
% 169.62/25.84 | | | | | inconsistent by sub-proof #309.
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | Case 2:
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | (40) all_58_1 = e1 & op(e3, e2) = e1
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | ALPHA: (40) implies:
% 169.62/25.84 | | | | | (41) all_58_1 = e1
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | REF_CLOSE: (5), (8), (13), (16), (18), (20), (30), (41) are
% 169.62/25.84 | | | | | inconsistent by sub-proof #315.
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | End of split
% 169.62/25.84 | | | |
% 169.62/25.84 | | | Case 2:
% 169.62/25.84 | | | |
% 169.62/25.84 | | | | (42) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 169.62/25.84 | | | | = e1)
% 169.62/25.84 | | | |
% 169.62/25.84 | | | | BETA: splitting (42) gives:
% 169.62/25.84 | | | |
% 169.62/25.84 | | | | Case 1:
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | (43) all_58_4 = e1 & op(e3, e1) = e1
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | ALPHA: (43) implies:
% 169.62/25.84 | | | | | (44) all_58_4 = e1
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | COMBINE_EQS: (18), (44) imply:
% 169.62/25.84 | | | | | (45) e3 = e1
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | COMBINE_EQS: (16), (45) imply:
% 169.62/25.84 | | | | | (46) all_58_0 = e1
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | REF_CLOSE: (3), (6), (9), (11), (13), (29), (36), (46) are
% 169.62/25.84 | | | | | inconsistent by sub-proof #309.
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | Case 2:
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | (47) all_58_9 = e1 & op(e3, e0) = e1
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | ALPHA: (47) implies:
% 169.62/25.84 | | | | | (48) all_58_9 = e1
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | BETA: splitting (25) gives:
% 169.62/25.84 | | | | |
% 169.62/25.84 | | | | | Case 1:
% 169.62/25.84 | | | | | |
% 169.62/25.84 | | | | | | (49) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 169.62/25.84 | | | | | | e2) = e2)
% 169.62/25.84 | | | | | |
% 169.62/25.84 | | | | | | BETA: splitting (49) gives:
% 169.62/25.84 | | | | | |
% 169.62/25.84 | | | | | | Case 1:
% 169.62/25.84 | | | | | | |
% 169.62/25.84 | | | | | | | (50) all_58_0 = e2 & op(e3, e3) = e2
% 169.62/25.84 | | | | | | |
% 169.62/25.84 | | | | | | | REF_CLOSE: (1), (3), (6), (8), (10), (12), (13), (14), (16), (19),
% 169.62/25.84 | | | | | | | (20), (21), (23), (24), (29), (50) are inconsistent by
% 169.62/25.84 | | | | | | | sub-proof #317.
% 169.62/25.84 | | | | | | |
% 169.62/25.84 | | | | | | Case 2:
% 169.62/25.84 | | | | | | |
% 169.62/25.84 | | | | | | | (51) all_58_1 = e2 & op(e3, e2) = e2
% 169.62/25.84 | | | | | | |
% 169.62/25.84 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (12), (13), (14),
% 169.62/25.84 | | | | | | | (15), (16), (18), (19), (20), (21), (23), (24), (25),
% 169.62/25.84 | | | | | | | (28), (29), (51) are inconsistent by sub-proof #313.
% 169.62/25.84 | | | | | | |
% 169.62/25.84 | | | | | | End of split
% 169.62/25.84 | | | | | |
% 169.62/25.84 | | | | | Case 2:
% 169.62/25.84 | | | | | |
% 169.62/25.84 | | | | | | (52) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 169.62/25.84 | | | | | | e0) = e2)
% 169.62/25.84 | | | | | |
% 169.62/25.85 | | | | | | REF_CLOSE: (1), (3), (6), (8), (10), (12), (13), (14), (18), (19),
% 169.62/25.85 | | | | | | (20), (21), (23), (24), (29), (48), (52) are inconsistent
% 169.62/25.85 | | | | | | by sub-proof #379.
% 169.62/25.85 | | | | | |
% 169.62/25.85 | | | | | End of split
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | End of split
% 169.62/25.85 | | | |
% 169.62/25.85 | | | End of split
% 169.62/25.85 | | |
% 169.62/25.85 | | End of split
% 169.62/25.85 | |
% 169.62/25.85 | End of split
% 169.62/25.85 |
% 169.62/25.85 End of proof
% 169.62/25.85
% 169.62/25.85 Sub-proof #309 shows that the following formulas are inconsistent:
% 169.62/25.85 ----------------------------------------------------------------
% 169.62/25.85 (1) all_58_2 = e2
% 169.62/25.85 (2) all_58_0 = e1
% 169.62/25.85 (3) ~ (e3 = e1)
% 169.62/25.85 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.62/25.85 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.62/25.85 (5) all_58_6 = e2
% 169.62/25.85 (6) ~ (e3 = e0)
% 169.62/25.85 (7) all_58_12 = e0
% 169.62/25.85 (8) ~ (e3 = e2)
% 169.62/25.85
% 169.62/25.85 Begin of proof
% 169.62/25.85 |
% 169.62/25.85 | BETA: splitting (4) gives:
% 169.62/25.85 |
% 169.62/25.85 | Case 1:
% 169.62/25.85 | |
% 169.62/25.85 | | (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 169.62/25.85 | |
% 169.62/25.85 | | BETA: splitting (9) gives:
% 169.62/25.85 | |
% 169.62/25.85 | | Case 1:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (10) all_58_0 = e3 & op(e3, e3) = e3
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (2), (3), (10) are inconsistent by sub-proof #905.
% 169.62/25.85 | | |
% 169.62/25.85 | | Case 2:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (11) all_58_2 = e3 & op(e2, e3) = e3
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (1), (8), (11) are inconsistent by sub-proof #786.
% 169.62/25.85 | | |
% 169.62/25.85 | | End of split
% 169.62/25.85 | |
% 169.62/25.85 | Case 2:
% 169.62/25.85 | |
% 169.62/25.85 | | (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 169.62/25.85 | | e3)
% 169.62/25.85 | |
% 169.62/25.85 | | BETA: splitting (12) gives:
% 169.62/25.85 | |
% 169.62/25.85 | | Case 1:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (13) all_58_6 = e3 & op(e1, e3) = e3
% 169.62/25.85 | | |
% 169.62/25.85 | | | ALPHA: (13) implies:
% 169.62/25.85 | | | (14) all_58_6 = e3
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (5), (8), (14) are inconsistent by sub-proof #822.
% 169.62/25.85 | | |
% 169.62/25.85 | | Case 2:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (15) all_58_12 = e3 & op(e0, e3) = e3
% 169.62/25.85 | | |
% 169.62/25.85 | | | ALPHA: (15) implies:
% 169.62/25.85 | | | (16) all_58_12 = e3
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (6), (7), (16) are inconsistent by sub-proof #608.
% 169.62/25.85 | | |
% 169.62/25.85 | | End of split
% 169.62/25.85 | |
% 169.62/25.85 | End of split
% 169.62/25.85 |
% 169.62/25.85 End of proof
% 169.62/25.85
% 169.62/25.85 Sub-proof #310 shows that the following formulas are inconsistent:
% 169.62/25.85 ----------------------------------------------------------------
% 169.62/25.85 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.85 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.85 (2) all_58_2 = e2
% 169.62/25.85 (3) ~ (e3 = e1)
% 169.62/25.85 (4) ~ (e1 = e0)
% 169.62/25.85 (5) op(e2, e3) = all_52_1
% 169.62/25.85 (6) op(e2, e3) = e2
% 169.62/25.85 (7) ~ (e3 = e0)
% 169.62/25.85 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.85 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.85 (9) all_58_15 = e2 & op(e0, e0) = e2
% 169.62/25.85 (10) all_58_15 = e3
% 169.62/25.85 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.85 (12) ~ (e2 = e0)
% 169.62/25.85 (13) all_58_3 = e3
% 169.62/25.85 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.85 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.85 (15) ~ (e2 = e1)
% 169.62/25.85 (16) ~ (e3 = e2)
% 169.62/25.85
% 169.62/25.85 Begin of proof
% 169.62/25.85 |
% 169.62/25.85 | ALPHA: (9) implies:
% 169.62/25.85 | (17) all_58_15 = e2
% 169.62/25.85 |
% 169.62/25.85 | COMBINE_EQS: (10), (17) imply:
% 169.62/25.85 | (18) e3 = e2
% 169.62/25.85 |
% 169.62/25.85 | COMBINE_EQS: (13), (18) imply:
% 169.62/25.85 | (19) all_58_3 = e2
% 169.62/25.85 |
% 169.62/25.85 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (14), (15),
% 169.62/25.85 | (16), (19) are inconsistent by sub-proof #779.
% 169.62/25.85 |
% 169.62/25.85 End of proof
% 169.62/25.85
% 169.62/25.85 Sub-proof #311 shows that the following formulas are inconsistent:
% 169.62/25.85 ----------------------------------------------------------------
% 169.62/25.85 (1) op(e1, e3) = all_52_2
% 169.62/25.85 (2) ~ (e1 = e0)
% 169.62/25.85 (3) all_58_11 = e2
% 169.62/25.85 (4) ~ (e3 = e0)
% 169.62/25.85 (5) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.62/25.85 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.62/25.85 (6) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 169.62/25.85 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.85 (8) ~ (e2 = e0)
% 169.62/25.85 (9) ~ (e2 = e1)
% 169.62/25.85 (10) op(e1, e3) = e1
% 169.62/25.85 (11) all_58_7 = e3
% 169.62/25.85
% 169.62/25.85 Begin of proof
% 169.62/25.85 |
% 169.62/25.85 | BETA: splitting (6) gives:
% 169.62/25.85 |
% 169.62/25.85 | Case 1:
% 169.62/25.85 | |
% 169.62/25.85 | | (12) all_58_8 = e1 & op(e1, e1) = e1
% 169.62/25.85 | |
% 169.62/25.85 | | ALPHA: (12) implies:
% 169.62/25.85 | | (13) all_58_8 = e1
% 169.62/25.85 | |
% 169.62/25.85 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (13) are
% 169.62/25.85 | | inconsistent by sub-proof #312.
% 169.62/25.85 | |
% 169.62/25.85 | Case 2:
% 169.62/25.85 | |
% 169.62/25.85 | | (14) all_58_11 = e1 & op(e1, e0) = e1
% 169.62/25.85 | |
% 169.62/25.85 | | REF_CLOSE: (3), (9), (14) are inconsistent by sub-proof #547.
% 169.62/25.85 | |
% 169.62/25.85 | End of split
% 169.62/25.85 |
% 169.62/25.85 End of proof
% 169.62/25.85
% 169.62/25.85 Sub-proof #312 shows that the following formulas are inconsistent:
% 169.62/25.85 ----------------------------------------------------------------
% 169.62/25.85 (1) all_58_8 = e1
% 169.62/25.85 (2) op(e1, e3) = all_52_2
% 169.62/25.85 (3) ~ (e1 = e0)
% 169.62/25.85 (4) all_58_11 = e2
% 169.62/25.85 (5) ~ (e3 = e0)
% 169.62/25.85 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.62/25.85 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.62/25.85 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.85 (8) ~ (e2 = e0)
% 169.62/25.85 (9) op(e1, e3) = e1
% 169.62/25.85 (10) all_58_7 = e3
% 169.62/25.85
% 169.62/25.85 Begin of proof
% 169.62/25.85 |
% 169.62/25.85 | BETA: splitting (6) gives:
% 169.62/25.85 |
% 169.62/25.85 | Case 1:
% 169.62/25.85 | |
% 169.62/25.85 | | (11) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 169.62/25.85 | | e0)
% 169.62/25.85 | |
% 169.62/25.85 | | REF_CLOSE: (2), (3), (5), (7), (9), (10), (11) are inconsistent by sub-proof
% 169.62/25.85 | | #747.
% 169.62/25.85 | |
% 169.62/25.85 | Case 2:
% 169.62/25.85 | |
% 169.62/25.85 | | (12) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 169.62/25.85 | | e0)
% 169.62/25.85 | |
% 169.62/25.85 | | BETA: splitting (12) gives:
% 169.62/25.85 | |
% 169.62/25.85 | | Case 1:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (13) all_58_8 = e0 & op(e1, e1) = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | ALPHA: (13) implies:
% 169.62/25.85 | | | (14) all_58_8 = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (1), (3), (14) are inconsistent by sub-proof #818.
% 169.62/25.85 | | |
% 169.62/25.85 | | Case 2:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (15) all_58_11 = e0 & op(e1, e0) = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (4), (8), (15) are inconsistent by sub-proof #848.
% 169.62/25.85 | | |
% 169.62/25.85 | | End of split
% 169.62/25.85 | |
% 169.62/25.85 | End of split
% 169.62/25.85 |
% 169.62/25.85 End of proof
% 169.62/25.85
% 169.62/25.85 Sub-proof #313 shows that the following formulas are inconsistent:
% 169.62/25.85 ----------------------------------------------------------------
% 169.62/25.85 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.85 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.85 (2) all_58_2 = e2
% 169.62/25.85 (3) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.85 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.62/25.85 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.62/25.85 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.85 (5) ~ (e3 = e1)
% 169.62/25.85 (6) ~ (e1 = e0)
% 169.62/25.85 (7) op(e2, e3) = all_52_1
% 169.62/25.85 (8) op(e2, e3) = e2
% 169.62/25.85 (9) ~ (e3 = e0)
% 169.62/25.85 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.85 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.85 (11) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.85 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.62/25.85 (12) all_58_0 = e3
% 169.62/25.85 (13) all_58_4 = e3
% 169.62/25.85 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.85 (15) ~ (e2 = e0)
% 169.62/25.85 (16) all_58_1 = e2 & op(e3, e2) = e2
% 169.62/25.85 (17) all_58_3 = e3
% 169.62/25.85 (18) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.85 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.85 (19) ~ (e2 = e1)
% 169.62/25.85 (20) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.62/25.85 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.62/25.85 (21) all_58_7 = e3
% 169.62/25.85 (22) ~ (e3 = e2)
% 169.62/25.85
% 169.62/25.85 Begin of proof
% 169.62/25.85 |
% 169.62/25.85 | ALPHA: (16) implies:
% 169.62/25.85 | (23) all_58_1 = e2
% 169.62/25.85 |
% 169.62/25.85 | BETA: splitting (11) gives:
% 169.62/25.85 |
% 169.62/25.85 | Case 1:
% 169.62/25.85 | |
% 169.62/25.85 | | (24) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 169.62/25.85 | | e0)
% 169.62/25.85 | |
% 169.62/25.85 | | BETA: splitting (24) gives:
% 169.62/25.85 | |
% 169.62/25.85 | | Case 1:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (25) all_58_1 = e0 & op(e3, e2) = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (15), (23), (25) are inconsistent by sub-proof #906.
% 169.62/25.85 | | |
% 169.62/25.85 | | Case 2:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (26) all_58_3 = e0 & op(e2, e2) = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (9), (17), (26) are inconsistent by sub-proof #869.
% 169.62/25.85 | | |
% 169.62/25.85 | | End of split
% 169.62/25.85 | |
% 169.62/25.85 | Case 2:
% 169.62/25.85 | |
% 169.62/25.85 | | (27) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.62/25.85 | | e0)
% 169.62/25.85 | |
% 169.62/25.85 | | BETA: splitting (27) gives:
% 169.62/25.85 | |
% 169.62/25.85 | | Case 1:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (28) all_58_7 = e0 & op(e1, e2) = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (9), (21), (28) are inconsistent by sub-proof #890.
% 169.62/25.85 | | |
% 169.62/25.85 | | Case 2:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (29) all_58_13 = e0 & op(e0, e2) = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | ALPHA: (29) implies:
% 169.62/25.85 | | | (30) all_58_13 = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | BETA: splitting (3) gives:
% 169.62/25.85 | | |
% 169.62/25.85 | | | Case 1:
% 169.62/25.85 | | | |
% 169.62/25.85 | | | | (31) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 169.62/25.85 | | | | = e1)
% 169.62/25.85 | | | |
% 169.62/25.85 | | | | BETA: splitting (31) gives:
% 169.62/25.85 | | | |
% 169.62/25.85 | | | | Case 1:
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | | (32) all_58_1 = e1 & op(e3, e2) = e1
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 169.62/25.85 | | | | | (14), (15), (17), (18), (19), (20), (22), (32) are
% 169.62/25.85 | | | | | inconsistent by sub-proof #314.
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | Case 2:
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | | (33) all_58_3 = e1 & op(e2, e2) = e1
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | | REF_CLOSE: (5), (17), (33) are inconsistent by sub-proof #868.
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | End of split
% 169.62/25.85 | | | |
% 169.62/25.85 | | | Case 2:
% 169.62/25.85 | | | |
% 169.62/25.85 | | | | (34) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 169.62/25.85 | | | | = e1)
% 169.62/25.85 | | | |
% 169.62/25.85 | | | | BETA: splitting (34) gives:
% 169.62/25.85 | | | |
% 169.62/25.85 | | | | Case 1:
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | | (35) all_58_7 = e1 & op(e1, e2) = e1
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | | REF_CLOSE: (5), (21), (35) are inconsistent by sub-proof #757.
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | Case 2:
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | | (36) all_58_13 = e1 & op(e0, e2) = e1
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | | ALPHA: (36) implies:
% 169.62/25.85 | | | | | (37) all_58_13 = e1
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | | REF_CLOSE: (6), (30), (37) are inconsistent by sub-proof #546.
% 169.62/25.85 | | | | |
% 169.62/25.85 | | | | End of split
% 169.62/25.85 | | | |
% 169.62/25.85 | | | End of split
% 169.62/25.85 | | |
% 169.62/25.85 | | End of split
% 169.62/25.85 | |
% 169.62/25.85 | End of split
% 169.62/25.85 |
% 169.62/25.85 End of proof
% 169.62/25.85
% 169.62/25.85 Sub-proof #314 shows that the following formulas are inconsistent:
% 169.62/25.85 ----------------------------------------------------------------
% 169.62/25.85 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.85 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.85 (2) all_58_2 = e2
% 169.62/25.85 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.62/25.85 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.85 (4) ~ (e3 = e1)
% 169.62/25.85 (5) ~ (e1 = e0)
% 169.62/25.85 (6) all_58_1 = e1 & op(e3, e2) = e1
% 169.62/25.85 (7) op(e2, e3) = all_52_1
% 169.62/25.85 (8) op(e2, e3) = e2
% 169.62/25.85 (9) ~ (e3 = e0)
% 169.62/25.85 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.85 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.85 (11) all_58_0 = e3
% 169.62/25.85 (12) all_58_4 = e3
% 169.62/25.85 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.85 (14) ~ (e2 = e0)
% 169.62/25.85 (15) all_58_3 = e3
% 169.62/25.85 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.85 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.85 (17) ~ (e2 = e1)
% 169.62/25.85 (18) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.62/25.85 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.62/25.85 (19) ~ (e3 = e2)
% 169.62/25.85
% 169.62/25.85 Begin of proof
% 169.62/25.85 |
% 169.62/25.85 | ALPHA: (6) implies:
% 169.62/25.85 | (20) all_58_1 = e1
% 169.62/25.85 |
% 169.62/25.85 | BETA: splitting (18) gives:
% 169.62/25.85 |
% 169.62/25.85 | Case 1:
% 169.62/25.85 | |
% 169.62/25.85 | | (21) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 169.62/25.85 | | e2)
% 169.62/25.85 | |
% 169.62/25.85 | | BETA: splitting (21) gives:
% 169.62/25.85 | |
% 169.62/25.85 | | Case 1:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (22) all_58_0 = e2 & op(e3, e3) = e2
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 169.62/25.85 | | | (15), (16), (17), (19), (22) are inconsistent by sub-proof
% 169.62/25.85 | | | #317.
% 169.62/25.85 | | |
% 169.62/25.85 | | Case 2:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (23) all_58_1 = e2 & op(e3, e2) = e2
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (17), (20), (23) are inconsistent by sub-proof #316.
% 169.62/25.85 | | |
% 169.62/25.85 | | End of split
% 169.62/25.85 | |
% 169.62/25.85 | Case 2:
% 169.62/25.85 | |
% 169.62/25.85 | | (24) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 169.62/25.85 | | e2)
% 169.62/25.85 | |
% 169.62/25.85 | | BETA: splitting (24) gives:
% 169.62/25.85 | |
% 169.62/25.85 | | Case 1:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (25) all_58_4 = e2 & op(e3, e1) = e2
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 169.62/25.85 | | | (15), (16), (17), (19), (25) are inconsistent by sub-proof
% 169.62/25.85 | | | #409.
% 169.62/25.85 | | |
% 169.62/25.85 | | Case 2:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (26) all_58_9 = e2 & op(e3, e0) = e2
% 169.62/25.85 | | |
% 169.62/25.85 | | | ALPHA: (26) implies:
% 169.62/25.85 | | | (27) all_58_9 = e2
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (3), (5), (9), (11), (12), (14), (20), (27) are inconsistent by
% 169.62/25.85 | | | sub-proof #315.
% 169.62/25.85 | | |
% 169.62/25.85 | | End of split
% 169.62/25.85 | |
% 169.62/25.85 | End of split
% 169.62/25.85 |
% 169.62/25.85 End of proof
% 169.62/25.85
% 169.62/25.85 Sub-proof #315 shows that the following formulas are inconsistent:
% 169.62/25.85 ----------------------------------------------------------------
% 169.62/25.85 (1) all_58_1 = e1
% 169.62/25.85 (2) all_58_9 = e2
% 169.62/25.85 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.62/25.85 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.85 (4) ~ (e1 = e0)
% 169.62/25.85 (5) ~ (e3 = e0)
% 169.62/25.85 (6) all_58_0 = e3
% 169.62/25.85 (7) all_58_4 = e3
% 169.62/25.85 (8) ~ (e2 = e0)
% 169.62/25.85
% 169.62/25.85 Begin of proof
% 169.62/25.85 |
% 169.62/25.85 | BETA: splitting (3) gives:
% 169.62/25.85 |
% 169.62/25.85 | Case 1:
% 169.62/25.85 | |
% 169.62/25.85 | | (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 169.62/25.85 | |
% 169.62/25.85 | | BETA: splitting (9) gives:
% 169.62/25.85 | |
% 169.62/25.85 | | Case 1:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (10) all_58_0 = e0 & op(e3, e3) = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (5), (6), (10) are inconsistent by sub-proof #898.
% 169.62/25.85 | | |
% 169.62/25.85 | | Case 2:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (11) all_58_1 = e0 & op(e3, e2) = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #948.
% 169.62/25.85 | | |
% 169.62/25.85 | | End of split
% 169.62/25.85 | |
% 169.62/25.85 | Case 2:
% 169.62/25.85 | |
% 169.62/25.85 | | (12) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 169.62/25.85 | | e0)
% 169.62/25.85 | |
% 169.62/25.85 | | BETA: splitting (12) gives:
% 169.62/25.85 | |
% 169.62/25.85 | | Case 1:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (13) all_58_4 = e0 & op(e3, e1) = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #704.
% 169.62/25.85 | | |
% 169.62/25.85 | | Case 2:
% 169.62/25.85 | | |
% 169.62/25.85 | | | (14) all_58_9 = e0 & op(e3, e0) = e0
% 169.62/25.85 | | |
% 169.62/25.85 | | | REF_CLOSE: (2), (8), (14) are inconsistent by sub-proof #745.
% 169.62/25.85 | | |
% 169.62/25.85 | | End of split
% 169.62/25.85 | |
% 169.62/25.85 | End of split
% 169.62/25.85 |
% 169.62/25.85 End of proof
% 169.62/25.85
% 169.62/25.85 Sub-proof #316 shows that the following formulas are inconsistent:
% 169.62/25.85 ----------------------------------------------------------------
% 169.62/25.85 (1) all_58_1 = e2 & op(e3, e2) = e2
% 169.62/25.85 (2) all_58_1 = e1
% 169.62/25.85 (3) ~ (e2 = e1)
% 169.62/25.85
% 169.62/25.85 Begin of proof
% 169.62/25.85 |
% 169.62/25.85 | ALPHA: (1) implies:
% 169.62/25.85 | (4) all_58_1 = e2
% 169.62/25.85 |
% 169.62/25.85 | COMBINE_EQS: (2), (4) imply:
% 169.62/25.85 | (5) e2 = e1
% 169.62/25.85 |
% 169.62/25.85 | SIMP: (5) implies:
% 169.62/25.85 | (6) e2 = e1
% 169.62/25.85 |
% 169.62/25.85 | REDUCE: (3), (6) imply:
% 169.62/25.86 | (7) $false
% 169.62/25.86 |
% 169.62/25.86 | CLOSE: (7) is inconsistent.
% 169.62/25.86 |
% 169.62/25.86 End of proof
% 169.62/25.86
% 169.62/25.86 Sub-proof #317 shows that the following formulas are inconsistent:
% 169.62/25.86 ----------------------------------------------------------------
% 169.62/25.86 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.86 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.86 (2) all_58_2 = e2
% 169.62/25.86 (3) ~ (e3 = e1)
% 169.62/25.86 (4) ~ (e1 = e0)
% 169.62/25.86 (5) op(e2, e3) = all_52_1
% 169.62/25.86 (6) op(e2, e3) = e2
% 169.62/25.86 (7) ~ (e3 = e0)
% 169.62/25.86 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.86 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.86 (9) all_58_0 = e3
% 169.62/25.86 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.86 (11) ~ (e2 = e0)
% 169.62/25.86 (12) all_58_3 = e3
% 169.62/25.86 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.86 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.86 (14) ~ (e2 = e1)
% 169.62/25.86 (15) all_58_0 = e2 & op(e3, e3) = e2
% 169.62/25.86 (16) ~ (e3 = e2)
% 169.62/25.86
% 169.62/25.86 Begin of proof
% 169.62/25.86 |
% 169.62/25.86 | ALPHA: (15) implies:
% 169.62/25.86 | (17) all_58_0 = e2
% 169.62/25.86 |
% 169.62/25.86 | COMBINE_EQS: (9), (17) imply:
% 169.62/25.86 | (18) e3 = e2
% 169.62/25.86 |
% 169.62/25.86 | COMBINE_EQS: (12), (18) imply:
% 169.62/25.86 | (19) all_58_3 = e2
% 169.62/25.86 |
% 169.62/25.86 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (14),
% 169.62/25.86 | (16), (19) are inconsistent by sub-proof #779.
% 169.62/25.86 |
% 169.62/25.86 End of proof
% 169.62/25.86
% 169.62/25.86 Sub-proof #318 shows that the following formulas are inconsistent:
% 169.62/25.86 ----------------------------------------------------------------
% 169.62/25.86 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.62/25.86 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.62/25.86 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.86 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.86 (3) all_58_14 = e2
% 169.62/25.86 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.62/25.86 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.62/25.86 (5) all_58_2 = e2
% 169.62/25.86 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.86 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.62/25.86 (7) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.62/25.86 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.62/25.86 (8) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.62/25.86 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.86 (9) ~ (e3 = e1)
% 169.62/25.86 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.62/25.86 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.62/25.86 e1)
% 169.62/25.86 (11) op(e1, e3) = all_52_2
% 169.62/25.86 (12) ~ (e1 = e0)
% 169.62/25.86 (13) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.62/25.86 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.62/25.86 e3)
% 169.62/25.86 (14) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.62/25.86 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.62/25.86 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.62/25.86 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.62/25.86 (16) op(e2, e3) = all_52_1
% 169.62/25.86 (17) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.62/25.86 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.62/25.86 (18) ~ (all_52_7 = e3)
% 169.62/25.86 (19) op(e2, e3) = e2
% 169.62/25.86 (20) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.62/25.86 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.62/25.86 (21) ~ (e3 = e0)
% 169.62/25.86 (22) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.86 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.86 (23) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.62/25.86 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.62/25.86 (24) all_58_11 = e3
% 169.62/25.86 (25) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.86 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.62/25.86 (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.62/25.86 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.62/25.86 (27) all_58_4 = e3
% 169.62/25.86 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.86 (29) ~ (e2 = e0)
% 169.62/25.86 (30) all_58_3 = e3
% 169.62/25.86 (31) op(e3, e3) = e3
% 169.62/25.86 (32) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.86 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.86 (33) ~ (e2 = e1)
% 169.62/25.86 (34) op(e0, e2) = all_52_7
% 169.62/25.86 (35) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.62/25.86 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.62/25.86 (36) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.62/25.86 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.62/25.86 (37) op(e1, e3) = e1
% 169.62/25.86 (38) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.86 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.86 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.86 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.86 (39) ~ (e3 = e2)
% 169.62/25.86
% 169.62/25.86 Begin of proof
% 169.62/25.86 |
% 169.62/25.86 | BETA: splitting (13) gives:
% 169.62/25.86 |
% 169.62/25.86 | Case 1:
% 169.62/25.86 | |
% 169.62/25.86 | | (40) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 169.62/25.86 | | e3)
% 169.62/25.86 | |
% 169.62/25.86 | | BETA: splitting (40) gives:
% 169.62/25.86 | |
% 169.62/25.86 | | Case 1:
% 169.62/25.86 | | |
% 169.62/25.86 | | | (41) all_58_12 = e3 & op(e0, e3) = e3
% 169.62/25.86 | | |
% 169.62/25.86 | | | ALPHA: (41) implies:
% 169.62/25.86 | | | (42) all_58_12 = e3
% 169.62/25.86 | | |
% 169.62/25.86 | | | BETA: splitting (7) gives:
% 169.62/25.86 | | |
% 169.62/25.86 | | | Case 1:
% 169.62/25.86 | | | |
% 169.62/25.86 | | | | (43) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 169.62/25.86 | | | | = e2)
% 169.62/25.86 | | | |
% 169.62/25.86 | | | | BETA: splitting (43) gives:
% 169.62/25.86 | | | |
% 169.62/25.86 | | | | Case 1:
% 169.62/25.86 | | | | |
% 169.62/25.86 | | | | | (44) all_58_6 = e2 & op(e1, e3) = e2
% 169.62/25.86 | | | | |
% 169.62/25.86 | | | | | ALPHA: (44) implies:
% 169.62/25.86 | | | | | (45) all_58_6 = e2
% 169.62/25.86 | | | | |
% 169.62/25.86 | | | | | REF_CLOSE: (4), (9), (12), (16), (19), (20), (21), (28), (29), (33),
% 169.62/25.86 | | | | | (42), (45) are inconsistent by sub-proof #329.
% 169.62/25.86 | | | | |
% 169.62/25.86 | | | | Case 2:
% 169.62/25.86 | | | | |
% 169.62/25.86 | | | | | (46) all_58_7 = e2 & op(e1, e2) = e2
% 169.62/25.86 | | | | |
% 169.62/25.86 | | | | | ALPHA: (46) implies:
% 169.62/25.86 | | | | | (47) all_58_7 = e2
% 169.62/25.86 | | | | |
% 169.62/25.86 | | | | | BETA: splitting (15) gives:
% 169.62/25.86 | | | | |
% 169.62/25.86 | | | | | Case 1:
% 169.62/25.86 | | | | | |
% 169.62/25.86 | | | | | | (48) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 169.62/25.86 | | | | | | e0) = e2)
% 169.62/25.86 | | | | | |
% 169.62/25.86 | | | | | | BETA: splitting (48) gives:
% 169.62/25.86 | | | | | |
% 169.62/25.86 | | | | | | Case 1:
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | (49) all_58_9 = e2 & op(e3, e0) = e2
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | ALPHA: (49) implies:
% 169.62/25.86 | | | | | | | (50) all_58_9 = e2
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | BETA: splitting (36) gives:
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | (51) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 &
% 169.62/25.86 | | | | | | | | op(e2, e1) = e1)
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | BETA: splitting (51) gives:
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | (52) all_58_4 = e1 & op(e3, e1) = e1
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | ALPHA: (52) implies:
% 169.62/25.86 | | | | | | | | | (53) all_58_4 = e1
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | REF_CLOSE: (9), (27), (53) are inconsistent by sub-proof #767.
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | (54) all_58_5 = e1 & op(e2, e1) = e1
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | ALPHA: (54) implies:
% 169.62/25.86 | | | | | | | | | (55) all_58_5 = e1
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | BETA: splitting (8) gives:
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | (56) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 &
% 169.62/25.86 | | | | | | | | | | op(e3, e2) = e0)
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | BETA: splitting (56) gives:
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | (57) all_58_0 = e0 & op(e3, e3) = e0
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | ALPHA: (57) implies:
% 169.62/25.86 | | | | | | | | | | | (58) op(e3, e3) = e0
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | REF_CLOSE: (21), (28), (31), (58) are inconsistent by
% 169.62/25.86 | | | | | | | | | | | sub-proof #949.
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | (59) all_58_1 = e0 & op(e3, e2) = e0
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | ALPHA: (59) implies:
% 169.62/25.86 | | | | | | | | | | | (60) all_58_1 = e0
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | BETA: splitting (1) gives:
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | (61) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 169.62/25.86 | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 169.62/25.86 | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | BETA: splitting (61) gives:
% 169.62/25.86 | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | (62) all_58_9 = e1 & op(e3, e0) = e1
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | REF_CLOSE: (33), (50), (62) are inconsistent by sub-proof
% 169.62/25.86 | | | | | | | | | | | | | #701.
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | (63) all_58_10 = e1 & op(e2, e0) = e1
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | ALPHA: (63) implies:
% 169.62/25.86 | | | | | | | | | | | | | (64) all_58_10 = e1
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | BETA: splitting (6) gives:
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | (65) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 169.62/25.86 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 169.62/25.86 | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 169.62/25.86 | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | | (66) all_58_1 = e1 & op(e3, e2) = e1
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | | REF_CLOSE: (12), (60), (66) are inconsistent by sub-proof
% 169.62/25.86 | | | | | | | | | | | | | | | #658.
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | | (67) all_58_3 = e1 & op(e2, e2) = e1
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | | ALPHA: (67) implies:
% 169.62/25.86 | | | | | | | | | | | | | | | (68) all_58_3 = e1
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | | REF_CLOSE: (9), (30), (68) are inconsistent by sub-proof
% 169.62/25.86 | | | | | | | | | | | | | | | #328.
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | End of split
% 169.62/25.86 | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | (69) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 169.62/25.86 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 169.62/25.86 | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 169.62/25.86 | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | | (70) all_58_7 = e1 & op(e1, e2) = e1
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | | ALPHA: (70) implies:
% 169.62/25.86 | | | | | | | | | | | | | | | (71) all_58_7 = e1
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | | REF_CLOSE: (33), (47), (71) are inconsistent by sub-proof
% 169.62/25.86 | | | | | | | | | | | | | | | #494.
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | | (72) all_58_13 = e1 & op(e0, e2) = e1
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (9), (12), (13), (16), (18), (19),
% 169.62/25.86 | | | | | | | | | | | | | | | (21), (22), (28), (29), (30), (32), (33), (34),
% 169.62/25.86 | | | | | | | | | | | | | | | (38), (39), (42), (55), (64), (72) are
% 169.62/25.86 | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 169.62/25.86 | | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | | End of split
% 169.62/25.86 | | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | End of split
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | End of split
% 169.62/25.86 | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | (73) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 169.62/25.86 | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.62/25.86 | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | BETA: splitting (73) gives:
% 169.62/25.86 | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | (74) all_58_11 = e1 & op(e1, e0) = e1
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | REF_CLOSE: (9), (24), (74) are inconsistent by sub-proof
% 169.62/25.86 | | | | | | | | | | | | | #721.
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | (75) all_58_15 = e1 & op(e0, e0) = e1
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | ALPHA: (75) implies:
% 169.62/25.86 | | | | | | | | | | | | | (76) all_58_15 = e1
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (6), (9), (12), (13), (16), (19),
% 169.62/25.86 | | | | | | | | | | | | | (21), (22), (28), (29), (30), (32), (33), (38),
% 169.62/25.86 | | | | | | | | | | | | | (39), (42), (47), (60), (76) are inconsistent by
% 169.62/25.86 | | | | | | | | | | | | | sub-proof #352.
% 169.62/25.86 | | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | | End of split
% 169.62/25.86 | | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | End of split
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | End of split
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | (77) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 &
% 169.62/25.86 | | | | | | | | | | op(e3, e0) = e0)
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | BETA: splitting (77) gives:
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | (78) all_58_4 = e0 & op(e3, e1) = e0
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | ALPHA: (78) implies:
% 169.62/25.86 | | | | | | | | | | | (79) all_58_4 = e0
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | REF_CLOSE: (21), (27), (79) are inconsistent by sub-proof
% 169.62/25.86 | | | | | | | | | | | #894.
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | (80) all_58_9 = e0 & op(e3, e0) = e0
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | ALPHA: (80) implies:
% 169.62/25.86 | | | | | | | | | | | (81) all_58_9 = e0
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | REF_CLOSE: (29), (50), (81) are inconsistent by sub-proof
% 169.62/25.86 | | | | | | | | | | | #945.
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | End of split
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | End of split
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | End of split
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | (82) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 &
% 169.62/25.86 | | | | | | | | op(e0, e1) = e1)
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | BETA: splitting (82) gives:
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | (83) all_58_8 = e1 & op(e1, e1) = e1
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | ALPHA: (83) implies:
% 169.62/25.86 | | | | | | | | | (84) all_58_8 = e1
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | REF_CLOSE: (11), (12), (21), (23), (24), (28), (29), (37),
% 169.62/25.86 | | | | | | | | | (47), (84) are inconsistent by sub-proof #325.
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | (85) all_58_14 = e1 & op(e0, e1) = e1
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | REF_CLOSE: (3), (33), (85) are inconsistent by sub-proof #396.
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | End of split
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | End of split
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | Case 2:
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | (86) all_58_10 = e2 & op(e2, e0) = e2
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | REF_CLOSE: (2), (9), (12), (16), (19), (21), (22), (28), (29),
% 169.62/25.86 | | | | | | | (30), (33), (86) are inconsistent by sub-proof #447.
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | End of split
% 169.62/25.86 | | | | | |
% 169.62/25.86 | | | | | Case 2:
% 169.62/25.86 | | | | | |
% 169.62/25.86 | | | | | | (87) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 169.62/25.86 | | | | | | op(e0, e0) = e2)
% 169.62/25.86 | | | | | |
% 169.62/25.86 | | | | | | BETA: splitting (87) gives:
% 169.62/25.86 | | | | | |
% 169.62/25.86 | | | | | | Case 1:
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | (88) all_58_11 = e2 & op(e1, e0) = e2
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | ALPHA: (88) implies:
% 169.62/25.86 | | | | | | | (89) all_58_11 = e2
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | REF_CLOSE: (2), (5), (9), (12), (16), (19), (21), (22), (24),
% 169.62/25.86 | | | | | | | (28), (29), (30), (32), (33), (39), (89) are
% 169.62/25.86 | | | | | | | inconsistent by sub-proof #421.
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | Case 2:
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | (90) all_58_15 = e2 & op(e0, e0) = e2
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | ALPHA: (90) implies:
% 169.62/25.86 | | | | | | | (91) all_58_15 = e2
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | BETA: splitting (38) gives:
% 169.62/25.86 | | | | | | |
% 169.62/25.86 | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | (92) all_58_15 = e0 & op(e0, e0) = e0
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | REF_CLOSE: (29), (91), (92) are inconsistent by sub-proof #874.
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | (93) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 &
% 169.62/25.86 | | | | | | | | op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 169.62/25.86 | | | | | | | | e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 169.62/25.86 | | | | | | | | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 &
% 169.62/25.86 | | | | | | | | op(e0, e1) = e0))
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | ALPHA: (93) implies:
% 169.62/25.86 | | | | | | | | (94) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.86 | | | | | | | | op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | BETA: splitting (23) gives:
% 169.62/25.86 | | | | | | | |
% 169.62/25.86 | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | (95) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 169.62/25.86 | | | | | | | | | op(e1, e2) = e0)
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | REF_CLOSE: (11), (12), (28), (29), (37), (47), (95) are
% 169.62/25.86 | | | | | | | | | inconsistent by sub-proof #326.
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | Case 2:
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | (96) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 169.62/25.86 | | | | | | | | | op(e1, e0) = e0)
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | BETA: splitting (96) gives:
% 169.62/25.86 | | | | | | | | |
% 169.62/25.86 | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | (97) all_58_8 = e0 & op(e1, e1) = e0
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | ALPHA: (97) implies:
% 169.62/25.86 | | | | | | | | | | (98) all_58_8 = e0
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | BETA: splitting (36) gives:
% 169.62/25.86 | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | Case 1:
% 169.62/25.86 | | | | | | | | | | |
% 169.62/25.86 | | | | | | | | | | | (99) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 169.62/25.86 | | | | | | | | | | | & op(e2, e1) = e1)
% 169.62/25.87 | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | BETA: splitting (99) gives:
% 169.62/25.87 | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | (100) all_58_4 = e1 & op(e3, e1) = e1
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | ALPHA: (100) implies:
% 169.62/25.87 | | | | | | | | | | | | (101) all_58_4 = e1
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | REF_CLOSE: (9), (27), (101) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | #767.
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | (102) all_58_5 = e1 & op(e2, e1) = e1
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | ALPHA: (102) implies:
% 169.62/25.87 | | | | | | | | | | | | (103) all_58_5 = e1
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | BETA: splitting (10) gives:
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | (104) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 169.62/25.87 | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 169.62/25.87 | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | BETA: splitting (104) gives:
% 169.62/25.87 | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | (105) all_58_12 = e1 & op(e0, e3) = e1
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | REF_CLOSE: (9), (42), (105) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | | | #651.
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | (106) all_58_13 = e1 & op(e0, e2) = e1
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | ALPHA: (106) implies:
% 169.62/25.87 | | | | | | | | | | | | | | (107) all_58_13 = e1
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | (108) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 169.62/25.87 | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 169.62/25.87 | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 169.62/25.87 | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | (109) all_58_0 = e0 & op(e3, e3) = e0
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | (110) all_58_0 = e0
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | (111) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 169.62/25.87 | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 169.62/25.87 | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 169.62/25.87 | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | (112) all_58_1 = e0 & op(e3, e2) = e0
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | (113) all_58_1 = e0
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | (114) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 169.62/25.87 | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | (115) all_58_0 = e1 & op(e3, e3) = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | (116) all_58_0 = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (12), (16), (19), (21), (28), (29),
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | (37), (42), (116) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | #324.
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | (117) all_58_1 = e1 & op(e3, e2) = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (113), (117) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | #658.
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | (118) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 169.62/25.87 | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | (119) all_58_4 = e1 & op(e3, e1) = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | (120) all_58_4 = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (27), (120) imply:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | (121) e3 = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (121) imply:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | (122) all_58_12 = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (29), (94), (107), (122) are
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #530.
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | (123) all_58_9 = e1 & op(e3, e0) = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | (124) all_58_9 = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | (125) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | (126) all_58_0 = e2 & op(e3, e3) = e2
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (110), (126) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | #390.
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | (127) all_58_1 = e2 & op(e3, e2) = e2
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (113), (127) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | #392.
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | (128) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | (129) all_58_4 = e2 & op(e3, e1) = e2
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | (130) all_58_4 = e2
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (9), (12), (14), (17), (21), (29), (39),
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | (103), (130) are inconsistent by sub-proof #321.
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | (131) all_58_9 = e2 & op(e3, e0) = e2
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | (132) all_58_9 = e2
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (132) imply:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | (133) e2 = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | SIMP: (133) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | (134) e2 = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (134) imply:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | (135) all_58_14 = e1
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (21), (42), (94), (107), (135) are
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #581.
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | (136) all_58_3 = e0 & op(e2, e2) = e0
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | (137) all_58_3 = e0
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (30), (137) imply:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | (138) e3 = e0
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | SIMP: (138) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | (139) e3 = e0
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (139) imply:
% 169.62/25.87 | | | | | | | | | | | | | | | | | | (140) all_58_12 = e0
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (9), (12), (13), (16), (18), (19),
% 169.62/25.87 | | | | | | | | | | | | | | | | | | (21), (22), (28), (29), (30), (32), (33), (34),
% 169.62/25.87 | | | | | | | | | | | | | | | | | | (39), (91), (140) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | | | | | | | #358.
% 169.62/25.87 | | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | (141) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 169.62/25.87 | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 169.62/25.87 | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (29), (47), (107), (141) are inconsistent by
% 169.62/25.87 | | | | | | | | | | | | | | | | | sub-proof #376.
% 169.62/25.87 | | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | (142) all_58_2 = e0 & op(e2, e3) = e0
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (19), (28), (29), (142) are inconsistent by
% 169.62/25.87 | | | | | | | | | | | | | | | | sub-proof #782.
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | (143) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 169.62/25.87 | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 169.62/25.87 | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 169.62/25.87 | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | (144) all_58_6 = e0 & op(e1, e3) = e0
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | (145) op(e1, e3) = e0
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (28), (37), (145) are inconsistent by
% 169.62/25.87 | | | | | | | | | | | | | | | | sub-proof #749.
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | (146) all_58_12 = e0 & op(e0, e3) = e0
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 169.62/25.87 | | | | | | | | | | | | | | | | (147) all_58_12 = e0
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (9), (12), (13), (16), (18), (19),
% 169.62/25.87 | | | | | | | | | | | | | | | | (21), (22), (28), (29), (30), (32), (33), (34),
% 169.62/25.87 | | | | | | | | | | | | | | | | (39), (91), (147) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | | | | | #358.
% 169.62/25.87 | | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | (148) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 169.62/25.87 | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.62/25.87 | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | BETA: splitting (148) gives:
% 169.62/25.87 | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | (149) all_58_14 = e1 & op(e0, e1) = e1
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | REF_CLOSE: (3), (33), (149) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | | | #396.
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | (150) all_58_15 = e1 & op(e0, e0) = e1
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | ALPHA: (150) implies:
% 169.62/25.87 | | | | | | | | | | | | | | (151) all_58_15 = e1
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | | REF_CLOSE: (33), (91), (151) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | | | #645.
% 169.62/25.87 | | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | (152) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 169.62/25.87 | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 169.62/25.87 | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | BETA: splitting (152) gives:
% 169.62/25.87 | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | Case 1:
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | (153) all_58_8 = e1 & op(e1, e1) = e1
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | ALPHA: (153) implies:
% 169.62/25.87 | | | | | | | | | | | | (154) all_58_8 = e1
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | REF_CLOSE: (12), (98), (154) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | #818.
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | (155) all_58_14 = e1 & op(e0, e1) = e1
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | | REF_CLOSE: (3), (33), (155) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | | | #396.
% 169.62/25.87 | | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | Case 2:
% 169.62/25.87 | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | (156) all_58_11 = e0 & op(e1, e0) = e0
% 169.62/25.87 | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | ALPHA: (156) implies:
% 169.62/25.87 | | | | | | | | | | (157) all_58_11 = e0
% 169.62/25.87 | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | COMBINE_EQS: (24), (157) imply:
% 169.62/25.87 | | | | | | | | | | (158) e3 = e0
% 169.62/25.87 | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | SIMP: (158) implies:
% 169.62/25.87 | | | | | | | | | | (159) e3 = e0
% 169.62/25.87 | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | COMBINE_EQS: (42), (159) imply:
% 169.62/25.87 | | | | | | | | | | (160) all_58_12 = e0
% 169.62/25.87 | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | | REF_CLOSE: (2), (3), (5), (9), (12), (13), (16), (18), (19),
% 169.62/25.87 | | | | | | | | | | (21), (22), (28), (29), (30), (32), (33), (34),
% 169.62/25.87 | | | | | | | | | | (39), (91), (160) are inconsistent by sub-proof
% 169.62/25.87 | | | | | | | | | | #358.
% 169.62/25.87 | | | | | | | | | |
% 169.62/25.87 | | | | | | | | | End of split
% 169.62/25.87 | | | | | | | | |
% 169.62/25.87 | | | | | | | | End of split
% 169.62/25.87 | | | | | | | |
% 169.62/25.87 | | | | | | | End of split
% 169.62/25.87 | | | | | | |
% 169.62/25.87 | | | | | | End of split
% 169.62/25.87 | | | | | |
% 169.62/25.87 | | | | | End of split
% 169.62/25.87 | | | | |
% 169.62/25.87 | | | | End of split
% 169.62/25.87 | | | |
% 169.62/25.87 | | | Case 2:
% 169.62/25.87 | | | |
% 169.62/25.87 | | | | (161) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 169.62/25.87 | | | | e0) = e2)
% 169.62/25.87 | | | |
% 169.62/25.87 | | | | BETA: splitting (161) gives:
% 169.62/25.87 | | | |
% 169.62/25.87 | | | | Case 1:
% 169.62/25.87 | | | | |
% 169.62/25.87 | | | | | (162) all_58_8 = e2 & op(e1, e1) = e2
% 169.62/25.87 | | | | |
% 169.62/25.87 | | | | | ALPHA: (162) implies:
% 169.62/25.87 | | | | | (163) all_58_8 = e2
% 169.62/25.87 | | | | |
% 169.62/25.87 | | | | | REF_CLOSE: (3), (9), (12), (17), (21), (27), (29), (33), (36), (163)
% 169.62/25.87 | | | | | are inconsistent by sub-proof #395.
% 169.62/25.87 | | | | |
% 169.62/25.87 | | | | Case 2:
% 169.62/25.87 | | | | |
% 169.62/25.87 | | | | | (164) all_58_11 = e2 & op(e1, e0) = e2
% 169.62/25.87 | | | | |
% 169.62/25.87 | | | | | REF_CLOSE: (2), (5), (9), (12), (16), (19), (21), (22), (24), (28),
% 169.62/25.87 | | | | | (29), (30), (32), (33), (39), (164) are inconsistent by
% 169.62/25.87 | | | | | sub-proof #419.
% 169.62/25.87 | | | | |
% 169.62/25.87 | | | | End of split
% 169.62/25.87 | | | |
% 169.62/25.87 | | | End of split
% 169.62/25.87 | | |
% 169.62/25.87 | | Case 2:
% 169.62/25.87 | | |
% 169.62/25.87 | | | (165) all_58_13 = e3 & op(e0, e2) = e3
% 169.62/25.87 | | |
% 169.62/25.87 | | | REF_CLOSE: (18), (28), (34), (165) are inconsistent by sub-proof #962.
% 169.62/25.87 | | |
% 169.62/25.87 | | End of split
% 169.62/25.87 | |
% 169.62/25.87 | Case 2:
% 169.62/25.87 | |
% 169.62/25.87 | | (166) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.62/25.87 | | e3)
% 169.62/25.87 | |
% 169.62/25.87 | | BETA: splitting (166) gives:
% 169.62/25.87 | |
% 169.62/25.87 | | Case 1:
% 169.62/25.87 | | |
% 169.62/25.87 | | | (167) all_58_14 = e3 & op(e0, e1) = e3
% 169.62/25.87 | | |
% 169.62/25.87 | | | REF_CLOSE: (2), (3), (5), (9), (12), (16), (19), (21), (22), (28), (29),
% 169.62/25.87 | | | (30), (32), (33), (39), (167) are inconsistent by sub-proof
% 169.62/25.87 | | | #405.
% 169.62/25.87 | | |
% 169.62/25.87 | | Case 2:
% 169.62/25.87 | | |
% 169.62/25.87 | | | (168) all_58_15 = e3 & op(e0, e0) = e3
% 169.62/25.87 | | |
% 169.62/25.87 | | | ALPHA: (168) implies:
% 169.62/25.87 | | | (169) all_58_15 = e3
% 169.62/25.87 | | |
% 169.62/25.87 | | | REF_CLOSE: (1), (2), (5), (9), (12), (15), (16), (19), (21), (22), (24),
% 169.62/25.87 | | | (28), (29), (30), (32), (33), (38), (39), (169) are
% 169.62/25.87 | | | inconsistent by sub-proof #319.
% 169.62/25.87 | | |
% 169.62/25.87 | | End of split
% 169.62/25.87 | |
% 169.62/25.87 | End of split
% 169.62/25.87 |
% 169.62/25.87 End of proof
% 169.62/25.87
% 169.62/25.87 Sub-proof #319 shows that the following formulas are inconsistent:
% 169.62/25.87 ----------------------------------------------------------------
% 169.62/25.87 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.62/25.87 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.62/25.87 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.87 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.87 (3) all_58_2 = e2
% 169.62/25.87 (4) ~ (e3 = e1)
% 169.62/25.87 (5) ~ (e1 = e0)
% 169.62/25.87 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.62/25.87 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.62/25.87 (7) op(e2, e3) = all_52_1
% 169.62/25.87 (8) op(e2, e3) = e2
% 169.62/25.87 (9) ~ (e3 = e0)
% 169.62/25.87 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.87 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.87 (11) all_58_11 = e3
% 169.62/25.87 (12) all_58_15 = e3
% 169.62/25.87 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.87 (14) ~ (e2 = e0)
% 169.62/25.87 (15) all_58_3 = e3
% 169.62/25.87 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.87 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.87 (17) ~ (e2 = e1)
% 169.62/25.87 (18) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.87 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.87 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.87 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.87 (19) ~ (e3 = e2)
% 169.62/25.87
% 169.62/25.87 Begin of proof
% 169.62/25.87 |
% 169.62/25.87 | BETA: splitting (6) gives:
% 169.62/25.87 |
% 169.62/25.87 | Case 1:
% 169.62/25.87 | |
% 169.62/25.87 | | (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 169.62/25.87 | | e2)
% 169.62/25.87 | |
% 169.62/25.87 | | BETA: splitting (20) gives:
% 169.62/25.87 | |
% 169.62/25.87 | | Case 1:
% 169.62/25.87 | | |
% 169.62/25.87 | | | (21) all_58_9 = e2 & op(e3, e0) = e2
% 169.62/25.87 | | |
% 169.62/25.87 | | | ALPHA: (21) implies:
% 169.62/25.87 | | | (22) all_58_9 = e2
% 169.62/25.87 | | |
% 169.62/25.87 | | | REF_CLOSE: (1), (4), (5), (9), (11), (12), (14), (17), (18), (22) are
% 169.62/25.87 | | | inconsistent by sub-proof #374.
% 169.62/25.87 | | |
% 169.62/25.87 | | Case 2:
% 169.62/25.87 | | |
% 169.62/25.87 | | | (23) all_58_10 = e2 & op(e2, e0) = e2
% 169.62/25.87 | | |
% 169.62/25.87 | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (13), (14), (15), (17),
% 169.62/25.87 | | | (23) are inconsistent by sub-proof #447.
% 169.62/25.87 | | |
% 169.62/25.87 | | End of split
% 169.62/25.87 | |
% 169.62/25.87 | Case 2:
% 169.62/25.87 | |
% 169.62/25.87 | | (24) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.62/25.87 | | e2)
% 169.62/25.87 | |
% 169.62/25.87 | | BETA: splitting (24) gives:
% 169.62/25.87 | |
% 169.62/25.87 | | Case 1:
% 169.62/25.87 | | |
% 169.62/25.87 | | | (25) all_58_11 = e2 & op(e1, e0) = e2
% 169.62/25.87 | | |
% 169.62/25.87 | | | ALPHA: (25) implies:
% 169.62/25.87 | | | (26) all_58_11 = e2
% 169.62/25.87 | | |
% 169.62/25.87 | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 169.62/25.87 | | | (15), (16), (17), (19), (26) are inconsistent by sub-proof
% 169.62/25.87 | | | #421.
% 169.62/25.87 | | |
% 169.62/25.87 | | Case 2:
% 169.62/25.87 | | |
% 169.62/25.87 | | | (27) all_58_15 = e2 & op(e0, e0) = e2
% 169.62/25.87 | | |
% 169.62/25.87 | | | ALPHA: (27) implies:
% 169.62/25.87 | | | (28) all_58_15 = e2
% 169.62/25.87 | | |
% 169.62/25.87 | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 169.62/25.87 | | | (15), (16), (17), (19), (28) are inconsistent by sub-proof
% 169.62/25.87 | | | #320.
% 169.62/25.87 | | |
% 169.62/25.87 | | End of split
% 169.62/25.87 | |
% 169.62/25.87 | End of split
% 169.62/25.87 |
% 169.62/25.87 End of proof
% 169.62/25.87
% 169.62/25.87 Sub-proof #320 shows that the following formulas are inconsistent:
% 169.62/25.87 ----------------------------------------------------------------
% 169.62/25.87 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.87 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.87 (2) all_58_15 = e2
% 169.62/25.87 (3) all_58_2 = e2
% 169.62/25.87 (4) ~ (e3 = e1)
% 169.62/25.87 (5) ~ (e1 = e0)
% 169.62/25.87 (6) op(e2, e3) = all_52_1
% 169.62/25.87 (7) op(e2, e3) = e2
% 169.62/25.87 (8) ~ (e3 = e0)
% 169.62/25.87 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.87 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.87 (10) all_58_15 = e3
% 169.62/25.87 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.87 (12) ~ (e2 = e0)
% 169.62/25.87 (13) all_58_3 = e3
% 169.62/25.87 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.87 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.87 (15) ~ (e2 = e1)
% 169.62/25.87 (16) ~ (e3 = e2)
% 169.62/25.87
% 169.62/25.87 Begin of proof
% 169.62/25.87 |
% 169.62/25.87 | COMBINE_EQS: (2), (10) imply:
% 169.62/25.87 | (17) e3 = e2
% 169.62/25.87 |
% 169.62/25.87 | SIMP: (17) implies:
% 169.62/25.87 | (18) e3 = e2
% 169.62/25.87 |
% 169.62/25.87 | COMBINE_EQS: (13), (18) imply:
% 169.62/25.87 | (19) all_58_3 = e2
% 169.62/25.87 |
% 169.62/25.88 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15),
% 169.62/25.88 | (16), (19) are inconsistent by sub-proof #779.
% 169.62/25.88 |
% 169.62/25.88 End of proof
% 169.62/25.88
% 169.62/25.88 Sub-proof #321 shows that the following formulas are inconsistent:
% 169.62/25.88 ----------------------------------------------------------------
% 169.62/25.88 (1) all_58_14 = e2
% 169.62/25.88 (2) ~ (e3 = e1)
% 169.62/25.88 (3) ~ (e1 = e0)
% 169.62/25.88 (4) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.62/25.88 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.62/25.88 (5) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.62/25.88 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.62/25.88 (6) ~ (e3 = e0)
% 169.62/25.88 (7) ~ (e2 = e0)
% 169.62/25.88 (8) all_58_5 = e1
% 169.62/25.88 (9) all_58_4 = e2
% 169.62/25.88 (10) ~ (e3 = e2)
% 169.62/25.88
% 169.62/25.88 Begin of proof
% 169.62/25.88 |
% 169.62/25.88 | BETA: splitting (4) gives:
% 169.62/25.88 |
% 169.62/25.88 | Case 1:
% 169.62/25.88 | |
% 169.62/25.88 | | (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 169.62/25.88 | | e3)
% 169.62/25.88 | |
% 169.62/25.88 | | REF_CLOSE: (2), (8), (9), (10), (11) are inconsistent by sub-proof #323.
% 169.62/25.88 | |
% 169.62/25.88 | Case 2:
% 169.62/25.88 | |
% 169.62/25.88 | | (12) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 169.62/25.88 | | e3)
% 169.62/25.88 | |
% 169.62/25.88 | | BETA: splitting (12) gives:
% 169.62/25.88 | |
% 169.62/25.88 | | Case 1:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (13) all_58_8 = e3 & op(e1, e1) = e3
% 169.62/25.88 | | |
% 169.62/25.88 | | | ALPHA: (13) implies:
% 169.62/25.88 | | | (14) all_58_8 = e3
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (14) are inconsistent by
% 169.62/25.88 | | | sub-proof #322.
% 169.62/25.88 | | |
% 169.62/25.88 | | Case 2:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (15) all_58_14 = e3 & op(e0, e1) = e3
% 169.62/25.88 | | |
% 169.62/25.88 | | | ALPHA: (15) implies:
% 169.62/25.88 | | | (16) all_58_14 = e3
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (1), (10), (16) are inconsistent by sub-proof #855.
% 169.62/25.88 | | |
% 169.62/25.88 | | End of split
% 169.62/25.88 | |
% 169.62/25.88 | End of split
% 169.62/25.88 |
% 169.62/25.88 End of proof
% 169.62/25.88
% 169.62/25.88 Sub-proof #322 shows that the following formulas are inconsistent:
% 169.62/25.88 ----------------------------------------------------------------
% 169.62/25.88 (1) all_58_14 = e2
% 169.62/25.88 (2) ~ (e1 = e0)
% 169.62/25.88 (3) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.62/25.88 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.62/25.88 (4) ~ (e3 = e0)
% 169.62/25.88 (5) ~ (e2 = e0)
% 169.62/25.88 (6) all_58_8 = e3
% 169.62/25.88 (7) all_58_5 = e1
% 169.62/25.88 (8) all_58_4 = e2
% 169.62/25.88
% 169.62/25.88 Begin of proof
% 169.62/25.88 |
% 169.62/25.88 | BETA: splitting (3) gives:
% 169.62/25.88 |
% 169.62/25.88 | Case 1:
% 169.62/25.88 | |
% 169.62/25.88 | | (9) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 169.62/25.88 | |
% 169.62/25.88 | | BETA: splitting (9) gives:
% 169.62/25.88 | |
% 169.62/25.88 | | Case 1:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (10) all_58_4 = e0 & op(e3, e1) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (5), (8), (10) are inconsistent by sub-proof #902.
% 169.62/25.88 | | |
% 169.62/25.88 | | Case 2:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (11) all_58_5 = e0 & op(e2, e1) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (2), (7), (11) are inconsistent by sub-proof #781.
% 169.62/25.88 | | |
% 169.62/25.88 | | End of split
% 169.62/25.88 | |
% 169.62/25.88 | Case 2:
% 169.62/25.88 | |
% 169.62/25.88 | | (12) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 169.62/25.88 | | e0)
% 169.62/25.88 | |
% 169.62/25.88 | | BETA: splitting (12) gives:
% 169.62/25.88 | |
% 169.62/25.88 | | Case 1:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (13) all_58_8 = e0 & op(e1, e1) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | ALPHA: (13) implies:
% 169.62/25.88 | | | (14) all_58_8 = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (4), (6), (14) are inconsistent by sub-proof #480.
% 169.62/25.88 | | |
% 169.62/25.88 | | Case 2:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (15) all_58_14 = e0 & op(e0, e1) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (1), (5), (15) are inconsistent by sub-proof #858.
% 169.62/25.88 | | |
% 169.62/25.88 | | End of split
% 169.62/25.88 | |
% 169.62/25.88 | End of split
% 169.62/25.88 |
% 169.62/25.88 End of proof
% 169.62/25.88
% 169.62/25.88 Sub-proof #323 shows that the following formulas are inconsistent:
% 169.62/25.88 ----------------------------------------------------------------
% 169.62/25.88 (1) ~ (e3 = e1)
% 169.62/25.88 (2) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 169.62/25.88 (3) all_58_5 = e1
% 169.62/25.88 (4) all_58_4 = e2
% 169.62/25.88 (5) ~ (e3 = e2)
% 169.62/25.88
% 169.62/25.88 Begin of proof
% 169.62/25.88 |
% 169.62/25.88 | BETA: splitting (2) gives:
% 169.62/25.88 |
% 169.62/25.88 | Case 1:
% 169.62/25.88 | |
% 169.62/25.88 | | (6) all_58_4 = e3 & op(e3, e1) = e3
% 169.62/25.88 | |
% 169.62/25.88 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #952.
% 169.62/25.88 | |
% 169.62/25.88 | Case 2:
% 169.62/25.88 | |
% 169.62/25.88 | | (7) all_58_5 = e3 & op(e2, e1) = e3
% 169.62/25.88 | |
% 169.62/25.88 | | ALPHA: (7) implies:
% 169.62/25.88 | | (8) all_58_5 = e3
% 169.62/25.88 | |
% 169.62/25.88 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #920.
% 169.62/25.88 | |
% 169.62/25.88 | End of split
% 169.62/25.88 |
% 169.62/25.88 End of proof
% 169.62/25.88
% 169.62/25.88 Sub-proof #324 shows that the following formulas are inconsistent:
% 169.62/25.88 ----------------------------------------------------------------
% 169.62/25.88 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.62/25.88 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.62/25.88 (2) all_58_0 = e1
% 169.62/25.88 (3) op(e1, e3) = all_52_2
% 169.62/25.88 (4) ~ (e1 = e0)
% 169.62/25.88 (5) op(e2, e3) = all_52_1
% 169.62/25.88 (6) op(e2, e3) = e2
% 169.62/25.88 (7) ~ (e3 = e0)
% 169.62/25.88 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.88 (9) ~ (e2 = e0)
% 169.62/25.88 (10) all_58_12 = e3
% 169.62/25.88 (11) op(e1, e3) = e1
% 169.62/25.88
% 169.62/25.88 Begin of proof
% 169.62/25.88 |
% 169.62/25.88 | BETA: splitting (1) gives:
% 169.62/25.88 |
% 169.62/25.88 | Case 1:
% 169.62/25.88 | |
% 169.62/25.88 | | (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.62/25.88 | | e0)
% 169.62/25.88 | |
% 169.62/25.88 | | BETA: splitting (12) gives:
% 169.62/25.88 | |
% 169.62/25.88 | | Case 1:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (13) all_58_0 = e0 & op(e3, e3) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (2), (4), (13) are inconsistent by sub-proof #903.
% 169.62/25.88 | | |
% 169.62/25.88 | | Case 2:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (14) all_58_2 = e0 & op(e2, e3) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (5), (6), (8), (9), (14) are inconsistent by sub-proof #782.
% 169.62/25.88 | | |
% 169.62/25.88 | | End of split
% 169.62/25.88 | |
% 169.62/25.88 | Case 2:
% 169.62/25.88 | |
% 169.62/25.88 | | (15) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.62/25.88 | | e0)
% 169.62/25.88 | |
% 169.62/25.88 | | BETA: splitting (15) gives:
% 169.62/25.88 | |
% 169.62/25.88 | | Case 1:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (16) all_58_6 = e0 & op(e1, e3) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | ALPHA: (16) implies:
% 169.62/25.88 | | | (17) op(e1, e3) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (3), (4), (8), (11), (17) are inconsistent by sub-proof #749.
% 169.62/25.88 | | |
% 169.62/25.88 | | Case 2:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (18) all_58_12 = e0 & op(e0, e3) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | ALPHA: (18) implies:
% 169.62/25.88 | | | (19) all_58_12 = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (7), (10), (19) are inconsistent by sub-proof #608.
% 169.62/25.88 | | |
% 169.62/25.88 | | End of split
% 169.62/25.88 | |
% 169.62/25.88 | End of split
% 169.62/25.88 |
% 169.62/25.88 End of proof
% 169.62/25.88
% 169.62/25.88 Sub-proof #325 shows that the following formulas are inconsistent:
% 169.62/25.88 ----------------------------------------------------------------
% 169.62/25.88 (1) all_58_7 = e2
% 169.62/25.88 (2) all_58_8 = e1
% 169.62/25.88 (3) op(e1, e3) = all_52_2
% 169.62/25.88 (4) ~ (e1 = e0)
% 169.62/25.88 (5) ~ (e3 = e0)
% 169.62/25.88 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.62/25.88 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.62/25.88 (7) all_58_11 = e3
% 169.62/25.88 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.88 (9) ~ (e2 = e0)
% 169.62/25.88 (10) op(e1, e3) = e1
% 169.62/25.88
% 169.62/25.88 Begin of proof
% 169.62/25.88 |
% 169.62/25.88 | BETA: splitting (6) gives:
% 169.62/25.88 |
% 169.62/25.88 | Case 1:
% 169.62/25.88 | |
% 169.62/25.88 | | (11) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 169.62/25.88 | | e0)
% 169.62/25.88 | |
% 169.62/25.88 | | REF_CLOSE: (1), (3), (4), (8), (9), (10), (11) are inconsistent by sub-proof
% 169.62/25.88 | | #326.
% 169.62/25.88 | |
% 169.62/25.88 | Case 2:
% 169.62/25.88 | |
% 169.62/25.88 | | (12) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 169.62/25.88 | | e0)
% 169.62/25.88 | |
% 169.62/25.88 | | BETA: splitting (12) gives:
% 169.62/25.88 | |
% 169.62/25.88 | | Case 1:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (13) all_58_8 = e0 & op(e1, e1) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | ALPHA: (13) implies:
% 169.62/25.88 | | | (14) all_58_8 = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #818.
% 169.62/25.88 | | |
% 169.62/25.88 | | Case 2:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (15) all_58_11 = e0 & op(e1, e0) = e0
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (5), (7), (15) are inconsistent by sub-proof #724.
% 169.62/25.88 | | |
% 169.62/25.88 | | End of split
% 169.62/25.88 | |
% 169.62/25.88 | End of split
% 169.62/25.88 |
% 169.62/25.88 End of proof
% 169.62/25.88
% 169.62/25.88 Sub-proof #326 shows that the following formulas are inconsistent:
% 169.62/25.88 ----------------------------------------------------------------
% 169.62/25.88 (1) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 169.62/25.88 (2) all_58_7 = e2
% 169.62/25.88 (3) op(e1, e3) = all_52_2
% 169.62/25.88 (4) ~ (e1 = e0)
% 169.62/25.88 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.88 (6) ~ (e2 = e0)
% 169.62/25.88 (7) op(e1, e3) = e1
% 169.62/25.88
% 169.62/25.88 Begin of proof
% 169.62/25.88 |
% 169.62/25.88 | BETA: splitting (1) gives:
% 169.62/25.88 |
% 169.62/25.88 | Case 1:
% 169.62/25.88 | |
% 169.62/25.88 | | (8) all_58_6 = e0 & op(e1, e3) = e0
% 169.62/25.88 | |
% 169.62/25.88 | | ALPHA: (8) implies:
% 169.62/25.88 | | (9) op(e1, e3) = e0
% 169.62/25.88 | |
% 169.62/25.88 | | REF_CLOSE: (3), (4), (5), (7), (9) are inconsistent by sub-proof #749.
% 169.62/25.88 | |
% 169.62/25.88 | Case 2:
% 169.62/25.88 | |
% 169.62/25.88 | | (10) all_58_7 = e0 & op(e1, e2) = e0
% 169.62/25.88 | |
% 169.62/25.88 | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #363.
% 169.62/25.88 | |
% 169.62/25.88 | End of split
% 169.62/25.88 |
% 169.62/25.88 End of proof
% 169.62/25.88
% 169.62/25.88 Sub-proof #327 shows that the following formulas are inconsistent:
% 169.62/25.88 ----------------------------------------------------------------
% 169.62/25.88 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.88 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.88 (2) all_58_14 = e2
% 169.62/25.88 (3) all_58_2 = e2
% 169.62/25.88 (4) ~ (e3 = e1)
% 169.62/25.88 (5) ~ (e1 = e0)
% 169.62/25.88 (6) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.62/25.88 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.62/25.88 (7) op(e2, e3) = all_52_1
% 169.62/25.88 (8) all_58_13 = e1 & op(e0, e2) = e1
% 169.62/25.88 (9) ~ (all_52_7 = e3)
% 169.62/25.88 (10) op(e2, e3) = e2
% 169.62/25.88 (11) ~ (e3 = e0)
% 169.62/25.88 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.88 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.88 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.88 (14) ~ (e2 = e0)
% 169.62/25.88 (15) all_58_5 = e1
% 169.62/25.88 (16) all_58_12 = e3
% 169.62/25.88 (17) all_58_3 = e3
% 169.62/25.88 (18) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.88 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.88 (19) ~ (e2 = e1)
% 169.62/25.88 (20) all_58_10 = e1
% 169.62/25.88 (21) op(e0, e2) = all_52_7
% 169.62/25.88 (22) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.88 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.88 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.88 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.88 (23) ~ (e3 = e2)
% 169.62/25.88
% 169.62/25.88 Begin of proof
% 169.62/25.88 |
% 169.62/25.88 | ALPHA: (8) implies:
% 169.62/25.88 | (24) all_58_13 = e1
% 169.62/25.88 |
% 169.62/25.88 | BETA: splitting (22) gives:
% 169.62/25.88 |
% 169.62/25.88 | Case 1:
% 169.62/25.88 | |
% 169.62/25.88 | | (25) all_58_15 = e0 & op(e0, e0) = e0
% 169.62/25.88 | |
% 169.62/25.88 | | ALPHA: (25) implies:
% 169.62/25.88 | | (26) all_58_15 = e0
% 169.62/25.88 | |
% 169.62/25.88 | | BETA: splitting (12) gives:
% 169.62/25.88 | |
% 169.62/25.88 | | Case 1:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (27) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 169.62/25.88 | | | e0)
% 169.62/25.88 | | |
% 169.62/25.88 | | | BETA: splitting (27) gives:
% 169.62/25.88 | | |
% 169.62/25.88 | | | Case 1:
% 169.62/25.88 | | | |
% 169.62/25.88 | | | | (28) all_58_2 = e0 & op(e2, e3) = e0
% 169.62/25.88 | | | |
% 169.62/25.88 | | | | REF_CLOSE: (7), (10), (13), (14), (28) are inconsistent by sub-proof
% 169.62/25.88 | | | | #782.
% 169.62/25.88 | | | |
% 169.62/25.88 | | | Case 2:
% 169.62/25.88 | | | |
% 169.62/25.88 | | | | (29) all_58_3 = e0 & op(e2, e2) = e0
% 169.62/25.88 | | | |
% 169.62/25.88 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 169.62/25.88 | | | | (13), (14), (16), (17), (18), (19), (21), (23), (26), (29)
% 169.62/25.88 | | | | are inconsistent by sub-proof #377.
% 169.62/25.88 | | | |
% 169.62/25.88 | | | End of split
% 169.62/25.88 | | |
% 169.62/25.88 | | Case 2:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (30) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 169.62/25.88 | | | e0)
% 169.62/25.88 | | |
% 169.62/25.88 | | | BETA: splitting (30) gives:
% 169.62/25.88 | | |
% 169.62/25.88 | | | Case 1:
% 169.62/25.88 | | | |
% 169.62/25.88 | | | | (31) all_58_5 = e0 & op(e2, e1) = e0
% 169.62/25.88 | | | |
% 169.62/25.88 | | | | REF_CLOSE: (5), (15), (31) are inconsistent by sub-proof #781.
% 169.62/25.88 | | | |
% 169.62/25.88 | | | Case 2:
% 169.62/25.88 | | | |
% 169.62/25.88 | | | | (32) all_58_10 = e0 & op(e2, e0) = e0
% 169.62/25.88 | | | |
% 169.62/25.88 | | | | REF_CLOSE: (5), (20), (32) are inconsistent by sub-proof #925.
% 169.62/25.88 | | | |
% 169.62/25.88 | | | End of split
% 169.62/25.88 | | |
% 169.62/25.88 | | End of split
% 169.62/25.88 | |
% 169.62/25.88 | Case 2:
% 169.62/25.88 | |
% 169.62/25.88 | | (33) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 169.62/25.88 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 169.62/25.88 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 169.62/25.88 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.62/25.88 | |
% 169.62/25.88 | | ALPHA: (33) implies:
% 169.62/25.88 | | (34) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.62/25.88 | | e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.62/25.88 | |
% 169.62/25.88 | | REF_CLOSE: (2), (5), (11), (14), (16), (24), (34) are inconsistent by
% 169.62/25.88 | | sub-proof #545.
% 169.62/25.88 | |
% 169.62/25.88 | End of split
% 169.62/25.88 |
% 169.62/25.88 End of proof
% 169.62/25.88
% 169.62/25.88 Sub-proof #328 shows that the following formulas are inconsistent:
% 169.62/25.88 ----------------------------------------------------------------
% 169.62/25.88 (1) all_58_3 = e3
% 169.62/25.88 (2) all_58_3 = e1
% 169.62/25.88 (3) ~ (e3 = e1)
% 169.62/25.88
% 169.62/25.88 Begin of proof
% 169.62/25.88 |
% 169.62/25.88 | COMBINE_EQS: (1), (2) imply:
% 169.62/25.88 | (4) e3 = e1
% 169.62/25.88 |
% 169.62/25.88 | SIMP: (4) implies:
% 169.62/25.88 | (5) e3 = e1
% 169.62/25.88 |
% 169.62/25.88 | REDUCE: (3), (5) imply:
% 169.62/25.88 | (6) $false
% 169.62/25.88 |
% 169.62/25.88 | CLOSE: (6) is inconsistent.
% 169.62/25.88 |
% 169.62/25.88 End of proof
% 169.62/25.88
% 169.62/25.88 Sub-proof #329 shows that the following formulas are inconsistent:
% 169.62/25.88 ----------------------------------------------------------------
% 169.62/25.88 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.62/25.88 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.62/25.88 (2) ~ (e3 = e1)
% 169.62/25.88 (3) ~ (e1 = e0)
% 169.62/25.88 (4) op(e2, e3) = all_52_1
% 169.62/25.88 (5) all_58_6 = e2
% 169.62/25.88 (6) op(e2, e3) = e2
% 169.62/25.88 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.62/25.88 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.62/25.88 (8) ~ (e3 = e0)
% 169.62/25.88 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.88 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.88 (10) ~ (e2 = e0)
% 169.62/25.88 (11) all_58_12 = e3
% 169.62/25.88 (12) ~ (e2 = e1)
% 169.62/25.88
% 169.62/25.88 Begin of proof
% 169.62/25.88 |
% 169.62/25.88 | BETA: splitting (7) gives:
% 169.62/25.88 |
% 169.62/25.88 | Case 1:
% 169.62/25.88 | |
% 169.62/25.88 | | (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 169.62/25.88 | | e1)
% 169.62/25.88 | |
% 169.62/25.88 | | BETA: splitting (13) gives:
% 169.62/25.88 | |
% 169.62/25.88 | | Case 1:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (14) all_58_0 = e1 & op(e3, e3) = e1
% 169.62/25.88 | | |
% 169.62/25.88 | | | ALPHA: (14) implies:
% 169.62/25.88 | | | (15) all_58_0 = e1
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (15) are
% 169.62/25.88 | | | inconsistent by sub-proof #401.
% 169.62/25.88 | | |
% 169.62/25.88 | | Case 2:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (16) all_58_2 = e1 & op(e2, e3) = e1
% 169.62/25.88 | | |
% 169.62/25.88 | | | ALPHA: (16) implies:
% 169.62/25.88 | | | (17) op(e2, e3) = e1
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (4), (6), (9), (12), (17) are inconsistent by sub-proof #784.
% 169.62/25.88 | | |
% 169.62/25.88 | | End of split
% 169.62/25.88 | |
% 169.62/25.88 | Case 2:
% 169.62/25.88 | |
% 169.62/25.88 | | (18) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 169.62/25.88 | | e1)
% 169.62/25.88 | |
% 169.62/25.88 | | BETA: splitting (18) gives:
% 169.62/25.88 | |
% 169.62/25.88 | | Case 1:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (19) all_58_6 = e1 & op(e1, e3) = e1
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (5), (12), (19) are inconsistent by sub-proof #774.
% 169.62/25.88 | | |
% 169.62/25.88 | | Case 2:
% 169.62/25.88 | | |
% 169.62/25.88 | | | (20) all_58_12 = e1 & op(e0, e3) = e1
% 169.62/25.88 | | |
% 169.62/25.88 | | | ALPHA: (20) implies:
% 169.62/25.88 | | | (21) all_58_12 = e1
% 169.62/25.88 | | |
% 169.62/25.88 | | | REF_CLOSE: (2), (11), (21) are inconsistent by sub-proof #600.
% 169.62/25.88 | | |
% 169.62/25.88 | | End of split
% 169.62/25.88 | |
% 169.62/25.88 | End of split
% 169.62/25.88 |
% 169.62/25.88 End of proof
% 169.62/25.88
% 169.62/25.88 Sub-proof #330 shows that the following formulas are inconsistent:
% 169.62/25.88 ----------------------------------------------------------------
% 169.62/25.88 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.88 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.88 (2) all_58_14 = e2
% 169.62/25.88 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.62/25.88 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.62/25.88 (4) all_58_2 = e2
% 169.62/25.88 (5) ~ (e3 = e1)
% 169.62/25.88 (6) all_58_6 = e3
% 169.62/25.88 (7) op(e1, e3) = all_52_2
% 169.62/25.88 (8) ~ (e1 = e0)
% 169.62/25.88 (9) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.62/25.88 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.62/25.88 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.62/25.88 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.62/25.88 (11) op(e2, e3) = all_52_1
% 169.62/25.89 (12) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.62/25.89 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.62/25.89 (13) ~ (all_52_7 = e3)
% 169.62/25.89 (14) op(e2, e3) = e2
% 169.62/25.89 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.62/25.89 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.62/25.89 (16) ~ (e3 = e0)
% 169.62/25.89 (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.89 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.89 (18) all_58_4 = e3
% 169.62/25.89 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.89 (20) ~ (e2 = e0)
% 169.62/25.89 (21) all_58_15 = e3 & op(e0, e0) = e3
% 169.62/25.89 (22) op(e1, e3) = e3
% 169.62/25.89 (23) all_58_3 = e3
% 169.62/25.89 (24) op(e3, e3) = e3
% 169.62/25.89 (25) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.89 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.89 (26) ~ (e2 = e1)
% 169.62/25.89 (27) op(e0, e2) = all_52_7
% 169.62/25.89 (28) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.62/25.89 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.62/25.89 (29) op(e1, e3) = e1
% 169.62/25.89 (30) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.89 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.89 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.89 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.89 (31) ~ (e3 = e2)
% 169.62/25.89
% 169.62/25.89 Begin of proof
% 169.62/25.89 |
% 169.62/25.89 | ALPHA: (21) implies:
% 169.62/25.89 | (32) all_58_15 = e3
% 169.62/25.89 |
% 169.62/25.89 | BETA: splitting (28) gives:
% 169.62/25.89 |
% 169.62/25.89 | Case 1:
% 169.62/25.89 | |
% 169.62/25.89 | | (33) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 169.62/25.89 | | e1)
% 169.62/25.89 | |
% 169.62/25.89 | | BETA: splitting (33) gives:
% 169.62/25.89 | |
% 169.62/25.89 | | Case 1:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (34) all_58_4 = e1 & op(e3, e1) = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (34) implies:
% 169.62/25.89 | | | (35) all_58_4 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | COMBINE_EQS: (18), (35) imply:
% 169.62/25.89 | | | (36) e3 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | SIMP: (36) implies:
% 169.62/25.89 | | | (37) e3 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | COMBINE_EQS: (32), (37) imply:
% 169.62/25.89 | | | (38) all_58_15 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 169.62/25.89 | | | (15), (16), (17), (19), (20), (23), (25), (26), (27), (30),
% 169.62/25.89 | | | (31), (38) are inconsistent by sub-proof #361.
% 169.62/25.89 | | |
% 169.62/25.89 | | Case 2:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (39) all_58_5 = e1 & op(e2, e1) = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (39) implies:
% 169.62/25.89 | | | (40) all_58_5 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 169.62/25.89 | | | (14), (15), (16), (17), (19), (20), (22), (23), (24), (25),
% 169.62/25.89 | | | (26), (27), (29), (30), (31), (32), (40) are inconsistent by
% 169.62/25.89 | | | sub-proof #332.
% 169.62/25.89 | | |
% 169.62/25.89 | | End of split
% 169.62/25.89 | |
% 169.62/25.89 | Case 2:
% 169.62/25.89 | |
% 169.62/25.89 | | (41) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 169.62/25.89 | | e1)
% 169.62/25.89 | |
% 169.62/25.89 | | BETA: splitting (41) gives:
% 169.62/25.89 | |
% 169.62/25.89 | | Case 1:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (42) all_58_8 = e1 & op(e1, e1) = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (42) implies:
% 169.62/25.89 | | | (43) all_58_8 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.62/25.89 | | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23),
% 169.62/25.89 | | | (24), (25), (26), (27), (29), (30), (31), (32), (43) are
% 169.62/25.89 | | | inconsistent by sub-proof #331.
% 169.62/25.89 | | |
% 169.62/25.89 | | Case 2:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (44) all_58_14 = e1 & op(e0, e1) = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (44) implies:
% 169.62/25.89 | | | (45) all_58_14 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (2), (26), (45) are inconsistent by sub-proof #649.
% 169.62/25.89 | | |
% 169.62/25.89 | | End of split
% 169.62/25.89 | |
% 169.62/25.89 | End of split
% 169.62/25.89 |
% 169.62/25.89 End of proof
% 169.62/25.89
% 169.62/25.89 Sub-proof #331 shows that the following formulas are inconsistent:
% 169.62/25.89 ----------------------------------------------------------------
% 169.62/25.89 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.89 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.89 (2) all_58_14 = e2
% 169.62/25.89 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.62/25.89 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.62/25.89 (4) all_58_2 = e2
% 169.62/25.89 (5) all_58_8 = e1
% 169.62/25.89 (6) ~ (e3 = e1)
% 169.62/25.89 (7) all_58_6 = e3
% 169.62/25.89 (8) op(e1, e3) = all_52_2
% 169.62/25.89 (9) ~ (e1 = e0)
% 169.62/25.89 (10) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.62/25.89 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.62/25.89 e3)
% 169.62/25.89 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.62/25.89 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.62/25.89 (12) op(e2, e3) = all_52_1
% 169.62/25.89 (13) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.62/25.89 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.62/25.89 (14) ~ (all_52_7 = e3)
% 169.62/25.89 (15) op(e2, e3) = e2
% 169.62/25.89 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.62/25.89 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.62/25.89 (17) ~ (e3 = e0)
% 169.62/25.89 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.89 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.89 (19) all_58_15 = e3
% 169.62/25.89 (20) all_58_4 = e3
% 169.62/25.89 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.89 (22) ~ (e2 = e0)
% 169.62/25.89 (23) op(e1, e3) = e3
% 169.62/25.89 (24) all_58_3 = e3
% 169.62/25.89 (25) op(e3, e3) = e3
% 169.62/25.89 (26) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.89 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.89 (27) ~ (e2 = e1)
% 169.62/25.89 (28) op(e0, e2) = all_52_7
% 169.62/25.89 (29) op(e1, e3) = e1
% 169.62/25.89 (30) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.89 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.89 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.89 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.89 (31) ~ (e3 = e2)
% 169.62/25.89
% 169.62/25.89 Begin of proof
% 169.62/25.89 |
% 169.62/25.89 | BETA: splitting (13) gives:
% 169.62/25.89 |
% 169.62/25.89 | Case 1:
% 169.62/25.89 | |
% 169.62/25.89 | | (32) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 169.62/25.89 | | e0)
% 169.62/25.89 | |
% 169.62/25.89 | | BETA: splitting (32) gives:
% 169.62/25.89 | |
% 169.62/25.89 | | Case 1:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (33) all_58_4 = e0 & op(e3, e1) = e0
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (33) implies:
% 169.62/25.89 | | | (34) all_58_4 = e0
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (17), (20), (34) are inconsistent by sub-proof #894.
% 169.62/25.89 | | |
% 169.62/25.89 | | Case 2:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (35) all_58_5 = e0 & op(e2, e1) = e0
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (35) implies:
% 169.62/25.89 | | | (36) all_58_5 = e0
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 169.62/25.89 | | | (15), (16), (17), (18), (19), (21), (22), (23), (24), (25),
% 169.62/25.89 | | | (26), (27), (28), (29), (30), (31), (36) are inconsistent by
% 169.62/25.89 | | | sub-proof #333.
% 169.62/25.89 | | |
% 169.62/25.89 | | End of split
% 169.62/25.89 | |
% 169.62/25.89 | Case 2:
% 169.62/25.89 | |
% 169.62/25.89 | | (37) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 169.62/25.89 | | e0)
% 169.62/25.89 | |
% 169.62/25.89 | | BETA: splitting (37) gives:
% 169.62/25.89 | |
% 169.62/25.89 | | Case 1:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (38) all_58_8 = e0 & op(e1, e1) = e0
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (38) implies:
% 169.62/25.89 | | | (39) all_58_8 = e0
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (5), (9), (39) are inconsistent by sub-proof #818.
% 169.62/25.89 | | |
% 169.62/25.89 | | Case 2:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (40) all_58_14 = e0 & op(e0, e1) = e0
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (40) implies:
% 169.62/25.89 | | | (41) all_58_14 = e0
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (2), (22), (41) are inconsistent by sub-proof #806.
% 169.62/25.89 | | |
% 169.62/25.89 | | End of split
% 169.62/25.89 | |
% 169.62/25.89 | End of split
% 169.62/25.89 |
% 169.62/25.89 End of proof
% 169.62/25.89
% 169.62/25.89 Sub-proof #332 shows that the following formulas are inconsistent:
% 169.62/25.89 ----------------------------------------------------------------
% 169.62/25.89 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.89 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.89 (2) all_58_14 = e2
% 169.62/25.89 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.62/25.89 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.62/25.89 (4) all_58_2 = e2
% 169.62/25.89 (5) ~ (e3 = e1)
% 169.62/25.89 (6) all_58_6 = e3
% 169.62/25.89 (7) op(e1, e3) = all_52_2
% 169.62/25.89 (8) ~ (e1 = e0)
% 169.62/25.89 (9) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.62/25.89 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.62/25.89 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.62/25.89 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.62/25.89 (11) op(e2, e3) = all_52_1
% 169.62/25.89 (12) ~ (all_52_7 = e3)
% 169.62/25.89 (13) op(e2, e3) = e2
% 169.62/25.89 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.62/25.89 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.62/25.89 (15) ~ (e3 = e0)
% 169.62/25.89 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.89 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.89 (17) all_58_15 = e3
% 169.62/25.89 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.89 (19) ~ (e2 = e0)
% 169.62/25.89 (20) all_58_5 = e1
% 169.62/25.89 (21) op(e1, e3) = e3
% 169.62/25.89 (22) all_58_3 = e3
% 169.62/25.89 (23) op(e3, e3) = e3
% 169.62/25.89 (24) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.89 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.89 (25) ~ (e2 = e1)
% 169.62/25.89 (26) op(e0, e2) = all_52_7
% 169.62/25.89 (27) op(e1, e3) = e1
% 169.62/25.89 (28) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.89 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.89 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.89 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.89 (29) ~ (e3 = e2)
% 169.62/25.89
% 169.62/25.89 Begin of proof
% 169.62/25.89 |
% 169.62/25.89 | BETA: splitting (14) gives:
% 169.62/25.89 |
% 169.62/25.89 | Case 1:
% 169.62/25.89 | |
% 169.62/25.89 | | (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 169.62/25.89 | | e1)
% 169.62/25.89 | |
% 169.62/25.89 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.62/25.89 | | (13), (15), (16), (18), (19), (21), (22), (23), (24), (25), (26),
% 169.62/25.89 | | (27), (28), (29), (30) are inconsistent by sub-proof #336.
% 169.62/25.89 | |
% 169.62/25.89 | Case 2:
% 169.62/25.89 | |
% 169.62/25.89 | | (31) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 169.62/25.89 | | e1)
% 169.62/25.89 | |
% 169.62/25.89 | | BETA: splitting (31) gives:
% 169.62/25.89 | |
% 169.62/25.89 | | Case 1:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (32) all_58_6 = e1 & op(e1, e3) = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (32) implies:
% 169.62/25.89 | | | (33) all_58_6 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | COMBINE_EQS: (6), (33) imply:
% 169.62/25.89 | | | (34) e3 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | SIMP: (34) implies:
% 169.62/25.89 | | | (35) e3 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | COMBINE_EQS: (17), (35) imply:
% 169.62/25.89 | | | (36) all_58_15 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 169.62/25.89 | | | (14), (15), (16), (18), (19), (22), (24), (25), (26), (28),
% 169.62/25.89 | | | (29), (36) are inconsistent by sub-proof #361.
% 169.62/25.89 | | |
% 169.62/25.89 | | Case 2:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (37) all_58_12 = e1 & op(e0, e3) = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (37) implies:
% 169.62/25.89 | | | (38) all_58_12 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | BETA: splitting (16) gives:
% 169.62/25.89 | | |
% 169.62/25.89 | | | Case 1:
% 169.62/25.89 | | | |
% 169.62/25.89 | | | | (39) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2)
% 169.62/25.89 | | | | = e0)
% 169.62/25.89 | | | |
% 169.62/25.89 | | | | BETA: splitting (39) gives:
% 169.62/25.89 | | | |
% 169.62/25.89 | | | | Case 1:
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | (40) all_58_2 = e0 & op(e2, e3) = e0
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | REF_CLOSE: (11), (13), (18), (19), (40) are inconsistent by sub-proof
% 169.62/25.89 | | | | | #782.
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | Case 2:
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | (41) all_58_3 = e0 & op(e2, e2) = e0
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | ALPHA: (41) implies:
% 169.62/25.89 | | | | | (42) all_58_3 = e0
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | COMBINE_EQS: (22), (42) imply:
% 169.62/25.89 | | | | | (43) e3 = e0
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | COMBINE_EQS: (17), (43) imply:
% 169.62/25.89 | | | | | (44) all_58_15 = e0
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (11), (12), (13), (15), (16),
% 169.62/25.89 | | | | | (18), (19), (22), (24), (25), (26), (29), (38), (44) are
% 169.62/25.89 | | | | | inconsistent by sub-proof #380.
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | End of split
% 169.62/25.89 | | | |
% 169.62/25.89 | | | Case 2:
% 169.62/25.89 | | | |
% 169.62/25.89 | | | | (45) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0)
% 169.62/25.89 | | | | = e0)
% 169.62/25.89 | | | |
% 169.62/25.89 | | | | BETA: splitting (45) gives:
% 169.62/25.89 | | | |
% 169.62/25.89 | | | | Case 1:
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | (46) all_58_5 = e0 & op(e2, e1) = e0
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | ALPHA: (46) implies:
% 169.62/25.89 | | | | | (47) all_58_5 = e0
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 169.62/25.89 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (21), (22),
% 169.62/25.89 | | | | | (23), (24), (25), (26), (27), (28), (29), (47) are
% 169.62/25.89 | | | | | inconsistent by sub-proof #333.
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | Case 2:
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | (48) all_58_10 = e0 & op(e2, e0) = e0
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | ALPHA: (48) implies:
% 169.62/25.89 | | | | | (49) all_58_10 = e0
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | BETA: splitting (3) gives:
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | | Case 1:
% 169.62/25.89 | | | | | |
% 169.62/25.89 | | | | | | (50) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 169.62/25.89 | | | | | | e3) = e0)
% 169.62/25.89 | | | | | |
% 169.62/25.89 | | | | | | REF_CLOSE: (11), (13), (15), (18), (19), (23), (50) are inconsistent
% 169.62/25.89 | | | | | | by sub-proof #460.
% 169.62/25.89 | | | | | |
% 169.62/25.89 | | | | | Case 2:
% 169.62/25.89 | | | | | |
% 169.62/25.89 | | | | | | (51) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 169.62/25.89 | | | | | | e3) = e0)
% 169.62/25.89 | | | | | |
% 169.62/25.89 | | | | | | BETA: splitting (51) gives:
% 169.62/25.89 | | | | | |
% 169.62/25.89 | | | | | | Case 1:
% 169.62/25.89 | | | | | | |
% 169.62/25.89 | | | | | | | (52) all_58_6 = e0 & op(e1, e3) = e0
% 169.62/25.89 | | | | | | |
% 169.62/25.89 | | | | | | | ALPHA: (52) implies:
% 169.62/25.89 | | | | | | | (53) op(e1, e3) = e0
% 169.62/25.89 | | | | | | |
% 169.62/25.89 | | | | | | | REF_CLOSE: (7), (8), (18), (27), (53) are inconsistent by
% 169.62/25.89 | | | | | | | sub-proof #749.
% 169.62/25.89 | | | | | | |
% 169.62/25.89 | | | | | | Case 2:
% 169.62/25.89 | | | | | | |
% 169.62/25.89 | | | | | | | (54) all_58_12 = e0 & op(e0, e3) = e0
% 169.62/25.89 | | | | | | |
% 169.62/25.89 | | | | | | | ALPHA: (54) implies:
% 169.62/25.89 | | | | | | | (55) all_58_12 = e0
% 169.62/25.89 | | | | | | |
% 169.62/25.89 | | | | | | | COMBINE_EQS: (38), (55) imply:
% 169.62/25.89 | | | | | | | (56) e1 = e0
% 169.62/25.89 | | | | | | |
% 169.62/25.89 | | | | | | | COMBINE_EQS: (20), (56) imply:
% 169.62/25.89 | | | | | | | (57) all_58_5 = e0
% 169.62/25.89 | | | | | | |
% 169.62/25.89 | | | | | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (11), (13), (15), (16),
% 169.62/25.89 | | | | | | | (17), (18), (19), (22), (24), (25), (28), (29), (38),
% 169.62/25.89 | | | | | | | (49), (57) are inconsistent by sub-proof #334.
% 169.62/25.89 | | | | | | |
% 169.62/25.89 | | | | | | End of split
% 169.62/25.89 | | | | | |
% 169.62/25.89 | | | | | End of split
% 169.62/25.89 | | | | |
% 169.62/25.89 | | | | End of split
% 169.62/25.89 | | | |
% 169.62/25.89 | | | End of split
% 169.62/25.89 | | |
% 169.62/25.89 | | End of split
% 169.62/25.89 | |
% 169.62/25.89 | End of split
% 169.62/25.89 |
% 169.62/25.89 End of proof
% 169.62/25.89
% 169.62/25.89 Sub-proof #333 shows that the following formulas are inconsistent:
% 169.62/25.89 ----------------------------------------------------------------
% 169.62/25.89 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.89 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.89 (2) all_58_14 = e2
% 169.62/25.89 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.62/25.89 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.62/25.89 (4) all_58_2 = e2
% 169.62/25.89 (5) ~ (e3 = e1)
% 169.62/25.89 (6) all_58_6 = e3
% 169.62/25.89 (7) op(e1, e3) = all_52_2
% 169.62/25.89 (8) ~ (e1 = e0)
% 169.62/25.89 (9) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.62/25.89 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.62/25.89 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.62/25.89 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.62/25.89 (11) op(e2, e3) = all_52_1
% 169.62/25.89 (12) ~ (all_52_7 = e3)
% 169.62/25.89 (13) op(e2, e3) = e2
% 169.62/25.89 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.62/25.89 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.62/25.89 (15) ~ (e3 = e0)
% 169.62/25.89 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.89 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.89 (17) all_58_15 = e3
% 169.62/25.89 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.89 (19) ~ (e2 = e0)
% 169.62/25.89 (20) op(e1, e3) = e3
% 169.62/25.89 (21) all_58_3 = e3
% 169.62/25.89 (22) op(e3, e3) = e3
% 169.62/25.89 (23) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.89 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.89 (24) ~ (e2 = e1)
% 169.62/25.89 (25) all_58_5 = e0
% 169.62/25.89 (26) op(e0, e2) = all_52_7
% 169.62/25.89 (27) op(e1, e3) = e1
% 169.62/25.89 (28) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.89 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.89 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.89 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.89 (29) ~ (e3 = e2)
% 169.62/25.89
% 169.62/25.89 Begin of proof
% 169.62/25.89 |
% 169.62/25.89 | BETA: splitting (1) gives:
% 169.62/25.89 |
% 169.62/25.89 | Case 1:
% 169.62/25.89 | |
% 169.62/25.89 | | (30) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.62/25.89 | | e1)
% 169.62/25.89 | |
% 169.62/25.89 | | BETA: splitting (30) gives:
% 169.62/25.89 | |
% 169.62/25.89 | | Case 1:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (31) all_58_2 = e1 & op(e2, e3) = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (31) implies:
% 169.62/25.89 | | | (32) op(e2, e3) = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (11), (13), (18), (24), (32) are inconsistent by sub-proof
% 169.62/25.89 | | | #784.
% 169.62/25.89 | | |
% 169.62/25.89 | | Case 2:
% 169.62/25.89 | | |
% 169.62/25.89 | | | (33) all_58_3 = e1 & op(e2, e2) = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | ALPHA: (33) implies:
% 169.62/25.89 | | | (34) all_58_3 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | COMBINE_EQS: (21), (34) imply:
% 169.62/25.89 | | | (35) e3 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | COMBINE_EQS: (17), (35) imply:
% 169.62/25.89 | | | (36) all_58_15 = e1
% 169.62/25.89 | | |
% 169.62/25.89 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 169.62/25.89 | | | (14), (15), (16), (18), (19), (21), (23), (24), (26), (28),
% 169.62/25.89 | | | (29), (36) are inconsistent by sub-proof #361.
% 169.62/25.89 | | |
% 169.62/25.89 | | End of split
% 169.62/25.89 | |
% 169.62/25.89 | Case 2:
% 169.62/25.89 | |
% 169.62/25.90 | | (37) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 169.62/25.90 | | e1)
% 169.62/25.90 | |
% 169.62/25.90 | | BETA: splitting (37) gives:
% 169.62/25.90 | |
% 169.62/25.90 | | Case 1:
% 169.62/25.90 | | |
% 169.62/25.90 | | | (38) all_58_5 = e1 & op(e2, e1) = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | ALPHA: (38) implies:
% 169.62/25.90 | | | (39) all_58_5 = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | REF_CLOSE: (8), (25), (39) are inconsistent by sub-proof #449.
% 169.62/25.90 | | |
% 169.62/25.90 | | Case 2:
% 169.62/25.90 | | |
% 169.62/25.90 | | | (40) all_58_10 = e1 & op(e2, e0) = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | ALPHA: (40) implies:
% 169.62/25.90 | | | (41) all_58_10 = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | BETA: splitting (14) gives:
% 169.62/25.90 | | |
% 169.62/25.90 | | | Case 1:
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | (42) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 169.62/25.90 | | | | = e1)
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 169.62/25.90 | | | | (12), (13), (15), (16), (18), (19), (20), (21), (22), (23),
% 169.62/25.90 | | | | (24), (26), (27), (28), (29), (42) are inconsistent by
% 169.62/25.90 | | | | sub-proof #336.
% 169.62/25.90 | | | |
% 169.62/25.90 | | | Case 2:
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | (43) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 169.62/25.90 | | | | = e1)
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | BETA: splitting (43) gives:
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | Case 1:
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | (44) all_58_6 = e1 & op(e1, e3) = e1
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | ALPHA: (44) implies:
% 169.62/25.90 | | | | | (45) all_58_6 = e1
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | COMBINE_EQS: (6), (45) imply:
% 169.62/25.90 | | | | | (46) e3 = e1
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | COMBINE_EQS: (17), (46) imply:
% 169.62/25.90 | | | | | (47) all_58_15 = e1
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 169.62/25.90 | | | | | (13), (14), (15), (16), (18), (19), (21), (23), (24), (26),
% 169.62/25.90 | | | | | (28), (29), (47) are inconsistent by sub-proof #361.
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | Case 2:
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | (48) all_58_12 = e1 & op(e0, e3) = e1
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | ALPHA: (48) implies:
% 169.62/25.90 | | | | | (49) all_58_12 = e1
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | BETA: splitting (3) gives:
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | Case 1:
% 169.62/25.90 | | | | | |
% 169.62/25.90 | | | | | | (50) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 169.62/25.90 | | | | | | e3) = e0)
% 169.62/25.90 | | | | | |
% 169.62/25.90 | | | | | | REF_CLOSE: (11), (13), (15), (18), (19), (22), (50) are inconsistent
% 169.62/25.90 | | | | | | by sub-proof #460.
% 169.62/25.90 | | | | | |
% 169.62/25.90 | | | | | Case 2:
% 169.62/25.90 | | | | | |
% 169.62/25.90 | | | | | | (51) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 169.62/25.90 | | | | | | e3) = e0)
% 169.62/25.90 | | | | | |
% 169.62/25.90 | | | | | | BETA: splitting (51) gives:
% 169.62/25.90 | | | | | |
% 169.62/25.90 | | | | | | Case 1:
% 169.62/25.90 | | | | | | |
% 169.62/25.90 | | | | | | | (52) all_58_6 = e0 & op(e1, e3) = e0
% 169.62/25.90 | | | | | | |
% 169.62/25.90 | | | | | | | ALPHA: (52) implies:
% 169.62/25.90 | | | | | | | (53) op(e1, e3) = e0
% 169.62/25.90 | | | | | | |
% 169.62/25.90 | | | | | | | REF_CLOSE: (7), (8), (18), (27), (53) are inconsistent by
% 169.62/25.90 | | | | | | | sub-proof #749.
% 169.62/25.90 | | | | | | |
% 169.62/25.90 | | | | | | Case 2:
% 169.62/25.90 | | | | | | |
% 169.62/25.90 | | | | | | | (54) all_58_12 = e0 & op(e0, e3) = e0
% 169.62/25.90 | | | | | | |
% 169.62/25.90 | | | | | | | ALPHA: (54) implies:
% 169.62/25.90 | | | | | | | (55) all_58_12 = e0
% 169.62/25.90 | | | | | | |
% 169.62/25.90 | | | | | | | COMBINE_EQS: (49), (55) imply:
% 169.62/25.90 | | | | | | | (56) e1 = e0
% 169.62/25.90 | | | | | | |
% 169.62/25.90 | | | | | | | COMBINE_EQS: (41), (56) imply:
% 169.62/25.90 | | | | | | | (57) all_58_10 = e0
% 169.62/25.90 | | | | | | |
% 169.62/25.90 | | | | | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (11), (13), (15), (16),
% 169.62/25.90 | | | | | | | (17), (18), (19), (21), (23), (24), (25), (28), (29),
% 169.62/25.90 | | | | | | | (49), (57) are inconsistent by sub-proof #334.
% 169.62/25.90 | | | | | | |
% 169.62/25.90 | | | | | | End of split
% 169.62/25.90 | | | | | |
% 169.62/25.90 | | | | | End of split
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | End of split
% 169.62/25.90 | | | |
% 169.62/25.90 | | | End of split
% 169.62/25.90 | | |
% 169.62/25.90 | | End of split
% 169.62/25.90 | |
% 169.62/25.90 | End of split
% 169.62/25.90 |
% 169.62/25.90 End of proof
% 169.62/25.90
% 169.62/25.90 Sub-proof #334 shows that the following formulas are inconsistent:
% 169.62/25.90 ----------------------------------------------------------------
% 169.62/25.90 (1) all_58_10 = e0
% 169.62/25.90 (2) all_58_12 = e1
% 169.62/25.90 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.90 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.90 (4) all_58_14 = e2
% 169.62/25.90 (5) all_58_2 = e2
% 169.62/25.90 (6) ~ (e3 = e1)
% 169.62/25.90 (7) ~ (e1 = e0)
% 169.62/25.90 (8) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.62/25.90 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.62/25.90 (9) op(e2, e3) = all_52_1
% 169.62/25.90 (10) op(e2, e3) = e2
% 169.62/25.90 (11) ~ (e3 = e0)
% 169.62/25.90 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.90 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.90 (13) all_58_15 = e3
% 169.62/25.90 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.90 (15) ~ (e2 = e0)
% 169.62/25.90 (16) all_58_3 = e3
% 169.62/25.90 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.90 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.90 (18) ~ (e2 = e1)
% 169.62/25.90 (19) all_58_5 = e0
% 169.62/25.90 (20) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.90 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.90 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.90 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.90 (21) ~ (e3 = e2)
% 169.62/25.90
% 169.62/25.90 Begin of proof
% 169.62/25.90 |
% 169.62/25.90 | BETA: splitting (3) gives:
% 169.62/25.90 |
% 169.62/25.90 | Case 1:
% 169.62/25.90 | |
% 169.62/25.90 | | (22) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.62/25.90 | | e1)
% 169.62/25.90 | |
% 169.62/25.90 | | BETA: splitting (22) gives:
% 169.62/25.90 | |
% 169.62/25.90 | | Case 1:
% 169.62/25.90 | | |
% 169.62/25.90 | | | (23) all_58_2 = e1 & op(e2, e3) = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | ALPHA: (23) implies:
% 169.62/25.90 | | | (24) op(e2, e3) = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | REF_CLOSE: (9), (10), (14), (18), (24) are inconsistent by sub-proof #784.
% 169.62/25.90 | | |
% 169.62/25.90 | | Case 2:
% 169.62/25.90 | | |
% 169.62/25.90 | | | (25) all_58_3 = e1 & op(e2, e2) = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.62/25.90 | | | (14), (15), (16), (17), (18), (20), (21), (25) are inconsistent
% 169.62/25.90 | | | by sub-proof #335.
% 169.62/25.90 | | |
% 169.62/25.90 | | End of split
% 169.62/25.90 | |
% 169.62/25.90 | Case 2:
% 169.62/25.90 | |
% 169.62/25.90 | | (26) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 169.62/25.90 | | e1)
% 169.62/25.90 | |
% 169.62/25.90 | | BETA: splitting (26) gives:
% 169.62/25.90 | |
% 169.62/25.90 | | Case 1:
% 169.62/25.90 | | |
% 169.62/25.90 | | | (27) all_58_5 = e1 & op(e2, e1) = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | ALPHA: (27) implies:
% 169.62/25.90 | | | (28) all_58_5 = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | REF_CLOSE: (7), (19), (28) are inconsistent by sub-proof #449.
% 169.62/25.90 | | |
% 169.62/25.90 | | Case 2:
% 169.62/25.90 | | |
% 169.62/25.90 | | | (29) all_58_10 = e1 & op(e2, e0) = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | ALPHA: (29) implies:
% 169.62/25.90 | | | (30) all_58_10 = e1
% 169.62/25.90 | | |
% 169.62/25.90 | | | REF_CLOSE: (1), (7), (30) are inconsistent by sub-proof #834.
% 169.62/25.90 | | |
% 169.62/25.90 | | End of split
% 169.62/25.90 | |
% 169.62/25.90 | End of split
% 169.62/25.90 |
% 169.62/25.90 End of proof
% 169.62/25.90
% 169.62/25.90 Sub-proof #335 shows that the following formulas are inconsistent:
% 169.62/25.90 ----------------------------------------------------------------
% 169.62/25.90 (1) all_58_12 = e1
% 169.62/25.90 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.90 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.90 (3) all_58_14 = e2
% 169.62/25.90 (4) all_58_2 = e2
% 169.62/25.90 (5) ~ (e3 = e1)
% 169.62/25.90 (6) ~ (e1 = e0)
% 169.62/25.90 (7) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.62/25.90 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.62/25.90 (8) op(e2, e3) = all_52_1
% 169.62/25.90 (9) op(e2, e3) = e2
% 169.62/25.90 (10) all_58_3 = e1 & op(e2, e2) = e1
% 169.62/25.90 (11) ~ (e3 = e0)
% 169.62/25.90 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.90 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.90 (13) all_58_15 = e3
% 169.62/25.90 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.90 (15) ~ (e2 = e0)
% 169.62/25.90 (16) all_58_3 = e3
% 169.62/25.90 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.90 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.90 (18) ~ (e2 = e1)
% 169.62/25.90 (19) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.90 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.90 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.90 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.90 (20) ~ (e3 = e2)
% 169.62/25.90
% 169.62/25.90 Begin of proof
% 169.62/25.90 |
% 169.62/25.90 | ALPHA: (10) implies:
% 169.62/25.90 | (21) all_58_3 = e1
% 169.62/25.90 |
% 169.62/25.90 | COMBINE_EQS: (16), (21) imply:
% 169.62/25.90 | (22) e3 = e1
% 169.62/25.90 |
% 169.62/25.90 | COMBINE_EQS: (13), (22) imply:
% 169.62/25.90 | (23) all_58_15 = e1
% 169.62/25.90 |
% 169.62/25.90 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14),
% 169.62/25.90 | (15), (16), (17), (18), (19), (20), (23) are inconsistent by
% 169.62/25.90 | sub-proof #362.
% 169.62/25.90 |
% 169.62/25.90 End of proof
% 169.62/25.90
% 169.62/25.90 Sub-proof #336 shows that the following formulas are inconsistent:
% 169.62/25.90 ----------------------------------------------------------------
% 169.62/25.90 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.90 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.62/25.90 (2) all_58_14 = e2
% 169.62/25.90 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.62/25.90 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.62/25.90 (4) all_58_2 = e2
% 169.62/25.90 (5) ~ (e3 = e1)
% 169.62/25.90 (6) all_58_6 = e3
% 169.62/25.90 (7) op(e1, e3) = all_52_2
% 169.62/25.90 (8) ~ (e1 = e0)
% 169.62/25.90 (9) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.62/25.90 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.62/25.90 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.62/25.90 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.62/25.90 (11) op(e2, e3) = all_52_1
% 169.62/25.90 (12) ~ (all_52_7 = e3)
% 169.62/25.90 (13) op(e2, e3) = e2
% 169.62/25.90 (14) ~ (e3 = e0)
% 169.62/25.90 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.62/25.90 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.62/25.90 (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 169.62/25.90 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.62/25.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.62/25.90 (18) ~ (e2 = e0)
% 169.62/25.90 (19) op(e1, e3) = e3
% 169.62/25.90 (20) all_58_3 = e3
% 169.62/25.90 (21) op(e3, e3) = e3
% 169.62/25.90 (22) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.62/25.90 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.62/25.90 (23) ~ (e2 = e1)
% 169.62/25.90 (24) op(e0, e2) = all_52_7
% 169.62/25.90 (25) op(e1, e3) = e1
% 169.62/25.90 (26) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.62/25.90 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.62/25.90 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.62/25.90 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.62/25.90 (27) ~ (e3 = e2)
% 169.62/25.90
% 169.62/25.90 Begin of proof
% 169.62/25.90 |
% 169.62/25.90 | BETA: splitting (16) gives:
% 169.62/25.90 |
% 169.62/25.90 | Case 1:
% 169.62/25.90 | |
% 169.62/25.90 | | (28) all_58_0 = e1 & op(e3, e3) = e1
% 169.62/25.90 | |
% 169.62/25.90 | | ALPHA: (28) implies:
% 169.62/25.90 | | (29) all_58_0 = e1
% 169.62/25.90 | |
% 169.62/25.90 | | BETA: splitting (3) gives:
% 169.62/25.90 | |
% 169.62/25.90 | | Case 1:
% 169.62/25.90 | | |
% 169.62/25.90 | | | (30) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.62/25.90 | | | e0)
% 169.62/25.90 | | |
% 169.62/25.90 | | | REF_CLOSE: (11), (13), (14), (17), (18), (21), (30) are inconsistent by
% 169.62/25.90 | | | sub-proof #460.
% 169.62/25.90 | | |
% 169.62/25.90 | | Case 2:
% 169.62/25.90 | | |
% 169.62/25.90 | | | (31) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.62/25.90 | | | e0)
% 169.62/25.90 | | |
% 169.62/25.90 | | | BETA: splitting (31) gives:
% 169.62/25.90 | | |
% 169.62/25.90 | | | Case 1:
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | (32) all_58_6 = e0 & op(e1, e3) = e0
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | ALPHA: (32) implies:
% 169.62/25.90 | | | | (33) op(e1, e3) = e0
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | REF_CLOSE: (7), (8), (17), (25), (33) are inconsistent by sub-proof
% 169.62/25.90 | | | | #749.
% 169.62/25.90 | | | |
% 169.62/25.90 | | | Case 2:
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | (34) all_58_12 = e0 & op(e0, e3) = e0
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | ALPHA: (34) implies:
% 169.62/25.90 | | | | (35) all_58_12 = e0
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | BETA: splitting (26) gives:
% 169.62/25.90 | | | |
% 169.62/25.90 | | | | Case 1:
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | (36) all_58_15 = e0 & op(e0, e0) = e0
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | ALPHA: (36) implies:
% 169.62/25.90 | | | | | (37) all_58_15 = e0
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (11), (12), (13), (14), (15),
% 169.62/25.90 | | | | | (17), (18), (20), (22), (23), (24), (27), (35), (37) are
% 169.62/25.90 | | | | | inconsistent by sub-proof #404.
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | Case 2:
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | GROUND_INST: instantiating (17) with all_52_2, e1, e3, e1, simplifying
% 169.62/25.90 | | | | | with (7), (25) gives:
% 169.62/25.90 | | | | | (38) all_52_2 = e1
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | GROUND_INST: instantiating (17) with all_52_2, e3, e3, e1, simplifying
% 169.62/25.90 | | | | | with (7), (19) gives:
% 169.62/25.90 | | | | | (39) all_52_2 = e3
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | COMBINE_EQS: (38), (39) imply:
% 169.62/25.90 | | | | | (40) e3 = e1
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | SIMP: (40) implies:
% 169.62/25.90 | | | | | (41) e3 = e1
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | COMBINE_EQS: (6), (41) imply:
% 169.62/25.90 | | | | | (42) all_58_6 = e1
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | | REF_CLOSE: (4), (5), (10), (14), (27), (29), (35), (42) are
% 169.62/25.90 | | | | | inconsistent by sub-proof #456.
% 169.62/25.90 | | | | |
% 169.62/25.90 | | | | End of split
% 169.62/25.90 | | | |
% 169.62/25.90 | | | End of split
% 169.62/25.90 | | |
% 169.62/25.90 | | End of split
% 169.62/25.90 | |
% 169.62/25.90 | Case 2:
% 169.62/25.90 | |
% 169.62/25.90 | | (43) all_58_2 = e1 & op(e2, e3) = e1
% 169.62/25.90 | |
% 169.62/25.90 | | ALPHA: (43) implies:
% 169.62/25.90 | | (44) op(e2, e3) = e1
% 169.62/25.90 | |
% 169.62/25.90 | | REF_CLOSE: (11), (13), (17), (23), (44) are inconsistent by sub-proof #784.
% 169.62/25.90 | |
% 169.62/25.90 | End of split
% 169.62/25.90 |
% 169.62/25.90 End of proof
% 169.62/25.90
% 169.62/25.90 Sub-proof #337 shows that the following formulas are inconsistent:
% 169.62/25.90 ----------------------------------------------------------------
% 169.62/25.90 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.62/25.90 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.90 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.69/25.90 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.69/25.90 (3) all_58_2 = e2
% 169.69/25.90 (4) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.69/25.90 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.69/25.90 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.69/25.90 (6) ~ (e3 = e1)
% 169.69/25.90 (7) ~ (e1 = e0)
% 169.69/25.90 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.69/25.90 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.69/25.90 (9) op(e2, e3) = all_52_1
% 169.69/25.90 (10) ~ (all_52_7 = e3)
% 169.69/25.90 (11) op(e2, e3) = e2
% 169.69/25.90 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.69/25.90 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.69/25.90 (13) ~ (e3 = e0)
% 169.69/25.90 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.90 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.90 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.69/25.90 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.69/25.90 (16) all_58_4 = e3
% 169.69/25.90 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.90 (18) ~ (e2 = e0)
% 169.69/25.90 (19) all_58_3 = e3
% 169.69/25.90 (20) all_58_9 = e3
% 169.69/25.90 (21) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.90 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.90 (22) ~ (e2 = e1)
% 169.69/25.90 (23) op(e0, e2) = all_52_7
% 169.69/25.90 (24) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.69/25.90 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.69/25.90 (25) ~ (e3 = e2)
% 169.69/25.90
% 169.69/25.90 Begin of proof
% 169.69/25.90 |
% 169.69/25.90 | BETA: splitting (4) gives:
% 169.69/25.90 |
% 169.69/25.90 | Case 1:
% 169.69/25.90 | |
% 169.69/25.90 | | (26) all_58_12 = e3 & op(e0, e3) = e3
% 169.69/25.90 | |
% 169.69/25.90 | | ALPHA: (26) implies:
% 169.69/25.90 | | (27) all_58_12 = e3
% 169.69/25.90 | |
% 169.69/25.90 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 169.69/25.90 | | (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (27)
% 169.69/25.90 | | are inconsistent by sub-proof #388.
% 169.69/25.90 | |
% 169.69/25.90 | Case 2:
% 169.69/25.90 | |
% 169.69/25.90 | | (28) all_58_13 = e3 & op(e0, e2) = e3
% 169.69/25.90 | |
% 169.69/25.90 | | REF_CLOSE: (10), (17), (23), (28) are inconsistent by sub-proof #962.
% 169.69/25.90 | |
% 169.69/25.90 | End of split
% 169.69/25.90 |
% 169.69/25.90 End of proof
% 169.69/25.90
% 169.69/25.90 Sub-proof #338 shows that the following formulas are inconsistent:
% 169.69/25.90 ----------------------------------------------------------------
% 169.69/25.90 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.90 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.90 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.69/25.90 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.69/25.90 (3) all_58_2 = e2
% 169.69/25.90 (4) op(e3, e3) = all_10_2
% 169.69/25.90 (5) all_58_8 = e2 & op(e1, e1) = e2
% 169.69/25.90 (6) op(e1, e3) = all_52_2
% 169.69/25.90 (7) ~ (all_10_2 = e0)
% 169.69/25.90 (8) ~ (e1 = e0)
% 169.69/25.90 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.69/25.90 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.69/25.90 (10) op(e2, e3) = all_52_1
% 169.69/25.90 (11) op(e2, e3) = e2
% 169.69/25.90 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.69/25.90 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.69/25.90 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.90 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.90 (14) op(e1, e1) = e3
% 169.69/25.90 (15) ~ (all_10_2 = e1)
% 169.69/25.90 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.90 (17) ~ (e2 = e0)
% 169.69/25.90 (18) ~ (all_10_2 = e2)
% 169.69/25.90 (19) all_58_3 = e3
% 169.69/25.90 (20) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.90 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.90 (21) ~ (e2 = e1)
% 169.69/25.90 (22) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.69/25.90 (23) all_54_0 = all_10_2
% 169.69/25.90 (24) op(e1, e3) = e1
% 169.69/25.90
% 169.69/25.90 Begin of proof
% 169.69/25.90 |
% 169.69/25.90 | ALPHA: (5) implies:
% 169.69/25.90 | (25) op(e1, e1) = e2
% 169.69/25.90 |
% 169.69/25.90 | BETA: splitting (22) gives:
% 169.69/25.90 |
% 169.69/25.90 | Case 1:
% 169.69/25.90 | |
% 169.69/25.90 | | (26) all_54_0 = e3
% 169.69/25.90 | |
% 169.69/25.90 | | COMBINE_EQS: (23), (26) imply:
% 169.69/25.90 | | (27) all_10_2 = e3
% 169.69/25.90 | |
% 169.69/25.90 | | SIMP: (27) implies:
% 169.69/25.90 | | (28) all_10_2 = e3
% 169.69/25.90 | |
% 169.69/25.90 | | REDUCE: (18), (28) imply:
% 169.69/25.90 | | (29) ~ (e3 = e2)
% 169.69/25.90 | |
% 169.69/25.90 | | REDUCE: (15), (28) imply:
% 169.69/25.90 | | (30) ~ (e3 = e1)
% 169.69/25.90 | |
% 169.69/25.90 | | REDUCE: (7), (28) imply:
% 169.69/25.90 | | (31) ~ (e3 = e0)
% 169.69/25.90 | |
% 169.69/25.90 | | REDUCE: (4), (28) imply:
% 169.69/25.90 | | (32) op(e3, e3) = e3
% 169.69/25.90 | |
% 169.69/25.90 | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (11), (12), (13), (14), (16),
% 169.69/25.90 | | (17), (19), (20), (21), (24), (25), (29), (30), (31), (32) are
% 169.69/25.90 | | inconsistent by sub-proof #339.
% 169.69/25.90 | |
% 169.69/25.90 | Case 2:
% 169.69/25.90 | |
% 169.69/25.90 | | (33) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 169.69/25.90 | |
% 169.69/25.90 | | REF_CLOSE: (7), (15), (18), (23), (33) are inconsistent by sub-proof #958.
% 169.69/25.90 | |
% 169.69/25.90 | End of split
% 169.69/25.90 |
% 169.69/25.90 End of proof
% 169.69/25.90
% 169.69/25.90 Sub-proof #339 shows that the following formulas are inconsistent:
% 169.69/25.90 ----------------------------------------------------------------
% 169.69/25.90 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.90 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.90 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.69/25.90 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.69/25.90 (3) all_58_2 = e2
% 169.69/25.90 (4) ~ (e3 = e1)
% 169.69/25.90 (5) op(e1, e3) = all_52_2
% 169.69/25.90 (6) ~ (e1 = e0)
% 169.69/25.90 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.69/25.90 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.69/25.90 (8) op(e1, e1) = e2
% 169.69/25.90 (9) op(e2, e3) = all_52_1
% 169.69/25.91 (10) op(e2, e3) = e2
% 169.69/25.91 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.69/25.91 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.69/25.91 (12) ~ (e3 = e0)
% 169.69/25.91 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.91 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.91 (14) op(e1, e1) = e3
% 169.69/25.91 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.91 (16) ~ (e2 = e0)
% 169.69/25.91 (17) all_58_3 = e3
% 169.69/25.91 (18) op(e3, e3) = e3
% 169.69/25.91 (19) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.91 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.91 (20) ~ (e2 = e1)
% 169.69/25.91 (21) op(e1, e3) = e1
% 169.69/25.91 (22) ~ (e3 = e2)
% 169.69/25.91
% 169.69/25.91 Begin of proof
% 169.69/25.91 |
% 169.69/25.91 | BETA: splitting (7) gives:
% 169.69/25.91 |
% 169.69/25.91 | Case 1:
% 169.69/25.91 | |
% 169.69/25.91 | | (23) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 169.69/25.91 | | e3)
% 169.69/25.91 | |
% 169.69/25.91 | | BETA: splitting (23) gives:
% 169.69/25.91 | |
% 169.69/25.91 | | Case 1:
% 169.69/25.91 | | |
% 169.69/25.91 | | |
% 169.69/25.91 | | | GROUND_INST: instantiating (15) with e2, e3, e1, e1, simplifying with (8),
% 169.69/25.91 | | | (14) gives:
% 169.69/25.91 | | | (24) e3 = e2
% 169.69/25.91 | | |
% 169.69/25.91 | | | COMBINE_EQS: (17), (24) imply:
% 169.69/25.91 | | | (25) all_58_3 = e2
% 169.69/25.91 | | |
% 169.69/25.91 | | | REF_CLOSE: (1), (3), (4), (6), (9), (10), (12), (13), (15), (16), (19),
% 169.69/25.91 | | | (20), (22), (25) are inconsistent by sub-proof #779.
% 169.69/25.91 | | |
% 169.69/25.91 | | Case 2:
% 169.69/25.91 | | |
% 169.69/25.91 | | | (26) all_58_2 = e3 & op(e2, e3) = e3
% 169.69/25.91 | | |
% 169.69/25.91 | | | ALPHA: (26) implies:
% 169.69/25.91 | | | (27) op(e2, e3) = e3
% 169.69/25.91 | | |
% 169.69/25.91 | | | REF_CLOSE: (9), (10), (15), (22), (27) are inconsistent by sub-proof #462.
% 169.69/25.91 | | |
% 169.69/25.91 | | End of split
% 169.69/25.91 | |
% 169.69/25.91 | Case 2:
% 169.69/25.91 | |
% 169.69/25.91 | | (28) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 169.69/25.91 | | e3)
% 169.69/25.91 | |
% 169.69/25.91 | | BETA: splitting (28) gives:
% 169.69/25.91 | |
% 169.69/25.91 | | Case 1:
% 169.69/25.91 | | |
% 169.69/25.91 | | | (29) all_58_6 = e3 & op(e1, e3) = e3
% 169.69/25.91 | | |
% 169.69/25.91 | | | ALPHA: (29) implies:
% 169.69/25.91 | | | (30) all_58_6 = e3
% 169.69/25.91 | | | (31) op(e1, e3) = e3
% 169.69/25.91 | | |
% 169.69/25.91 | | | BETA: splitting (11) gives:
% 169.69/25.91 | | |
% 169.69/25.91 | | | Case 1:
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | (32) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 169.69/25.91 | | | | = e1)
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | BETA: splitting (32) gives:
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | Case 1:
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | (33) all_58_0 = e1 & op(e3, e3) = e1
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | ALPHA: (33) implies:
% 169.69/25.91 | | | | | (34) all_58_0 = e1
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14),
% 169.69/25.91 | | | | | (15), (16), (18), (21), (22), (30), (31), (34) are
% 169.69/25.91 | | | | | inconsistent by sub-proof #342.
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | Case 2:
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | (35) all_58_2 = e1 & op(e2, e3) = e1
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | ALPHA: (35) implies:
% 169.69/25.91 | | | | | (36) op(e2, e3) = e1
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | REF_CLOSE: (9), (10), (15), (20), (36) are inconsistent by sub-proof
% 169.69/25.91 | | | | | #784.
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | End of split
% 169.69/25.91 | | | |
% 169.69/25.91 | | | Case 2:
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | (37) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 169.69/25.91 | | | | = e1)
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | BETA: splitting (37) gives:
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | Case 1:
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | (38) all_58_6 = e1 & op(e1, e3) = e1
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | REF_CLOSE: (4), (30), (38) are inconsistent by sub-proof #487.
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | Case 2:
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | (39) all_58_12 = e1 & op(e0, e3) = e1
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | ALPHA: (39) implies:
% 169.69/25.91 | | | | | (40) all_58_12 = e1
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | BETA: splitting (2) gives:
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | Case 1:
% 169.69/25.91 | | | | | |
% 169.69/25.91 | | | | | | (41) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2,
% 169.69/25.91 | | | | | | e3) = e0)
% 169.69/25.91 | | | | | |
% 169.69/25.91 | | | | | | REF_CLOSE: (8), (9), (10), (14), (15), (16), (18), (41) are
% 169.69/25.91 | | | | | | inconsistent by sub-proof #343.
% 169.69/25.91 | | | | | |
% 169.69/25.91 | | | | | Case 2:
% 169.69/25.91 | | | | | |
% 169.69/25.91 | | | | | | (42) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 169.69/25.91 | | | | | | e3) = e0)
% 169.69/25.91 | | | | | |
% 169.69/25.91 | | | | | | REF_CLOSE: (5), (6), (15), (21), (40), (42) are inconsistent by
% 169.69/25.91 | | | | | | sub-proof #341.
% 169.69/25.91 | | | | | |
% 169.69/25.91 | | | | | End of split
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | End of split
% 169.69/25.91 | | | |
% 169.69/25.91 | | | End of split
% 169.69/25.91 | | |
% 169.69/25.91 | | Case 2:
% 169.69/25.91 | | |
% 169.69/25.91 | | | (43) all_58_12 = e3 & op(e0, e3) = e3
% 169.69/25.91 | | |
% 169.69/25.91 | | | ALPHA: (43) implies:
% 169.69/25.91 | | | (44) all_58_12 = e3
% 169.69/25.91 | | |
% 169.69/25.91 | | | BETA: splitting (2) gives:
% 169.69/25.91 | | |
% 169.69/25.91 | | | Case 1:
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | (45) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 169.69/25.91 | | | | = e0)
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | BETA: splitting (45) gives:
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | Case 1:
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | (46) all_58_0 = e0 & op(e3, e3) = e0
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | ALPHA: (46) implies:
% 169.69/25.91 | | | | | (47) op(e3, e3) = e0
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | REF_CLOSE: (8), (14), (15), (16), (18), (47) are inconsistent by
% 169.69/25.91 | | | | | sub-proof #344.
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | Case 2:
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | (48) all_58_2 = e0 & op(e2, e3) = e0
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | | REF_CLOSE: (9), (10), (15), (16), (48) are inconsistent by sub-proof
% 169.69/25.91 | | | | | #782.
% 169.69/25.91 | | | | |
% 169.69/25.91 | | | | End of split
% 169.69/25.91 | | | |
% 169.69/25.91 | | | Case 2:
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | (49) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 169.69/25.91 | | | | = e0)
% 169.69/25.91 | | | |
% 169.69/25.91 | | | | REF_CLOSE: (5), (6), (12), (15), (21), (44), (49) are inconsistent by
% 169.69/25.91 | | | | sub-proof #340.
% 169.69/25.91 | | | |
% 169.69/25.91 | | | End of split
% 169.69/25.91 | | |
% 169.69/25.91 | | End of split
% 169.69/25.91 | |
% 169.69/25.91 | End of split
% 169.69/25.91 |
% 169.69/25.91 End of proof
% 169.69/25.91
% 169.69/25.91 Sub-proof #340 shows that the following formulas are inconsistent:
% 169.69/25.91 ----------------------------------------------------------------
% 169.69/25.91 (1) op(e1, e3) = all_52_2
% 169.69/25.91 (2) ~ (e1 = e0)
% 169.69/25.91 (3) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.69/25.91 (4) ~ (e3 = e0)
% 169.69/25.91 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.91 (6) all_58_12 = e3
% 169.69/25.91 (7) op(e1, e3) = e1
% 169.69/25.91
% 169.69/25.91 Begin of proof
% 169.69/25.91 |
% 169.69/25.91 | BETA: splitting (3) gives:
% 169.69/25.91 |
% 169.69/25.91 | Case 1:
% 169.69/25.91 | |
% 169.69/25.91 | | (8) all_58_6 = e0 & op(e1, e3) = e0
% 169.69/25.91 | |
% 169.69/25.91 | | ALPHA: (8) implies:
% 169.69/25.91 | | (9) op(e1, e3) = e0
% 169.69/25.91 | |
% 169.69/25.91 | | REF_CLOSE: (1), (2), (5), (7), (9) are inconsistent by sub-proof #749.
% 169.69/25.91 | |
% 169.69/25.91 | Case 2:
% 169.69/25.91 | |
% 169.69/25.91 | | (10) all_58_12 = e0 & op(e0, e3) = e0
% 169.69/25.91 | |
% 169.69/25.91 | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #646.
% 169.69/25.91 | |
% 169.69/25.91 | End of split
% 169.69/25.91 |
% 169.69/25.91 End of proof
% 169.69/25.91
% 169.69/25.91 Sub-proof #341 shows that the following formulas are inconsistent:
% 169.69/25.91 ----------------------------------------------------------------
% 169.69/25.91 (1) all_58_12 = e1
% 169.69/25.91 (2) op(e1, e3) = all_52_2
% 169.69/25.91 (3) ~ (e1 = e0)
% 169.69/25.91 (4) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.69/25.91 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.91 (6) op(e1, e3) = e1
% 169.69/25.91
% 169.69/25.91 Begin of proof
% 169.69/25.91 |
% 169.69/25.91 | BETA: splitting (4) gives:
% 169.69/25.91 |
% 169.69/25.91 | Case 1:
% 169.69/25.91 | |
% 169.69/25.91 | | (7) all_58_6 = e0 & op(e1, e3) = e0
% 169.69/25.91 | |
% 169.69/25.91 | | ALPHA: (7) implies:
% 169.69/25.91 | | (8) op(e1, e3) = e0
% 169.69/25.91 | |
% 169.69/25.91 | | REF_CLOSE: (2), (3), (5), (6), (8) are inconsistent by sub-proof #749.
% 169.69/25.91 | |
% 169.69/25.91 | Case 2:
% 169.69/25.91 | |
% 169.69/25.91 | | (9) all_58_12 = e0 & op(e0, e3) = e0
% 169.69/25.91 | |
% 169.69/25.91 | | ALPHA: (9) implies:
% 169.69/25.91 | | (10) all_58_12 = e0
% 169.69/25.91 | |
% 169.69/25.91 | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #873.
% 169.69/25.91 | |
% 169.69/25.91 | End of split
% 169.69/25.91 |
% 169.69/25.91 End of proof
% 169.69/25.91
% 169.69/25.91 Sub-proof #342 shows that the following formulas are inconsistent:
% 169.69/25.91 ----------------------------------------------------------------
% 169.69/25.91 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.69/25.91 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.69/25.91 (2) all_58_2 = e2
% 169.69/25.91 (3) all_58_0 = e1
% 169.69/25.91 (4) ~ (e3 = e1)
% 169.69/25.91 (5) all_58_6 = e3
% 169.69/25.91 (6) op(e1, e3) = all_52_2
% 169.69/25.91 (7) ~ (e1 = e0)
% 169.69/25.91 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.69/25.91 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.69/25.91 (9) op(e1, e1) = e2
% 169.69/25.91 (10) op(e2, e3) = all_52_1
% 169.69/25.91 (11) op(e2, e3) = e2
% 169.69/25.91 (12) ~ (e3 = e0)
% 169.69/25.91 (13) op(e1, e1) = e3
% 169.69/25.91 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.91 (15) ~ (e2 = e0)
% 169.69/25.91 (16) op(e1, e3) = e3
% 169.69/25.91 (17) op(e3, e3) = e3
% 169.69/25.91 (18) op(e1, e3) = e1
% 169.69/25.91 (19) ~ (e3 = e2)
% 169.69/25.91
% 169.69/25.91 Begin of proof
% 169.69/25.91 |
% 169.69/25.91 | BETA: splitting (1) gives:
% 169.69/25.91 |
% 169.69/25.91 | Case 1:
% 169.69/25.91 | |
% 169.69/25.91 | | (20) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.69/25.91 | | e0)
% 169.69/25.91 | |
% 169.69/25.91 | | REF_CLOSE: (9), (10), (11), (13), (14), (15), (17), (20) are inconsistent by
% 169.69/25.91 | | sub-proof #343.
% 169.69/25.91 | |
% 169.69/25.91 | Case 2:
% 169.69/25.91 | |
% 169.69/25.91 | | (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.69/25.91 | | e0)
% 169.69/25.91 | |
% 169.69/25.91 | | BETA: splitting (21) gives:
% 169.69/25.91 | |
% 169.69/25.91 | | Case 1:
% 169.69/25.91 | | |
% 169.69/25.91 | | | (22) all_58_6 = e0 & op(e1, e3) = e0
% 169.69/25.91 | | |
% 169.69/25.91 | | | ALPHA: (22) implies:
% 169.69/25.91 | | | (23) op(e1, e3) = e0
% 169.69/25.91 | | |
% 169.69/25.91 | | | REF_CLOSE: (6), (7), (14), (18), (23) are inconsistent by sub-proof #749.
% 169.69/25.91 | | |
% 169.69/25.91 | | Case 2:
% 169.69/25.91 | | |
% 169.69/25.91 | | | (24) all_58_12 = e0 & op(e0, e3) = e0
% 169.69/25.91 | | |
% 169.69/25.91 | | | ALPHA: (24) implies:
% 169.69/25.91 | | | (25) all_58_12 = e0
% 169.69/25.91 | | |
% 169.69/25.91 | | | GROUND_INST: instantiating (14) with e2, e3, e1, e1, simplifying with (9),
% 169.69/25.91 | | | (13) gives:
% 169.69/25.91 | | | (26) e3 = e2
% 169.69/25.91 | | |
% 169.69/25.91 | | | GROUND_INST: instantiating (14) with all_52_2, e1, e3, e1, simplifying
% 169.69/25.91 | | | with (6), (18) gives:
% 169.69/25.91 | | | (27) all_52_2 = e1
% 169.69/25.91 | | |
% 169.69/25.91 | | | GROUND_INST: instantiating (14) with all_52_2, e3, e3, e1, simplifying
% 169.69/25.91 | | | with (6), (16) gives:
% 169.69/25.91 | | | (28) all_52_2 = e3
% 169.69/25.91 | | |
% 169.69/25.91 | | | COMBINE_EQS: (27), (28) imply:
% 169.69/25.91 | | | (29) e3 = e1
% 169.69/25.91 | | |
% 169.69/25.91 | | | SIMP: (29) implies:
% 169.69/25.91 | | | (30) e3 = e1
% 169.69/25.91 | | |
% 169.69/25.91 | | | COMBINE_EQS: (26), (30) imply:
% 169.69/25.91 | | | (31) e2 = e1
% 169.69/25.91 | | |
% 169.69/25.91 | | | COMBINE_EQS: (5), (30) imply:
% 169.69/25.91 | | | (32) all_58_6 = e1
% 169.69/25.91 | | |
% 169.69/25.91 | | | REF_CLOSE: (2), (3), (4), (8), (12), (19), (25), (32) are inconsistent by
% 169.69/25.91 | | | sub-proof #456.
% 169.69/25.91 | | |
% 169.69/25.91 | | End of split
% 169.69/25.91 | |
% 169.69/25.91 | End of split
% 169.69/25.91 |
% 169.69/25.91 End of proof
% 169.69/25.91
% 169.69/25.91 Sub-proof #343 shows that the following formulas are inconsistent:
% 169.69/25.91 ----------------------------------------------------------------
% 169.69/25.91 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 169.69/25.91 (2) op(e1, e1) = e2
% 169.69/25.91 (3) op(e2, e3) = all_52_1
% 169.69/25.91 (4) op(e2, e3) = e2
% 169.69/25.91 (5) op(e1, e1) = e3
% 169.69/25.91 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.91 (7) ~ (e2 = e0)
% 169.69/25.91 (8) op(e3, e3) = e3
% 169.69/25.91
% 169.69/25.91 Begin of proof
% 169.69/25.91 |
% 169.69/25.91 | BETA: splitting (1) gives:
% 169.69/25.91 |
% 169.69/25.91 | Case 1:
% 169.69/25.91 | |
% 169.69/25.91 | | (9) all_58_0 = e0 & op(e3, e3) = e0
% 169.69/25.91 | |
% 169.69/25.91 | | ALPHA: (9) implies:
% 169.69/25.91 | | (10) op(e3, e3) = e0
% 169.69/25.91 | |
% 169.69/25.91 | | REF_CLOSE: (2), (5), (6), (7), (8), (10) are inconsistent by sub-proof #344.
% 169.69/25.91 | |
% 169.69/25.91 | Case 2:
% 169.69/25.91 | |
% 169.69/25.91 | | (11) all_58_2 = e0 & op(e2, e3) = e0
% 169.69/25.91 | |
% 169.69/25.91 | | REF_CLOSE: (3), (4), (6), (7), (11) are inconsistent by sub-proof #782.
% 169.69/25.91 | |
% 169.69/25.91 | End of split
% 169.69/25.91 |
% 169.69/25.91 End of proof
% 169.69/25.91
% 169.69/25.91 Sub-proof #344 shows that the following formulas are inconsistent:
% 169.69/25.91 ----------------------------------------------------------------
% 169.69/25.91 (1) op(e3, e3) = e0
% 169.69/25.91 (2) op(e1, e1) = e2
% 169.69/25.91 (3) op(e1, e1) = e3
% 169.69/25.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.91 (5) ~ (e2 = e0)
% 169.69/25.91 (6) op(e3, e3) = e3
% 169.69/25.91
% 169.69/25.91 Begin of proof
% 169.69/25.91 |
% 169.69/25.91 | GROUND_INST: instantiating (4) with e2, e3, e1, e1, simplifying with (2), (3)
% 169.69/25.91 | gives:
% 169.69/25.91 | (7) e3 = e2
% 169.69/25.91 |
% 169.69/25.91 | GROUND_INST: instantiating (4) with e0, e3, e3, e3, simplifying with (1), (6)
% 169.69/25.91 | gives:
% 169.69/25.91 | (8) e3 = e0
% 169.69/25.91 |
% 169.69/25.91 | COMBINE_EQS: (7), (8) imply:
% 169.69/25.91 | (9) e2 = e0
% 169.69/25.91 |
% 169.69/25.91 | SIMP: (9) implies:
% 169.69/25.91 | (10) e2 = e0
% 169.69/25.91 |
% 169.69/25.91 | REDUCE: (5), (10) imply:
% 169.69/25.91 | (11) $false
% 169.69/25.91 |
% 169.69/25.91 | CLOSE: (11) is inconsistent.
% 169.69/25.91 |
% 169.69/25.91 End of proof
% 169.69/25.91
% 169.69/25.91 Sub-proof #345 shows that the following formulas are inconsistent:
% 169.69/25.91 ----------------------------------------------------------------
% 169.69/25.91 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.69/25.91 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.69/25.91 (2) op(e2, e1) = all_52_9
% 169.69/25.91 (3) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.69/25.91 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.69/25.91 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.91 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.69/25.91 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.69/25.91 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.69/25.91 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.91 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.69/25.91 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.69/25.91 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 169.69/25.91 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 169.69/25.91 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.69/25.91 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.69/25.91 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.69/25.91 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.69/25.91 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 169.69/25.91 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.69/25.91 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.69/25.91 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.69/25.91 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.69/25.91 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.69/25.91 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.91 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.69/25.91 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.69/25.91 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 169.69/25.91 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 169.69/25.91 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.69/25.91 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.91 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.69/25.91 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.69/25.91 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 169.69/25.91 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.91 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.69/25.91 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.69/25.91 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 169.69/25.91 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 169.69/25.91 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.69/25.91 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.91 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.69/25.91 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.69/25.91 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 169.69/25.91 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.69/25.91 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.69/25.91 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.69/25.91 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 169.69/25.91 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.69/25.91 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.69/25.91 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 169.69/25.91 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.69/25.91 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 169.69/25.91 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.69/25.91 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.69/25.91 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.69/25.91 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.91 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.91 (6) ~ (all_52_13 = e3)
% 169.69/25.91 (7) ~ (all_4_2 = e2)
% 169.69/25.91 (8) all_56_0 = e2
% 169.69/25.91 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.69/25.91 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.69/25.91 (10) all_58_2 = e2
% 169.69/25.91 (11) all_54_6 = all_52_9
% 169.69/25.91 (12) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.91 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.69/25.91 (13) all_58_0 = e1
% 169.69/25.91 (14) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.69/25.91 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.69/25.91 (15) ~ (all_56_15 = e3) | (all_56_6 = e0 & op(e0, e3) = e0)
% 169.69/25.91 (16) ~ (all_4_2 = e1)
% 169.69/25.91 (17) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.69/25.91 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.69/25.91 (18) all_56_14 = all_6_2
% 169.69/25.91 (19) op(e3, e3) = e1
% 169.69/25.91 (20) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.69/25.91 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 169.69/25.91 e1)
% 169.69/25.91 (21) all_56_4 = e3
% 169.69/25.91 (22) op(e3, e1) = all_52_8
% 169.69/25.91 (23) ~ (e1 = e0)
% 169.69/25.91 (24) all_56_10 = e1
% 169.69/25.91 (25) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.69/25.91 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.69/25.91 e3)
% 169.69/25.91 (26) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.69/25.91 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.69/25.91 (27) op(e1, e2) = all_52_6
% 169.69/25.91 (28) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.69/25.91 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.69/25.91 (29) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.69/25.91 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.69/25.91 (30) op(e2, e3) = all_52_1
% 169.69/25.91 (31) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.69/25.91 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.69/25.91 (32) op(e3, e1) = e3
% 169.69/25.91 (33) ~ (all_52_7 = e3)
% 169.69/25.91 (34) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 169.69/25.91 (35) all_54_15 = all_4_2
% 169.69/25.91 (36) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 169.69/25.91 (37) ~ (all_6_2 = e2)
% 169.69/25.91 (38) op(e1, e1) = all_6_2
% 169.69/25.91 (39) op(e2, e3) = e2
% 169.69/25.91 (40) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.69/25.91 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.69/25.91 (41) all_56_15 = all_4_2
% 169.69/25.91 (42) ~ (e3 = e0)
% 169.69/25.91 (43) ~ (all_52_8 = e1)
% 169.69/25.91 (44) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.91 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.91 (45) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 169.69/25.91 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.69/25.91 (46) op(e0, e0) = all_4_2
% 169.69/25.91 (47) ~ (all_52_9 = all_6_2)
% 169.69/25.91 (48) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 169.69/25.91 (49) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.69/25.91 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.69/25.91 e2) = all_22_1 & $i(all_22_1))
% 169.69/25.92 (50) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.92 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.69/25.92 (51) ~ (all_52_8 = all_52_9)
% 169.69/25.92 (52) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.69/25.92 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.69/25.92 (53) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.69/25.92 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.69/25.92 (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.92 (55) ~ (all_52_8 = all_6_2)
% 169.69/25.92 (56) ~ (e2 = e0)
% 169.69/25.92 (57) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.69/25.92 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.69/25.92 (58) all_58_3 = e3
% 169.69/25.92 (59) ~ (all_52_4 = all_52_8)
% 169.69/25.92 (60) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.92 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.92 (61) ~ (e2 = e1)
% 169.69/25.92 (62) op(e3, e2) = all_52_4
% 169.69/25.92 (63) op(e0, e2) = all_52_7
% 169.69/25.92 (64) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.69/25.92 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.69/25.92 (65) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.69/25.92 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.69/25.92 (66) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.69/25.92 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.69/25.92 (67) all_56_12 = e3
% 169.69/25.92 (68) ~ (all_52_9 = e2)
% 169.69/25.92 (69) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.69/25.92 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.69/25.92 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.69/25.92 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.69/25.92 (70) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.69/25.92 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.69/25.92 (71) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.69/25.92 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.69/25.92 e2) = all_14_1 & $i(all_14_1))
% 169.69/25.92 (72) op(e2, e0) = all_52_13
% 169.69/25.92 (73) ~ (e3 = e2)
% 169.69/25.92
% 169.69/25.92 Begin of proof
% 169.69/25.92 |
% 169.69/25.92 | GROUND_INST: instantiating (54) with all_52_8, e3, e1, e3, simplifying with
% 169.69/25.92 | (22), (32) gives:
% 169.69/25.92 | (74) all_52_8 = e3
% 169.69/25.92 |
% 169.69/25.92 | REDUCE: (59), (74) imply:
% 169.69/25.92 | (75) ~ (all_52_4 = e3)
% 169.69/25.92 |
% 169.69/25.92 | REDUCE: (51), (74) imply:
% 169.69/25.92 | (76) ~ (all_52_9 = e3)
% 169.69/25.92 |
% 169.69/25.92 | SIMP: (76) implies:
% 169.69/25.92 | (77) ~ (all_52_9 = e3)
% 169.69/25.92 |
% 169.69/25.92 | REDUCE: (55), (74) imply:
% 169.69/25.92 | (78) ~ (all_6_2 = e3)
% 169.69/25.92 |
% 169.69/25.92 | SIMP: (78) implies:
% 169.69/25.92 | (79) ~ (all_6_2 = e3)
% 169.69/25.92 |
% 169.69/25.92 | REDUCE: (43), (74) imply:
% 169.69/25.92 | (80) ~ (e3 = e1)
% 169.69/25.92 |
% 169.69/25.92 | BETA: splitting (28) gives:
% 169.69/25.92 |
% 169.69/25.92 | Case 1:
% 169.69/25.92 | |
% 169.69/25.92 | | (81) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 169.69/25.92 | | e3)
% 169.69/25.92 | |
% 169.69/25.92 | | BETA: splitting (81) gives:
% 169.69/25.92 | |
% 169.69/25.92 | | Case 1:
% 169.69/25.92 | | |
% 169.69/25.92 | | | (82) all_58_4 = e3 & op(e3, e1) = e3
% 169.69/25.92 | | |
% 169.69/25.92 | | | ALPHA: (82) implies:
% 169.69/25.92 | | | (83) all_58_4 = e3
% 169.69/25.92 | | |
% 169.69/25.92 | | | BETA: splitting (70) gives:
% 169.69/25.92 | | |
% 169.69/25.92 | | | Case 1:
% 169.69/25.92 | | | |
% 169.69/25.92 | | | | (84) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1)
% 169.69/25.92 | | | | = e2)
% 169.69/25.92 | | | |
% 169.69/25.92 | | | | BETA: splitting (84) gives:
% 169.69/25.92 | | | |
% 169.69/25.92 | | | | Case 1:
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | | (85) all_58_4 = e2 & op(e3, e1) = e2
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | | REF_CLOSE: (5), (10), (23), (30), (39), (42), (44), (54), (56), (58),
% 169.69/25.92 | | | | | (60), (61), (73), (80), (83), (85) are inconsistent by
% 169.69/25.92 | | | | | sub-proof #409.
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | Case 2:
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | | (86) all_58_5 = e2 & op(e2, e1) = e2
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | | REF_CLOSE: (5), (23), (30), (39), (42), (44), (54), (56), (58), (61),
% 169.69/25.92 | | | | | (80), (86) are inconsistent by sub-proof #412.
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | End of split
% 169.69/25.92 | | | |
% 169.69/25.92 | | | Case 2:
% 169.69/25.92 | | | |
% 169.69/25.92 | | | | (87) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1)
% 169.69/25.92 | | | | = e2)
% 169.69/25.92 | | | |
% 169.69/25.92 | | | | BETA: splitting (87) gives:
% 169.69/25.92 | | | |
% 169.69/25.92 | | | | Case 1:
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | | (88) all_58_8 = e2 & op(e1, e1) = e2
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | | REF_CLOSE: (37), (38), (54), (88) are inconsistent by sub-proof #845.
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | Case 2:
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | | (89) all_58_14 = e2 & op(e0, e1) = e2
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | | ALPHA: (89) implies:
% 169.69/25.92 | | | | | (90) all_58_14 = e2
% 169.69/25.92 | | | | | (91) op(e0, e1) = e2
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | | BETA: splitting (20) gives:
% 169.69/25.92 | | | | |
% 169.69/25.92 | | | | | Case 1:
% 169.69/25.92 | | | | | |
% 169.69/25.92 | | | | | | (92) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 169.69/25.92 | | | | | | op(e0, e2) = e1)
% 169.69/25.92 | | | | | |
% 169.69/25.92 | | | | | | BETA: splitting (92) gives:
% 169.69/25.92 | | | | | |
% 169.69/25.92 | | | | | | Case 1:
% 169.69/25.92 | | | | | | |
% 169.69/25.92 | | | | | | | (93) all_58_12 = e1 & op(e0, e3) = e1
% 169.69/25.92 | | | | | | |
% 169.69/25.92 | | | | | | | ALPHA: (93) implies:
% 169.69/25.92 | | | | | | | (94) all_58_12 = e1
% 169.69/25.92 | | | | | | |
% 169.69/25.92 | | | | | | | BETA: splitting (26) gives:
% 169.69/25.92 | | | | | | |
% 169.69/25.92 | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | | (95) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 169.69/25.92 | | | | | | | | op(e2, e3) = e3)
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | | REF_CLOSE: (2), (5), (10), (13), (23), (28), (30), (37), (38),
% 169.69/25.92 | | | | | | | | (39), (42), (44), (54), (56), (58), (60), (61), (70),
% 169.69/25.92 | | | | | | | | (73), (77), (79), (80), (83), (95) are inconsistent
% 169.69/25.92 | | | | | | | | by sub-proof #406.
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | | (96) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 169.69/25.92 | | | | | | | | op(e0, e3) = e3)
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | | BETA: splitting (96) gives:
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | (97) all_58_6 = e3 & op(e1, e3) = e3
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | ALPHA: (97) implies:
% 169.69/25.92 | | | | | | | | | (98) all_58_6 = e3
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | REF_CLOSE: (9), (13), (23), (30), (39), (42), (54), (56),
% 169.69/25.92 | | | | | | | | | (94), (98) are inconsistent by sub-proof #459.
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | (99) all_58_12 = e3 & op(e0, e3) = e3
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | ALPHA: (99) implies:
% 169.69/25.92 | | | | | | | | | (100) all_58_12 = e3
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | COMBINE_EQS: (94), (100) imply:
% 169.69/25.92 | | | | | | | | | (101) e3 = e1
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | COMBINE_EQS: (83), (101) imply:
% 169.69/25.92 | | | | | | | | | (102) all_58_4 = e1
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | REF_CLOSE: (2), (5), (10), (23), (28), (30), (37), (38), (39),
% 169.69/25.92 | | | | | | | | | (42), (44), (54), (56), (58), (60), (61), (70),
% 169.69/25.92 | | | | | | | | | (73), (77), (79), (80), (102) are inconsistent by
% 169.69/25.92 | | | | | | | | | sub-proof #407.
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | End of split
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | End of split
% 169.69/25.92 | | | | | | |
% 169.69/25.92 | | | | | | Case 2:
% 169.69/25.92 | | | | | | |
% 169.69/25.92 | | | | | | | (103) all_58_13 = e1 & op(e0, e2) = e1
% 169.69/25.92 | | | | | | |
% 169.69/25.92 | | | | | | | ALPHA: (103) implies:
% 169.69/25.92 | | | | | | | (104) all_58_13 = e1
% 169.69/25.92 | | | | | | | (105) op(e0, e2) = e1
% 169.69/25.92 | | | | | | |
% 169.69/25.92 | | | | | | | BETA: splitting (34) gives:
% 169.69/25.92 | | | | | | |
% 169.69/25.92 | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | | (106) all_54_15 = e3
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | | COMBINE_EQS: (35), (106) imply:
% 169.69/25.92 | | | | | | | | (107) all_4_2 = e3
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | | COMBINE_EQS: (41), (107) imply:
% 169.69/25.92 | | | | | | | | (108) all_56_15 = e3
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | | BETA: splitting (69) gives:
% 169.69/25.92 | | | | | | | |
% 169.69/25.92 | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | (109) all_58_15 = e0 & op(e0, e0) = e0
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (12),
% 169.69/25.92 | | | | | | | | | (13), (14), (17), (23), (25), (26), (27), (28),
% 169.69/25.92 | | | | | | | | | (29), (30), (31), (33), (37), (38), (39), (40),
% 169.69/25.92 | | | | | | | | | (42), (44), (46), (49), (50), (52), (54), (56),
% 169.69/25.92 | | | | | | | | | (57), (58), (60), (61), (62), (63), (64), (65),
% 169.69/25.92 | | | | | | | | | (66), (69), (70), (71), (72), (73), (77), (79),
% 169.69/25.92 | | | | | | | | | (80), (83), (90), (104), (109) are inconsistent by
% 169.69/25.92 | | | | | | | | | sub-proof #373.
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | (110) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0
% 169.69/25.92 | | | | | | | | | & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.69/25.92 | | | | | | | | | = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) |
% 169.69/25.92 | | | | | | | | | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 169.69/25.92 | | | | | | | | | e0 & op(e0, e1) = e0))
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | ALPHA: (110) implies:
% 169.69/25.92 | | | | | | | | | (111) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0
% 169.69/25.92 | | | | | | | | | & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 169.69/25.92 | | | | | | | | | e0)
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | BETA: splitting (15) gives:
% 169.69/25.92 | | | | | | | | |
% 169.69/25.92 | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | (112) ~ (all_56_15 = e3)
% 169.69/25.92 | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | REDUCE: (108), (112) imply:
% 169.69/25.92 | | | | | | | | | | (113) $false
% 169.69/25.92 | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | CLOSE: (113) is inconsistent.
% 169.69/25.92 | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | (114) all_56_6 = e0 & op(e0, e3) = e0
% 169.69/25.92 | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | ALPHA: (114) implies:
% 169.69/25.92 | | | | | | | | | | (115) all_56_6 = e0
% 169.69/25.92 | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | BETA: splitting (26) gives:
% 169.69/25.92 | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | (116) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 169.69/25.92 | | | | | | | | | | | & op(e2, e3) = e3)
% 169.69/25.92 | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (13), (23), (28), (30), (37),
% 169.69/25.92 | | | | | | | | | | | (38), (39), (42), (44), (54), (56), (58), (60),
% 169.69/25.92 | | | | | | | | | | | (61), (70), (73), (77), (79), (80), (83), (116)
% 169.69/25.92 | | | | | | | | | | | are inconsistent by sub-proof #406.
% 169.69/25.92 | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | (117) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 169.69/25.92 | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 169.69/25.92 | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | BETA: splitting (117) gives:
% 169.69/25.92 | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | (118) all_58_6 = e3 & op(e1, e3) = e3
% 169.69/25.92 | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | ALPHA: (118) implies:
% 169.69/25.92 | | | | | | | | | | | | (119) all_58_6 = e3
% 169.69/25.92 | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | BETA: splitting (48) gives:
% 169.69/25.92 | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | (120) all_56_10 = e3
% 169.69/25.92 | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | COMBINE_EQS: (24), (120) imply:
% 169.69/25.92 | | | | | | | | | | | | | (121) e3 = e1
% 169.69/25.92 | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | COMBINE_EQS: (83), (121) imply:
% 169.69/25.92 | | | | | | | | | | | | | (122) all_58_4 = e1
% 169.69/25.92 | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (23), (28), (30), (37), (38),
% 169.69/25.92 | | | | | | | | | | | | | (39), (42), (44), (54), (56), (58), (60), (61),
% 169.69/25.92 | | | | | | | | | | | | | (70), (73), (77), (79), (80), (122) are
% 169.69/25.92 | | | | | | | | | | | | | inconsistent by sub-proof #407.
% 169.69/25.92 | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | (123) ~ (all_56_10 = e3)
% 169.69/25.92 | | | | | | | | | | | | | (124) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 169.69/25.92 | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | REDUCE: (24), (123) imply:
% 169.69/25.92 | | | | | | | | | | | | | (125) ~ (e3 = e1)
% 169.69/25.92 | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | BETA: splitting (124) gives:
% 169.69/25.92 | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | (126) all_56_12 = e2
% 169.69/25.92 | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (39), (42), (44), (54),
% 169.69/25.92 | | | | | | | | | | | | | | (56), (58), (60), (61), (67), (73), (80), (126)
% 169.69/25.92 | | | | | | | | | | | | | | are inconsistent by sub-proof #372.
% 169.69/25.92 | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | (127) ~ (all_56_12 = e2)
% 169.69/25.92 | | | | | | | | | | | | | | (128) all_56_14 = e1 | all_56_15 = e0
% 169.69/25.92 | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 169.69/25.92 | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | (129) all_56_14 = e1
% 169.69/25.92 | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | COMBINE_EQS: (18), (129) imply:
% 169.69/25.92 | | | | | | | | | | | | | | | (130) all_6_2 = e1
% 169.69/25.92 | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | SIMP: (130) implies:
% 169.69/25.92 | | | | | | | | | | | | | | | (131) all_6_2 = e1
% 169.69/25.92 | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | REDUCE: (47), (131) imply:
% 169.69/25.92 | | | | | | | | | | | | | | | (132) ~ (all_52_9 = e1)
% 169.69/25.92 | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | REDUCE: (37), (131) imply:
% 169.69/25.92 | | | | | | | | | | | | | | | (133) ~ (e2 = e1)
% 169.69/25.92 | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 169.69/25.92 | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | (134) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 169.69/25.92 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 169.69/25.92 | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | BETA: splitting (134) gives:
% 169.69/25.92 | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | (135) all_58_9 = e1 & op(e3, e0) = e1
% 169.69/25.92 | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 169.69/25.92 | | | | | | | | | | | | | | | | | (136) all_58_9 = e1
% 169.69/25.92 | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 169.69/25.92 | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (137) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 169.69/25.92 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (23), (30), (39), (54), (56), (137) are
% 169.69/25.92 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #371.
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (138) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (139) all_58_6 = e0 & op(e1, e3) = e0
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (140) all_58_6 = e0
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (119), (140) are inconsistent by sub-proof
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | #537.
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (141) all_58_12 = e0 & op(e0, e3) = e0
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (142) all_58_12 = e0
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (143) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (33), (42), (54), (56), (63), (90), (104),
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (111), (143) are inconsistent by sub-proof #517.
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (144) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | (145) all_58_14 = e3 & op(e0, e1) = e3
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | (146) all_58_14 = e3
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (31), (39), (42), (44),
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | (54), (56), (58), (60), (61), (66), (70), (73),
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | (80), (83), (146) are inconsistent by sub-proof
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | #375.
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | (147) all_58_15 = e3 & op(e0, e0) = e3
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | (148) all_58_15 = e3
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (13), (17), (19), (23), (25), (30),
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | (33), (39), (42), (44), (54), (56), (58), (60),
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | (61), (63), (65), (73), (80), (83), (90), (136),
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | | (142), (148) are inconsistent by sub-proof #369.
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | End of split
% 169.69/25.92 | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | (149) all_58_10 = e1 & op(e2, e0) = e1
% 169.69/25.92 | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 169.69/25.92 | | | | | | | | | | | | | | | | | (150) op(e2, e0) = e1
% 169.69/25.92 | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 169.69/25.92 | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (151) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 169.69/25.92 | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 169.69/25.92 | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 169.69/25.92 | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21), (24), (30), (39), (54), (67), (73),
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (151) are inconsistent by sub-proof #366.
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (152) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 169.69/25.92 | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.69/25.92 | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 169.69/25.92 | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 169.69/25.92 | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 169.69/25.92 | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (153) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (154) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (155) op(e2, e1) = e1
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (30), (39), (42), (44), (54), (56), (58),
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (150), (155) are inconsistent by sub-proof #365.
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (156) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | (157) ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2,
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | e3) = all_56_0 & $i(all_56_0))
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (67), (157) are inconsistent by sub-proof
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | | #368.
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.92 | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.92 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (158) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (159) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (160) op(e2, e0) = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (54), (150), (160) are inconsistent by
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | sub-proof #849.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (161) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (162) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (163) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (24), (163) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | #795.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (164) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (165) ~ (all_56_15 = e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (166) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | = e1)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (54), (61), (91), (105), (115), (166) are
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #966.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | (167) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 169.69/25.93 | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.69/25.93 | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | (168) all_58_11 = e1 & op(e1, e0) = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | (169) all_58_11 = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | (170) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 169.69/25.93 | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (171) all_58_6 = e2 & op(e1, e3) = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (172) all_58_6 = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (13), (23), (26), (30), (39),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (42), (44), (54), (56), (58), (60), (61), (73),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (80), (172) are inconsistent by sub-proof #400.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (173) all_58_7 = e2 & op(e1, e2) = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (174) all_58_7 = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (175) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (176) all_58_9 = e2 & op(e3, e0) = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (177) all_58_9 = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | (178) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (23), (30), (39), (54), (56), (178) are
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #371.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | (179) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | (180) all_58_6 = e0 & op(e1, e3) = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | (181) all_58_6 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (119), (181) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | #537.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | (182) all_58_12 = e0 & op(e0, e3) = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | (183) all_58_12 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | (184) all_54_6 = e3
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (77), (184) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | #681.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | (185) ~ (all_54_6 = e3)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | (186) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | (187) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (33), (42), (54), (56), (63), (90), (104),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | (111), (187) are inconsistent by sub-proof #517.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | (188) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_58_14 = e3 & op(e0, e1) = e3
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_58_14 = e3
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (31), (39), (42), (44),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (54), (56), (58), (60), (61), (66), (70), (73),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (83), (190) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | #375.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (191) all_58_15 = e3 & op(e0, e0) = e3
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (191) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_58_15 = e3
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_54_6 = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (68), (193) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | #680.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (194) ~ (all_54_6 = e2)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_54_6 = e1 | all_54_6 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_54_6 = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (132), (196) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #364.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197) all_54_6 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11), (197) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_52_9 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (198) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) all_52_9 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (77), (199) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) ~ (e3 = e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (199) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) ~ (e2 = e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (199) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) ~ (e1 = e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2), (199) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) op(e2, e1) = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_58_4 = e1 & op(e3, e1) = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_4 = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (23), (28), (30), (37), (38),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (39), (42), (44), (54), (56), (58), (60), (61),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (70), (73), (77), (79), (80), (206) are
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #407.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_58_5 = e1 & op(e2, e1) = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) op(e2, e1) = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (54), (203), (208) are inconsistent by
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #911.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_58_8 = e1 & op(e1, e1) = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (210) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_58_8 = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_58_6 = e0 & op(e1, e3) = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_58_6 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (119), (214) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) e3 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (215) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) e3 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (192), (216) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) all_58_15 = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (23), (25), (30), (33), (39), (42),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (44), (54), (56), (58), (60), (61), (63), (73),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (80), (90), (183), (217) are inconsistent by
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #404.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_58_7 = e0 & op(e1, e2) = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (174), (218) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #363.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) all_58_8 = e0 & op(e1, e1) = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (211), (220) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #718.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) all_58_11 = e0 & op(e1, e0) = e0
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (169), (221) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #513.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) all_58_14 = e1 & op(e0, e1) = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_58_14 = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (223) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) e2 = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (224) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) e2 = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (177), (225) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_58_9 = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (13), (17), (19), (23), (25), (30),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (33), (39), (42), (44), (54), (56), (58), (60),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (61), (63), (65), (73), (80), (83), (90), (183),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (226) are inconsistent by sub-proof #369.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (227) all_58_10 = e2 & op(e2, e0) = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (23), (30), (39), (42), (44), (54), (56),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | (58), (61), (80), (227) are inconsistent by
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | | sub-proof #447.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | (228) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (46), (54), (61), (169), (228) are
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | (229) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 169.69/25.93 | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 169.69/25.93 | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 169.69/25.93 | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (230) all_58_8 = e2 & op(e1, e1) = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (231) all_58_8 = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (31), (42), (56), (61), (66), (80), (83),
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (90), (231) are inconsistent by sub-proof #395.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | (232) all_58_11 = e2 & op(e1, e0) = e2
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (169), (232) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | | | | | | | #471.
% 169.69/25.93 | | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | (233) all_58_15 = e1 & op(e0, e0) = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | | | (234) all_58_15 = e1
% 169.69/25.93 | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (23), (25), (26), (30), (33),
% 169.69/25.93 | | | | | | | | | | | | | | | | | (39), (40), (42), (44), (54), (56), (58), (60),
% 169.69/25.93 | | | | | | | | | | | | | | | | | (61), (63), (69), (73), (80), (90), (119), (234)
% 169.69/25.93 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #361.
% 169.69/25.93 | | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | (235) all_56_15 = e0
% 169.69/25.93 | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | COMBINE_EQS: (108), (235) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | (236) e3 = e0
% 169.69/25.93 | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | SIMP: (236) implies:
% 169.69/25.93 | | | | | | | | | | | | | | | (237) e3 = e0
% 169.69/25.93 | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | REDUCE: (42), (237) imply:
% 169.69/25.93 | | | | | | | | | | | | | | | (238) $false
% 169.69/25.93 | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | | CLOSE: (238) is inconsistent.
% 169.69/25.93 | | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | (239) all_58_12 = e3 & op(e0, e3) = e3
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | ALPHA: (239) implies:
% 169.69/25.93 | | | | | | | | | | | | (240) all_58_12 = e3
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | REF_CLOSE: (23), (42), (56), (90), (104), (111), (240) are
% 169.69/25.93 | | | | | | | | | | | | inconsistent by sub-proof #545.
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | |
% 169.69/25.93 | | | | | | | | End of split
% 169.69/25.93 | | | | | | | |
% 169.69/25.93 | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | |
% 169.69/25.93 | | | | | | | | (241) ~ (all_54_15 = e3)
% 169.69/25.93 | | | | | | | | (242) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 169.69/25.93 | | | | | | | |
% 169.69/25.93 | | | | | | | | REDUCE: (35), (241) imply:
% 169.69/25.93 | | | | | | | | (243) ~ (all_4_2 = e3)
% 169.69/25.93 | | | | | | | |
% 169.69/25.93 | | | | | | | | BETA: splitting (242) gives:
% 169.69/25.93 | | | | | | | |
% 169.69/25.93 | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | |
% 169.69/25.93 | | | | | | | | | (244) all_54_15 = e2
% 169.69/25.93 | | | | | | | | |
% 169.69/25.93 | | | | | | | | | COMBINE_EQS: (35), (244) imply:
% 169.69/25.93 | | | | | | | | | (245) all_4_2 = e2
% 169.69/25.93 | | | | | | | | |
% 169.69/25.93 | | | | | | | | | REDUCE: (7), (245) imply:
% 169.69/25.93 | | | | | | | | | (246) $false
% 169.69/25.93 | | | | | | | | |
% 169.69/25.93 | | | | | | | | | CLOSE: (246) is inconsistent.
% 169.69/25.93 | | | | | | | | |
% 169.69/25.93 | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | |
% 169.69/25.93 | | | | | | | | | (247) ~ (all_54_15 = e2)
% 169.69/25.93 | | | | | | | | | (248) all_54_15 = e1 | all_54_15 = e0
% 169.69/25.93 | | | | | | | | |
% 169.69/25.93 | | | | | | | | | BETA: splitting (25) gives:
% 169.69/25.93 | | | | | | | | |
% 169.69/25.93 | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | (249) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 169.69/25.93 | | | | | | | | | | e3 & op(e0, e2) = e3)
% 169.69/25.93 | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | BETA: splitting (249) gives:
% 169.69/25.93 | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | (250) all_58_12 = e3 & op(e0, e3) = e3
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | ALPHA: (250) implies:
% 169.69/25.93 | | | | | | | | | | | (251) all_58_12 = e3
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | BETA: splitting (69) gives:
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | (252) all_58_15 = e0 & op(e0, e0) = e0
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (12),
% 169.69/25.93 | | | | | | | | | | | | (13), (14), (17), (23), (25), (26), (27), (28),
% 169.69/25.93 | | | | | | | | | | | | (29), (30), (31), (33), (37), (38), (39), (40),
% 169.69/25.93 | | | | | | | | | | | | (42), (44), (46), (49), (50), (52), (54), (56),
% 169.69/25.93 | | | | | | | | | | | | (57), (58), (60), (61), (62), (63), (64), (65),
% 169.69/25.93 | | | | | | | | | | | | (66), (69), (70), (71), (72), (73), (77), (79),
% 169.69/25.93 | | | | | | | | | | | | (80), (83), (90), (104), (252) are inconsistent by
% 169.69/25.93 | | | | | | | | | | | | sub-proof #373.
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | (253) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 169.69/25.93 | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 169.69/25.93 | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 169.69/25.93 | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.69/25.93 | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | ALPHA: (253) implies:
% 169.69/25.93 | | | | | | | | | | | | (254) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 169.69/25.93 | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 169.69/25.93 | | | | | | | | | | | | e1) = e0)
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | REF_CLOSE: (23), (42), (56), (90), (104), (251), (254) are
% 169.69/25.93 | | | | | | | | | | | | inconsistent by sub-proof #545.
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | (255) all_58_13 = e3 & op(e0, e2) = e3
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | REF_CLOSE: (33), (54), (63), (255) are inconsistent by
% 169.69/25.93 | | | | | | | | | | | sub-proof #962.
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | End of split
% 169.69/25.93 | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | (256) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 169.69/25.93 | | | | | | | | | | e3 & op(e0, e0) = e3)
% 169.69/25.93 | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | BETA: splitting (256) gives:
% 169.69/25.93 | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | (257) all_58_14 = e3 & op(e0, e1) = e3
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | ALPHA: (257) implies:
% 169.69/25.93 | | | | | | | | | | | (258) all_58_14 = e3
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (31), (39), (42), (44),
% 169.69/25.93 | | | | | | | | | | | (54), (56), (58), (60), (61), (66), (70), (73),
% 169.69/25.93 | | | | | | | | | | | (80), (83), (258) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | #375.
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | (259) all_58_15 = e3 & op(e0, e0) = e3
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | ALPHA: (259) implies:
% 169.69/25.93 | | | | | | | | | | | (260) all_58_15 = e3
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | BETA: splitting (69) gives:
% 169.69/25.93 | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | (261) all_58_15 = e0 & op(e0, e0) = e0
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (12),
% 169.69/25.93 | | | | | | | | | | | | (13), (14), (17), (23), (25), (26), (27), (28),
% 169.69/25.93 | | | | | | | | | | | | (29), (30), (31), (33), (37), (38), (39), (40),
% 169.69/25.93 | | | | | | | | | | | | (42), (44), (46), (49), (50), (52), (54), (56),
% 169.69/25.93 | | | | | | | | | | | | (57), (58), (60), (61), (62), (63), (64), (65),
% 169.69/25.93 | | | | | | | | | | | | (66), (69), (70), (71), (72), (73), (77), (79),
% 169.69/25.93 | | | | | | | | | | | | (80), (83), (90), (104), (261) are inconsistent by
% 169.69/25.93 | | | | | | | | | | | | sub-proof #373.
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | (262) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 169.69/25.93 | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 169.69/25.93 | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 169.69/25.93 | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.69/25.93 | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | ALPHA: (262) implies:
% 169.69/25.93 | | | | | | | | | | | | (263) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 169.69/25.93 | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 169.69/25.93 | | | | | | | | | | | | e1) = e0)
% 169.69/25.93 | | | | | | | | | | | | (264) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 169.69/25.93 | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 169.69/25.93 | | | | | | | | | | | | e0) = e0)
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | BETA: splitting (248) gives:
% 169.69/25.93 | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | (265) all_54_15 = e1
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | REF_CLOSE: (16), (35), (265) are inconsistent by sub-proof
% 169.69/25.93 | | | | | | | | | | | | | #990.
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | Case 2:
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | (266) all_54_15 = e0
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | COMBINE_EQS: (35), (266) imply:
% 169.69/25.93 | | | | | | | | | | | | | (267) all_4_2 = e0
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | SIMP: (267) implies:
% 169.69/25.93 | | | | | | | | | | | | | (268) all_4_2 = e0
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | COMBINE_EQS: (41), (268) imply:
% 169.69/25.93 | | | | | | | | | | | | | (269) all_56_15 = e0
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | REDUCE: (243), (268) imply:
% 169.69/25.93 | | | | | | | | | | | | | (270) ~ (e3 = e0)
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | REDUCE: (7), (268) imply:
% 169.69/25.93 | | | | | | | | | | | | | (271) ~ (e2 = e0)
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | REDUCE: (16), (268) imply:
% 169.69/25.93 | | | | | | | | | | | | | (272) ~ (e1 = e0)
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | BETA: splitting (263) gives:
% 169.69/25.93 | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | (273) all_58_12 = e0 & op(e0, e3) = e0
% 169.69/25.93 | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | ALPHA: (273) implies:
% 169.69/25.93 | | | | | | | | | | | | | | (274) all_58_12 = e0
% 169.69/25.93 | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 169.69/25.93 | | | | | | | | | | | | | |
% 169.69/25.93 | | | | | | | | | | | | | | Case 1:
% 169.69/25.93 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | (275) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 169.69/25.94 | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.69/25.94 | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 169.69/25.94 | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.69/25.94 | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 169.69/25.94 | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 169.69/25.94 | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_6))))
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | REF_CLOSE: (8), (21), (24), (30), (39), (54), (67), (73),
% 169.69/25.94 | | | | | | | | | | | | | | | (275) are inconsistent by sub-proof #366.
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | (276) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 169.69/25.94 | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.69/25.94 | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.69/25.94 | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.69/25.94 | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.69/25.94 | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 169.69/25.94 | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.69/25.94 | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 169.69/25.94 | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 169.69/25.94 | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | BETA: splitting (276) gives:
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | (277) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 169.69/25.94 | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.69/25.94 | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.69/25.94 | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.94 | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.69/25.94 | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.69/25.94 | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.69/25.94 | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.69/25.94 | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | (278) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) =
% 169.69/25.94 | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 169.69/25.94 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 169.69/25.94 | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.69/25.94 | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | | | (279) ~ (all_56_12 = e2)
% 169.69/25.94 | | | | | | | | | | | | | | | | | (280) op(e2, e1) = e1
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | (281) all_58_9 = e0 & op(e3, e0) = e0
% 169.69/25.94 | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | (282) all_58_9 = e0
% 169.69/25.94 | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 169.69/25.94 | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (283) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (13), (17), (19), (23), (25), (30),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (33), (39), (42), (44), (54), (56), (58), (60),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (61), (63), (65), (73), (80), (83), (90), (260),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (274), (280), (283) are inconsistent by sub-proof
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | #360.
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (284) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (23), (25), (28), (29), (30),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (33), (37), (38), (39), (42), (44), (54), (56),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (58), (60), (61), (63), (70), (73), (77), (79),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (80), (83), (90), (260), (274), (282), (284) are
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #356.
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | (285) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 169.69/25.94 | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 169.69/25.94 | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 169.69/25.94 | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (286) all_58_10 = e0 & op(e2, e0) = e0
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (287) op(e2, e0) = e0
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (10), (13), (17), (19), (23), (25),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (28), (29), (30), (33), (37), (38), (39), (42),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (44), (49), (54), (56), (58), (60), (61), (63),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (65), (70), (73), (77), (79), (80), (83), (90),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (105), (260), (274), (287) are inconsistent by
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | sub-proof #355.
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (288) all_58_11 = e0 & op(e1, e0) = e0
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | (289) all_58_11 = e0
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | (290) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (13), (17), (19), (23), (25), (30),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | (33), (39), (42), (44), (54), (56), (58), (60),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | (61), (63), (65), (73), (80), (83), (90), (260),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | (274), (280), (290) are inconsistent by sub-proof
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | #360.
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | (291) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (291) gives:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | | (292) all_58_11 = e1 & op(e1, e0) = e1
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (289), (292) are inconsistent by sub-proof
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | | #354.
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | | (293) all_58_15 = e1 & op(e0, e0) = e1
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (23), (28), (30), (37), (38),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | | (39), (42), (44), (54), (56), (58), (60), (61),
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | | (70), (73), (77), (79), (80), (83), (260), (293)
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #357.
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | (294) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) =
% 169.69/25.94 | | | | | | | | | | | | | | | | | e0 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.69/25.94 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 169.69/25.94 | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 169.69/25.94 | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | ALPHA: (294) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | | | (295) ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2,
% 169.69/25.94 | | | | | | | | | | | | | | | | | e3) = all_56_0 & $i(all_56_0))
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (67), (295) are inconsistent by sub-proof
% 169.69/25.94 | | | | | | | | | | | | | | | | | #368.
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | (296) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.69/25.94 | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 169.69/25.94 | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 169.69/25.94 | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.69/25.94 | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 169.69/25.94 | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 169.69/25.94 | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.69/25.94 | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.69/25.94 | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 169.69/25.94 | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 169.69/25.94 | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 169.69/25.94 | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.69/25.94 | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 169.69/25.94 | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 169.69/25.94 | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | BETA: splitting (296) gives:
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | (297) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 169.69/25.94 | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 169.69/25.94 | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 169.69/25.94 | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 169.69/25.94 | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | ALPHA: (297) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | | | (298) op(e2, e0) = e0
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (10), (13), (17), (19), (23), (25),
% 169.69/25.94 | | | | | | | | | | | | | | | | | (28), (29), (30), (33), (37), (38), (39), (42),
% 169.69/25.94 | | | | | | | | | | | | | | | | | (44), (49), (54), (56), (58), (60), (61), (63),
% 169.69/25.94 | | | | | | | | | | | | | | | | | (65), (70), (73), (77), (79), (80), (83), (90),
% 169.69/25.94 | | | | | | | | | | | | | | | | | (105), (260), (274), (298) are inconsistent by
% 169.69/25.94 | | | | | | | | | | | | | | | | | sub-proof #355.
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | (299) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 169.69/25.94 | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 169.69/25.94 | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 169.69/25.94 | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.69/25.94 | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 169.69/25.94 | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 169.69/25.94 | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 169.69/25.94 | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 169.69/25.94 | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 169.69/25.94 | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 169.69/25.94 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 169.69/25.94 | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 169.69/25.94 | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 169.69/25.94 | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (24), (269), (299) are inconsistent by
% 169.69/25.94 | | | | | | | | | | | | | | | | | sub-proof #353.
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | (300) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 169.69/25.94 | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | BETA: splitting (300) gives:
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | (301) all_58_13 = e0 & op(e0, e2) = e0
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | REF_CLOSE: (23), (104), (301) are inconsistent by sub-proof
% 169.69/25.94 | | | | | | | | | | | | | | | #582.
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | (302) all_58_14 = e0 & op(e0, e1) = e0
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | REF_CLOSE: (56), (90), (302) are inconsistent by sub-proof
% 169.69/25.94 | | | | | | | | | | | | | | | #858.
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | End of split
% 169.69/25.94 | | | | | | | |
% 169.69/25.94 | | | | | | | End of split
% 169.69/25.94 | | | | | | |
% 169.69/25.94 | | | | | | End of split
% 169.69/25.94 | | | | | |
% 169.69/25.94 | | | | | Case 2:
% 169.69/25.94 | | | | | |
% 169.69/25.94 | | | | | | (303) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 169.69/25.94 | | | | | | op(e0, e0) = e1)
% 169.69/25.94 | | | | | |
% 169.69/25.94 | | | | | | BETA: splitting (303) gives:
% 169.69/25.94 | | | | | |
% 169.69/25.94 | | | | | | Case 1:
% 169.69/25.94 | | | | | | |
% 169.69/25.94 | | | | | | | (304) all_58_14 = e1 & op(e0, e1) = e1
% 169.69/25.94 | | | | | | |
% 169.69/25.94 | | | | | | | ALPHA: (304) implies:
% 169.69/25.94 | | | | | | | (305) op(e0, e1) = e1
% 169.69/25.94 | | | | | | |
% 169.69/25.94 | | | | | | | REF_CLOSE: (54), (61), (91), (305) are inconsistent by sub-proof
% 169.69/25.94 | | | | | | | #967.
% 169.69/25.94 | | | | | | |
% 169.69/25.94 | | | | | | Case 2:
% 169.69/25.94 | | | | | | |
% 169.69/25.94 | | | | | | | (306) all_58_15 = e1 & op(e0, e0) = e1
% 169.69/25.94 | | | | | | |
% 169.69/25.94 | | | | | | | ALPHA: (306) implies:
% 169.69/25.94 | | | | | | | (307) all_58_15 = e1
% 169.69/25.94 | | | | | | |
% 169.69/25.94 | | | | | | | BETA: splitting (25) gives:
% 169.69/25.94 | | | | | | |
% 169.69/25.94 | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | |
% 169.69/25.94 | | | | | | | | (308) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 169.69/25.94 | | | | | | | | op(e0, e2) = e3)
% 169.69/25.94 | | | | | | | |
% 169.69/25.94 | | | | | | | | BETA: splitting (308) gives:
% 169.69/25.94 | | | | | | | |
% 169.69/25.94 | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | (309) all_58_12 = e3 & op(e0, e3) = e3
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | ALPHA: (309) implies:
% 169.69/25.94 | | | | | | | | | (310) all_58_12 = e3
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | BETA: splitting (64) gives:
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | (311) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3
% 169.69/25.94 | | | | | | | | | | & op(e2, e0) = e3)
% 169.69/25.94 | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | REF_CLOSE: (5), (6), (9), (10), (17), (23), (26), (30), (39),
% 169.69/25.94 | | | | | | | | | | (40), (42), (44), (52), (54), (56), (58), (60),
% 169.69/25.94 | | | | | | | | | | (61), (65), (72), (73), (80), (83), (310), (311)
% 169.69/25.94 | | | | | | | | | | are inconsistent by sub-proof #387.
% 169.69/25.94 | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | (312) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 169.69/25.94 | | | | | | | | | | e3 & op(e0, e0) = e3)
% 169.69/25.94 | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | BETA: splitting (312) gives:
% 169.69/25.94 | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | (313) all_58_11 = e3 & op(e1, e0) = e3
% 169.69/25.94 | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | ALPHA: (313) implies:
% 169.69/25.94 | | | | | | | | | | | (314) all_58_11 = e3
% 169.69/25.94 | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | BETA: splitting (29) gives:
% 169.69/25.94 | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | (315) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 169.69/25.94 | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 169.69/25.94 | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | BETA: splitting (315) gives:
% 169.69/25.94 | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | (316) all_58_9 = e2 & op(e3, e0) = e2
% 169.69/25.94 | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | ALPHA: (316) implies:
% 169.69/25.94 | | | | | | | | | | | | | (317) all_58_9 = e2
% 169.69/25.94 | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | BETA: splitting (17) gives:
% 169.69/25.94 | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | (318) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 169.69/25.94 | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | (319) all_58_0 = e0 & op(e3, e3) = e0
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | (320) op(e3, e3) = e0
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | REF_CLOSE: (19), (23), (54), (320) are inconsistent by
% 169.69/25.94 | | | | | | | | | | | | | | | sub-proof #907.
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | (321) all_58_1 = e0 & op(e3, e2) = e0
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | ALPHA: (321) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | (322) all_58_1 = e0
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | (323) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2
% 169.69/25.94 | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | (324) all_58_6 = e2 & op(e1, e3) = e2
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | | | (325) all_58_6 = e2
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (13), (23), (26), (30), (39),
% 169.69/25.94 | | | | | | | | | | | | | | | | | (42), (44), (54), (56), (58), (60), (61), (73),
% 169.69/25.94 | | | | | | | | | | | | | | | | | (80), (325) are inconsistent by sub-proof #400.
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | (326) all_58_7 = e2 & op(e1, e2) = e2
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | ALPHA: (326) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | | | (327) all_58_7 = e2
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (12), (23), (25), (30), (39), (42),
% 169.69/25.94 | | | | | | | | | | | | | | | | | (44), (54), (56), (58), (60), (61), (69), (73),
% 169.69/25.94 | | | | | | | | | | | | | | | | | (80), (90), (307), (310), (322), (327) are
% 169.69/25.94 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #352.
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | (328) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 =
% 169.69/25.94 | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | BETA: splitting (328) gives:
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | (329) all_58_8 = e2 & op(e1, e1) = e2
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | ALPHA: (329) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | | | (330) all_58_8 = e2
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (31), (42), (56), (61), (66), (80), (83),
% 169.69/25.94 | | | | | | | | | | | | | | | | | (90), (330) are inconsistent by sub-proof #395.
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | (331) all_58_11 = e2 & op(e1, e0) = e2
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | ALPHA: (331) implies:
% 169.69/25.94 | | | | | | | | | | | | | | | | | (332) all_58_11 = e2
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (39), (42), (44), (54),
% 169.69/25.94 | | | | | | | | | | | | | | | | | (56), (58), (60), (61), (73), (80), (314), (332)
% 169.69/25.94 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #421.
% 169.69/25.94 | | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | (333) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 169.69/25.94 | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | | REF_CLOSE: (42), (56), (83), (317), (333) are inconsistent by
% 169.69/25.94 | | | | | | | | | | | | | | sub-proof #703.
% 169.69/25.94 | | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | (334) all_58_10 = e2 & op(e2, e0) = e2
% 169.69/25.94 | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | | REF_CLOSE: (5), (23), (30), (39), (42), (44), (54), (56),
% 169.69/25.94 | | | | | | | | | | | | | (58), (61), (80), (334) are inconsistent by
% 169.69/25.94 | | | | | | | | | | | | | sub-proof #447.
% 169.69/25.94 | | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | (335) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 169.69/25.94 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 169.69/25.94 | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | | REF_CLOSE: (5), (7), (10), (23), (30), (39), (42), (44),
% 169.69/25.94 | | | | | | | | | | | | (46), (54), (56), (58), (60), (61), (73), (80),
% 169.69/25.94 | | | | | | | | | | | | (314), (335) are inconsistent by sub-proof #420.
% 169.69/25.94 | | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | (336) all_58_15 = e3 & op(e0, e0) = e3
% 169.69/25.94 | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (23), (28), (30), (37), (38),
% 169.69/25.94 | | | | | | | | | | | (39), (42), (44), (54), (56), (58), (60), (61),
% 169.69/25.94 | | | | | | | | | | | (70), (73), (77), (79), (80), (83), (307), (336)
% 169.69/25.94 | | | | | | | | | | | are inconsistent by sub-proof #351.
% 169.69/25.94 | | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | | |
% 169.69/25.94 | | | | | | | | | End of split
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | (337) all_58_13 = e3 & op(e0, e2) = e3
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | REF_CLOSE: (33), (54), (63), (337) are inconsistent by
% 169.69/25.94 | | | | | | | | | sub-proof #962.
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | End of split
% 169.69/25.94 | | | | | | | |
% 169.69/25.94 | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | |
% 169.69/25.94 | | | | | | | | (338) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 169.69/25.94 | | | | | | | | op(e0, e0) = e3)
% 169.69/25.94 | | | | | | | |
% 169.69/25.94 | | | | | | | | BETA: splitting (338) gives:
% 169.69/25.94 | | | | | | | |
% 169.69/25.94 | | | | | | | | Case 1:
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | (339) all_58_14 = e3 & op(e0, e1) = e3
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | ALPHA: (339) implies:
% 169.69/25.94 | | | | | | | | | (340) all_58_14 = e3
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (31), (39), (42), (44),
% 169.69/25.94 | | | | | | | | | (54), (56), (58), (60), (61), (66), (70), (73),
% 169.69/25.94 | | | | | | | | | (80), (83), (340) are inconsistent by sub-proof
% 169.69/25.94 | | | | | | | | | #375.
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | Case 2:
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | (341) all_58_15 = e3 & op(e0, e0) = e3
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | | REF_CLOSE: (2), (5), (10), (23), (28), (30), (37), (38), (39),
% 169.69/25.94 | | | | | | | | | (42), (44), (54), (56), (58), (60), (61), (70),
% 169.69/25.94 | | | | | | | | | (73), (77), (79), (80), (83), (307), (341) are
% 169.69/25.94 | | | | | | | | | inconsistent by sub-proof #351.
% 169.69/25.94 | | | | | | | | |
% 169.69/25.94 | | | | | | | | End of split
% 169.69/25.94 | | | | | | | |
% 169.69/25.94 | | | | | | | End of split
% 169.69/25.94 | | | | | | |
% 169.69/25.94 | | | | | | End of split
% 169.69/25.94 | | | | | |
% 169.69/25.94 | | | | | End of split
% 169.69/25.94 | | | | |
% 169.69/25.94 | | | | End of split
% 169.69/25.94 | | | |
% 169.69/25.94 | | | End of split
% 169.69/25.94 | | |
% 169.69/25.94 | | Case 2:
% 169.69/25.94 | | |
% 169.69/25.94 | | | (342) all_58_5 = e3 & op(e2, e1) = e3
% 169.69/25.94 | | |
% 169.69/25.94 | | | ALPHA: (342) implies:
% 169.69/25.94 | | | (343) op(e2, e1) = e3
% 169.69/25.94 | | |
% 169.69/25.94 | | | REF_CLOSE: (2), (54), (77), (343) are inconsistent by sub-proof #951.
% 169.69/25.94 | | |
% 169.69/25.94 | | End of split
% 169.69/25.94 | |
% 169.69/25.94 | Case 2:
% 169.69/25.94 | |
% 169.69/25.94 | | (344) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 169.69/25.94 | | e3)
% 169.69/25.94 | |
% 169.69/25.94 | | BETA: splitting (344) gives:
% 169.69/25.94 | |
% 169.69/25.94 | | Case 1:
% 169.69/25.94 | | |
% 169.69/25.94 | | | (345) all_58_8 = e3 & op(e1, e1) = e3
% 169.69/25.94 | | |
% 169.69/25.94 | | | REF_CLOSE: (38), (54), (79), (345) are inconsistent by sub-proof #961.
% 169.69/25.94 | | |
% 169.69/25.94 | | Case 2:
% 169.69/25.94 | | |
% 169.69/25.94 | | | (346) all_58_14 = e3 & op(e0, e1) = e3
% 169.69/25.94 | | |
% 169.69/25.94 | | | ALPHA: (346) implies:
% 169.69/25.94 | | | (347) all_58_14 = e3
% 169.69/25.94 | | |
% 169.69/25.94 | | | BETA: splitting (53) gives:
% 169.69/25.94 | | |
% 169.69/25.94 | | | Case 1:
% 169.69/25.94 | | | |
% 169.69/25.94 | | | | (348) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 169.69/25.94 | | | | = e3)
% 169.69/25.94 | | | |
% 169.69/25.94 | | | | BETA: splitting (348) gives:
% 169.69/25.94 | | | |
% 169.69/25.94 | | | | Case 1:
% 169.69/25.94 | | | | |
% 169.69/25.94 | | | | | (349) all_58_0 = e3 & op(e3, e3) = e3
% 169.69/25.94 | | | | |
% 169.69/25.94 | | | | | ALPHA: (349) implies:
% 169.69/25.94 | | | | | (350) op(e3, e3) = e3
% 169.69/25.94 | | | | |
% 169.69/25.95 | | | | | REF_CLOSE: (1), (5), (7), (9), (10), (12), (17), (20), (23), (26),
% 169.69/25.95 | | | | | (27), (29), (30), (31), (37), (38), (39), (40), (42), (44),
% 169.69/25.95 | | | | | (46), (49), (50), (52), (53), (54), (56), (57), (58), (60),
% 169.69/25.95 | | | | | (61), (62), (66), (69), (70), (71), (73), (75), (80),
% 169.69/25.95 | | | | | (347), (350) are inconsistent by sub-proof #410.
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | Case 2:
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | | (351) all_58_1 = e3 & op(e3, e2) = e3
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | | ALPHA: (351) implies:
% 169.69/25.95 | | | | | (352) op(e3, e2) = e3
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | | REF_CLOSE: (54), (62), (75), (352) are inconsistent by sub-proof #974.
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | End of split
% 169.69/25.95 | | | |
% 169.69/25.95 | | | Case 2:
% 169.69/25.95 | | | |
% 169.69/25.95 | | | | (353) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 169.69/25.95 | | | | = e3)
% 169.69/25.95 | | | |
% 169.69/25.95 | | | | BETA: splitting (353) gives:
% 169.69/25.95 | | | |
% 169.69/25.95 | | | | Case 1:
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | | (354) all_58_4 = e3 & op(e3, e1) = e3
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | | ALPHA: (354) implies:
% 169.69/25.95 | | | | | (355) all_58_4 = e3
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | | REF_CLOSE: (5), (10), (23), (30), (31), (39), (42), (44), (54), (56),
% 169.69/25.95 | | | | | (58), (60), (61), (66), (70), (73), (80), (347), (355) are
% 169.69/25.95 | | | | | inconsistent by sub-proof #375.
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | Case 2:
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | | (356) all_58_9 = e3 & op(e3, e0) = e3
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | | ALPHA: (356) implies:
% 169.69/25.95 | | | | | (357) all_58_9 = e3
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | | BETA: splitting (20) gives:
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | | Case 1:
% 169.69/25.95 | | | | | |
% 169.69/25.95 | | | | | | (358) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 169.69/25.95 | | | | | | op(e0, e2) = e1)
% 169.69/25.95 | | | | | |
% 169.69/25.95 | | | | | | BETA: splitting (358) gives:
% 169.69/25.95 | | | | | |
% 169.69/25.95 | | | | | | Case 1:
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | (359) all_58_12 = e1 & op(e0, e3) = e1
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | ALPHA: (359) implies:
% 169.69/25.95 | | | | | | | (360) all_58_12 = e1
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | BETA: splitting (26) gives:
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | (361) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 169.69/25.95 | | | | | | | | op(e2, e3) = e3)
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | BETA: splitting (361) gives:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (362) all_58_0 = e3 & op(e3, e3) = e3
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | ALPHA: (362) implies:
% 169.69/25.95 | | | | | | | | | (363) op(e3, e3) = e3
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | REF_CLOSE: (1), (5), (7), (9), (10), (12), (17), (20), (23),
% 169.69/25.95 | | | | | | | | | (26), (27), (29), (30), (31), (37), (38), (39),
% 169.69/25.95 | | | | | | | | | (40), (42), (44), (46), (49), (50), (52), (53),
% 169.69/25.95 | | | | | | | | | (54), (56), (57), (58), (60), (61), (62), (66),
% 169.69/25.95 | | | | | | | | | (69), (70), (71), (73), (75), (80), (347), (363)
% 169.69/25.95 | | | | | | | | | are inconsistent by sub-proof #410.
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (364) all_58_2 = e3 & op(e2, e3) = e3
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | ALPHA: (364) implies:
% 169.69/25.95 | | | | | | | | | (365) op(e2, e3) = e3
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | REF_CLOSE: (30), (39), (54), (73), (365) are inconsistent by
% 169.69/25.95 | | | | | | | | | sub-proof #462.
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | End of split
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | (366) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 169.69/25.95 | | | | | | | | op(e0, e3) = e3)
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | BETA: splitting (366) gives:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (367) all_58_6 = e3 & op(e1, e3) = e3
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | ALPHA: (367) implies:
% 169.69/25.95 | | | | | | | | | (368) all_58_6 = e3
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | REF_CLOSE: (9), (13), (23), (30), (39), (42), (54), (56),
% 169.69/25.95 | | | | | | | | | (360), (368) are inconsistent by sub-proof #459.
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (369) all_58_12 = e3 & op(e0, e3) = e3
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | REF_CLOSE: (80), (360), (369) are inconsistent by sub-proof
% 169.69/25.95 | | | | | | | | | #490.
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | End of split
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | End of split
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | Case 2:
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | (370) all_58_13 = e1 & op(e0, e2) = e1
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | ALPHA: (370) implies:
% 169.69/25.95 | | | | | | | (371) all_58_13 = e1
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | BETA: splitting (65) gives:
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | (372) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 169.69/25.95 | | | | | | | | op(e3, e2) = e2)
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | BETA: splitting (372) gives:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (373) all_58_0 = e2 & op(e3, e3) = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | REF_CLOSE: (13), (61), (373) are inconsistent by sub-proof
% 169.69/25.95 | | | | | | | | | #393.
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (374) all_58_1 = e2 & op(e3, e2) = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | ALPHA: (374) implies:
% 169.69/25.95 | | | | | | | | | (375) all_58_1 = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | REF_CLOSE: (1), (5), (7), (9), (10), (12), (13), (23), (26),
% 169.69/25.95 | | | | | | | | | (30), (39), (42), (44), (46), (50), (54), (56),
% 169.69/25.95 | | | | | | | | | (58), (60), (61), (73), (80), (347), (375) are
% 169.69/25.95 | | | | | | | | | inconsistent by sub-proof #350.
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | End of split
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | (376) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 &
% 169.69/25.95 | | | | | | | | op(e3, e0) = e2)
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | BETA: splitting (376) gives:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (377) all_58_4 = e2 & op(e3, e1) = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | ALPHA: (377) implies:
% 169.69/25.95 | | | | | | | | | (378) all_58_4 = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | BETA: splitting (1) gives:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | (379) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 =
% 169.69/25.95 | | | | | | | | | | e2 & op(e0, e2) = e2)
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | BETA: splitting (379) gives:
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | (380) all_58_12 = e2 & op(e0, e3) = e2
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | ALPHA: (380) implies:
% 169.69/25.95 | | | | | | | | | | | (381) all_58_12 = e2
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | REF_CLOSE: (9), (10), (13), (23), (26), (42), (56), (73),
% 169.69/25.95 | | | | | | | | | | | (80), (381) are inconsistent by sub-proof #435.
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | (382) all_58_13 = e2 & op(e0, e2) = e2
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | ALPHA: (382) implies:
% 169.69/25.95 | | | | | | | | | | | (383) all_58_13 = e2
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | COMBINE_EQS: (371), (383) imply:
% 169.69/25.95 | | | | | | | | | | | (384) e2 = e1
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | COMBINE_EQS: (378), (384) imply:
% 169.69/25.95 | | | | | | | | | | | (385) all_58_4 = e1
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (37), (38), (39), (42),
% 169.69/25.95 | | | | | | | | | | | (44), (54), (56), (58), (60), (61), (70), (73),
% 169.69/25.95 | | | | | | | | | | | (80), (347), (385) are inconsistent by sub-proof
% 169.69/25.95 | | | | | | | | | | | #408.
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | (386) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 169.69/25.95 | | | | | | | | | | e2 & op(e0, e0) = e2)
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | REF_CLOSE: (5), (7), (10), (23), (30), (39), (42), (44),
% 169.69/25.95 | | | | | | | | | | (46), (54), (56), (58), (60), (61), (73), (80),
% 169.69/25.95 | | | | | | | | | | (347), (386) are inconsistent by sub-proof #437.
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (387) all_58_9 = e2 & op(e3, e0) = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (39), (42), (44), (54),
% 169.69/25.95 | | | | | | | | | (56), (58), (60), (61), (73), (80), (357), (387)
% 169.69/25.95 | | | | | | | | | are inconsistent by sub-proof #349.
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | End of split
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | End of split
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | End of split
% 169.69/25.95 | | | | | |
% 169.69/25.95 | | | | | Case 2:
% 169.69/25.95 | | | | | |
% 169.69/25.95 | | | | | | (388) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 169.69/25.95 | | | | | | op(e0, e0) = e1)
% 169.69/25.95 | | | | | |
% 169.69/25.95 | | | | | | BETA: splitting (388) gives:
% 169.69/25.95 | | | | | |
% 169.69/25.95 | | | | | | Case 1:
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | (389) all_58_14 = e1 & op(e0, e1) = e1
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | ALPHA: (389) implies:
% 169.69/25.95 | | | | | | | (390) all_58_14 = e1
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | REF_CLOSE: (80), (347), (390) are inconsistent by sub-proof #626.
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | Case 2:
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | (391) all_58_15 = e1 & op(e0, e0) = e1
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | ALPHA: (391) implies:
% 169.69/25.95 | | | | | | | (392) all_58_15 = e1
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | BETA: splitting (65) gives:
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | (393) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 &
% 169.69/25.95 | | | | | | | | op(e3, e2) = e2)
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | BETA: splitting (393) gives:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (394) all_58_0 = e2 & op(e3, e3) = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | REF_CLOSE: (13), (61), (394) are inconsistent by sub-proof
% 169.69/25.95 | | | | | | | | | #393.
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (395) all_58_1 = e2 & op(e3, e2) = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | ALPHA: (395) implies:
% 169.69/25.95 | | | | | | | | | (396) all_58_1 = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | REF_CLOSE: (1), (5), (7), (9), (10), (12), (13), (23), (26),
% 169.69/25.95 | | | | | | | | | (30), (39), (42), (44), (46), (50), (54), (56),
% 169.69/25.95 | | | | | | | | | (58), (60), (61), (73), (80), (347), (396) are
% 169.69/25.95 | | | | | | | | | inconsistent by sub-proof #350.
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | End of split
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | (397) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 &
% 169.69/25.95 | | | | | | | | op(e3, e0) = e2)
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | BETA: splitting (397) gives:
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (398) all_58_4 = e2 & op(e3, e1) = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | ALPHA: (398) implies:
% 169.69/25.95 | | | | | | | | | (399) all_58_4 = e2
% 169.69/25.95 | | | | | | | | | (400) op(e3, e1) = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | BETA: splitting (29) gives:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | (401) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2
% 169.69/25.95 | | | | | | | | | | & op(e2, e0) = e2)
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (39), (42), (44), (54),
% 169.69/25.95 | | | | | | | | | | (56), (58), (60), (61), (73), (80), (357), (401)
% 169.69/25.95 | | | | | | | | | | are inconsistent by sub-proof #446.
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | (402) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 169.69/25.95 | | | | | | | | | | e2 & op(e0, e0) = e2)
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | BETA: splitting (402) gives:
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | (403) all_58_11 = e2 & op(e1, e0) = e2
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | ALPHA: (403) implies:
% 169.69/25.95 | | | | | | | | | | | (404) all_58_11 = e2
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | BETA: splitting (57) gives:
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | (405) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 169.69/25.95 | | | | | | | | | | | | & op(e1, e2) = e3)
% 169.69/25.95 | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | BETA: splitting (405) gives:
% 169.69/25.95 | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | (406) all_58_6 = e3 & op(e1, e3) = e3
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | ALPHA: (406) implies:
% 169.69/25.95 | | | | | | | | | | | | | (407) all_58_6 = e3
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | BETA: splitting (69) gives:
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | (408) all_58_15 = e0 & op(e0, e0) = e0
% 169.69/25.95 | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | ALPHA: (408) implies:
% 169.69/25.95 | | | | | | | | | | | | | | (409) all_58_15 = e0
% 169.69/25.95 | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | REF_CLOSE: (23), (392), (409) are inconsistent by sub-proof
% 169.69/25.95 | | | | | | | | | | | | | | #881.
% 169.69/25.95 | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | (410) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 169.69/25.95 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 169.69/25.95 | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 169.69/25.95 | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.69/25.95 | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.69/25.95 | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | ALPHA: (410) implies:
% 169.69/25.95 | | | | | | | | | | | | | | (411) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 169.69/25.95 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 169.69/25.95 | | | | | | | | | | | | | | e0) = e0)
% 169.69/25.95 | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 169.69/25.95 | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | (412) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 169.69/25.95 | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 169.69/25.95 | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | BETA: splitting (412) gives:
% 169.69/25.95 | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | (413) all_58_2 = e1 & op(e2, e3) = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | ALPHA: (413) implies:
% 169.69/25.95 | | | | | | | | | | | | | | | | (414) op(e2, e3) = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (39), (54), (61), (414) are inconsistent by
% 169.69/25.95 | | | | | | | | | | | | | | | | sub-proof #784.
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | (415) all_58_3 = e1 & op(e2, e2) = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | ALPHA: (415) implies:
% 169.69/25.95 | | | | | | | | | | | | | | | | (416) all_58_3 = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (416) imply:
% 169.69/25.95 | | | | | | | | | | | | | | | | (417) e3 = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | SIMP: (417) implies:
% 169.69/25.95 | | | | | | | | | | | | | | | | (418) e3 = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | COMBINE_EQS: (407), (418) imply:
% 169.69/25.95 | | | | | | | | | | | | | | | | (419) all_58_6 = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (13), (23), (26), (30), (39), (42),
% 169.69/25.95 | | | | | | | | | | | | | | | | (54), (56), (73), (80), (419) are inconsistent by
% 169.69/25.95 | | | | | | | | | | | | | | | | sub-proof #455.
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | (420) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 169.69/25.95 | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 169.69/25.95 | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | BETA: splitting (420) gives:
% 169.69/25.95 | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | (421) all_58_5 = e1 & op(e2, e1) = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | ALPHA: (421) implies:
% 169.69/25.95 | | | | | | | | | | | | | | | | (422) op(e2, e1) = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | (423) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 169.69/25.95 | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 169.69/25.95 | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | BETA: splitting (423) gives:
% 169.69/25.95 | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | (424) all_58_4 = e0 & op(e3, e1) = e0
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (399), (424) are inconsistent by sub-proof
% 169.69/25.95 | | | | | | | | | | | | | | | | | | #902.
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | (425) all_58_5 = e0 & op(e2, e1) = e0
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | ALPHA: (425) implies:
% 169.69/25.95 | | | | | | | | | | | | | | | | | | (426) op(e2, e1) = e0
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (54), (422), (426) are inconsistent by
% 169.69/25.95 | | | | | | | | | | | | | | | | | | sub-proof #911.
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | (427) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 169.69/25.95 | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 169.69/25.95 | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | BETA: splitting (427) gives:
% 169.69/25.95 | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (54) with e3, e2, e1, e3,
% 169.69/25.95 | | | | | | | | | | | | | | | | | | simplifying with (32), (400) gives:
% 169.69/25.95 | | | | | | | | | | | | | | | | | | (428) e3 = e2
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (428) imply:
% 169.69/25.95 | | | | | | | | | | | | | | | | | | (429) all_58_3 = e2
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (39), (42), (44), (54),
% 169.69/25.95 | | | | | | | | | | | | | | | | | | (56), (60), (61), (73), (80), (429) are
% 169.69/25.95 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #779.
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | (430) all_58_14 = e0 & op(e0, e1) = e0
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | ALPHA: (430) implies:
% 169.69/25.95 | | | | | | | | | | | | | | | | | | (431) all_58_14 = e0
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (347), (431) are inconsistent by sub-proof
% 169.69/25.95 | | | | | | | | | | | | | | | | | | #423.
% 169.69/25.95 | | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | (432) all_58_10 = e1 & op(e2, e0) = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | ALPHA: (432) implies:
% 169.69/25.95 | | | | | | | | | | | | | | | | (433) all_58_10 = e1
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | | REF_CLOSE: (23), (42), (56), (357), (404), (411), (433) are
% 169.69/25.95 | | | | | | | | | | | | | | | | inconsistent by sub-proof #833.
% 169.69/25.95 | | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | (434) all_58_7 = e3 & op(e1, e2) = e3
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | ALPHA: (434) implies:
% 169.69/25.95 | | | | | | | | | | | | | (435) all_58_7 = e3
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (5), (7), (9), (10), (12), (23), (26),
% 169.69/25.95 | | | | | | | | | | | | | (27), (28), (30), (38), (39), (40), (42), (44),
% 169.69/25.95 | | | | | | | | | | | | | (46), (49), (50), (54), (56), (58), (60), (61),
% 169.69/25.95 | | | | | | | | | | | | | (62), (71), (73), (77), (79), (80), (399), (435)
% 169.69/25.95 | | | | | | | | | | | | | are inconsistent by sub-proof #346.
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | (436) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 169.69/25.95 | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 169.69/25.95 | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | BETA: splitting (436) gives:
% 169.69/25.95 | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | Case 1:
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | (437) all_58_8 = e3 & op(e1, e1) = e3
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | ALPHA: (437) implies:
% 169.69/25.95 | | | | | | | | | | | | | (438) all_58_8 = e3
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | REF_CLOSE: (23), (31), (42), (56), (61), (66), (80), (347),
% 169.69/25.95 | | | | | | | | | | | | | (399), (438) are inconsistent by sub-proof #422.
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | (439) all_58_11 = e3 & op(e1, e0) = e3
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | ALPHA: (439) implies:
% 169.69/25.95 | | | | | | | | | | | | | (440) all_58_11 = e3
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (10), (23), (29), (30), (39), (42),
% 169.69/25.95 | | | | | | | | | | | | | (44), (46), (54), (56), (58), (60), (61), (73),
% 169.69/25.95 | | | | | | | | | | | | | (80), (357), (440) are inconsistent by sub-proof
% 169.69/25.95 | | | | | | | | | | | | | #418.
% 169.69/25.95 | | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | (441) all_58_15 = e2 & op(e0, e0) = e2
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | | REF_CLOSE: (7), (46), (54), (441) are inconsistent by
% 169.69/25.95 | | | | | | | | | | | sub-proof #854.
% 169.69/25.95 | | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | | |
% 169.69/25.95 | | | | | | | | | End of split
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | Case 2:
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | (442) all_58_9 = e2 & op(e3, e0) = e2
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | | REF_CLOSE: (5), (10), (23), (30), (39), (42), (44), (54),
% 169.69/25.95 | | | | | | | | | (56), (58), (60), (61), (73), (80), (357), (442)
% 169.69/25.95 | | | | | | | | | are inconsistent by sub-proof #349.
% 169.69/25.95 | | | | | | | | |
% 169.69/25.95 | | | | | | | | End of split
% 169.69/25.95 | | | | | | | |
% 169.69/25.95 | | | | | | | End of split
% 169.69/25.95 | | | | | | |
% 169.69/25.95 | | | | | | End of split
% 169.69/25.95 | | | | | |
% 169.69/25.95 | | | | | End of split
% 169.69/25.95 | | | | |
% 169.69/25.95 | | | | End of split
% 169.69/25.95 | | | |
% 169.69/25.95 | | | End of split
% 169.69/25.95 | | |
% 169.69/25.95 | | End of split
% 169.69/25.95 | |
% 169.69/25.95 | End of split
% 169.69/25.95 |
% 169.69/25.95 End of proof
% 169.69/25.95
% 169.69/25.95 Sub-proof #346 shows that the following formulas are inconsistent:
% 169.69/25.95 ----------------------------------------------------------------
% 169.69/25.95 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.69/25.95 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.69/25.95 (2) op(e2, e1) = all_52_9
% 169.69/25.95 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.95 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.95 (4) ~ (all_52_9 = e3)
% 169.69/25.95 (5) ~ (all_4_2 = e2)
% 169.69/25.95 (6) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.69/25.95 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.69/25.95 (7) all_58_2 = e2
% 169.69/25.95 (8) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.95 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.69/25.95 (9) ~ (all_6_2 = e3)
% 169.69/25.95 (10) ~ (e3 = e1)
% 169.69/25.95 (11) ~ (e1 = e0)
% 169.69/25.95 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.69/25.95 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.69/25.95 (13) op(e1, e2) = all_52_6
% 169.69/25.95 (14) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.69/25.95 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.69/25.95 (15) op(e2, e3) = all_52_1
% 169.69/25.95 (16) op(e1, e1) = all_6_2
% 169.69/25.95 (17) op(e2, e3) = e2
% 169.69/25.95 (18) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.69/25.95 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.69/25.95 (19) ~ (e3 = e0)
% 169.69/25.95 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.95 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.95 (21) op(e0, e0) = all_4_2
% 169.69/25.95 (22) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.69/25.95 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.69/25.95 e2) = all_22_1 & $i(all_22_1))
% 169.69/25.95 (23) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.95 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.69/25.95 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.95 (25) ~ (e2 = e0)
% 169.69/25.95 (26) all_58_3 = e3
% 169.69/25.95 (27) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.95 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.95 (28) ~ (e2 = e1)
% 169.69/25.95 (29) op(e3, e2) = all_52_4
% 169.69/25.95 (30) all_58_4 = e2
% 169.69/25.95 (31) all_58_7 = e3
% 169.69/25.95 (32) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.69/25.95 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.69/25.95 e2) = all_14_1 & $i(all_14_1))
% 169.69/25.95 (33) ~ (e3 = e2)
% 169.69/25.95
% 169.69/25.95 Begin of proof
% 169.69/25.95 |
% 169.69/25.95 | BETA: splitting (14) gives:
% 169.69/25.95 |
% 169.69/25.95 | Case 1:
% 169.69/25.95 | |
% 169.69/25.95 | | (34) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 169.69/25.95 | | e3)
% 169.69/25.95 | |
% 169.69/25.95 | | REF_CLOSE: (2), (3), (4), (7), (10), (11), (15), (17), (19), (20), (24),
% 169.69/25.95 | | (25), (26), (27), (28), (30), (33), (34) are inconsistent by
% 169.69/25.95 | | sub-proof #347.
% 169.69/25.95 | |
% 169.69/25.95 | Case 2:
% 169.69/25.95 | |
% 169.69/25.95 | | (35) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 169.69/25.95 | | e3)
% 169.69/25.95 | |
% 169.69/25.95 | | BETA: splitting (35) gives:
% 169.69/25.95 | |
% 169.69/25.95 | | Case 1:
% 169.69/25.95 | | |
% 169.69/25.95 | | | (36) all_58_8 = e3 & op(e1, e1) = e3
% 169.69/25.95 | | |
% 169.69/25.95 | | | REF_CLOSE: (9), (16), (24), (36) are inconsistent by sub-proof #961.
% 169.69/25.95 | | |
% 169.69/25.95 | | Case 2:
% 169.69/25.95 | | |
% 169.69/25.95 | | | (37) all_58_14 = e3 & op(e0, e1) = e3
% 169.69/25.95 | | |
% 169.69/25.95 | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (10), (11), (12), (13), (15),
% 169.69/25.95 | | | (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 169.69/25.95 | | | (27), (28), (29), (31), (32), (33), (37) are inconsistent by
% 169.69/25.95 | | | sub-proof #386.
% 169.69/25.95 | | |
% 169.69/25.95 | | End of split
% 169.69/25.95 | |
% 169.69/25.95 | End of split
% 169.69/25.95 |
% 169.69/25.95 End of proof
% 169.69/25.95
% 169.69/25.95 Sub-proof #347 shows that the following formulas are inconsistent:
% 169.69/25.95 ----------------------------------------------------------------
% 169.69/25.95 (1) op(e2, e1) = all_52_9
% 169.69/25.95 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.95 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.95 (3) ~ (all_52_9 = e3)
% 169.69/25.95 (4) all_58_2 = e2
% 169.69/25.95 (5) ~ (e3 = e1)
% 169.69/25.95 (6) ~ (e1 = e0)
% 169.69/25.95 (7) op(e2, e3) = all_52_1
% 169.69/25.95 (8) op(e2, e3) = e2
% 169.69/25.95 (9) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 169.69/25.95 (10) ~ (e3 = e0)
% 169.69/25.95 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.95 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.95 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.95 (13) ~ (e2 = e0)
% 169.69/25.95 (14) all_58_3 = e3
% 169.69/25.95 (15) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.96 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.96 (16) ~ (e2 = e1)
% 169.69/25.96 (17) all_58_4 = e2
% 169.69/25.96 (18) ~ (e3 = e2)
% 169.69/25.96
% 169.69/25.96 Begin of proof
% 169.69/25.96 |
% 169.69/25.96 | BETA: splitting (9) gives:
% 169.69/25.96 |
% 169.69/25.96 | Case 1:
% 169.69/25.96 | |
% 169.69/25.96 | | (19) all_58_4 = e3 & op(e3, e1) = e3
% 169.69/25.96 | |
% 169.69/25.96 | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 169.69/25.96 | | (16), (17), (18), (19) are inconsistent by sub-proof #348.
% 169.69/25.96 | |
% 169.69/25.96 | Case 2:
% 169.69/25.96 | |
% 169.69/25.96 | | (20) all_58_5 = e3 & op(e2, e1) = e3
% 169.69/25.96 | |
% 169.69/25.96 | | ALPHA: (20) implies:
% 169.69/25.96 | | (21) op(e2, e1) = e3
% 169.69/25.96 | |
% 169.69/25.96 | | REF_CLOSE: (1), (3), (12), (21) are inconsistent by sub-proof #951.
% 169.69/25.96 | |
% 169.69/25.96 | End of split
% 169.69/25.96 |
% 169.69/25.96 End of proof
% 169.69/25.96
% 169.69/25.96 Sub-proof #348 shows that the following formulas are inconsistent:
% 169.69/25.96 ----------------------------------------------------------------
% 169.69/25.96 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.96 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.96 (2) all_58_2 = e2
% 169.69/25.96 (3) all_58_4 = e3 & op(e3, e1) = e3
% 169.69/25.96 (4) ~ (e3 = e1)
% 169.69/25.96 (5) ~ (e1 = e0)
% 169.69/25.96 (6) op(e2, e3) = all_52_1
% 169.69/25.96 (7) op(e2, e3) = e2
% 169.69/25.96 (8) ~ (e3 = e0)
% 169.69/25.96 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.96 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.96 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.96 (11) ~ (e2 = e0)
% 169.69/25.96 (12) all_58_3 = e3
% 169.69/25.96 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.96 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.96 (14) ~ (e2 = e1)
% 169.69/25.96 (15) all_58_4 = e2
% 169.69/25.96 (16) ~ (e3 = e2)
% 169.69/25.96
% 169.69/25.96 Begin of proof
% 169.69/25.96 |
% 169.69/25.96 | ALPHA: (3) implies:
% 169.69/25.96 | (17) all_58_4 = e3
% 169.69/25.96 |
% 169.69/25.96 | COMBINE_EQS: (15), (17) imply:
% 169.69/25.96 | (18) e3 = e2
% 169.69/25.96 |
% 169.69/25.96 | COMBINE_EQS: (12), (18) imply:
% 169.69/25.96 | (19) all_58_3 = e2
% 169.69/25.96 |
% 169.69/25.96 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 169.69/25.96 | (16), (19) are inconsistent by sub-proof #779.
% 169.69/25.96 |
% 169.69/25.96 End of proof
% 169.69/25.96
% 169.69/25.96 Sub-proof #349 shows that the following formulas are inconsistent:
% 169.69/25.96 ----------------------------------------------------------------
% 169.69/25.96 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.96 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.96 (2) all_58_2 = e2
% 169.69/25.96 (3) ~ (e3 = e1)
% 169.69/25.96 (4) ~ (e1 = e0)
% 169.69/25.96 (5) op(e2, e3) = all_52_1
% 169.69/25.96 (6) op(e2, e3) = e2
% 169.69/25.96 (7) ~ (e3 = e0)
% 169.69/25.96 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.96 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.96 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.96 (10) ~ (e2 = e0)
% 169.69/25.96 (11) all_58_3 = e3
% 169.69/25.96 (12) all_58_9 = e3
% 169.69/25.96 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.96 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.96 (14) ~ (e2 = e1)
% 169.69/25.96 (15) all_58_9 = e2 & op(e3, e0) = e2
% 169.69/25.96 (16) ~ (e3 = e2)
% 169.69/25.96
% 169.69/25.96 Begin of proof
% 169.69/25.96 |
% 169.69/25.96 | ALPHA: (15) implies:
% 169.69/25.96 | (17) all_58_9 = e2
% 169.69/25.96 |
% 169.69/25.96 | COMBINE_EQS: (12), (17) imply:
% 169.69/25.96 | (18) e3 = e2
% 169.69/25.96 |
% 169.69/25.96 | COMBINE_EQS: (11), (18) imply:
% 169.69/25.96 | (19) all_58_3 = e2
% 169.69/25.96 |
% 169.69/25.96 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 169.69/25.96 | (16), (19) are inconsistent by sub-proof #779.
% 169.69/25.96 |
% 169.69/25.96 End of proof
% 169.69/25.96
% 169.69/25.96 Sub-proof #350 shows that the following formulas are inconsistent:
% 169.69/25.96 ----------------------------------------------------------------
% 169.69/25.96 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.69/25.96 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.69/25.96 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.96 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.96 (3) ~ (all_4_2 = e2)
% 169.69/25.96 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.69/25.96 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.69/25.96 (5) all_58_2 = e2
% 169.69/25.96 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.96 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.69/25.96 (7) all_58_0 = e1
% 169.69/25.96 (8) ~ (e3 = e1)
% 169.69/25.96 (9) ~ (e1 = e0)
% 169.69/25.96 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.69/25.96 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.69/25.96 (11) op(e2, e3) = all_52_1
% 169.69/25.96 (12) all_58_1 = e2
% 169.69/25.96 (13) op(e2, e3) = e2
% 169.69/25.96 (14) ~ (e3 = e0)
% 169.69/25.96 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.96 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.96 (16) op(e0, e0) = all_4_2
% 169.69/25.96 (17) all_58_14 = e3
% 169.69/25.96 (18) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.96 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.69/25.96 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.96 (20) ~ (e2 = e0)
% 169.69/25.96 (21) all_58_3 = e3
% 169.69/25.96 (22) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.96 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.96 (23) ~ (e2 = e1)
% 169.69/25.96 (24) ~ (e3 = e2)
% 169.69/25.96
% 169.69/25.96 Begin of proof
% 169.69/25.96 |
% 169.69/25.96 | BETA: splitting (1) gives:
% 169.69/25.96 |
% 169.69/25.96 | Case 1:
% 169.69/25.96 | |
% 169.69/25.96 | | (25) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 169.69/25.96 | | e2)
% 169.69/25.96 | |
% 169.69/25.96 | | BETA: splitting (25) gives:
% 169.69/25.96 | |
% 169.69/25.96 | | Case 1:
% 169.69/25.96 | | |
% 169.69/25.96 | | | (26) all_58_12 = e2 & op(e0, e3) = e2
% 169.69/25.96 | | |
% 169.69/25.96 | | | ALPHA: (26) implies:
% 169.69/25.96 | | | (27) all_58_12 = e2
% 169.69/25.96 | | |
% 169.69/25.96 | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (14), (20), (24), (27) are
% 169.69/25.96 | | | inconsistent by sub-proof #435.
% 169.69/25.96 | | |
% 169.69/25.96 | | Case 2:
% 169.69/25.96 | | |
% 169.69/25.96 | | | (28) all_58_13 = e2 & op(e0, e2) = e2
% 169.69/25.96 | | |
% 169.69/25.96 | | | ALPHA: (28) implies:
% 169.69/25.96 | | | (29) all_58_13 = e2
% 169.69/25.96 | | |
% 169.69/25.96 | | | REF_CLOSE: (6), (8), (9), (12), (14), (18), (20), (21), (23), (29) are
% 169.69/25.96 | | | inconsistent by sub-proof #864.
% 169.69/25.96 | | |
% 169.69/25.96 | | End of split
% 169.69/25.96 | |
% 169.69/25.96 | Case 2:
% 169.69/25.96 | |
% 169.69/25.96 | | (30) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.69/25.96 | | e2)
% 169.69/25.96 | |
% 169.69/25.96 | | REF_CLOSE: (2), (3), (5), (8), (9), (11), (13), (14), (15), (16), (17),
% 169.69/25.96 | | (19), (20), (21), (22), (23), (24), (30) are inconsistent by
% 169.69/25.96 | | sub-proof #437.
% 169.69/25.96 | |
% 169.69/25.96 | End of split
% 169.69/25.96 |
% 169.69/25.96 End of proof
% 169.69/25.96
% 169.69/25.96 Sub-proof #351 shows that the following formulas are inconsistent:
% 169.69/25.96 ----------------------------------------------------------------
% 169.69/25.96 (1) op(e2, e1) = all_52_9
% 169.69/25.96 (2) all_58_15 = e1
% 169.69/25.96 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.96 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.96 (4) ~ (all_52_9 = e3)
% 169.69/25.96 (5) all_58_2 = e2
% 169.69/25.96 (6) ~ (all_6_2 = e3)
% 169.69/25.96 (7) ~ (e3 = e1)
% 169.69/25.96 (8) ~ (e1 = e0)
% 169.69/25.96 (9) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.69/25.96 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.69/25.96 (10) op(e2, e3) = all_52_1
% 169.69/25.96 (11) ~ (all_6_2 = e2)
% 169.69/25.96 (12) op(e1, e1) = all_6_2
% 169.69/25.96 (13) op(e2, e3) = e2
% 169.69/25.96 (14) ~ (e3 = e0)
% 169.69/25.96 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.96 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.96 (16) all_58_4 = e3
% 169.69/25.96 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.96 (18) ~ (e2 = e0)
% 169.69/25.96 (19) all_58_15 = e3 & op(e0, e0) = e3
% 169.69/25.96 (20) all_58_3 = e3
% 169.69/25.96 (21) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.96 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.96 (22) ~ (e2 = e1)
% 169.69/25.96 (23) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.69/25.96 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.69/25.96 (24) ~ (e3 = e2)
% 169.69/25.96
% 169.69/25.96 Begin of proof
% 169.69/25.96 |
% 169.69/25.96 | ALPHA: (19) implies:
% 169.69/25.96 | (25) all_58_15 = e3
% 169.69/25.96 |
% 169.69/25.96 | COMBINE_EQS: (2), (25) imply:
% 169.69/25.96 | (26) e3 = e1
% 169.69/25.96 |
% 169.69/25.96 | COMBINE_EQS: (16), (26) imply:
% 169.69/25.96 | (27) all_58_4 = e1
% 169.69/25.96 |
% 169.69/25.96 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.69/25.96 | (14), (15), (17), (18), (20), (21), (22), (23), (24), (27) are
% 169.69/25.96 | inconsistent by sub-proof #407.
% 169.69/25.96 |
% 169.69/25.96 End of proof
% 169.69/25.96
% 169.69/25.96 Sub-proof #352 shows that the following formulas are inconsistent:
% 169.69/25.96 ----------------------------------------------------------------
% 169.69/25.96 (1) all_58_15 = e1
% 169.69/25.96 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.96 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.96 (3) all_58_14 = e2
% 169.69/25.96 (4) all_58_7 = e2
% 169.69/25.96 (5) all_58_2 = e2
% 169.69/25.96 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.96 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.69/25.96 (7) ~ (e3 = e1)
% 169.69/25.96 (8) ~ (e1 = e0)
% 169.69/25.96 (9) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.69/25.96 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.69/25.96 (10) op(e2, e3) = all_52_1
% 169.69/25.96 (11) op(e2, e3) = e2
% 169.69/25.96 (12) ~ (e3 = e0)
% 169.69/25.96 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.96 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.96 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.96 (15) ~ (e2 = e0)
% 169.69/25.96 (16) all_58_12 = e3
% 169.69/25.96 (17) all_58_3 = e3
% 169.69/25.96 (18) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.96 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.96 (19) ~ (e2 = e1)
% 169.69/25.96 (20) all_58_1 = e0
% 169.69/25.96 (21) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.69/25.96 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.69/25.96 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.69/25.96 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.69/25.96 (22) ~ (e3 = e2)
% 169.69/25.96
% 169.69/25.96 Begin of proof
% 169.69/25.96 |
% 169.69/25.96 | BETA: splitting (6) gives:
% 169.69/25.96 |
% 169.69/25.96 | Case 1:
% 169.69/25.96 | |
% 169.69/25.96 | | (23) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 169.69/25.96 | | e1)
% 169.69/25.96 | |
% 169.69/25.96 | | BETA: splitting (23) gives:
% 169.69/25.96 | |
% 169.69/25.96 | | Case 1:
% 169.69/25.96 | | |
% 169.69/25.96 | | | (24) all_58_1 = e1 & op(e3, e2) = e1
% 169.69/25.96 | | |
% 169.69/25.96 | | | REF_CLOSE: (8), (20), (24) are inconsistent by sub-proof #658.
% 169.69/25.96 | | |
% 169.69/25.96 | | Case 2:
% 169.69/25.96 | | |
% 169.69/25.96 | | | (25) all_58_3 = e1 & op(e2, e2) = e1
% 169.69/25.96 | | |
% 169.69/25.96 | | | ALPHA: (25) implies:
% 169.69/25.96 | | | (26) all_58_3 = e1
% 169.69/25.96 | | |
% 169.69/25.96 | | | COMBINE_EQS: (17), (26) imply:
% 169.69/25.96 | | | (27) e3 = e1
% 169.69/25.96 | | |
% 169.69/25.96 | | | SIMP: (27) implies:
% 169.69/25.96 | | | (28) e3 = e1
% 169.69/25.96 | | |
% 169.69/25.96 | | | COMBINE_EQS: (16), (28) imply:
% 169.69/25.96 | | | (29) all_58_12 = e1
% 169.69/25.96 | | |
% 169.69/25.96 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13),
% 169.69/25.96 | | | (14), (15), (17), (18), (19), (21), (22), (29) are inconsistent
% 169.69/25.96 | | | by sub-proof #362.
% 169.69/25.96 | | |
% 169.69/25.96 | | End of split
% 169.69/25.96 | |
% 169.69/25.96 | Case 2:
% 169.69/25.96 | |
% 169.69/25.96 | | (30) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 169.69/25.96 | | e1)
% 169.69/25.96 | |
% 169.69/25.96 | | BETA: splitting (30) gives:
% 169.69/25.96 | |
% 169.69/25.96 | | Case 1:
% 169.69/25.96 | | |
% 169.69/25.96 | | | (31) all_58_7 = e1 & op(e1, e2) = e1
% 169.69/25.96 | | |
% 169.69/25.96 | | | ALPHA: (31) implies:
% 169.69/25.96 | | | (32) all_58_7 = e1
% 169.69/25.96 | | |
% 169.69/25.96 | | | REF_CLOSE: (4), (19), (32) are inconsistent by sub-proof #494.
% 169.69/25.96 | | |
% 169.69/25.96 | | Case 2:
% 169.69/25.96 | | |
% 169.69/25.96 | | | (33) all_58_13 = e1 & op(e0, e2) = e1
% 169.69/25.96 | | |
% 169.69/25.96 | | | ALPHA: (33) implies:
% 169.69/25.96 | | | (34) all_58_13 = e1
% 169.69/25.96 | | |
% 169.69/25.96 | | | REF_CLOSE: (1), (3), (8), (12), (15), (16), (21), (34) are inconsistent by
% 169.69/25.96 | | | sub-proof #544.
% 169.69/25.96 | | |
% 169.69/25.96 | | End of split
% 169.69/25.96 | |
% 169.69/25.96 | End of split
% 169.69/25.96 |
% 169.69/25.96 End of proof
% 169.69/25.96
% 169.69/25.96 Sub-proof #353 shows that the following formulas are inconsistent:
% 169.69/25.96 ----------------------------------------------------------------
% 169.69/25.96 (1) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10
% 169.69/25.96 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.69/25.96 $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.69/25.96 op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 169.69/25.96 (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~
% 169.69/25.96 (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3,
% 169.69/25.96 e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 169.69/25.96 (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~
% 169.69/25.96 (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 169.69/25.96 $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 169.69/25.96 e2 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 169.69/25.96 (2) all_56_10 = e1
% 169.69/25.96 (3) all_56_4 = e3
% 169.69/25.96 (4) all_56_15 = e0
% 169.69/25.96
% 169.69/25.96 Begin of proof
% 169.69/25.96 |
% 169.69/25.96 | BETA: splitting (1) gives:
% 169.69/25.96 |
% 169.69/25.96 | Case 1:
% 169.69/25.96 | |
% 169.69/25.96 | | (5) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 169.69/25.96 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.69/25.96 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.69/25.96 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | (
% 169.69/25.96 | | ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 169.69/25.96 | |
% 169.69/25.96 | | ALPHA: (5) implies:
% 169.69/25.96 | | (6) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.69/25.96 | | $i(all_56_4))
% 169.69/25.96 | |
% 169.69/25.96 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #795.
% 169.69/25.96 | |
% 169.69/25.96 | Case 2:
% 169.69/25.96 | |
% 169.69/25.96 | | (7) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 169.69/25.96 | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) | (
% 169.69/25.96 | | ~ (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 169.69/25.96 | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) = all_56_13
% 169.69/25.96 | | & $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) = e3) |
% 169.69/25.96 | | (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) =
% 169.69/25.96 | | e1))
% 169.69/25.96 | |
% 169.69/25.96 | | ALPHA: (7) implies:
% 169.69/25.96 | | (8) ~ (all_56_15 = e0)
% 169.69/25.96 | |
% 169.69/25.96 | | REDUCE: (4), (8) imply:
% 169.69/25.96 | | (9) $false
% 169.69/25.96 | |
% 169.69/25.96 | | CLOSE: (9) is inconsistent.
% 169.69/25.96 | |
% 169.69/25.96 | End of split
% 169.69/25.96 |
% 169.69/25.96 End of proof
% 169.69/25.96
% 169.69/25.96 Sub-proof #354 shows that the following formulas are inconsistent:
% 169.69/25.96 ----------------------------------------------------------------
% 169.69/25.96 (1) all_58_11 = e1 & op(e1, e0) = e1
% 169.69/25.96 (2) all_58_11 = e0
% 169.69/25.96 (3) ~ (e1 = e0)
% 169.69/25.96
% 169.69/25.96 Begin of proof
% 169.69/25.96 |
% 169.69/25.96 | ALPHA: (1) implies:
% 169.69/25.96 | (4) all_58_11 = e1
% 169.69/25.96 |
% 169.69/25.96 | COMBINE_EQS: (2), (4) imply:
% 169.69/25.96 | (5) e1 = e0
% 169.69/25.96 |
% 169.69/25.96 | REDUCE: (3), (5) imply:
% 169.69/25.96 | (6) $false
% 169.69/25.96 |
% 169.69/25.96 | CLOSE: (6) is inconsistent.
% 169.69/25.96 |
% 169.69/25.96 End of proof
% 169.69/25.96
% 169.69/25.96 Sub-proof #355 shows that the following formulas are inconsistent:
% 169.69/25.96 ----------------------------------------------------------------
% 169.69/25.96 (1) op(e2, e1) = all_52_9
% 169.69/25.96 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.69/25.96 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.69/25.96 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.96 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.96 (4) all_58_14 = e2
% 169.69/25.96 (5) ~ (all_52_9 = e3)
% 169.69/25.96 (6) all_58_2 = e2
% 169.69/25.96 (7) all_58_0 = e1
% 169.69/25.96 (8) ~ (all_6_2 = e3)
% 169.69/25.96 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.69/25.96 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.69/25.96 (10) ~ (e3 = e1)
% 169.69/25.96 (11) op(e3, e3) = e1
% 169.69/25.96 (12) ~ (e1 = e0)
% 169.69/25.96 (13) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.69/25.96 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.69/25.96 e3)
% 169.69/25.96 (14) op(e0, e2) = e1
% 169.69/25.96 (15) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.69/25.96 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.69/25.96 (16) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.69/25.96 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.69/25.96 (17) op(e2, e3) = all_52_1
% 169.69/25.96 (18) ~ (all_52_7 = e3)
% 169.69/25.96 (19) op(e2, e0) = e0
% 169.69/25.96 (20) ~ (all_6_2 = e2)
% 169.69/25.96 (21) op(e1, e1) = all_6_2
% 169.69/25.96 (22) op(e2, e3) = e2
% 169.69/25.96 (23) ~ (e3 = e0)
% 169.69/25.96 (24) all_58_12 = e0
% 169.69/25.96 (25) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.96 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.96 (26) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.69/25.96 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.69/25.96 e2) = all_22_1 & $i(all_22_1))
% 169.69/25.96 (27) all_58_15 = e3
% 169.69/25.96 (28) all_58_4 = e3
% 169.69/25.96 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.96 (30) ~ (e2 = e0)
% 169.69/25.96 (31) all_58_3 = e3
% 169.69/25.96 (32) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.96 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.96 (33) ~ (e2 = e1)
% 169.69/25.96 (34) op(e0, e2) = all_52_7
% 169.69/25.96 (35) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.69/25.96 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.69/25.96 (36) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.69/25.96 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.69/25.96 (37) ~ (e3 = e2)
% 169.69/25.96
% 169.69/25.96 Begin of proof
% 169.69/25.96 |
% 169.69/25.96 | BETA: splitting (9) gives:
% 169.69/25.96 |
% 169.69/25.96 | Case 1:
% 169.69/25.96 | |
% 169.69/25.96 | | (38) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 169.69/25.96 | | e0)
% 169.69/25.96 | |
% 169.69/25.96 | | BETA: splitting (38) gives:
% 169.69/25.96 | |
% 169.69/25.96 | | Case 1:
% 169.69/25.96 | | |
% 169.69/25.96 | | | (39) all_58_0 = e0 & op(e3, e3) = e0
% 169.69/25.96 | | |
% 169.69/25.96 | | | ALPHA: (39) implies:
% 169.69/25.96 | | | (40) op(e3, e3) = e0
% 169.69/25.96 | | |
% 169.69/25.96 | | | REF_CLOSE: (11), (12), (29), (40) are inconsistent by sub-proof #907.
% 169.69/25.96 | | |
% 169.69/25.96 | | Case 2:
% 169.69/25.96 | | |
% 169.69/25.96 | | | (41) all_58_1 = e0 & op(e3, e2) = e0
% 169.69/25.96 | | |
% 169.69/25.96 | | | ALPHA: (41) implies:
% 169.69/25.96 | | | (42) op(e3, e2) = e0
% 169.69/25.96 | | |
% 169.69/25.96 | | | REF_CLOSE: (14), (26), (29), (42) are inconsistent by sub-proof #443.
% 169.69/25.96 | | |
% 169.69/25.96 | | End of split
% 169.69/25.96 | |
% 169.69/25.96 | Case 2:
% 169.69/25.96 | |
% 169.69/25.96 | | (43) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 169.69/25.96 | | e0)
% 169.69/25.96 | |
% 169.69/25.96 | | BETA: splitting (43) gives:
% 169.69/25.96 | |
% 169.69/25.96 | | Case 1:
% 169.69/25.96 | | |
% 169.69/25.96 | | | (44) all_58_4 = e0 & op(e3, e1) = e0
% 169.69/25.96 | | |
% 169.69/25.96 | | | REF_CLOSE: (3), (4), (6), (10), (12), (13), (17), (18), (22), (23), (24),
% 169.69/25.96 | | | (25), (27), (28), (29), (30), (31), (32), (33), (34), (37),
% 169.69/25.96 | | | (44) are inconsistent by sub-proof #370.
% 169.69/25.96 | | |
% 169.69/25.96 | | Case 2:
% 169.69/25.96 | | |
% 169.69/25.96 | | | (45) all_58_9 = e0 & op(e3, e0) = e0
% 169.69/25.96 | | |
% 169.69/25.96 | | | ALPHA: (45) implies:
% 169.69/25.96 | | | (46) all_58_9 = e0
% 169.69/25.96 | | |
% 169.69/25.96 | | | BETA: splitting (2) gives:
% 169.69/25.96 | | |
% 169.69/25.96 | | | Case 1:
% 169.69/25.96 | | | |
% 169.69/25.97 | | | | (47) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 169.69/25.97 | | | | = e1)
% 169.69/25.97 | | | |
% 169.69/25.97 | | | | BETA: splitting (47) gives:
% 169.69/25.97 | | | |
% 169.69/25.97 | | | | Case 1:
% 169.69/25.97 | | | | |
% 169.69/25.97 | | | | | (48) all_58_9 = e1 & op(e3, e0) = e1
% 169.69/25.97 | | | | |
% 169.69/25.97 | | | | | ALPHA: (48) implies:
% 169.69/25.97 | | | | | (49) all_58_9 = e1
% 169.69/25.97 | | | | |
% 169.69/25.97 | | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (13), (17),
% 169.69/25.97 | | | | | (18), (22), (23), (24), (25), (27), (28), (29), (30), (31),
% 169.69/25.97 | | | | | (32), (33), (34), (35), (37), (49) are inconsistent by
% 169.69/25.97 | | | | | sub-proof #369.
% 169.69/25.97 | | | | |
% 169.69/25.97 | | | | Case 2:
% 169.69/25.97 | | | | |
% 169.69/25.97 | | | | | (50) all_58_10 = e1 & op(e2, e0) = e1
% 169.69/25.97 | | | | |
% 169.69/25.97 | | | | | ALPHA: (50) implies:
% 169.69/25.97 | | | | | (51) op(e2, e0) = e1
% 169.69/25.97 | | | | |
% 169.69/25.97 | | | | | REF_CLOSE: (12), (19), (29), (51) are inconsistent by sub-proof #849.
% 169.69/25.97 | | | | |
% 169.69/25.97 | | | | End of split
% 169.69/25.97 | | | |
% 169.69/25.97 | | | Case 2:
% 169.69/25.97 | | | |
% 169.69/25.97 | | | | (52) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 169.69/25.97 | | | | e0) = e1)
% 169.69/25.97 | | | |
% 169.69/25.97 | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (12), (13), (15), (16),
% 169.69/25.97 | | | | (17), (18), (20), (21), (22), (23), (24), (25), (27), (28),
% 169.69/25.97 | | | | (29), (30), (31), (32), (33), (34), (36), (37), (46), (52)
% 169.69/25.97 | | | | are inconsistent by sub-proof #356.
% 169.69/25.97 | | | |
% 169.69/25.97 | | | End of split
% 169.69/25.97 | | |
% 169.69/25.97 | | End of split
% 169.69/25.97 | |
% 169.69/25.97 | End of split
% 169.69/25.97 |
% 169.69/25.97 End of proof
% 169.69/25.97
% 169.69/25.97 Sub-proof #356 shows that the following formulas are inconsistent:
% 169.69/25.97 ----------------------------------------------------------------
% 169.69/25.97 (1) op(e2, e1) = all_52_9
% 169.69/25.97 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.69/25.97 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.69/25.97 (3) all_58_14 = e2
% 169.69/25.97 (4) ~ (all_52_9 = e3)
% 169.69/25.97 (5) all_58_2 = e2
% 169.69/25.97 (6) ~ (all_6_2 = e3)
% 169.69/25.97 (7) all_58_9 = e0
% 169.69/25.97 (8) ~ (e3 = e1)
% 169.69/25.97 (9) ~ (e1 = e0)
% 169.69/25.97 (10) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.69/25.97 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.69/25.97 e3)
% 169.69/25.97 (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.69/25.97 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.69/25.97 (12) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.69/25.97 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.69/25.97 (13) op(e2, e3) = all_52_1
% 169.69/25.97 (14) ~ (all_52_7 = e3)
% 169.69/25.97 (15) ~ (all_6_2 = e2)
% 169.69/25.97 (16) op(e1, e1) = all_6_2
% 169.69/25.97 (17) op(e2, e3) = e2
% 169.69/25.97 (18) ~ (e3 = e0)
% 169.69/25.97 (19) all_58_12 = e0
% 169.69/25.97 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.69/25.97 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.69/25.97 (21) all_58_15 = e3
% 169.69/25.97 (22) all_58_4 = e3
% 169.69/25.97 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.69/25.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.69/25.97 (24) ~ (e2 = e0)
% 169.69/25.97 (25) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.69/25.97 (26) all_58_3 = e3
% 169.69/25.97 (27) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.69/25.97 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.69/25.97 (28) ~ (e2 = e1)
% 169.69/25.97 (29) op(e0, e2) = all_52_7
% 169.84/25.97 (30) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.84/25.97 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.84/25.97 (31) ~ (e3 = e2)
% 169.84/25.97
% 169.84/25.97 Begin of proof
% 169.84/25.97 |
% 169.84/25.97 | BETA: splitting (25) gives:
% 169.84/25.97 |
% 169.84/25.97 | Case 1:
% 169.84/25.97 | |
% 169.84/25.97 | | (32) all_58_11 = e1 & op(e1, e0) = e1
% 169.84/25.97 | |
% 169.84/25.97 | | ALPHA: (32) implies:
% 169.84/25.97 | | (33) all_58_11 = e1
% 169.84/25.97 | |
% 169.84/25.97 | | BETA: splitting (12) gives:
% 169.84/25.97 | |
% 169.84/25.97 | | Case 1:
% 169.84/25.97 | | |
% 169.84/25.97 | | | (34) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 169.84/25.97 | | | e2)
% 169.84/25.97 | | |
% 169.84/25.97 | | | BETA: splitting (34) gives:
% 169.84/25.97 | | |
% 169.84/25.97 | | | Case 1:
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | (35) all_58_9 = e2 & op(e3, e0) = e2
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | ALPHA: (35) implies:
% 169.84/25.97 | | | | (36) all_58_9 = e2
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | REF_CLOSE: (7), (24), (36) are inconsistent by sub-proof #945.
% 169.84/25.97 | | | |
% 169.84/25.97 | | | Case 2:
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | (37) all_58_10 = e2 & op(e2, e0) = e2
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | REF_CLOSE: (2), (8), (9), (13), (17), (18), (20), (23), (24), (26),
% 169.84/25.97 | | | | (28), (37) are inconsistent by sub-proof #447.
% 169.84/25.97 | | | |
% 169.84/25.97 | | | End of split
% 169.84/25.97 | | |
% 169.84/25.97 | | Case 2:
% 169.84/25.97 | | |
% 169.84/25.97 | | | (38) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0)
% 169.84/25.97 | | | = e2)
% 169.84/25.97 | | |
% 169.84/25.97 | | | BETA: splitting (38) gives:
% 169.84/25.97 | | |
% 169.84/25.97 | | | Case 1:
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | (39) all_58_11 = e2 & op(e1, e0) = e2
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | ALPHA: (39) implies:
% 169.84/25.97 | | | | (40) all_58_11 = e2
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | REF_CLOSE: (28), (33), (40) are inconsistent by sub-proof #832.
% 169.84/25.97 | | | |
% 169.84/25.97 | | | Case 2:
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | (41) all_58_15 = e2 & op(e0, e0) = e2
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | ALPHA: (41) implies:
% 169.84/25.97 | | | | (42) all_58_15 = e2
% 169.84/25.97 | | | |
% 169.84/25.97 | | | | REF_CLOSE: (2), (3), (5), (8), (9), (10), (13), (14), (17), (18), (19),
% 169.84/25.97 | | | | (20), (23), (24), (26), (27), (28), (29), (31), (42) are
% 169.84/25.97 | | | | inconsistent by sub-proof #358.
% 169.84/25.97 | | | |
% 169.84/25.97 | | | End of split
% 169.84/25.97 | | |
% 169.84/25.97 | | End of split
% 169.84/25.97 | |
% 169.84/25.97 | Case 2:
% 169.84/25.97 | |
% 169.84/25.97 | | (43) all_58_15 = e1 & op(e0, e0) = e1
% 169.84/25.97 | |
% 169.84/25.97 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (11), (13), (15), (16), (17),
% 169.84/25.97 | | (18), (20), (21), (22), (23), (24), (26), (27), (28), (30), (31),
% 169.84/25.97 | | (43) are inconsistent by sub-proof #357.
% 169.84/25.97 | |
% 169.84/25.97 | End of split
% 169.84/25.97 |
% 169.84/25.97 End of proof
% 169.84/25.97
% 169.84/25.97 Sub-proof #357 shows that the following formulas are inconsistent:
% 169.84/25.97 ----------------------------------------------------------------
% 169.84/25.97 (1) op(e2, e1) = all_52_9
% 169.84/25.97 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.97 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.97 (3) ~ (all_52_9 = e3)
% 169.84/25.97 (4) all_58_2 = e2
% 169.84/25.97 (5) ~ (all_6_2 = e3)
% 169.84/25.97 (6) ~ (e3 = e1)
% 169.84/25.97 (7) ~ (e1 = e0)
% 169.84/25.97 (8) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.84/25.97 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.84/25.97 (9) op(e2, e3) = all_52_1
% 169.84/25.97 (10) ~ (all_6_2 = e2)
% 169.84/25.97 (11) op(e1, e1) = all_6_2
% 169.84/25.97 (12) op(e2, e3) = e2
% 169.84/25.97 (13) ~ (e3 = e0)
% 169.84/25.97 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/25.97 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/25.97 (15) all_58_15 = e1 & op(e0, e0) = e1
% 169.84/25.97 (16) all_58_15 = e3
% 169.84/25.97 (17) all_58_4 = e3
% 169.84/25.97 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.97 (19) ~ (e2 = e0)
% 169.84/25.97 (20) all_58_3 = e3
% 169.84/25.97 (21) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/25.97 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/25.97 (22) ~ (e2 = e1)
% 169.84/25.97 (23) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.84/25.97 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.84/25.97 (24) ~ (e3 = e2)
% 169.84/25.97
% 169.84/25.97 Begin of proof
% 169.84/25.97 |
% 169.84/25.97 | ALPHA: (15) implies:
% 169.84/25.97 | (25) all_58_15 = e1
% 169.84/25.97 |
% 169.84/25.97 | COMBINE_EQS: (16), (25) imply:
% 169.84/25.97 | (26) e3 = e1
% 169.84/25.97 |
% 169.84/25.97 | SIMP: (26) implies:
% 169.84/25.97 | (27) e3 = e1
% 169.84/25.97 |
% 169.84/25.97 | COMBINE_EQS: (17), (27) imply:
% 169.84/25.97 | (28) all_58_4 = e1
% 169.84/25.97 |
% 169.84/25.97 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.84/25.97 | (13), (14), (18), (19), (20), (21), (22), (23), (24), (28) are
% 169.84/25.97 | inconsistent by sub-proof #407.
% 169.84/25.97 |
% 169.84/25.97 End of proof
% 169.84/25.97
% 169.84/25.97 Sub-proof #358 shows that the following formulas are inconsistent:
% 169.84/25.97 ----------------------------------------------------------------
% 169.84/25.97 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.97 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.97 (2) all_58_14 = e2
% 169.84/25.97 (3) all_58_15 = e2
% 169.84/25.97 (4) all_58_2 = e2
% 169.84/25.97 (5) ~ (e3 = e1)
% 169.84/25.97 (6) ~ (e1 = e0)
% 169.84/25.97 (7) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.84/25.97 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/25.97 (8) op(e2, e3) = all_52_1
% 169.84/25.97 (9) ~ (all_52_7 = e3)
% 169.84/25.97 (10) op(e2, e3) = e2
% 169.84/25.97 (11) ~ (e3 = e0)
% 169.84/25.97 (12) all_58_12 = e0
% 169.84/25.97 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/25.97 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/25.97 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.97 (15) ~ (e2 = e0)
% 169.84/25.97 (16) all_58_3 = e3
% 169.84/25.97 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/25.97 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/25.97 (18) ~ (e2 = e1)
% 169.84/25.97 (19) op(e0, e2) = all_52_7
% 169.84/25.97 (20) ~ (e3 = e2)
% 169.84/25.97
% 169.84/25.97 Begin of proof
% 169.84/25.97 |
% 169.84/25.97 | BETA: splitting (7) gives:
% 169.84/25.97 |
% 169.84/25.97 | Case 1:
% 169.84/25.97 | |
% 169.84/25.97 | | (21) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 169.84/25.97 | | e3)
% 169.84/25.97 | |
% 169.84/25.97 | | REF_CLOSE: (9), (11), (12), (14), (19), (21) are inconsistent by sub-proof
% 169.84/25.97 | | #557.
% 169.84/25.97 | |
% 169.84/25.97 | Case 2:
% 169.84/25.97 | |
% 169.84/25.97 | | (22) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.84/25.97 | | e3)
% 169.84/25.97 | |
% 169.84/25.97 | | BETA: splitting (22) gives:
% 169.84/25.97 | |
% 169.84/25.97 | | Case 1:
% 169.84/25.97 | | |
% 169.84/25.97 | | | (23) all_58_14 = e3 & op(e0, e1) = e3
% 169.84/25.97 | | |
% 169.84/25.97 | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (13), (14), (15),
% 169.84/25.97 | | | (16), (17), (18), (20), (23) are inconsistent by sub-proof
% 169.84/25.97 | | | #405.
% 169.84/25.97 | | |
% 169.84/25.97 | | Case 2:
% 169.84/25.97 | | |
% 169.84/25.97 | | | (24) all_58_15 = e3 & op(e0, e0) = e3
% 169.84/25.97 | | |
% 169.84/25.97 | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (11), (13), (14), (15),
% 169.84/25.97 | | | (16), (17), (18), (20), (24) are inconsistent by sub-proof
% 169.84/25.97 | | | #359.
% 169.84/25.97 | | |
% 169.84/25.97 | | End of split
% 169.84/25.97 | |
% 169.84/25.97 | End of split
% 169.84/25.97 |
% 169.84/25.97 End of proof
% 169.84/25.97
% 169.84/25.97 Sub-proof #359 shows that the following formulas are inconsistent:
% 169.84/25.97 ----------------------------------------------------------------
% 169.84/25.97 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.97 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.97 (2) all_58_15 = e2
% 169.84/25.97 (3) all_58_2 = e2
% 169.84/25.97 (4) ~ (e3 = e1)
% 169.84/25.97 (5) ~ (e1 = e0)
% 169.84/25.97 (6) op(e2, e3) = all_52_1
% 169.84/25.97 (7) op(e2, e3) = e2
% 169.84/25.97 (8) ~ (e3 = e0)
% 169.84/25.97 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/25.97 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/25.97 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.97 (11) ~ (e2 = e0)
% 169.84/25.97 (12) all_58_15 = e3 & op(e0, e0) = e3
% 169.84/25.97 (13) all_58_3 = e3
% 169.84/25.97 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/25.97 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/25.97 (15) ~ (e2 = e1)
% 169.84/25.97 (16) ~ (e3 = e2)
% 169.84/25.97
% 169.84/25.97 Begin of proof
% 169.84/25.97 |
% 169.84/25.97 | ALPHA: (12) implies:
% 169.84/25.97 | (17) all_58_15 = e3
% 169.84/25.97 |
% 169.84/25.97 | COMBINE_EQS: (2), (17) imply:
% 169.84/25.97 | (18) e3 = e2
% 169.84/25.97 |
% 169.84/25.97 | COMBINE_EQS: (13), (18) imply:
% 169.84/25.97 | (19) all_58_3 = e2
% 169.84/25.97 |
% 169.84/25.97 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), (15),
% 169.84/25.97 | (16), (19) are inconsistent by sub-proof #779.
% 169.84/25.97 |
% 169.84/25.97 End of proof
% 169.84/25.97
% 169.84/25.97 Sub-proof #360 shows that the following formulas are inconsistent:
% 169.84/25.97 ----------------------------------------------------------------
% 169.84/25.97 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.97 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.97 (2) all_58_14 = e2
% 169.84/25.97 (3) all_58_2 = e2
% 169.84/25.97 (4) all_58_0 = e1
% 169.84/25.97 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.84/25.97 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/25.97 (6) ~ (e3 = e1)
% 169.84/25.97 (7) op(e3, e3) = e1
% 169.84/25.97 (8) ~ (e1 = e0)
% 169.84/25.97 (9) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.84/25.97 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/25.97 (10) op(e2, e3) = all_52_1
% 169.84/25.97 (11) ~ (all_52_7 = e3)
% 169.84/25.97 (12) op(e2, e3) = e2
% 169.84/25.97 (13) ~ (e3 = e0)
% 169.84/25.97 (14) all_58_12 = e0
% 169.84/25.97 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/25.97 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/25.97 (16) all_58_15 = e3
% 169.84/25.97 (17) op(e2, e1) = e1
% 169.84/25.97 (18) all_58_4 = e3
% 169.84/25.97 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.97 (20) ~ (e2 = e0)
% 169.84/25.97 (21) all_58_3 = e3
% 169.84/25.97 (22) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/25.97 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/25.97 (23) ~ (e2 = e1)
% 169.84/25.97 (24) op(e0, e2) = all_52_7
% 169.84/25.97 (25) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.84/25.97 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.84/25.97 (26) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.97 (27) ~ (e3 = e2)
% 169.84/25.97
% 169.84/25.97 Begin of proof
% 169.84/25.97 |
% 169.84/25.97 | BETA: splitting (26) gives:
% 169.84/25.97 |
% 169.84/25.97 | Case 1:
% 169.84/25.97 | |
% 169.84/25.97 | | (28) all_58_9 = e1 & op(e3, e0) = e1
% 169.84/25.97 | |
% 169.84/25.97 | | ALPHA: (28) implies:
% 169.84/25.97 | | (29) all_58_9 = e1
% 169.84/25.97 | |
% 169.84/25.97 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.84/25.97 | | (13), (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 169.84/25.97 | | (25), (27), (29) are inconsistent by sub-proof #369.
% 169.84/25.97 | |
% 169.84/25.97 | Case 2:
% 169.84/25.97 | |
% 169.84/25.97 | | (30) all_58_10 = e1 & op(e2, e0) = e1
% 169.84/25.97 | |
% 169.84/25.97 | | ALPHA: (30) implies:
% 169.84/25.97 | | (31) op(e2, e0) = e1
% 169.84/25.97 | |
% 169.84/25.97 | | REF_CLOSE: (8), (10), (12), (13), (15), (17), (19), (20), (21), (31) are
% 169.84/25.97 | | inconsistent by sub-proof #365.
% 169.84/25.97 | |
% 169.84/25.97 | End of split
% 169.84/25.97 |
% 169.84/25.97 End of proof
% 169.84/25.97
% 169.84/25.97 Sub-proof #361 shows that the following formulas are inconsistent:
% 169.84/25.98 ----------------------------------------------------------------
% 169.84/25.98 (1) all_58_15 = e1
% 169.84/25.98 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.98 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.98 (3) all_58_14 = e2
% 169.84/25.98 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/25.98 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/25.98 (5) all_58_2 = e2
% 169.84/25.98 (6) ~ (e3 = e1)
% 169.84/25.98 (7) all_58_6 = e3
% 169.84/25.98 (8) ~ (e1 = e0)
% 169.84/25.98 (9) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.84/25.98 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/25.98 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.84/25.98 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.84/25.98 (11) op(e2, e3) = all_52_1
% 169.84/25.98 (12) ~ (all_52_7 = e3)
% 169.84/25.98 (13) op(e2, e3) = e2
% 169.84/25.98 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.84/25.98 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.84/25.98 (15) ~ (e3 = e0)
% 169.84/25.98 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/25.98 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/25.98 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.98 (18) ~ (e2 = e0)
% 169.84/25.98 (19) all_58_3 = e3
% 169.84/25.98 (20) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/25.98 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/25.98 (21) ~ (e2 = e1)
% 169.84/25.98 (22) op(e0, e2) = all_52_7
% 169.84/25.98 (23) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/25.98 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.84/25.98 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.84/25.98 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.84/25.98 (24) ~ (e3 = e2)
% 169.84/25.98
% 169.84/25.98 Begin of proof
% 169.84/25.98 |
% 169.84/25.98 | BETA: splitting (14) gives:
% 169.84/25.98 |
% 169.84/25.98 | Case 1:
% 169.84/25.98 | |
% 169.84/25.98 | | (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 169.84/25.98 | | e1)
% 169.84/25.98 | |
% 169.84/25.98 | | BETA: splitting (25) gives:
% 169.84/25.98 | |
% 169.84/25.98 | | Case 1:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (26) all_58_0 = e1 & op(e3, e3) = e1
% 169.84/25.98 | | |
% 169.84/25.98 | | | ALPHA: (26) implies:
% 169.84/25.98 | | | (27) all_58_0 = e1
% 169.84/25.98 | | |
% 169.84/25.98 | | | BETA: splitting (4) gives:
% 169.84/25.98 | | |
% 169.84/25.98 | | | Case 1:
% 169.84/25.98 | | | |
% 169.84/25.98 | | | | (28) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 169.84/25.98 | | | | = e0)
% 169.84/25.98 | | | |
% 169.84/25.98 | | | | BETA: splitting (28) gives:
% 169.84/25.98 | | | |
% 169.84/25.98 | | | | Case 1:
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | (29) all_58_0 = e0 & op(e3, e3) = e0
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | REF_CLOSE: (8), (27), (29) are inconsistent by sub-proof #903.
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | Case 2:
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | (30) all_58_2 = e0 & op(e2, e3) = e0
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | REF_CLOSE: (11), (13), (17), (18), (30) are inconsistent by sub-proof
% 169.84/25.98 | | | | | #782.
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | End of split
% 169.84/25.98 | | | |
% 169.84/25.98 | | | Case 2:
% 169.84/25.98 | | | |
% 169.84/25.98 | | | | (31) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 169.84/25.98 | | | | = e0)
% 169.84/25.98 | | | |
% 169.84/25.98 | | | | BETA: splitting (31) gives:
% 169.84/25.98 | | | |
% 169.84/25.98 | | | | Case 1:
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | (32) all_58_6 = e0 & op(e1, e3) = e0
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | ALPHA: (32) implies:
% 169.84/25.98 | | | | | (33) all_58_6 = e0
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | REF_CLOSE: (7), (15), (33) are inconsistent by sub-proof #537.
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | Case 2:
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | (34) all_58_12 = e0 & op(e0, e3) = e0
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | ALPHA: (34) implies:
% 169.84/25.98 | | | | | (35) all_58_12 = e0
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | BETA: splitting (9) gives:
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | | Case 1:
% 169.84/25.98 | | | | | |
% 169.84/25.98 | | | | | | (36) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 169.84/25.98 | | | | | | op(e0, e2) = e3)
% 169.84/25.98 | | | | | |
% 169.84/25.98 | | | | | | REF_CLOSE: (12), (15), (17), (22), (35), (36) are inconsistent by
% 169.84/25.98 | | | | | | sub-proof #557.
% 169.84/25.98 | | | | | |
% 169.84/25.98 | | | | | Case 2:
% 169.84/25.98 | | | | | |
% 169.84/25.98 | | | | | | (37) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 169.84/25.98 | | | | | | op(e0, e0) = e3)
% 169.84/25.98 | | | | | |
% 169.84/25.98 | | | | | | BETA: splitting (37) gives:
% 169.84/25.98 | | | | | |
% 169.84/25.98 | | | | | | Case 1:
% 169.84/25.98 | | | | | | |
% 169.84/25.98 | | | | | | | (38) all_58_14 = e3 & op(e0, e1) = e3
% 169.84/25.98 | | | | | | |
% 169.84/25.98 | | | | | | | ALPHA: (38) implies:
% 169.84/25.98 | | | | | | | (39) all_58_14 = e3
% 169.84/25.98 | | | | | | |
% 169.84/25.98 | | | | | | | REF_CLOSE: (2), (3), (5), (6), (8), (11), (13), (15), (16), (17),
% 169.84/25.98 | | | | | | | (18), (19), (20), (21), (24), (39) are inconsistent by
% 169.84/25.98 | | | | | | | sub-proof #438.
% 169.84/25.98 | | | | | | |
% 169.84/25.98 | | | | | | Case 2:
% 169.84/25.98 | | | | | | |
% 169.84/25.98 | | | | | | | (40) all_58_15 = e3 & op(e0, e0) = e3
% 169.84/25.98 | | | | | | |
% 169.84/25.98 | | | | | | | ALPHA: (40) implies:
% 169.84/25.98 | | | | | | | (41) all_58_15 = e3
% 169.84/25.98 | | | | | | |
% 169.84/25.98 | | | | | | | COMBINE_EQS: (1), (41) imply:
% 169.84/25.98 | | | | | | | (42) e3 = e1
% 169.84/25.98 | | | | | | |
% 169.84/25.98 | | | | | | | COMBINE_EQS: (7), (42) imply:
% 169.84/25.98 | | | | | | | (43) all_58_6 = e1
% 169.84/25.98 | | | | | | |
% 169.84/25.98 | | | | | | | REF_CLOSE: (5), (6), (10), (15), (24), (27), (35), (43) are
% 169.84/25.98 | | | | | | | inconsistent by sub-proof #456.
% 169.84/25.98 | | | | | | |
% 169.84/25.98 | | | | | | End of split
% 169.84/25.98 | | | | | |
% 169.84/25.98 | | | | | End of split
% 169.84/25.98 | | | | |
% 169.84/25.98 | | | | End of split
% 169.84/25.98 | | | |
% 169.84/25.98 | | | End of split
% 169.84/25.98 | | |
% 169.84/25.98 | | Case 2:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (44) all_58_2 = e1 & op(e2, e3) = e1
% 169.84/25.98 | | |
% 169.84/25.98 | | | ALPHA: (44) implies:
% 169.84/25.98 | | | (45) op(e2, e3) = e1
% 169.84/25.98 | | |
% 169.84/25.98 | | | REF_CLOSE: (11), (13), (17), (21), (45) are inconsistent by sub-proof
% 169.84/25.98 | | | #784.
% 169.84/25.98 | | |
% 169.84/25.98 | | End of split
% 169.84/25.98 | |
% 169.84/25.98 | Case 2:
% 169.84/25.98 | |
% 169.84/25.98 | | (46) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 169.84/25.98 | | e1)
% 169.84/25.98 | |
% 169.84/25.98 | | BETA: splitting (46) gives:
% 169.84/25.98 | |
% 169.84/25.98 | | Case 1:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (47) all_58_6 = e1 & op(e1, e3) = e1
% 169.84/25.98 | | |
% 169.84/25.98 | | | REF_CLOSE: (6), (7), (47) are inconsistent by sub-proof #487.
% 169.84/25.98 | | |
% 169.84/25.98 | | Case 2:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (48) all_58_12 = e1 & op(e0, e3) = e1
% 169.84/25.98 | | |
% 169.84/25.98 | | | ALPHA: (48) implies:
% 169.84/25.98 | | | (49) all_58_12 = e1
% 169.84/25.98 | | |
% 169.84/25.98 | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (11), (13), (15), (16),
% 169.84/25.98 | | | (17), (18), (19), (20), (21), (23), (24), (49) are inconsistent
% 169.84/25.98 | | | by sub-proof #362.
% 169.84/25.98 | | |
% 169.84/25.98 | | End of split
% 169.84/25.98 | |
% 169.84/25.98 | End of split
% 169.84/25.98 |
% 169.84/25.98 End of proof
% 169.84/25.98
% 169.84/25.98 Sub-proof #362 shows that the following formulas are inconsistent:
% 169.84/25.98 ----------------------------------------------------------------
% 169.84/25.98 (1) all_58_12 = e1
% 169.84/25.98 (2) all_58_15 = e1
% 169.84/25.98 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.98 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.98 (4) all_58_14 = e2
% 169.84/25.98 (5) all_58_2 = e2
% 169.84/25.98 (6) ~ (e3 = e1)
% 169.84/25.98 (7) ~ (e1 = e0)
% 169.84/25.98 (8) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.84/25.98 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/25.98 (9) op(e2, e3) = all_52_1
% 169.84/25.98 (10) op(e2, e3) = e2
% 169.84/25.98 (11) ~ (e3 = e0)
% 169.84/25.98 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/25.98 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/25.98 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.98 (14) ~ (e2 = e0)
% 169.84/25.98 (15) all_58_3 = e3
% 169.84/25.98 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/25.98 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/25.98 (17) ~ (e2 = e1)
% 169.84/25.98 (18) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/25.98 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.84/25.98 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.84/25.98 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.84/25.98 (19) ~ (e3 = e2)
% 169.84/25.98
% 169.84/25.98 Begin of proof
% 169.84/25.98 |
% 169.84/25.98 | BETA: splitting (8) gives:
% 169.84/25.98 |
% 169.84/25.98 | Case 1:
% 169.84/25.98 | |
% 169.84/25.98 | | (20) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 169.84/25.98 | | e3)
% 169.84/25.98 | |
% 169.84/25.98 | | BETA: splitting (20) gives:
% 169.84/25.98 | |
% 169.84/25.98 | | Case 1:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (21) all_58_12 = e3 & op(e0, e3) = e3
% 169.84/25.98 | | |
% 169.84/25.98 | | | ALPHA: (21) implies:
% 169.84/25.98 | | | (22) all_58_12 = e3
% 169.84/25.98 | | |
% 169.84/25.98 | | | REF_CLOSE: (1), (6), (22) are inconsistent by sub-proof #600.
% 169.84/25.98 | | |
% 169.84/25.98 | | Case 2:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (23) all_58_13 = e3 & op(e0, e2) = e3
% 169.84/25.98 | | |
% 169.84/25.98 | | | ALPHA: (23) implies:
% 169.84/25.98 | | | (24) all_58_13 = e3
% 169.84/25.98 | | |
% 169.84/25.98 | | | BETA: splitting (18) gives:
% 169.84/25.98 | | |
% 169.84/25.98 | | | Case 1:
% 169.84/25.98 | | | |
% 169.84/25.98 | | | | (25) all_58_15 = e0 & op(e0, e0) = e0
% 169.84/25.98 | | | |
% 169.84/25.98 | | | | REF_CLOSE: (2), (7), (25) are inconsistent by sub-proof #541.
% 169.84/25.98 | | | |
% 169.84/25.98 | | | Case 2:
% 169.84/25.98 | | | |
% 169.84/25.98 | | | | (26) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 169.84/25.98 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 169.84/25.98 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 169.84/25.98 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.84/25.98 | | | |
% 169.84/25.98 | | | | REF_CLOSE: (1), (4), (7), (11), (14), (24), (26) are inconsistent by
% 169.84/25.98 | | | | sub-proof #857.
% 169.84/25.98 | | | |
% 169.84/25.98 | | | End of split
% 169.84/25.98 | | |
% 169.84/25.98 | | End of split
% 169.84/25.98 | |
% 169.84/25.98 | Case 2:
% 169.84/25.98 | |
% 169.84/25.98 | | (27) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.84/25.98 | | e3)
% 169.84/25.98 | |
% 169.84/25.98 | | BETA: splitting (27) gives:
% 169.84/25.98 | |
% 169.84/25.98 | | Case 1:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (28) all_58_14 = e3 & op(e0, e1) = e3
% 169.84/25.98 | | |
% 169.84/25.98 | | | ALPHA: (28) implies:
% 169.84/25.98 | | | (29) all_58_14 = e3
% 169.84/25.98 | | |
% 169.84/25.98 | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 169.84/25.98 | | | (15), (16), (17), (19), (29) are inconsistent by sub-proof
% 169.84/25.98 | | | #438.
% 169.84/25.98 | | |
% 169.84/25.98 | | Case 2:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (30) all_58_15 = e3 & op(e0, e0) = e3
% 169.84/25.98 | | |
% 169.84/25.98 | | | ALPHA: (30) implies:
% 169.84/25.98 | | | (31) all_58_15 = e3
% 169.84/25.98 | | |
% 169.84/25.98 | | | REF_CLOSE: (2), (6), (31) are inconsistent by sub-proof #556.
% 169.84/25.98 | | |
% 169.84/25.98 | | End of split
% 169.84/25.98 | |
% 169.84/25.98 | End of split
% 169.84/25.98 |
% 169.84/25.98 End of proof
% 169.84/25.98
% 169.84/25.98 Sub-proof #363 shows that the following formulas are inconsistent:
% 169.84/25.98 ----------------------------------------------------------------
% 169.84/25.98 (1) all_58_7 = e0 & op(e1, e2) = e0
% 169.84/25.98 (2) all_58_7 = e2
% 169.84/25.98 (3) ~ (e2 = e0)
% 169.84/25.98
% 169.84/25.98 Begin of proof
% 169.84/25.98 |
% 169.84/25.98 | ALPHA: (1) implies:
% 169.84/25.98 | (4) all_58_7 = e0
% 169.84/25.98 |
% 169.84/25.98 | COMBINE_EQS: (2), (4) imply:
% 169.84/25.98 | (5) e2 = e0
% 169.84/25.98 |
% 169.84/25.98 | REDUCE: (3), (5) imply:
% 169.84/25.98 | (6) $false
% 169.84/25.98 |
% 169.84/25.98 | CLOSE: (6) is inconsistent.
% 169.84/25.98 |
% 169.84/25.98 End of proof
% 169.84/25.98
% 169.84/25.98 Sub-proof #364 shows that the following formulas are inconsistent:
% 169.84/25.98 ----------------------------------------------------------------
% 169.84/25.98 (1) all_54_6 = all_52_9
% 169.84/25.98 (2) all_54_6 = e1
% 169.84/25.98 (3) ~ (all_52_9 = e1)
% 169.84/25.98
% 169.84/25.98 Begin of proof
% 169.84/25.98 |
% 169.84/25.98 | COMBINE_EQS: (1), (2) imply:
% 169.84/25.98 | (4) all_52_9 = e1
% 169.84/25.98 |
% 169.84/25.98 | SIMP: (4) implies:
% 169.84/25.98 | (5) all_52_9 = e1
% 169.84/25.98 |
% 169.84/25.98 | REDUCE: (3), (5) imply:
% 169.84/25.98 | (6) $false
% 169.84/25.98 |
% 169.84/25.98 | CLOSE: (6) is inconsistent.
% 169.84/25.98 |
% 169.84/25.98 End of proof
% 169.84/25.98
% 169.84/25.98 Sub-proof #365 shows that the following formulas are inconsistent:
% 169.84/25.98 ----------------------------------------------------------------
% 169.84/25.98 (1) ~ (e1 = e0)
% 169.84/25.98 (2) op(e2, e3) = all_52_1
% 169.84/25.98 (3) op(e2, e3) = e2
% 169.84/25.98 (4) ~ (e3 = e0)
% 169.84/25.98 (5) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/25.98 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/25.98 (6) op(e2, e1) = e1
% 169.84/25.98 (7) op(e2, e0) = e1
% 169.84/25.98 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.98 (9) ~ (e2 = e0)
% 169.84/25.98 (10) all_58_3 = e3
% 169.84/25.98
% 169.84/25.98 Begin of proof
% 169.84/25.98 |
% 169.84/25.98 | BETA: splitting (5) gives:
% 169.84/25.98 |
% 169.84/25.98 | Case 1:
% 169.84/25.98 | |
% 169.84/25.98 | | (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 169.84/25.98 | | e0)
% 169.84/25.98 | |
% 169.84/25.98 | | BETA: splitting (11) gives:
% 169.84/25.98 | |
% 169.84/25.98 | | Case 1:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (12) all_58_2 = e0 & op(e2, e3) = e0
% 169.84/25.98 | | |
% 169.84/25.98 | | | REF_CLOSE: (2), (3), (8), (9), (12) are inconsistent by sub-proof #782.
% 169.84/25.98 | | |
% 169.84/25.98 | | Case 2:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (13) all_58_3 = e0 & op(e2, e2) = e0
% 169.84/25.98 | | |
% 169.84/25.98 | | | REF_CLOSE: (4), (10), (13) are inconsistent by sub-proof #427.
% 169.84/25.98 | | |
% 169.84/25.98 | | End of split
% 169.84/25.98 | |
% 169.84/25.98 | Case 2:
% 169.84/25.98 | |
% 169.84/25.98 | | (14) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 169.84/25.98 | | e0)
% 169.84/25.98 | |
% 169.84/25.98 | | BETA: splitting (14) gives:
% 169.84/25.98 | |
% 169.84/25.98 | | Case 1:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (15) all_58_5 = e0 & op(e2, e1) = e0
% 169.84/25.98 | | |
% 169.84/25.98 | | | ALPHA: (15) implies:
% 169.84/25.98 | | | (16) op(e2, e1) = e0
% 169.84/25.98 | | |
% 169.84/25.98 | | | REF_CLOSE: (1), (6), (8), (16) are inconsistent by sub-proof #911.
% 169.84/25.98 | | |
% 169.84/25.98 | | Case 2:
% 169.84/25.98 | | |
% 169.84/25.98 | | | (17) all_58_10 = e0 & op(e2, e0) = e0
% 169.84/25.98 | | |
% 169.84/25.98 | | | ALPHA: (17) implies:
% 169.84/25.98 | | | (18) op(e2, e0) = e0
% 169.84/25.98 | | |
% 169.84/25.98 | | | REF_CLOSE: (1), (7), (8), (18) are inconsistent by sub-proof #849.
% 169.84/25.98 | | |
% 169.84/25.98 | | End of split
% 169.84/25.98 | |
% 169.84/25.98 | End of split
% 169.84/25.98 |
% 169.84/25.98 End of proof
% 169.84/25.98
% 169.84/25.98 Sub-proof #366 shows that the following formulas are inconsistent:
% 169.84/25.98 ----------------------------------------------------------------
% 169.84/25.98 (1) all_56_0 = e2
% 169.84/25.98 (2) all_56_4 = e3
% 169.84/25.98 (3) all_56_10 = e1
% 169.84/25.98 (4) op(e2, e3) = all_52_1
% 169.84/25.98 (5) op(e2, e3) = e2
% 169.84/25.98 (6) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.84/25.98 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.84/25.98 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.84/25.98 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.84/25.98 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.84/25.98 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.84/25.98 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.84/25.98 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.84/25.98 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.84/25.98 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 169.84/25.98 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 169.84/25.98 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.84/25.98 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.84/25.98 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.84/25.98 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 169.84/25.98 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 169.84/25.98 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 169.84/25.98 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 169.84/25.98 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 169.84/25.98 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 169.84/25.98 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 169.84/25.98 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.84/25.98 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.84/25.98 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.84/25.98 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.84/25.98 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.98 (8) all_56_12 = e3
% 169.84/25.98 (9) ~ (e3 = e2)
% 169.84/25.98
% 169.84/25.98 Begin of proof
% 169.84/25.98 |
% 169.84/25.98 | BETA: splitting (6) gives:
% 169.84/25.98 |
% 169.84/25.98 | Case 1:
% 169.84/25.98 | |
% 169.84/25.98 | | (10) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 169.84/25.98 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 169.84/25.98 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 169.84/25.98 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2)
% 169.84/25.98 | | | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7))))
% 169.84/25.98 | | | (all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.84/25.98 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.84/25.98 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.84/25.98 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 169.84/25.98 | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.84/25.98 | |
% 169.84/25.98 | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10) are inconsistent by sub-proof
% 169.84/25.98 | | #367.
% 169.84/25.98 | |
% 169.84/25.98 | Case 2:
% 169.84/25.98 | |
% 169.84/25.99 | | (11) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 169.84/25.99 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.84/25.99 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.84/25.99 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 169.84/25.99 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8))))
% 169.84/25.99 | | | (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.84/25.99 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.84/25.99 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.84/25.99 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 169.84/25.99 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8))))
% 169.84/25.99 | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 169.84/25.99 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.84/25.99 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.84/25.99 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 169.84/25.99 | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.84/25.99 | |
% 169.84/25.99 | | BETA: splitting (11) gives:
% 169.84/25.99 | |
% 169.84/25.99 | | Case 1:
% 169.84/25.99 | | |
% 169.84/25.99 | | | (12) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 169.84/25.99 | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 169.84/25.99 | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 169.84/25.99 | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 169.84/25.99 | | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 169.84/25.99 | | |
% 169.84/25.99 | | | ALPHA: (12) implies:
% 169.84/25.99 | | | (13) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4
% 169.84/25.99 | | | & $i(all_56_4))
% 169.84/25.99 | | |
% 169.84/25.99 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #795.
% 169.84/25.99 | | |
% 169.84/25.99 | | Case 2:
% 169.84/25.99 | | |
% 169.84/25.99 | | | (14) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.84/25.99 | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4
% 169.84/25.99 | | | & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 =
% 169.84/25.99 | | | e2) & op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.84/25.99 | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8
% 169.84/25.99 | | | & $i(all_56_8)))) | (all_56_4 = e1 & ~ (all_56_10 = e3) &
% 169.84/25.99 | | | op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 169.84/25.99 | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~ (all_56_14 =
% 169.84/25.99 | | | e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.84/25.99 | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0)
% 169.84/25.99 | | | & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.84/25.99 | | |
% 169.84/25.99 | | | BETA: splitting (14) gives:
% 169.84/25.99 | | |
% 169.84/25.99 | | | Case 1:
% 169.84/25.99 | | | |
% 169.84/25.99 | | | | (15) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 169.84/25.99 | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4
% 169.84/25.99 | | | | & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 =
% 169.84/25.99 | | | | e2) & op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 169.84/25.99 | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8
% 169.84/25.99 | | | | & $i(all_56_8)))
% 169.84/25.99 | | | |
% 169.84/25.99 | | | | ALPHA: (15) implies:
% 169.84/25.99 | | | | (16) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) =
% 169.84/25.99 | | | | all_56_4 & $i(all_56_4))
% 169.84/25.99 | | | |
% 169.84/25.99 | | | | REF_CLOSE: (2), (3), (16) are inconsistent by sub-proof #795.
% 169.84/25.99 | | | |
% 169.84/25.99 | | | Case 2:
% 169.84/25.99 | | | |
% 169.84/25.99 | | | | (17) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 169.84/25.99 | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0
% 169.84/25.99 | | | | & $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 =
% 169.84/25.99 | | | | e1) & op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 169.84/25.99 | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6
% 169.84/25.99 | | | | & $i(all_56_6)))
% 169.84/25.99 | | | |
% 169.84/25.99 | | | | ALPHA: (17) implies:
% 169.84/25.99 | | | | (18) ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) =
% 169.84/25.99 | | | | all_56_0 & $i(all_56_0))
% 169.84/25.99 | | | |
% 169.84/25.99 | | | | REF_CLOSE: (1), (8), (18) are inconsistent by sub-proof #368.
% 169.84/25.99 | | | |
% 169.84/25.99 | | | End of split
% 169.84/25.99 | | |
% 169.84/25.99 | | End of split
% 169.84/25.99 | |
% 169.84/25.99 | End of split
% 169.84/25.99 |
% 169.84/25.99 End of proof
% 169.84/25.99
% 169.84/25.99 Sub-proof #367 shows that the following formulas are inconsistent:
% 169.84/25.99 ----------------------------------------------------------------
% 169.84/25.99 (1) all_56_0 = e2
% 169.84/25.99 (2) op(e2, e3) = all_52_1
% 169.84/25.99 (3) op(e2, e3) = e2
% 169.84/25.99 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.99 (5) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 169.84/25.99 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 169.84/25.99 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 169.84/25.99 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 169.84/25.99 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 169.84/25.99 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 169.84/25.99 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 169.84/25.99 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 169.84/25.99 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 169.84/25.99 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 169.84/25.99 (6) all_56_12 = e3
% 169.84/25.99 (7) ~ (e3 = e2)
% 169.84/25.99
% 169.84/25.99 Begin of proof
% 169.84/25.99 |
% 169.84/25.99 | BETA: splitting (5) gives:
% 169.84/25.99 |
% 169.84/25.99 | Case 1:
% 169.84/25.99 | |
% 169.84/25.99 | | (8) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 169.84/25.99 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 169.84/25.99 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 169.84/25.99 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 169.84/25.99 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 169.84/25.99 | |
% 169.84/25.99 | | ALPHA: (8) implies:
% 169.84/25.99 | | (9) op(e2, e3) = e3
% 169.84/25.99 | |
% 169.84/25.99 | | REF_CLOSE: (2), (3), (4), (7), (9) are inconsistent by sub-proof #462.
% 169.84/25.99 | |
% 169.84/25.99 | Case 2:
% 169.84/25.99 | |
% 169.84/25.99 | | (10) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 169.84/25.99 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.84/25.99 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 169.84/25.99 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) |
% 169.84/25.99 | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 169.84/25.99 | |
% 169.84/25.99 | | ALPHA: (10) implies:
% 169.84/25.99 | | (11) ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.84/25.99 | | $i(all_56_0))
% 169.84/25.99 | |
% 169.84/25.99 | | REF_CLOSE: (1), (6), (11) are inconsistent by sub-proof #368.
% 169.84/25.99 | |
% 169.84/25.99 | End of split
% 169.84/25.99 |
% 169.84/25.99 End of proof
% 169.84/25.99
% 169.84/25.99 Sub-proof #368 shows that the following formulas are inconsistent:
% 169.84/25.99 ----------------------------------------------------------------
% 169.84/25.99 (1) ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 169.84/25.99 $i(all_56_0))
% 169.84/25.99 (2) all_56_12 = e3
% 169.84/25.99 (3) all_56_0 = e2
% 169.84/25.99
% 169.84/25.99 Begin of proof
% 169.84/25.99 |
% 169.84/25.99 | BETA: splitting (1) gives:
% 169.84/25.99 |
% 169.84/25.99 | Case 1:
% 169.84/25.99 | |
% 169.84/25.99 | | (4) ~ (all_56_12 = e3)
% 169.84/25.99 | |
% 169.84/25.99 | | REDUCE: (2), (4) imply:
% 169.84/25.99 | | (5) $false
% 169.84/25.99 | |
% 169.84/25.99 | | CLOSE: (5) is inconsistent.
% 169.84/25.99 | |
% 169.84/25.99 | Case 2:
% 169.84/25.99 | |
% 169.84/25.99 | | (6) ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0)
% 169.84/25.99 | |
% 169.84/25.99 | | ALPHA: (6) implies:
% 169.84/25.99 | | (7) ~ (all_56_0 = e2)
% 169.84/25.99 | |
% 169.84/25.99 | | REDUCE: (3), (7) imply:
% 169.84/25.99 | | (8) $false
% 169.84/25.99 | |
% 169.84/25.99 | | CLOSE: (8) is inconsistent.
% 169.84/25.99 | |
% 169.84/25.99 | End of split
% 169.84/25.99 |
% 169.84/25.99 End of proof
% 169.84/25.99
% 169.84/25.99 Sub-proof #369 shows that the following formulas are inconsistent:
% 169.84/25.99 ----------------------------------------------------------------
% 169.84/25.99 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.99 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.99 (2) all_58_14 = e2
% 169.84/25.99 (3) all_58_2 = e2
% 169.84/25.99 (4) all_58_0 = e1
% 169.84/25.99 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.84/25.99 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/25.99 (6) ~ (e3 = e1)
% 169.84/25.99 (7) op(e3, e3) = e1
% 169.84/25.99 (8) ~ (e1 = e0)
% 169.84/25.99 (9) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.84/25.99 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/25.99 (10) op(e2, e3) = all_52_1
% 169.84/25.99 (11) ~ (all_52_7 = e3)
% 169.84/25.99 (12) op(e2, e3) = e2
% 169.84/25.99 (13) ~ (e3 = e0)
% 169.84/25.99 (14) all_58_12 = e0
% 169.84/25.99 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/25.99 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/25.99 (16) all_58_15 = e3
% 169.84/25.99 (17) all_58_4 = e3
% 169.84/25.99 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.99 (19) ~ (e2 = e0)
% 169.84/25.99 (20) all_58_3 = e3
% 169.84/25.99 (21) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/25.99 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/25.99 (22) ~ (e2 = e1)
% 169.84/25.99 (23) all_58_9 = e1
% 169.84/25.99 (24) op(e0, e2) = all_52_7
% 169.84/25.99 (25) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.84/25.99 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.84/25.99 (26) ~ (e3 = e2)
% 169.84/25.99
% 169.84/25.99 Begin of proof
% 169.84/25.99 |
% 169.84/25.99 | BETA: splitting (5) gives:
% 169.84/25.99 |
% 169.84/25.99 | Case 1:
% 169.84/25.99 | |
% 169.84/25.99 | | (27) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 169.84/25.99 | | e0)
% 169.84/25.99 | |
% 169.84/25.99 | | BETA: splitting (27) gives:
% 169.84/25.99 | |
% 169.84/25.99 | | Case 1:
% 169.84/25.99 | | |
% 169.84/25.99 | | | (28) all_58_0 = e0 & op(e3, e3) = e0
% 169.84/25.99 | | |
% 169.84/25.99 | | | ALPHA: (28) implies:
% 169.84/25.99 | | | (29) op(e3, e3) = e0
% 169.84/25.99 | | |
% 169.84/25.99 | | | REF_CLOSE: (7), (8), (18), (29) are inconsistent by sub-proof #907.
% 169.84/25.99 | | |
% 169.84/25.99 | | Case 2:
% 169.84/25.99 | | |
% 169.84/25.99 | | | (30) all_58_1 = e0 & op(e3, e2) = e0
% 169.84/25.99 | | |
% 169.84/25.99 | | | ALPHA: (30) implies:
% 169.84/25.99 | | | (31) all_58_1 = e0
% 169.84/25.99 | | |
% 169.84/25.99 | | | REF_CLOSE: (1), (3), (4), (6), (8), (10), (12), (13), (15), (17), (18),
% 169.84/25.99 | | | (19), (20), (21), (22), (23), (25), (26), (31) are inconsistent
% 169.84/25.99 | | | by sub-proof #378.
% 169.84/25.99 | | |
% 169.84/25.99 | | End of split
% 169.84/25.99 | |
% 169.84/25.99 | Case 2:
% 169.84/25.99 | |
% 169.84/25.99 | | (32) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 169.84/25.99 | | e0)
% 169.84/25.99 | |
% 169.84/25.99 | | BETA: splitting (32) gives:
% 169.84/25.99 | |
% 169.84/25.99 | | Case 1:
% 169.84/25.99 | | |
% 169.84/25.99 | | | (33) all_58_4 = e0 & op(e3, e1) = e0
% 169.84/25.99 | | |
% 169.84/25.99 | | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (11), (12), (13), (14),
% 169.84/25.99 | | | (15), (16), (17), (18), (19), (20), (21), (22), (24), (26),
% 169.84/25.99 | | | (33) are inconsistent by sub-proof #370.
% 169.84/25.99 | | |
% 169.84/25.99 | | Case 2:
% 169.84/25.99 | | |
% 169.84/25.99 | | | (34) all_58_9 = e0 & op(e3, e0) = e0
% 169.84/25.99 | | |
% 169.84/25.99 | | | REF_CLOSE: (8), (23), (34) are inconsistent by sub-proof #897.
% 169.84/25.99 | | |
% 169.84/25.99 | | End of split
% 169.84/25.99 | |
% 169.84/25.99 | End of split
% 169.84/25.99 |
% 169.84/25.99 End of proof
% 169.84/25.99
% 169.84/25.99 Sub-proof #370 shows that the following formulas are inconsistent:
% 169.84/25.99 ----------------------------------------------------------------
% 169.84/25.99 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.99 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.99 (2) all_58_14 = e2
% 169.84/25.99 (3) all_58_2 = e2
% 169.84/25.99 (4) ~ (e3 = e1)
% 169.84/25.99 (5) ~ (e1 = e0)
% 169.84/25.99 (6) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.84/25.99 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/25.99 (7) op(e2, e3) = all_52_1
% 169.84/25.99 (8) ~ (all_52_7 = e3)
% 169.84/25.99 (9) all_58_4 = e0 & op(e3, e1) = e0
% 169.84/25.99 (10) op(e2, e3) = e2
% 169.84/25.99 (11) ~ (e3 = e0)
% 169.84/25.99 (12) all_58_12 = e0
% 169.84/25.99 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/25.99 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/25.99 (14) all_58_15 = e3
% 169.84/25.99 (15) all_58_4 = e3
% 169.84/25.99 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.99 (17) ~ (e2 = e0)
% 169.84/25.99 (18) all_58_3 = e3
% 169.84/25.99 (19) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/25.99 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/25.99 (20) ~ (e2 = e1)
% 169.84/25.99 (21) op(e0, e2) = all_52_7
% 169.84/25.99 (22) ~ (e3 = e2)
% 169.84/25.99
% 169.84/25.99 Begin of proof
% 169.84/25.99 |
% 169.84/25.99 | ALPHA: (9) implies:
% 169.84/25.99 | (23) all_58_4 = e0
% 169.84/25.99 |
% 169.84/25.99 | COMBINE_EQS: (15), (23) imply:
% 169.84/25.99 | (24) e3 = e0
% 169.84/25.99 |
% 169.84/25.99 | COMBINE_EQS: (14), (24) imply:
% 169.84/25.99 | (25) all_58_15 = e0
% 169.84/25.99 |
% 169.84/25.99 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 169.84/25.99 | (16), (17), (18), (19), (20), (21), (22), (25) are inconsistent by
% 169.84/25.99 | sub-proof #404.
% 169.84/25.99 |
% 169.84/25.99 End of proof
% 169.84/25.99
% 169.84/25.99 Sub-proof #371 shows that the following formulas are inconsistent:
% 169.84/25.99 ----------------------------------------------------------------
% 169.84/25.99 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 169.84/25.99 (2) op(e3, e3) = e1
% 169.84/25.99 (3) ~ (e1 = e0)
% 169.84/25.99 (4) op(e2, e3) = all_52_1
% 169.84/25.99 (5) op(e2, e3) = e2
% 169.84/25.99 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.99 (7) ~ (e2 = e0)
% 169.84/25.99
% 169.84/25.99 Begin of proof
% 169.84/25.99 |
% 169.84/25.99 | BETA: splitting (1) gives:
% 169.84/25.99 |
% 169.84/25.99 | Case 1:
% 169.84/25.99 | |
% 169.84/25.99 | | (8) all_58_0 = e0 & op(e3, e3) = e0
% 169.84/25.99 | |
% 169.84/25.99 | | ALPHA: (8) implies:
% 169.84/25.99 | | (9) op(e3, e3) = e0
% 169.84/25.99 | |
% 169.84/25.99 | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #907.
% 169.84/25.99 | |
% 169.84/25.99 | Case 2:
% 169.84/25.99 | |
% 169.84/25.99 | | (10) all_58_2 = e0 & op(e2, e3) = e0
% 169.84/25.99 | |
% 169.84/25.99 | | REF_CLOSE: (4), (5), (6), (7), (10) are inconsistent by sub-proof #782.
% 169.84/25.99 | |
% 169.84/25.99 | End of split
% 169.84/25.99 |
% 169.84/25.99 End of proof
% 169.84/25.99
% 169.84/25.99 Sub-proof #372 shows that the following formulas are inconsistent:
% 169.84/25.99 ----------------------------------------------------------------
% 169.84/25.99 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.99 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.99 (2) all_58_2 = e2
% 169.84/25.99 (3) ~ (e3 = e1)
% 169.84/25.99 (4) ~ (e1 = e0)
% 169.84/25.99 (5) op(e2, e3) = all_52_1
% 169.84/25.99 (6) all_56_12 = e2
% 169.84/25.99 (7) op(e2, e3) = e2
% 169.84/25.99 (8) ~ (e3 = e0)
% 169.84/25.99 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/25.99 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/25.99 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/25.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/25.99 (11) ~ (e2 = e0)
% 169.84/25.99 (12) all_58_3 = e3
% 169.84/25.99 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/25.99 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/25.99 (14) ~ (e2 = e1)
% 169.84/25.99 (15) all_56_12 = e3
% 169.84/25.99 (16) ~ (e3 = e2)
% 169.84/25.99
% 169.84/25.99 Begin of proof
% 169.84/25.99 |
% 169.84/25.99 | COMBINE_EQS: (6), (15) imply:
% 169.84/25.99 | (17) e3 = e2
% 169.84/25.99 |
% 169.84/25.99 | SIMP: (17) implies:
% 169.84/25.99 | (18) e3 = e2
% 169.84/25.99 |
% 169.84/25.99 | COMBINE_EQS: (12), (18) imply:
% 169.84/25.99 | (19) all_58_3 = e2
% 169.84/25.99 |
% 169.84/25.99 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 169.84/25.99 | (16), (19) are inconsistent by sub-proof #779.
% 169.84/25.99 |
% 169.84/25.99 End of proof
% 169.84/25.99
% 169.84/25.99 Sub-proof #373 shows that the following formulas are inconsistent:
% 169.84/25.99 ----------------------------------------------------------------
% 169.84/25.99 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.84/25.99 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.84/25.99 (2) op(e2, e1) = all_52_9
% 169.84/25.99 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.84/25.99 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.84/25.99 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.99 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/25.99 (5) all_58_14 = e2
% 169.84/25.99 (6) ~ (all_52_9 = e3)
% 169.84/25.99 (7) ~ (all_52_13 = e3)
% 169.84/25.99 (8) ~ (all_4_2 = e2)
% 169.84/25.99 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/25.99 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/25.99 (10) all_58_2 = e2
% 169.84/25.99 (11) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/25.99 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.84/25.99 (12) all_58_0 = e1
% 169.84/26.00 (13) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 169.84/26.00 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 169.84/26.00 (14) ~ (all_6_2 = e3)
% 169.84/26.00 (15) all_58_15 = e0 & op(e0, e0) = e0
% 169.84/26.00 (16) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.84/26.00 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/26.00 (17) ~ (e3 = e1)
% 169.84/26.00 (18) ~ (e1 = e0)
% 169.84/26.00 (19) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 169.84/26.00 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.84/26.00 e3)
% 169.84/26.00 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.84/26.00 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.84/26.00 (21) op(e1, e2) = all_52_6
% 169.84/26.00 (22) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.84/26.00 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.84/26.00 (23) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.84/26.00 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.84/26.00 (24) op(e2, e3) = all_52_1
% 169.84/26.00 (25) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.84/26.00 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.84/26.00 (26) ~ (all_52_7 = e3)
% 169.84/26.00 (27) ~ (all_6_2 = e2)
% 169.84/26.00 (28) op(e1, e1) = all_6_2
% 169.84/26.00 (29) op(e2, e3) = e2
% 169.84/26.00 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.84/26.00 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.84/26.00 (31) ~ (e3 = e0)
% 169.84/26.00 (32) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.00 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.00 (33) op(e0, e0) = all_4_2
% 169.84/26.00 (34) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.84/26.00 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.84/26.00 e2) = all_22_1 & $i(all_22_1))
% 169.84/26.00 (35) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.00 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.84/26.00 (36) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.84/26.00 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.84/26.00 (37) all_58_4 = e3
% 169.84/26.00 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.00 (39) ~ (e2 = e0)
% 169.84/26.00 (40) all_58_13 = e1
% 169.84/26.00 (41) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.84/26.00 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.84/26.00 (42) all_58_3 = e3
% 169.84/26.00 (43) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.00 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.00 (44) ~ (e2 = e1)
% 169.84/26.00 (45) op(e3, e2) = all_52_4
% 169.84/26.00 (46) op(e0, e2) = all_52_7
% 169.84/26.00 (47) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 169.84/26.00 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/26.00 (48) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.84/26.00 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.84/26.00 (49) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.84/26.00 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.84/26.00 (50) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/26.00 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.84/26.00 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.84/26.00 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.84/26.00 (51) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.84/26.00 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.84/26.00 (52) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.84/26.00 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.84/26.00 e2) = all_14_1 & $i(all_14_1))
% 169.84/26.00 (53) op(e2, e0) = all_52_13
% 169.84/26.00 (54) ~ (e3 = e2)
% 169.84/26.00
% 169.84/26.00 Begin of proof
% 169.84/26.00 |
% 169.84/26.00 | ALPHA: (15) implies:
% 169.84/26.00 | (55) all_58_15 = e0
% 169.84/26.00 |
% 169.84/26.00 | BETA: splitting (41) gives:
% 169.84/26.00 |
% 169.84/26.00 | Case 1:
% 169.84/26.00 | |
% 169.84/26.00 | | (56) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 169.84/26.00 | | e3)
% 169.84/26.00 | |
% 169.84/26.00 | | BETA: splitting (56) gives:
% 169.84/26.00 | |
% 169.84/26.00 | | Case 1:
% 169.84/26.00 | | |
% 169.84/26.00 | | | (57) all_58_6 = e3 & op(e1, e3) = e3
% 169.84/26.00 | | |
% 169.84/26.00 | | | ALPHA: (57) implies:
% 169.84/26.00 | | | (58) all_58_6 = e3
% 169.84/26.00 | | |
% 169.84/26.00 | | | REF_CLOSE: (4), (5), (9), (10), (12), (17), (18), (19), (24), (26), (29),
% 169.84/26.00 | | | (31), (32), (38), (39), (42), (43), (44), (46), (54), (55),
% 169.84/26.00 | | | (58) are inconsistent by sub-proof #403.
% 169.84/26.00 | | |
% 169.84/26.00 | | Case 2:
% 169.84/26.00 | | |
% 169.84/26.00 | | | (59) all_58_7 = e3 & op(e1, e2) = e3
% 169.84/26.00 | | |
% 169.84/26.00 | | | ALPHA: (59) implies:
% 169.84/26.00 | | | (60) all_58_7 = e3
% 169.84/26.00 | | |
% 169.84/26.00 | | | BETA: splitting (13) gives:
% 169.84/26.00 | | |
% 169.84/26.00 | | | Case 1:
% 169.84/26.00 | | | |
% 169.84/26.00 | | | | (61) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2)
% 169.84/26.00 | | | | = e2)
% 169.84/26.00 | | | |
% 169.84/26.00 | | | | BETA: splitting (61) gives:
% 169.84/26.00 | | | |
% 169.84/26.00 | | | | Case 1:
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | (62) all_58_6 = e2 & op(e1, e3) = e2
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | ALPHA: (62) implies:
% 169.84/26.00 | | | | | (63) all_58_6 = e2
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | REF_CLOSE: (4), (9), (10), (12), (17), (18), (20), (24), (29), (31),
% 169.84/26.00 | | | | | (32), (38), (39), (42), (43), (44), (54), (63) are
% 169.84/26.00 | | | | | inconsistent by sub-proof #400.
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | Case 2:
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | (64) all_58_7 = e2 & op(e1, e2) = e2
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | ALPHA: (64) implies:
% 169.84/26.00 | | | | | (65) all_58_7 = e2
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | REF_CLOSE: (4), (10), (17), (18), (24), (29), (31), (32), (38), (39),
% 169.84/26.00 | | | | | (42), (43), (44), (54), (60), (65) are inconsistent by
% 169.84/26.00 | | | | | sub-proof #399.
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | End of split
% 169.84/26.00 | | | |
% 169.84/26.00 | | | Case 2:
% 169.84/26.00 | | | |
% 169.84/26.00 | | | | (66) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0)
% 169.84/26.00 | | | | = e2)
% 169.84/26.00 | | | |
% 169.84/26.00 | | | | BETA: splitting (66) gives:
% 169.84/26.00 | | | |
% 169.84/26.00 | | | | Case 1:
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | (67) all_58_8 = e2 & op(e1, e1) = e2
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | REF_CLOSE: (1), (9), (10), (12), (17), (18), (20), (25), (31), (37),
% 169.84/26.00 | | | | | (39), (40), (44), (49), (54), (55), (67) are inconsistent
% 169.84/26.00 | | | | | by sub-proof #394.
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | Case 2:
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | (68) all_58_11 = e2 & op(e1, e0) = e2
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | ALPHA: (68) implies:
% 169.84/26.00 | | | | | (69) all_58_11 = e2
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | BETA: splitting (19) gives:
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | Case 1:
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | | (70) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 169.84/26.00 | | | | | | op(e0, e2) = e3)
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | | BETA: splitting (70) gives:
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | | Case 1:
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | (71) all_58_12 = e3 & op(e0, e3) = e3
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | ALPHA: (71) implies:
% 169.84/26.00 | | | | | | | (72) all_58_12 = e3
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | BETA: splitting (47) gives:
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | |
% 169.84/26.00 | | | | | | | | (73) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 169.84/26.00 | | | | | | | | op(e2, e0) = e3)
% 169.84/26.00 | | | | | | | |
% 169.84/26.00 | | | | | | | | REF_CLOSE: (4), (7), (9), (10), (16), (17), (18), (20), (24),
% 169.84/26.00 | | | | | | | | (29), (30), (31), (32), (36), (37), (38), (39), (42),
% 169.84/26.00 | | | | | | | | (43), (44), (48), (53), (54), (72), (73) are
% 169.84/26.00 | | | | | | | | inconsistent by sub-proof #387.
% 169.84/26.00 | | | | | | | |
% 169.84/26.00 | | | | | | | Case 2:
% 169.84/26.00 | | | | | | | |
% 169.84/26.00 | | | | | | | | (74) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 169.84/26.00 | | | | | | | | op(e0, e0) = e3)
% 169.84/26.00 | | | | | | | |
% 169.84/26.00 | | | | | | | | BETA: splitting (74) gives:
% 169.84/26.00 | | | | | | | |
% 169.84/26.00 | | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | (75) all_58_11 = e3 & op(e1, e0) = e3
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | ALPHA: (75) implies:
% 169.84/26.00 | | | | | | | | | (76) all_58_11 = e3
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | REF_CLOSE: (4), (10), (17), (18), (24), (29), (31), (32),
% 169.84/26.00 | | | | | | | | | (38), (39), (42), (43), (44), (54), (69), (76) are
% 169.84/26.00 | | | | | | | | | inconsistent by sub-proof #421.
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | Case 2:
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | (77) all_58_15 = e3 & op(e0, e0) = e3
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | ALPHA: (77) implies:
% 169.84/26.00 | | | | | | | | | (78) all_58_15 = e3
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | COMBINE_EQS: (55), (78) imply:
% 169.84/26.00 | | | | | | | | | (79) e3 = e0
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | COMBINE_EQS: (72), (79) imply:
% 169.84/26.00 | | | | | | | | | (80) all_58_12 = e0
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | REF_CLOSE: (4), (5), (10), (17), (18), (19), (24), (26), (29),
% 169.84/26.00 | | | | | | | | | (31), (32), (38), (39), (42), (43), (44), (46),
% 169.84/26.00 | | | | | | | | | (54), (55), (80) are inconsistent by sub-proof
% 169.84/26.00 | | | | | | | | | #404.
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | End of split
% 169.84/26.00 | | | | | | | |
% 169.84/26.00 | | | | | | | End of split
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | Case 2:
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | (81) all_58_13 = e3 & op(e0, e2) = e3
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | REF_CLOSE: (26), (38), (46), (81) are inconsistent by sub-proof
% 169.84/26.00 | | | | | | | #962.
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | End of split
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | Case 2:
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | | (82) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 169.84/26.00 | | | | | | op(e0, e0) = e3)
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | | BETA: splitting (82) gives:
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | | Case 1:
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | (83) all_58_14 = e3 & op(e0, e1) = e3
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | REF_CLOSE: (1), (4), (8), (9), (10), (11), (17), (18), (20), (21),
% 169.84/26.00 | | | | | | | (24), (29), (30), (31), (32), (33), (34), (35), (38),
% 169.84/26.00 | | | | | | | (39), (42), (43), (44), (45), (52), (54), (60), (83)
% 169.84/26.00 | | | | | | | are inconsistent by sub-proof #386.
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | Case 2:
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | (84) all_58_15 = e3 & op(e0, e0) = e3
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | ALPHA: (84) implies:
% 169.84/26.00 | | | | | | | (85) all_58_15 = e3
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | REF_CLOSE: (31), (55), (85) are inconsistent by sub-proof #860.
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | End of split
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | End of split
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | End of split
% 169.84/26.00 | | | |
% 169.84/26.00 | | | End of split
% 169.84/26.00 | | |
% 169.84/26.00 | | End of split
% 169.84/26.00 | |
% 169.84/26.00 | Case 2:
% 169.84/26.00 | |
% 169.84/26.00 | | (86) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 169.84/26.00 | | e3)
% 169.84/26.00 | |
% 169.84/26.00 | | BETA: splitting (86) gives:
% 169.84/26.00 | |
% 169.84/26.00 | | Case 1:
% 169.84/26.00 | | |
% 169.84/26.00 | | | (87) all_58_8 = e3 & op(e1, e1) = e3
% 169.84/26.00 | | |
% 169.84/26.00 | | | REF_CLOSE: (5), (17), (18), (25), (31), (37), (39), (44), (49), (87) are
% 169.84/26.00 | | | inconsistent by sub-proof #383.
% 169.84/26.00 | | |
% 169.84/26.00 | | Case 2:
% 169.84/26.00 | | |
% 169.84/26.00 | | | (88) all_58_11 = e3 & op(e1, e0) = e3
% 169.84/26.00 | | |
% 169.84/26.00 | | | ALPHA: (88) implies:
% 169.84/26.00 | | | (89) all_58_11 = e3
% 169.84/26.00 | | |
% 169.84/26.00 | | | BETA: splitting (3) gives:
% 169.84/26.00 | | |
% 169.84/26.00 | | | Case 1:
% 169.84/26.00 | | | |
% 169.84/26.00 | | | | (90) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0)
% 169.84/26.00 | | | | = e1)
% 169.84/26.00 | | | |
% 169.84/26.00 | | | | BETA: splitting (90) gives:
% 169.84/26.00 | | | |
% 169.84/26.00 | | | | Case 1:
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | (91) all_58_9 = e1 & op(e3, e0) = e1
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | ALPHA: (91) implies:
% 169.84/26.00 | | | | | (92) all_58_9 = e1
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | REF_CLOSE: (4), (8), (10), (17), (18), (23), (24), (29), (31), (32),
% 169.84/26.00 | | | | | (33), (38), (39), (42), (43), (44), (54), (89), (92) are
% 169.84/26.00 | | | | | inconsistent by sub-proof #381.
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | Case 2:
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | (93) all_58_10 = e1 & op(e2, e0) = e1
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | ALPHA: (93) implies:
% 169.84/26.00 | | | | | (94) op(e2, e0) = e1
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | BETA: splitting (13) gives:
% 169.84/26.00 | | | | |
% 169.84/26.00 | | | | | Case 1:
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | | (95) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 169.84/26.00 | | | | | | e2) = e2)
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | | BETA: splitting (95) gives:
% 169.84/26.00 | | | | | |
% 169.84/26.00 | | | | | | Case 1:
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | (96) all_58_6 = e2 & op(e1, e3) = e2
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | ALPHA: (96) implies:
% 169.84/26.00 | | | | | | | (97) all_58_6 = e2
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | REF_CLOSE: (4), (9), (10), (12), (17), (18), (20), (24), (29),
% 169.84/26.00 | | | | | | | (31), (32), (38), (39), (42), (43), (44), (54), (97)
% 169.84/26.00 | | | | | | | are inconsistent by sub-proof #400.
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | Case 2:
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | (98) all_58_7 = e2 & op(e1, e2) = e2
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | ALPHA: (98) implies:
% 169.84/26.00 | | | | | | | (99) all_58_7 = e2
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | BETA: splitting (23) gives:
% 169.84/26.00 | | | | | | |
% 169.84/26.00 | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | |
% 169.84/26.00 | | | | | | | | (100) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 169.84/26.00 | | | | | | | | op(e2, e0) = e2)
% 169.84/26.00 | | | | | | | |
% 169.84/26.00 | | | | | | | | BETA: splitting (100) gives:
% 169.84/26.00 | | | | | | | |
% 169.84/26.00 | | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | (101) all_58_9 = e2 & op(e3, e0) = e2
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | ALPHA: (101) implies:
% 169.84/26.00 | | | | | | | | | (102) all_58_9 = e2
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | BETA: splitting (19) gives:
% 169.84/26.00 | | | | | | | | |
% 169.84/26.00 | | | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | (103) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 169.84/26.00 | | | | | | | | | | e3 & op(e0, e2) = e3)
% 169.84/26.00 | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | BETA: splitting (103) gives:
% 169.84/26.00 | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | (104) all_58_12 = e3 & op(e0, e3) = e3
% 169.84/26.00 | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | ALPHA: (104) implies:
% 169.84/26.00 | | | | | | | | | | | (105) all_58_12 = e3
% 169.84/26.00 | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | BETA: splitting (35) gives:
% 169.84/26.00 | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | (106) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0
% 169.84/26.00 | | | | | | | | | | | | & op(e2, e2) = e0)
% 169.84/26.00 | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | BETA: splitting (106) gives:
% 169.84/26.00 | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | (107) all_58_1 = e0 & op(e3, e2) = e0
% 169.84/26.00 | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | ALPHA: (107) implies:
% 169.84/26.00 | | | | | | | | | | | | | (108) all_58_1 = e0
% 169.84/26.00 | | | | | | | | | | | | | (109) op(e3, e2) = e0
% 169.84/26.00 | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | BETA: splitting (50) gives:
% 169.84/26.00 | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 169.84/26.00 | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | (110) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 169.84/26.00 | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 169.84/26.00 | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | BETA: splitting (110) gives:
% 169.84/26.00 | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | (111) all_58_1 = e1 & op(e3, e2) = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | REF_CLOSE: (18), (108), (111) are inconsistent by sub-proof
% 169.84/26.00 | | | | | | | | | | | | | | | | #658.
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | Case 2:
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | (112) all_58_3 = e1 & op(e2, e2) = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 169.84/26.00 | | | | | | | | | | | | | | | | (113) all_58_3 = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | COMBINE_EQS: (42), (113) imply:
% 169.84/26.00 | | | | | | | | | | | | | | | | (114) e3 = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (114) imply:
% 169.84/26.00 | | | | | | | | | | | | | | | | (115) all_58_12 = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10), (17), (18), (19), (24), (26),
% 169.84/26.00 | | | | | | | | | | | | | | | | (29), (31), (32), (38), (39), (42), (43), (44),
% 169.84/26.00 | | | | | | | | | | | | | | | | (46), (54), (55), (115) are inconsistent by
% 169.84/26.00 | | | | | | | | | | | | | | | | sub-proof #380.
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | End of split
% 169.84/26.00 | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | Case 2:
% 169.84/26.00 | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | (116) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 169.84/26.00 | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 169.84/26.00 | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 169.84/26.00 | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | Case 1:
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | (117) all_58_7 = e1 & op(e1, e2) = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 169.84/26.00 | | | | | | | | | | | | | | | | (118) all_58_7 = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | COMBINE_EQS: (99), (118) imply:
% 169.84/26.00 | | | | | | | | | | | | | | | | (119) e2 = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (119) imply:
% 169.84/26.00 | | | | | | | | | | | | | | | | (120) all_58_9 = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (12), (17), (18), (24), (29), (31),
% 169.84/26.00 | | | | | | | | | | | | | | | | (32), (37), (38), (39), (42), (43), (44), (48),
% 169.84/26.00 | | | | | | | | | | | | | | | | (54), (108), (120) are inconsistent by sub-proof
% 169.84/26.00 | | | | | | | | | | | | | | | | #378.
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | Case 2:
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | (121) all_58_13 = e1 & op(e0, e2) = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 169.84/26.00 | | | | | | | | | | | | | | | | (122) op(e0, e2) = e1
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | | REF_CLOSE: (34), (38), (109), (122) are inconsistent by
% 169.84/26.00 | | | | | | | | | | | | | | | | sub-proof #443.
% 169.84/26.00 | | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | | End of split
% 169.84/26.00 | | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | End of split
% 169.84/26.00 | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | Case 2:
% 169.84/26.00 | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | (123) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 169.84/26.00 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 169.84/26.00 | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 169.84/26.00 | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.84/26.00 | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.84/26.00 | | | | | | | | | | | | | |
% 169.84/26.00 | | | | | | | | | | | | | | ALPHA: (123) implies:
% 169.84/26.01 | | | | | | | | | | | | | | (124) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 169.84/26.01 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 169.84/26.01 | | | | | | | | | | | | | | e0) = e0)
% 169.84/26.01 | | | | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | | | | REF_CLOSE: (18), (31), (38), (39), (89), (94), (102), (124)
% 169.84/26.01 | | | | | | | | | | | | | | are inconsistent by sub-proof #722.
% 169.84/26.01 | | | | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | | | End of split
% 169.84/26.01 | | | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | | Case 2:
% 169.84/26.01 | | | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | | | (125) all_58_3 = e0 & op(e2, e2) = e0
% 169.84/26.01 | | | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10), (17), (18), (19), (24), (26),
% 169.84/26.01 | | | | | | | | | | | | | (29), (31), (32), (38), (39), (42), (43), (44),
% 169.84/26.01 | | | | | | | | | | | | | (46), (54), (55), (105), (125) are inconsistent by
% 169.84/26.01 | | | | | | | | | | | | | sub-proof #377.
% 169.84/26.01 | | | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | | End of split
% 169.84/26.01 | | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | Case 2:
% 169.84/26.01 | | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | | (126) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 =
% 169.84/26.01 | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 169.84/26.01 | | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | | REF_CLOSE: (18), (39), (40), (99), (126) are inconsistent by
% 169.84/26.01 | | | | | | | | | | | | sub-proof #376.
% 169.84/26.01 | | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | End of split
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | Case 2:
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | (127) all_58_13 = e3 & op(e0, e2) = e3
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | REF_CLOSE: (26), (38), (46), (127) are inconsistent by
% 169.84/26.01 | | | | | | | | | | | sub-proof #962.
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | End of split
% 169.84/26.01 | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | Case 2:
% 169.84/26.01 | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | (128) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 169.84/26.01 | | | | | | | | | | e3 & op(e0, e0) = e3)
% 169.84/26.01 | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | BETA: splitting (128) gives:
% 169.84/26.01 | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | Case 1:
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | (129) all_58_14 = e3 & op(e0, e1) = e3
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | ALPHA: (129) implies:
% 169.84/26.01 | | | | | | | | | | | (130) all_58_14 = e3
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | REF_CLOSE: (4), (10), (17), (18), (24), (25), (29), (31),
% 169.84/26.01 | | | | | | | | | | | (32), (37), (38), (39), (42), (43), (44), (49),
% 169.84/26.01 | | | | | | | | | | | (51), (54), (130) are inconsistent by sub-proof
% 169.84/26.01 | | | | | | | | | | | #375.
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | Case 2:
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | (131) all_58_15 = e3 & op(e0, e0) = e3
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | ALPHA: (131) implies:
% 169.84/26.01 | | | | | | | | | | | (132) all_58_15 = e3
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | | REF_CLOSE: (3), (17), (18), (31), (39), (44), (50), (89),
% 169.84/26.01 | | | | | | | | | | | (102), (132) are inconsistent by sub-proof #374.
% 169.84/26.01 | | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | | End of split
% 169.84/26.01 | | | | | | | | | |
% 169.84/26.01 | | | | | | | | | End of split
% 169.84/26.01 | | | | | | | | |
% 169.84/26.01 | | | | | | | | Case 2:
% 169.84/26.01 | | | | | | | | |
% 169.84/26.01 | | | | | | | | | (133) all_58_10 = e2 & op(e2, e0) = e2
% 169.84/26.01 | | | | | | | | |
% 169.84/26.01 | | | | | | | | | REF_CLOSE: (4), (17), (18), (24), (29), (31), (32), (38),
% 169.84/26.01 | | | | | | | | | (39), (42), (44), (133) are inconsistent by
% 169.84/26.01 | | | | | | | | | sub-proof #447.
% 169.84/26.01 | | | | | | | | |
% 169.84/26.01 | | | | | | | | End of split
% 169.84/26.01 | | | | | | | |
% 169.84/26.01 | | | | | | | Case 2:
% 169.84/26.01 | | | | | | | |
% 169.84/26.01 | | | | | | | | (134) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 169.84/26.01 | | | | | | | | op(e0, e0) = e2)
% 169.84/26.01 | | | | | | | |
% 169.84/26.01 | | | | | | | | REF_CLOSE: (4), (8), (10), (17), (18), (24), (29), (31), (32),
% 169.84/26.01 | | | | | | | | (33), (38), (39), (42), (43), (44), (54), (89), (134)
% 169.84/26.01 | | | | | | | | are inconsistent by sub-proof #420.
% 169.84/26.01 | | | | | | | |
% 169.84/26.01 | | | | | | | End of split
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | End of split
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | Case 2:
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | (135) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 &
% 169.84/26.01 | | | | | | op(e1, e0) = e2)
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | BETA: splitting (135) gives:
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | Case 1:
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | | (136) all_58_8 = e2 & op(e1, e1) = e2
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | | REF_CLOSE: (1), (9), (10), (12), (17), (18), (20), (25), (31),
% 169.84/26.01 | | | | | | | (37), (39), (40), (44), (49), (54), (55), (136) are
% 169.84/26.01 | | | | | | | inconsistent by sub-proof #394.
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | Case 2:
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | | (137) all_58_11 = e2 & op(e1, e0) = e2
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | | ALPHA: (137) implies:
% 169.84/26.01 | | | | | | | (138) all_58_11 = e2
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | | REF_CLOSE: (4), (10), (17), (18), (24), (29), (31), (32), (38),
% 169.84/26.01 | | | | | | | (39), (42), (43), (44), (54), (89), (138) are
% 169.84/26.01 | | | | | | | inconsistent by sub-proof #421.
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | End of split
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | End of split
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | End of split
% 169.84/26.01 | | | |
% 169.84/26.01 | | | Case 2:
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | (139) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 169.84/26.01 | | | | e0) = e1)
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | BETA: splitting (139) gives:
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | Case 1:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | (140) all_58_11 = e1 & op(e1, e0) = e1
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | ALPHA: (140) implies:
% 169.84/26.01 | | | | | (141) all_58_11 = e1
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | COMBINE_EQS: (89), (141) imply:
% 169.84/26.01 | | | | | (142) e3 = e1
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | SIMP: (142) implies:
% 169.84/26.01 | | | | | (143) e3 = e1
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | COMBINE_EQS: (37), (143) imply:
% 169.84/26.01 | | | | | (144) all_58_4 = e1
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | REF_CLOSE: (2), (4), (6), (10), (14), (17), (18), (22), (24), (27),
% 169.84/26.01 | | | | | (28), (29), (31), (32), (38), (39), (42), (43), (44), (51),
% 169.84/26.01 | | | | | (54), (144) are inconsistent by sub-proof #407.
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | Case 2:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | (145) all_58_15 = e1 & op(e0, e0) = e1
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | ALPHA: (145) implies:
% 169.84/26.01 | | | | | (146) all_58_15 = e1
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | REF_CLOSE: (18), (55), (146) are inconsistent by sub-proof #881.
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | End of split
% 169.84/26.01 | | | |
% 169.84/26.01 | | | End of split
% 169.84/26.01 | | |
% 169.84/26.01 | | End of split
% 169.84/26.01 | |
% 169.84/26.01 | End of split
% 169.84/26.01 |
% 169.84/26.01 End of proof
% 169.84/26.01
% 169.84/26.01 Sub-proof #374 shows that the following formulas are inconsistent:
% 169.84/26.01 ----------------------------------------------------------------
% 169.84/26.01 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 169.84/26.01 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.84/26.01 (2) all_58_9 = e2
% 169.84/26.01 (3) ~ (e3 = e1)
% 169.84/26.01 (4) ~ (e1 = e0)
% 169.84/26.01 (5) ~ (e3 = e0)
% 169.84/26.01 (6) all_58_11 = e3
% 169.84/26.01 (7) all_58_15 = e3
% 169.84/26.01 (8) ~ (e2 = e0)
% 169.84/26.01 (9) ~ (e2 = e1)
% 169.84/26.01 (10) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/26.01 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.84/26.01 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.84/26.01 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.84/26.01
% 169.84/26.01 Begin of proof
% 169.84/26.01 |
% 169.84/26.01 | BETA: splitting (10) gives:
% 169.84/26.01 |
% 169.84/26.01 | Case 1:
% 169.84/26.01 | |
% 169.84/26.01 | | (11) all_58_15 = e0 & op(e0, e0) = e0
% 169.84/26.01 | |
% 169.84/26.01 | | ALPHA: (11) implies:
% 169.84/26.01 | | (12) all_58_15 = e0
% 169.84/26.01 | |
% 169.84/26.01 | | REF_CLOSE: (5), (7), (12) are inconsistent by sub-proof #860.
% 169.84/26.01 | |
% 169.84/26.01 | Case 2:
% 169.84/26.01 | |
% 169.84/26.01 | | (13) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 169.84/26.01 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 169.84/26.01 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 169.84/26.01 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.84/26.01 | |
% 169.84/26.01 | | ALPHA: (13) implies:
% 169.84/26.01 | | (14) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 169.84/26.01 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 169.84/26.01 | |
% 169.84/26.01 | | BETA: splitting (14) gives:
% 169.84/26.01 | |
% 169.84/26.01 | | Case 1:
% 169.84/26.01 | | |
% 169.84/26.01 | | | (15) all_58_9 = e0 & op(e3, e0) = e0
% 169.84/26.01 | | |
% 169.84/26.01 | | | ALPHA: (15) implies:
% 169.84/26.01 | | | (16) all_58_9 = e0
% 169.84/26.01 | | |
% 169.84/26.01 | | | REF_CLOSE: (2), (8), (16) are inconsistent by sub-proof #945.
% 169.84/26.01 | | |
% 169.84/26.01 | | Case 2:
% 169.84/26.01 | | |
% 169.84/26.01 | | | (17) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.84/26.01 | | | = e0)
% 169.84/26.01 | | |
% 169.84/26.01 | | | BETA: splitting (17) gives:
% 169.84/26.01 | | |
% 169.84/26.01 | | | Case 1:
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | (18) all_58_10 = e0 & op(e2, e0) = e0
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | ALPHA: (18) implies:
% 169.84/26.01 | | | | (19) all_58_10 = e0
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | BETA: splitting (1) gives:
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | Case 1:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | (20) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2,
% 169.84/26.01 | | | | | e0) = e1)
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | BETA: splitting (20) gives:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | Case 1:
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | (21) all_58_9 = e1 & op(e3, e0) = e1
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | REF_CLOSE: (2), (9), (21) are inconsistent by sub-proof #701.
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | Case 2:
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | (22) all_58_10 = e1 & op(e2, e0) = e1
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | ALPHA: (22) implies:
% 169.84/26.01 | | | | | | (23) all_58_10 = e1
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | REF_CLOSE: (4), (19), (23) are inconsistent by sub-proof #834.
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | End of split
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | Case 2:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | (24) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0,
% 169.84/26.01 | | | | | e0) = e1)
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | BETA: splitting (24) gives:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | Case 1:
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | (25) all_58_11 = e1 & op(e1, e0) = e1
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | REF_CLOSE: (3), (6), (25) are inconsistent by sub-proof #721.
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | Case 2:
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | (26) all_58_15 = e1 & op(e0, e0) = e1
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | ALPHA: (26) implies:
% 169.84/26.01 | | | | | | (27) all_58_15 = e1
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | REF_CLOSE: (3), (7), (27) are inconsistent by sub-proof #556.
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | End of split
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | End of split
% 169.84/26.01 | | | |
% 169.84/26.01 | | | Case 2:
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | (28) all_58_11 = e0 & op(e1, e0) = e0
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | ALPHA: (28) implies:
% 169.84/26.01 | | | | (29) all_58_11 = e0
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | REF_CLOSE: (5), (6), (29) are inconsistent by sub-proof #474.
% 169.84/26.01 | | | |
% 169.84/26.01 | | | End of split
% 169.84/26.01 | | |
% 169.84/26.01 | | End of split
% 169.84/26.01 | |
% 169.84/26.01 | End of split
% 169.84/26.01 |
% 169.84/26.01 End of proof
% 169.84/26.01
% 169.84/26.01 Sub-proof #375 shows that the following formulas are inconsistent:
% 169.84/26.01 ----------------------------------------------------------------
% 169.84/26.01 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.01 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.01 (2) all_58_2 = e2
% 169.84/26.01 (3) ~ (e3 = e1)
% 169.84/26.01 (4) ~ (e1 = e0)
% 169.84/26.01 (5) op(e2, e3) = all_52_1
% 169.84/26.01 (6) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.84/26.01 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.84/26.01 (7) op(e2, e3) = e2
% 169.84/26.01 (8) ~ (e3 = e0)
% 169.84/26.01 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.01 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.01 (10) all_58_14 = e3
% 169.84/26.01 (11) all_58_4 = e3
% 169.84/26.01 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.01 (13) ~ (e2 = e0)
% 169.84/26.01 (14) all_58_3 = e3
% 169.84/26.01 (15) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.01 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.01 (16) ~ (e2 = e1)
% 169.84/26.01 (17) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.84/26.01 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.84/26.01 (18) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.84/26.01 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.84/26.01 (19) ~ (e3 = e2)
% 169.84/26.01
% 169.84/26.01 Begin of proof
% 169.84/26.01 |
% 169.84/26.01 | BETA: splitting (18) gives:
% 169.84/26.01 |
% 169.84/26.01 | Case 1:
% 169.84/26.01 | |
% 169.84/26.01 | | (20) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 169.84/26.01 | | e2)
% 169.84/26.01 | |
% 169.84/26.01 | | BETA: splitting (20) gives:
% 169.84/26.01 | |
% 169.84/26.01 | | Case 1:
% 169.84/26.01 | | |
% 169.84/26.01 | | | (21) all_58_4 = e2 & op(e3, e1) = e2
% 169.84/26.01 | | |
% 169.84/26.01 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14),
% 169.84/26.01 | | | (15), (16), (19), (21) are inconsistent by sub-proof #409.
% 169.84/26.01 | | |
% 169.84/26.01 | | Case 2:
% 169.84/26.01 | | |
% 169.84/26.01 | | | (22) all_58_5 = e2 & op(e2, e1) = e2
% 169.84/26.01 | | |
% 169.84/26.01 | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (12), (13), (14), (16), (22)
% 169.84/26.01 | | | are inconsistent by sub-proof #412.
% 169.84/26.01 | | |
% 169.84/26.01 | | End of split
% 169.84/26.01 | |
% 169.84/26.01 | Case 2:
% 169.84/26.01 | |
% 169.84/26.01 | | (23) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 169.84/26.01 | | e2)
% 169.84/26.01 | |
% 169.84/26.01 | | BETA: splitting (23) gives:
% 169.84/26.01 | |
% 169.84/26.01 | | Case 1:
% 169.84/26.01 | | |
% 169.84/26.01 | | | (24) all_58_8 = e2 & op(e1, e1) = e2
% 169.84/26.01 | | |
% 169.84/26.01 | | | ALPHA: (24) implies:
% 169.84/26.01 | | | (25) all_58_8 = e2
% 169.84/26.01 | | |
% 169.84/26.01 | | | BETA: splitting (6) gives:
% 169.84/26.01 | | |
% 169.84/26.01 | | | Case 1:
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | (26) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 169.84/26.01 | | | | = e0)
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | BETA: splitting (26) gives:
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | Case 1:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | (27) all_58_4 = e0 & op(e3, e1) = e0
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | REF_CLOSE: (8), (11), (27) are inconsistent by sub-proof #704.
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | Case 2:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | (28) all_58_5 = e0 & op(e2, e1) = e0
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | ALPHA: (28) implies:
% 169.84/26.01 | | | | | (29) all_58_5 = e0
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | BETA: splitting (17) gives:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | Case 1:
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | (30) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2,
% 169.84/26.01 | | | | | | e1) = e1)
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | REF_CLOSE: (3), (4), (11), (29), (30) are inconsistent by sub-proof
% 169.84/26.01 | | | | | | #385.
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | Case 2:
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | (31) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0,
% 169.84/26.01 | | | | | | e1) = e1)
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | BETA: splitting (31) gives:
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | | Case 1:
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | | (32) all_58_8 = e1 & op(e1, e1) = e1
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | | REF_CLOSE: (16), (25), (32) are inconsistent by sub-proof #397.
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | Case 2:
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | | (33) all_58_14 = e1 & op(e0, e1) = e1
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | | ALPHA: (33) implies:
% 169.84/26.01 | | | | | | | (34) all_58_14 = e1
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | | REF_CLOSE: (3), (10), (34) are inconsistent by sub-proof #626.
% 169.84/26.01 | | | | | | |
% 169.84/26.01 | | | | | | End of split
% 169.84/26.01 | | | | | |
% 169.84/26.01 | | | | | End of split
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | End of split
% 169.84/26.01 | | | |
% 169.84/26.01 | | | Case 2:
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | (35) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1)
% 169.84/26.01 | | | | = e0)
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | BETA: splitting (35) gives:
% 169.84/26.01 | | | |
% 169.84/26.01 | | | | Case 1:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | (36) all_58_8 = e0 & op(e1, e1) = e0
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | REF_CLOSE: (13), (25), (36) are inconsistent by sub-proof #398.
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | Case 2:
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | (37) all_58_14 = e0 & op(e0, e1) = e0
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | ALPHA: (37) implies:
% 169.84/26.01 | | | | | (38) all_58_14 = e0
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | | REF_CLOSE: (8), (10), (38) are inconsistent by sub-proof #423.
% 169.84/26.01 | | | | |
% 169.84/26.01 | | | | End of split
% 169.84/26.01 | | | |
% 169.84/26.01 | | | End of split
% 169.84/26.01 | | |
% 169.84/26.01 | | Case 2:
% 169.84/26.01 | | |
% 169.84/26.01 | | | (39) all_58_14 = e2 & op(e0, e1) = e2
% 169.84/26.01 | | |
% 169.84/26.01 | | | ALPHA: (39) implies:
% 169.84/26.01 | | | (40) all_58_14 = e2
% 169.84/26.01 | | |
% 169.84/26.01 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 169.84/26.01 | | | (15), (16), (19), (40) are inconsistent by sub-proof #438.
% 169.84/26.01 | | |
% 169.84/26.01 | | End of split
% 169.84/26.01 | |
% 169.84/26.01 | End of split
% 169.84/26.01 |
% 169.84/26.01 End of proof
% 169.84/26.01
% 169.84/26.01 Sub-proof #376 shows that the following formulas are inconsistent:
% 169.84/26.01 ----------------------------------------------------------------
% 169.84/26.01 (1) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.84/26.01 (2) all_58_7 = e2
% 169.84/26.01 (3) ~ (e1 = e0)
% 169.84/26.01 (4) ~ (e2 = e0)
% 169.84/26.01 (5) all_58_13 = e1
% 169.84/26.01
% 169.84/26.01 Begin of proof
% 169.84/26.01 |
% 169.84/26.01 | BETA: splitting (1) gives:
% 169.84/26.01 |
% 169.84/26.01 | Case 1:
% 169.84/26.01 | |
% 169.84/26.01 | | (6) all_58_7 = e0 & op(e1, e2) = e0
% 169.84/26.01 | |
% 169.84/26.01 | | ALPHA: (6) implies:
% 169.84/26.01 | | (7) all_58_7 = e0
% 169.84/26.01 | |
% 169.84/26.01 | | REF_CLOSE: (2), (4), (7) are inconsistent by sub-proof #482.
% 169.84/26.01 | |
% 169.84/26.01 | Case 2:
% 169.84/26.01 | |
% 169.84/26.01 | | (8) all_58_13 = e0 & op(e0, e2) = e0
% 169.84/26.01 | |
% 169.84/26.01 | | ALPHA: (8) implies:
% 169.84/26.01 | | (9) all_58_13 = e0
% 169.84/26.01 | |
% 169.84/26.01 | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #546.
% 169.84/26.01 | |
% 169.84/26.01 | End of split
% 169.84/26.01 |
% 169.84/26.01 End of proof
% 169.84/26.01
% 169.84/26.01 Sub-proof #377 shows that the following formulas are inconsistent:
% 169.84/26.01 ----------------------------------------------------------------
% 169.84/26.01 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.01 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.01 (2) all_58_14 = e2
% 169.84/26.01 (3) all_58_2 = e2
% 169.84/26.01 (4) ~ (e3 = e1)
% 169.84/26.01 (5) ~ (e1 = e0)
% 169.84/26.01 (6) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.84/26.01 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/26.01 (7) all_58_3 = e0 & op(e2, e2) = e0
% 169.84/26.01 (8) op(e2, e3) = all_52_1
% 169.84/26.01 (9) ~ (all_52_7 = e3)
% 169.84/26.01 (10) op(e2, e3) = e2
% 169.84/26.01 (11) ~ (e3 = e0)
% 169.84/26.01 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.01 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.01 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.01 (14) ~ (e2 = e0)
% 169.84/26.01 (15) all_58_12 = e3
% 169.84/26.01 (16) all_58_3 = e3
% 169.84/26.01 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.01 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.01 (18) ~ (e2 = e1)
% 169.84/26.01 (19) all_58_15 = e0
% 169.84/26.01 (20) op(e0, e2) = all_52_7
% 169.84/26.01 (21) ~ (e3 = e2)
% 169.84/26.01
% 169.84/26.01 Begin of proof
% 169.84/26.01 |
% 169.84/26.01 | ALPHA: (7) implies:
% 169.84/26.01 | (22) all_58_3 = e0
% 169.84/26.01 |
% 169.84/26.01 | COMBINE_EQS: (16), (22) imply:
% 169.84/26.01 | (23) e3 = e0
% 169.84/26.01 |
% 169.84/26.01 | SIMP: (23) implies:
% 169.84/26.01 | (24) e3 = e0
% 169.84/26.01 |
% 169.84/26.02 | COMBINE_EQS: (15), (24) imply:
% 169.84/26.02 | (25) all_58_12 = e0
% 169.84/26.02 |
% 169.84/26.02 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 169.84/26.02 | (14), (16), (17), (18), (19), (20), (21), (25) are inconsistent by
% 169.84/26.02 | sub-proof #404.
% 169.84/26.02 |
% 169.84/26.02 End of proof
% 169.84/26.02
% 169.84/26.02 Sub-proof #378 shows that the following formulas are inconsistent:
% 169.84/26.02 ----------------------------------------------------------------
% 169.84/26.02 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.02 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.02 (2) all_58_2 = e2
% 169.84/26.02 (3) all_58_0 = e1
% 169.84/26.02 (4) ~ (e3 = e1)
% 169.84/26.02 (5) ~ (e1 = e0)
% 169.84/26.02 (6) op(e2, e3) = all_52_1
% 169.84/26.02 (7) op(e2, e3) = e2
% 169.84/26.02 (8) ~ (e3 = e0)
% 169.84/26.02 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.02 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.02 (10) all_58_4 = e3
% 169.84/26.02 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.02 (12) ~ (e2 = e0)
% 169.84/26.02 (13) all_58_3 = e3
% 169.84/26.02 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.02 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.02 (15) ~ (e2 = e1)
% 169.84/26.02 (16) all_58_9 = e1
% 169.84/26.02 (17) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.84/26.02 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.84/26.02 (18) all_58_1 = e0
% 169.84/26.02 (19) ~ (e3 = e2)
% 169.84/26.02
% 169.84/26.02 Begin of proof
% 169.84/26.02 |
% 169.84/26.02 | BETA: splitting (17) gives:
% 169.84/26.02 |
% 169.84/26.02 | Case 1:
% 169.84/26.02 | |
% 169.84/26.02 | | (20) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 169.84/26.02 | | e2)
% 169.84/26.02 | |
% 169.84/26.02 | | BETA: splitting (20) gives:
% 169.84/26.02 | |
% 169.84/26.02 | | Case 1:
% 169.84/26.02 | | |
% 169.84/26.02 | | | (21) all_58_0 = e2 & op(e3, e3) = e2
% 169.84/26.02 | | |
% 169.84/26.02 | | | REF_CLOSE: (3), (15), (21) are inconsistent by sub-proof #393.
% 169.84/26.02 | | |
% 169.84/26.02 | | Case 2:
% 169.84/26.02 | | |
% 169.84/26.02 | | | (22) all_58_1 = e2 & op(e3, e2) = e2
% 169.84/26.02 | | |
% 169.84/26.02 | | | REF_CLOSE: (12), (18), (22) are inconsistent by sub-proof #392.
% 169.84/26.02 | | |
% 169.84/26.02 | | End of split
% 169.84/26.02 | |
% 169.84/26.02 | Case 2:
% 169.84/26.02 | |
% 169.84/26.02 | | (23) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 169.84/26.02 | | e2)
% 169.84/26.02 | |
% 169.84/26.02 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.84/26.02 | | (14), (15), (16), (19), (23) are inconsistent by sub-proof #379.
% 169.84/26.02 | |
% 169.84/26.02 | End of split
% 169.84/26.02 |
% 169.84/26.02 End of proof
% 169.84/26.02
% 169.84/26.02 Sub-proof #379 shows that the following formulas are inconsistent:
% 169.84/26.02 ----------------------------------------------------------------
% 169.84/26.02 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.02 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.02 (2) all_58_2 = e2
% 169.84/26.02 (3) ~ (e3 = e1)
% 169.84/26.02 (4) ~ (e1 = e0)
% 169.84/26.02 (5) op(e2, e3) = all_52_1
% 169.84/26.02 (6) op(e2, e3) = e2
% 169.84/26.02 (7) ~ (e3 = e0)
% 169.84/26.02 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.02 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.02 (9) all_58_4 = e3
% 169.84/26.02 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.02 (11) ~ (e2 = e0)
% 169.84/26.02 (12) all_58_3 = e3
% 169.84/26.02 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.02 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.02 (14) ~ (e2 = e1)
% 169.84/26.02 (15) all_58_9 = e1
% 169.84/26.02 (16) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.84/26.02 (17) ~ (e3 = e2)
% 169.84/26.02
% 169.84/26.02 Begin of proof
% 169.84/26.02 |
% 169.84/26.02 | BETA: splitting (16) gives:
% 169.84/26.02 |
% 169.84/26.02 | Case 1:
% 169.84/26.02 | |
% 169.84/26.02 | | (18) all_58_4 = e2 & op(e3, e1) = e2
% 169.84/26.02 | |
% 169.84/26.02 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.84/26.02 | | (13), (14), (17), (18) are inconsistent by sub-proof #409.
% 169.84/26.02 | |
% 169.84/26.02 | Case 2:
% 169.84/26.02 | |
% 169.84/26.02 | | (19) all_58_9 = e2 & op(e3, e0) = e2
% 169.84/26.02 | |
% 169.84/26.02 | | ALPHA: (19) implies:
% 169.84/26.02 | | (20) all_58_9 = e2
% 169.84/26.02 | |
% 169.84/26.02 | | REF_CLOSE: (14), (15), (20) are inconsistent by sub-proof #942.
% 169.84/26.02 | |
% 169.84/26.02 | End of split
% 169.84/26.02 |
% 169.84/26.02 End of proof
% 169.84/26.02
% 169.84/26.02 Sub-proof #380 shows that the following formulas are inconsistent:
% 169.84/26.02 ----------------------------------------------------------------
% 169.84/26.02 (1) all_58_12 = e1
% 169.84/26.02 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.02 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.02 (3) all_58_14 = e2
% 169.84/26.02 (4) all_58_2 = e2
% 169.84/26.02 (5) ~ (e3 = e1)
% 169.84/26.02 (6) ~ (e1 = e0)
% 169.84/26.02 (7) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.84/26.02 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/26.02 (8) op(e2, e3) = all_52_1
% 169.84/26.02 (9) ~ (all_52_7 = e3)
% 169.84/26.02 (10) op(e2, e3) = e2
% 169.84/26.02 (11) ~ (e3 = e0)
% 169.84/26.02 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.02 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.02 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.02 (14) ~ (e2 = e0)
% 169.84/26.02 (15) all_58_3 = e3
% 169.84/26.02 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.02 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.02 (17) ~ (e2 = e1)
% 169.84/26.02 (18) all_58_15 = e0
% 169.84/26.02 (19) op(e0, e2) = all_52_7
% 169.84/26.02 (20) ~ (e3 = e2)
% 169.84/26.02
% 169.84/26.02 Begin of proof
% 169.84/26.02 |
% 169.84/26.02 | BETA: splitting (7) gives:
% 169.84/26.02 |
% 169.84/26.02 | Case 1:
% 169.84/26.02 | |
% 169.84/26.02 | | (21) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 169.84/26.02 | | e3)
% 169.84/26.02 | |
% 169.84/26.02 | | REF_CLOSE: (1), (5), (9), (13), (19), (21) are inconsistent by sub-proof
% 169.84/26.02 | | #470.
% 169.84/26.02 | |
% 169.84/26.02 | Case 2:
% 169.84/26.02 | |
% 169.84/26.02 | | (22) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.84/26.02 | | e3)
% 169.84/26.02 | |
% 169.84/26.02 | | BETA: splitting (22) gives:
% 169.84/26.02 | |
% 169.84/26.02 | | Case 1:
% 169.84/26.02 | | |
% 169.84/26.02 | | | (23) all_58_14 = e3 & op(e0, e1) = e3
% 169.84/26.02 | | |
% 169.84/26.02 | | | ALPHA: (23) implies:
% 169.84/26.02 | | | (24) all_58_14 = e3
% 169.84/26.02 | | |
% 169.84/26.02 | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (14),
% 169.84/26.02 | | | (15), (16), (17), (20), (24) are inconsistent by sub-proof
% 169.84/26.02 | | | #438.
% 169.84/26.02 | | |
% 169.84/26.02 | | Case 2:
% 169.84/26.02 | | |
% 169.84/26.02 | | | (25) all_58_15 = e3 & op(e0, e0) = e3
% 169.84/26.02 | | |
% 169.84/26.02 | | | REF_CLOSE: (11), (18), (25) are inconsistent by sub-proof #812.
% 169.84/26.02 | | |
% 169.84/26.02 | | End of split
% 169.84/26.02 | |
% 169.84/26.02 | End of split
% 169.84/26.02 |
% 169.84/26.02 End of proof
% 169.84/26.02
% 169.84/26.02 Sub-proof #381 shows that the following formulas are inconsistent:
% 169.84/26.02 ----------------------------------------------------------------
% 169.84/26.02 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.02 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.02 (2) ~ (all_4_2 = e2)
% 169.84/26.02 (3) all_58_2 = e2
% 169.84/26.02 (4) ~ (e3 = e1)
% 169.84/26.02 (5) ~ (e1 = e0)
% 169.84/26.02 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.84/26.02 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.84/26.02 (7) op(e2, e3) = all_52_1
% 169.84/26.02 (8) op(e2, e3) = e2
% 169.84/26.02 (9) ~ (e3 = e0)
% 169.84/26.02 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.02 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.02 (11) op(e0, e0) = all_4_2
% 169.84/26.02 (12) all_58_11 = e3
% 169.84/26.02 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.02 (14) ~ (e2 = e0)
% 169.84/26.02 (15) all_58_3 = e3
% 169.84/26.02 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.02 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.02 (17) ~ (e2 = e1)
% 169.84/26.02 (18) all_58_9 = e1
% 169.84/26.02 (19) ~ (e3 = e2)
% 169.84/26.02
% 169.84/26.02 Begin of proof
% 169.84/26.02 |
% 169.84/26.02 | BETA: splitting (6) gives:
% 169.84/26.02 |
% 169.84/26.02 | Case 1:
% 169.84/26.02 | |
% 169.84/26.02 | | (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 169.84/26.02 | | e2)
% 169.84/26.02 | |
% 169.84/26.02 | | BETA: splitting (20) gives:
% 169.84/26.02 | |
% 169.84/26.02 | | Case 1:
% 169.84/26.02 | | |
% 169.84/26.02 | | | (21) all_58_9 = e2 & op(e3, e0) = e2
% 169.84/26.02 | | |
% 169.84/26.02 | | | REF_CLOSE: (17), (18), (21) are inconsistent by sub-proof #382.
% 169.84/26.02 | | |
% 169.84/26.02 | | Case 2:
% 169.84/26.02 | | |
% 169.84/26.02 | | | (22) all_58_10 = e2 & op(e2, e0) = e2
% 169.84/26.02 | | |
% 169.84/26.02 | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (13), (14), (15), (17),
% 169.84/26.02 | | | (22) are inconsistent by sub-proof #447.
% 169.84/26.02 | | |
% 169.84/26.02 | | End of split
% 169.84/26.02 | |
% 169.84/26.02 | Case 2:
% 169.84/26.02 | |
% 169.84/26.02 | | (23) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.84/26.02 | | e2)
% 169.84/26.02 | |
% 169.84/26.02 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 169.84/26.02 | | (14), (15), (16), (17), (19), (23) are inconsistent by sub-proof
% 169.84/26.02 | | #420.
% 169.84/26.02 | |
% 169.84/26.02 | End of split
% 169.84/26.02 |
% 169.84/26.02 End of proof
% 169.84/26.02
% 169.84/26.02 Sub-proof #382 shows that the following formulas are inconsistent:
% 169.84/26.02 ----------------------------------------------------------------
% 169.84/26.02 (1) all_58_9 = e2 & op(e3, e0) = e2
% 169.84/26.02 (2) all_58_9 = e1
% 169.84/26.02 (3) ~ (e2 = e1)
% 169.84/26.02
% 169.84/26.02 Begin of proof
% 169.84/26.02 |
% 169.84/26.02 | ALPHA: (1) implies:
% 169.84/26.02 | (4) all_58_9 = e2
% 169.84/26.02 |
% 169.84/26.02 | COMBINE_EQS: (2), (4) imply:
% 169.84/26.02 | (5) e2 = e1
% 169.84/26.02 |
% 169.84/26.02 | REDUCE: (3), (5) imply:
% 169.84/26.02 | (6) $false
% 169.84/26.02 |
% 169.84/26.02 | CLOSE: (6) is inconsistent.
% 169.84/26.02 |
% 169.84/26.02 End of proof
% 169.84/26.02
% 169.84/26.02 Sub-proof #383 shows that the following formulas are inconsistent:
% 169.84/26.02 ----------------------------------------------------------------
% 169.84/26.02 (1) all_58_14 = e2
% 169.84/26.02 (2) ~ (e3 = e1)
% 169.84/26.02 (3) ~ (e1 = e0)
% 169.84/26.02 (4) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.84/26.02 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.84/26.02 (5) ~ (e3 = e0)
% 169.84/26.02 (6) all_58_8 = e3 & op(e1, e1) = e3
% 169.84/26.02 (7) all_58_4 = e3
% 169.84/26.02 (8) ~ (e2 = e0)
% 169.84/26.02 (9) ~ (e2 = e1)
% 169.84/26.02 (10) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.84/26.02 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.84/26.02
% 169.84/26.02 Begin of proof
% 169.84/26.02 |
% 169.84/26.02 | ALPHA: (6) implies:
% 169.84/26.02 | (11) all_58_8 = e3
% 169.84/26.02 |
% 169.84/26.02 | BETA: splitting (4) gives:
% 169.84/26.02 |
% 169.84/26.02 | Case 1:
% 169.84/26.02 | |
% 169.84/26.02 | | (12) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 169.84/26.02 | | e0)
% 169.84/26.02 | |
% 169.84/26.02 | | BETA: splitting (12) gives:
% 169.84/26.02 | |
% 169.84/26.02 | | Case 1:
% 169.84/26.02 | | |
% 169.84/26.02 | | | (13) all_58_4 = e0 & op(e3, e1) = e0
% 169.84/26.02 | | |
% 169.84/26.02 | | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #704.
% 169.84/26.02 | | |
% 169.84/26.02 | | Case 2:
% 169.84/26.02 | | |
% 169.84/26.02 | | | (14) all_58_5 = e0 & op(e2, e1) = e0
% 169.84/26.02 | | |
% 169.84/26.02 | | | ALPHA: (14) implies:
% 169.84/26.02 | | | (15) all_58_5 = e0
% 169.84/26.02 | | |
% 169.84/26.02 | | | BETA: splitting (10) gives:
% 169.84/26.02 | | |
% 169.84/26.02 | | | Case 1:
% 169.84/26.02 | | | |
% 169.84/26.02 | | | | (16) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 169.84/26.02 | | | | = e1)
% 169.84/26.02 | | | |
% 169.84/26.02 | | | | REF_CLOSE: (2), (3), (7), (15), (16) are inconsistent by sub-proof #385.
% 169.84/26.02 | | | |
% 169.84/26.02 | | | Case 2:
% 169.84/26.02 | | | |
% 169.84/26.02 | | | | (17) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 169.84/26.02 | | | | = e1)
% 169.84/26.02 | | | |
% 169.84/26.02 | | | | BETA: splitting (17) gives:
% 169.84/26.02 | | | |
% 169.84/26.02 | | | | Case 1:
% 169.84/26.02 | | | | |
% 169.84/26.02 | | | | | (18) all_58_8 = e1 & op(e1, e1) = e1
% 169.84/26.02 | | | | |
% 169.84/26.02 | | | | | REF_CLOSE: (2), (11), (18) are inconsistent by sub-proof #384.
% 169.84/26.02 | | | | |
% 169.84/26.02 | | | | Case 2:
% 169.84/26.02 | | | | |
% 169.84/26.02 | | | | | (19) all_58_14 = e1 & op(e0, e1) = e1
% 169.84/26.02 | | | | |
% 169.84/26.02 | | | | | ALPHA: (19) implies:
% 169.84/26.02 | | | | | (20) all_58_14 = e1
% 169.84/26.02 | | | | |
% 169.84/26.02 | | | | | REF_CLOSE: (1), (9), (20) are inconsistent by sub-proof #649.
% 169.84/26.02 | | | | |
% 169.84/26.02 | | | | End of split
% 169.84/26.02 | | | |
% 169.84/26.02 | | | End of split
% 169.84/26.02 | | |
% 169.84/26.02 | | End of split
% 169.84/26.02 | |
% 169.84/26.02 | Case 2:
% 169.84/26.02 | |
% 169.84/26.02 | | (21) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 169.84/26.02 | | e0)
% 169.84/26.02 | |
% 169.84/26.02 | | BETA: splitting (21) gives:
% 169.84/26.02 | |
% 169.84/26.02 | | Case 1:
% 169.84/26.02 | | |
% 169.84/26.02 | | | (22) all_58_8 = e0 & op(e1, e1) = e0
% 169.84/26.02 | | |
% 169.84/26.02 | | | REF_CLOSE: (5), (11), (22) are inconsistent by sub-proof #496.
% 169.84/26.02 | | |
% 169.84/26.02 | | Case 2:
% 169.84/26.02 | | |
% 169.84/26.02 | | | (23) all_58_14 = e0 & op(e0, e1) = e0
% 169.84/26.02 | | |
% 169.84/26.02 | | | REF_CLOSE: (1), (8), (23) are inconsistent by sub-proof #858.
% 169.84/26.02 | | |
% 169.84/26.02 | | End of split
% 169.84/26.02 | |
% 169.84/26.02 | End of split
% 169.84/26.02 |
% 169.84/26.02 End of proof
% 169.84/26.02
% 169.84/26.02 Sub-proof #384 shows that the following formulas are inconsistent:
% 169.84/26.02 ----------------------------------------------------------------
% 169.84/26.02 (1) all_58_8 = e1 & op(e1, e1) = e1
% 169.84/26.02 (2) all_58_8 = e3
% 169.84/26.02 (3) ~ (e3 = e1)
% 169.84/26.02
% 169.84/26.02 Begin of proof
% 169.84/26.02 |
% 169.84/26.02 | ALPHA: (1) implies:
% 169.84/26.02 | (4) all_58_8 = e1
% 169.84/26.02 |
% 169.84/26.02 | COMBINE_EQS: (2), (4) imply:
% 169.84/26.02 | (5) e3 = e1
% 169.84/26.02 |
% 169.84/26.02 | REDUCE: (3), (5) imply:
% 169.84/26.02 | (6) $false
% 169.84/26.02 |
% 169.84/26.02 | CLOSE: (6) is inconsistent.
% 169.84/26.02 |
% 169.84/26.02 End of proof
% 169.84/26.02
% 169.84/26.02 Sub-proof #385 shows that the following formulas are inconsistent:
% 169.84/26.02 ----------------------------------------------------------------
% 169.84/26.02 (1) ~ (e3 = e1)
% 169.84/26.02 (2) ~ (e1 = e0)
% 169.84/26.02 (3) all_58_4 = e3
% 169.84/26.02 (4) all_58_5 = e0
% 169.84/26.02 (5) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 169.84/26.02
% 169.84/26.02 Begin of proof
% 169.84/26.02 |
% 169.84/26.02 | BETA: splitting (5) gives:
% 169.84/26.02 |
% 169.84/26.02 | Case 1:
% 169.84/26.02 | |
% 169.84/26.02 | | (6) all_58_4 = e1 & op(e3, e1) = e1
% 169.84/26.02 | |
% 169.84/26.02 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #702.
% 169.84/26.02 | |
% 169.84/26.02 | Case 2:
% 169.84/26.02 | |
% 169.84/26.02 | | (7) all_58_5 = e1 & op(e2, e1) = e1
% 169.84/26.02 | |
% 169.84/26.02 | | ALPHA: (7) implies:
% 169.84/26.02 | | (8) all_58_5 = e1
% 169.84/26.02 | |
% 169.84/26.02 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #449.
% 169.84/26.02 | |
% 169.84/26.02 | End of split
% 169.84/26.02 |
% 169.84/26.02 End of proof
% 169.84/26.02
% 169.84/26.02 Sub-proof #386 shows that the following formulas are inconsistent:
% 169.84/26.02 ----------------------------------------------------------------
% 169.84/26.02 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.84/26.02 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.84/26.02 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.02 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.02 (3) ~ (all_4_2 = e2)
% 169.84/26.02 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/26.02 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/26.02 (5) all_58_2 = e2
% 169.84/26.02 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.02 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.84/26.02 (7) all_58_14 = e3 & op(e0, e1) = e3
% 169.84/26.02 (8) ~ (e3 = e1)
% 169.84/26.02 (9) ~ (e1 = e0)
% 169.84/26.02 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.84/26.02 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.84/26.02 (11) op(e1, e2) = all_52_6
% 169.84/26.02 (12) op(e2, e3) = all_52_1
% 169.84/26.02 (13) op(e2, e3) = e2
% 169.84/26.02 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.84/26.02 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.84/26.02 (15) ~ (e3 = e0)
% 169.84/26.02 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.02 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.02 (17) op(e0, e0) = all_4_2
% 169.84/26.02 (18) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.84/26.02 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.84/26.02 e2) = all_22_1 & $i(all_22_1))
% 169.84/26.03 (19) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.03 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.84/26.03 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.03 (21) ~ (e2 = e0)
% 169.84/26.03 (22) all_58_3 = e3
% 169.84/26.03 (23) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.03 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.03 (24) ~ (e2 = e1)
% 169.84/26.03 (25) op(e3, e2) = all_52_4
% 169.84/26.03 (26) all_58_7 = e3
% 169.84/26.03 (27) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.84/26.03 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.84/26.03 e2) = all_14_1 & $i(all_14_1))
% 169.84/26.03 (28) ~ (e3 = e2)
% 169.84/26.03
% 169.84/26.03 Begin of proof
% 169.84/26.03 |
% 169.84/26.03 | ALPHA: (7) implies:
% 169.84/26.03 | (29) all_58_14 = e3
% 169.84/26.03 |
% 169.84/26.03 | BETA: splitting (1) gives:
% 169.84/26.03 |
% 169.84/26.03 | Case 1:
% 169.84/26.03 | |
% 169.84/26.03 | | (30) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 169.84/26.03 | | e2)
% 169.84/26.03 | |
% 169.84/26.03 | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14), (15),
% 169.84/26.03 | | (16), (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 169.84/26.03 | | (28), (30) are inconsistent by sub-proof #424.
% 169.84/26.03 | |
% 169.84/26.03 | Case 2:
% 169.84/26.03 | |
% 169.84/26.03 | | (31) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.84/26.03 | | e2)
% 169.84/26.03 | |
% 169.84/26.03 | | REF_CLOSE: (2), (3), (5), (8), (9), (12), (13), (15), (16), (17), (20),
% 169.84/26.03 | | (21), (22), (23), (24), (28), (29), (31) are inconsistent by
% 169.84/26.03 | | sub-proof #437.
% 169.84/26.03 | |
% 169.84/26.03 | End of split
% 169.84/26.03 |
% 169.84/26.03 End of proof
% 169.84/26.03
% 169.84/26.03 Sub-proof #387 shows that the following formulas are inconsistent:
% 169.84/26.03 ----------------------------------------------------------------
% 169.84/26.03 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.03 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.03 (2) ~ (all_52_13 = e3)
% 169.84/26.03 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/26.03 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/26.03 (4) all_58_2 = e2
% 169.84/26.03 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.84/26.03 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/26.03 (6) ~ (e3 = e1)
% 169.84/26.03 (7) ~ (e1 = e0)
% 169.84/26.03 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.84/26.03 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.84/26.03 (9) op(e2, e3) = all_52_1
% 169.84/26.03 (10) op(e2, e3) = e2
% 169.84/26.03 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.84/26.03 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.84/26.03 (12) ~ (e3 = e0)
% 169.84/26.03 (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.03 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.03 (14) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.84/26.03 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.84/26.03 (15) all_58_4 = e3
% 169.84/26.03 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.03 (17) ~ (e2 = e0)
% 169.84/26.03 (18) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.03 (19) all_58_12 = e3
% 169.84/26.03 (20) all_58_3 = e3
% 169.84/26.03 (21) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.03 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.03 (22) ~ (e2 = e1)
% 169.84/26.03 (23) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.84/26.03 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.84/26.03 (24) op(e2, e0) = all_52_13
% 169.84/26.03 (25) ~ (e3 = e2)
% 169.84/26.03
% 169.84/26.03 Begin of proof
% 169.84/26.03 |
% 169.84/26.03 | BETA: splitting (18) gives:
% 169.84/26.03 |
% 169.84/26.03 | Case 1:
% 169.84/26.03 | |
% 169.84/26.03 | | (26) all_58_9 = e3 & op(e3, e0) = e3
% 169.84/26.03 | |
% 169.84/26.03 | | ALPHA: (26) implies:
% 169.84/26.03 | | (27) all_58_9 = e3
% 169.84/26.03 | |
% 169.84/26.03 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.84/26.03 | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (25), (27)
% 169.84/26.03 | | are inconsistent by sub-proof #388.
% 169.84/26.03 | |
% 169.84/26.03 | Case 2:
% 169.84/26.03 | |
% 169.84/26.03 | | (28) all_58_10 = e3 & op(e2, e0) = e3
% 169.84/26.03 | |
% 169.84/26.03 | | ALPHA: (28) implies:
% 169.84/26.03 | | (29) op(e2, e0) = e3
% 169.84/26.03 | |
% 169.84/26.03 | | REF_CLOSE: (2), (16), (24), (29) are inconsistent by sub-proof #562.
% 169.84/26.03 | |
% 169.84/26.03 | End of split
% 169.84/26.03 |
% 169.84/26.03 End of proof
% 169.84/26.03
% 169.84/26.03 Sub-proof #388 shows that the following formulas are inconsistent:
% 169.84/26.03 ----------------------------------------------------------------
% 169.84/26.03 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.03 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.03 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/26.03 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/26.03 (3) all_58_2 = e2
% 169.84/26.03 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.84/26.03 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/26.03 (5) ~ (e3 = e1)
% 169.84/26.03 (6) ~ (e1 = e0)
% 169.84/26.03 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.84/26.03 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.84/26.03 (8) op(e2, e3) = all_52_1
% 169.84/26.03 (9) op(e2, e3) = e2
% 169.84/26.03 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.84/26.03 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.84/26.03 (11) ~ (e3 = e0)
% 169.84/26.03 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.03 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.03 (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.84/26.03 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.84/26.03 (14) all_58_4 = e3
% 169.84/26.03 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.03 (16) ~ (e2 = e0)
% 169.84/26.03 (17) all_58_12 = e3
% 169.84/26.03 (18) all_58_3 = e3
% 169.84/26.03 (19) all_58_9 = e3
% 169.84/26.03 (20) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.03 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.03 (21) ~ (e2 = e1)
% 169.84/26.03 (22) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.84/26.03 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.84/26.03 (23) ~ (e3 = e2)
% 169.84/26.03
% 169.84/26.03 Begin of proof
% 169.84/26.03 |
% 169.84/26.03 | BETA: splitting (10) gives:
% 169.84/26.03 |
% 169.84/26.03 | Case 1:
% 169.84/26.03 | |
% 169.84/26.03 | | (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 169.84/26.03 | | e1)
% 169.84/26.03 | |
% 169.84/26.03 | | BETA: splitting (24) gives:
% 169.84/26.03 | |
% 169.84/26.03 | | Case 1:
% 169.84/26.03 | | |
% 169.84/26.03 | | | (25) all_58_0 = e1 & op(e3, e3) = e1
% 169.84/26.03 | | |
% 169.84/26.03 | | | ALPHA: (25) implies:
% 169.84/26.03 | | | (26) all_58_0 = e1
% 169.84/26.03 | | |
% 169.84/26.03 | | | BETA: splitting (4) gives:
% 169.84/26.03 | | |
% 169.84/26.03 | | | Case 1:
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | (27) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 169.84/26.03 | | | | = e0)
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | BETA: splitting (27) gives:
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | Case 1:
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | (28) all_58_0 = e0 & op(e3, e3) = e0
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | REF_CLOSE: (6), (26), (28) are inconsistent by sub-proof #903.
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | Case 2:
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | (29) all_58_1 = e0 & op(e3, e2) = e0
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | ALPHA: (29) implies:
% 169.84/26.03 | | | | | (30) all_58_1 = e0
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | BETA: splitting (22) gives:
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | Case 1:
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | (31) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3,
% 169.84/26.03 | | | | | | e2) = e2)
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | BETA: splitting (31) gives:
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | Case 1:
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | (32) all_58_0 = e2 & op(e3, e3) = e2
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | REF_CLOSE: (21), (26), (32) are inconsistent by sub-proof #393.
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | Case 2:
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | (33) all_58_1 = e2 & op(e3, e2) = e2
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | REF_CLOSE: (16), (30), (33) are inconsistent by sub-proof #392.
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | End of split
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | Case 2:
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | (34) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3,
% 169.84/26.03 | | | | | | e0) = e2)
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (14), (15),
% 169.84/26.03 | | | | | | (16), (18), (19), (20), (21), (23), (34) are inconsistent
% 169.84/26.03 | | | | | | by sub-proof #391.
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | End of split
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | End of split
% 169.84/26.03 | | | |
% 169.84/26.03 | | | Case 2:
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | (35) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 169.84/26.03 | | | | = e0)
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | BETA: splitting (35) gives:
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | Case 1:
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | (36) all_58_4 = e0 & op(e3, e1) = e0
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | REF_CLOSE: (11), (14), (36) are inconsistent by sub-proof #704.
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | Case 2:
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | (37) all_58_9 = e0 & op(e3, e0) = e0
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | ALPHA: (37) implies:
% 169.84/26.03 | | | | | (38) all_58_9 = e0
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | REF_CLOSE: (11), (19), (38) are inconsistent by sub-proof #835.
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | End of split
% 169.84/26.03 | | | |
% 169.84/26.03 | | | End of split
% 169.84/26.03 | | |
% 169.84/26.03 | | Case 2:
% 169.84/26.03 | | |
% 169.84/26.03 | | | (39) all_58_2 = e1 & op(e2, e3) = e1
% 169.84/26.03 | | |
% 169.84/26.03 | | | ALPHA: (39) implies:
% 169.84/26.03 | | | (40) op(e2, e3) = e1
% 169.84/26.03 | | |
% 169.84/26.03 | | | REF_CLOSE: (8), (9), (15), (21), (40) are inconsistent by sub-proof #784.
% 169.84/26.03 | | |
% 169.84/26.03 | | End of split
% 169.84/26.03 | |
% 169.84/26.03 | Case 2:
% 169.84/26.03 | |
% 169.84/26.03 | | (41) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 169.84/26.03 | | e1)
% 169.84/26.03 | |
% 169.84/26.03 | | BETA: splitting (41) gives:
% 169.84/26.03 | |
% 169.84/26.03 | | Case 1:
% 169.84/26.03 | | |
% 169.84/26.03 | | | (42) all_58_6 = e1 & op(e1, e3) = e1
% 169.84/26.03 | | |
% 169.84/26.03 | | | ALPHA: (42) implies:
% 169.84/26.03 | | | (43) all_58_6 = e1
% 169.84/26.03 | | |
% 169.84/26.03 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 169.84/26.03 | | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (43) are
% 169.84/26.03 | | | inconsistent by sub-proof #389.
% 169.84/26.03 | | |
% 169.84/26.03 | | Case 2:
% 169.84/26.03 | | |
% 169.84/26.03 | | | (44) all_58_12 = e1 & op(e0, e3) = e1
% 169.84/26.03 | | |
% 169.84/26.03 | | | ALPHA: (44) implies:
% 169.84/26.03 | | | (45) all_58_12 = e1
% 169.84/26.03 | | |
% 169.84/26.03 | | | REF_CLOSE: (5), (17), (45) are inconsistent by sub-proof #600.
% 169.84/26.03 | | |
% 169.84/26.03 | | End of split
% 169.84/26.03 | |
% 169.84/26.03 | End of split
% 169.84/26.03 |
% 169.84/26.03 End of proof
% 169.84/26.03
% 169.84/26.03 Sub-proof #389 shows that the following formulas are inconsistent:
% 169.84/26.03 ----------------------------------------------------------------
% 169.84/26.03 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.03 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.03 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/26.03 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/26.03 (3) all_58_2 = e2
% 169.84/26.03 (4) all_58_6 = e1
% 169.84/26.03 (5) ~ (e3 = e1)
% 169.84/26.03 (6) ~ (e1 = e0)
% 169.84/26.03 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.84/26.03 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.84/26.03 (8) op(e2, e3) = all_52_1
% 169.84/26.03 (9) op(e2, e3) = e2
% 169.84/26.03 (10) ~ (e3 = e0)
% 169.84/26.03 (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.03 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.03 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.84/26.03 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.84/26.03 (13) all_58_4 = e3
% 169.84/26.03 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.03 (15) ~ (e2 = e0)
% 169.84/26.03 (16) all_58_12 = e3
% 169.84/26.03 (17) all_58_3 = e3
% 169.84/26.03 (18) all_58_9 = e3
% 169.84/26.03 (19) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.03 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.03 (20) ~ (e2 = e1)
% 169.84/26.03 (21) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 169.84/26.03 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.84/26.03 (22) ~ (e3 = e2)
% 169.84/26.03
% 169.84/26.03 Begin of proof
% 169.84/26.03 |
% 169.84/26.03 | BETA: splitting (2) gives:
% 169.84/26.03 |
% 169.84/26.03 | Case 1:
% 169.84/26.03 | |
% 169.84/26.03 | | (23) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.84/26.03 | | e0)
% 169.84/26.03 | |
% 169.84/26.03 | | BETA: splitting (23) gives:
% 169.84/26.03 | |
% 169.84/26.03 | | Case 1:
% 169.84/26.03 | | |
% 169.84/26.03 | | | (24) all_58_0 = e0 & op(e3, e3) = e0
% 169.84/26.03 | | |
% 169.84/26.03 | | | ALPHA: (24) implies:
% 169.84/26.03 | | | (25) all_58_0 = e0
% 169.84/26.03 | | |
% 169.84/26.03 | | | BETA: splitting (21) gives:
% 169.84/26.03 | | |
% 169.84/26.03 | | | Case 1:
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | (26) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2)
% 169.84/26.03 | | | | = e2)
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | BETA: splitting (26) gives:
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | Case 1:
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | (27) all_58_0 = e2 & op(e3, e3) = e2
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | REF_CLOSE: (15), (25), (27) are inconsistent by sub-proof #390.
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | Case 2:
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | (28) all_58_1 = e2 & op(e3, e2) = e2
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | ALPHA: (28) implies:
% 169.84/26.03 | | | | | (29) all_58_1 = e2
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | BETA: splitting (12) gives:
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | | Case 1:
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3,
% 169.84/26.03 | | | | | | e2) = e1)
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | BETA: splitting (30) gives:
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | Case 1:
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | (31) all_58_0 = e1 & op(e3, e3) = e1
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | ALPHA: (31) implies:
% 169.84/26.03 | | | | | | | (32) all_58_0 = e1
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (14),
% 169.84/26.03 | | | | | | | (15), (22), (32) are inconsistent by sub-proof #455.
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | Case 2:
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | (33) all_58_1 = e1 & op(e3, e2) = e1
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | REF_CLOSE: (20), (29), (33) are inconsistent by sub-proof #899.
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | End of split
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | Case 2:
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | (34) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3,
% 169.84/26.03 | | | | | | e0) = e1)
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | BETA: splitting (34) gives:
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | | Case 1:
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | (35) all_58_4 = e1 & op(e3, e1) = e1
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | REF_CLOSE: (5), (13), (35) are inconsistent by sub-proof #702.
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | Case 2:
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | (36) all_58_9 = e1 & op(e3, e0) = e1
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | | REF_CLOSE: (5), (18), (36) are inconsistent by sub-proof #836.
% 169.84/26.03 | | | | | | |
% 169.84/26.03 | | | | | | End of split
% 169.84/26.03 | | | | | |
% 169.84/26.03 | | | | | End of split
% 169.84/26.03 | | | | |
% 169.84/26.03 | | | | End of split
% 169.84/26.03 | | | |
% 169.84/26.03 | | | Case 2:
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | (37) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0)
% 169.84/26.03 | | | | = e2)
% 169.84/26.03 | | | |
% 169.84/26.03 | | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (13), (14), (15),
% 169.84/26.03 | | | | (17), (18), (19), (20), (22), (37) are inconsistent by
% 169.84/26.03 | | | | sub-proof #391.
% 169.84/26.03 | | | |
% 169.84/26.03 | | | End of split
% 169.84/26.03 | | |
% 169.84/26.03 | | Case 2:
% 169.84/26.03 | | |
% 169.84/26.03 | | | (38) all_58_2 = e0 & op(e2, e3) = e0
% 169.84/26.03 | | |
% 169.84/26.03 | | | REF_CLOSE: (8), (9), (14), (15), (38) are inconsistent by sub-proof #782.
% 169.84/26.03 | | |
% 169.84/26.03 | | End of split
% 169.84/26.03 | |
% 169.84/26.03 | Case 2:
% 169.84/26.03 | |
% 169.84/26.03 | | (39) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.84/26.03 | | e0)
% 169.84/26.03 | |
% 169.84/26.03 | | BETA: splitting (39) gives:
% 169.84/26.03 | |
% 169.84/26.03 | | Case 1:
% 169.84/26.03 | | |
% 169.84/26.03 | | | (40) all_58_6 = e0 & op(e1, e3) = e0
% 169.84/26.03 | | |
% 169.84/26.03 | | | REF_CLOSE: (4), (6), (40) are inconsistent by sub-proof #415.
% 169.84/26.03 | | |
% 169.84/26.03 | | Case 2:
% 169.84/26.03 | | |
% 169.84/26.03 | | | (41) all_58_12 = e0 & op(e0, e3) = e0
% 169.84/26.03 | | |
% 169.84/26.03 | | | REF_CLOSE: (10), (16), (41) are inconsistent by sub-proof #646.
% 169.84/26.03 | | |
% 169.84/26.03 | | End of split
% 169.84/26.03 | |
% 169.84/26.03 | End of split
% 169.84/26.03 |
% 169.84/26.03 End of proof
% 169.84/26.03
% 169.84/26.03 Sub-proof #390 shows that the following formulas are inconsistent:
% 169.84/26.03 ----------------------------------------------------------------
% 169.84/26.04 (1) all_58_0 = e2 & op(e3, e3) = e2
% 169.84/26.04 (2) all_58_0 = e0
% 169.84/26.04 (3) ~ (e2 = e0)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | ALPHA: (1) implies:
% 169.84/26.04 | (4) all_58_0 = e2
% 169.84/26.04 |
% 169.84/26.04 | COMBINE_EQS: (2), (4) imply:
% 169.84/26.04 | (5) e2 = e0
% 169.84/26.04 |
% 169.84/26.04 | SIMP: (5) implies:
% 169.84/26.04 | (6) e2 = e0
% 169.84/26.04 |
% 169.84/26.04 | REDUCE: (3), (6) imply:
% 169.84/26.04 | (7) $false
% 169.84/26.04 |
% 169.84/26.04 | CLOSE: (7) is inconsistent.
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #391 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.04 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.04 (2) all_58_2 = e2
% 169.84/26.04 (3) ~ (e3 = e1)
% 169.84/26.04 (4) ~ (e1 = e0)
% 169.84/26.04 (5) op(e2, e3) = all_52_1
% 169.84/26.04 (6) op(e2, e3) = e2
% 169.84/26.04 (7) ~ (e3 = e0)
% 169.84/26.04 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.04 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.04 (9) all_58_4 = e3
% 169.84/26.04 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.04 (11) ~ (e2 = e0)
% 169.84/26.04 (12) all_58_3 = e3
% 169.84/26.04 (13) all_58_9 = e3
% 169.84/26.04 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.04 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.04 (15) ~ (e2 = e1)
% 169.84/26.04 (16) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 169.84/26.04 (17) ~ (e3 = e2)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | BETA: splitting (16) gives:
% 169.84/26.04 |
% 169.84/26.04 | Case 1:
% 169.84/26.04 | |
% 169.84/26.04 | | (18) all_58_4 = e2 & op(e3, e1) = e2
% 169.84/26.04 | |
% 169.84/26.04 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 169.84/26.04 | | (14), (15), (17), (18) are inconsistent by sub-proof #409.
% 169.84/26.04 | |
% 169.84/26.04 | Case 2:
% 169.84/26.04 | |
% 169.84/26.04 | | (19) all_58_9 = e2 & op(e3, e0) = e2
% 169.84/26.04 | |
% 169.84/26.04 | | ALPHA: (19) implies:
% 169.84/26.04 | | (20) all_58_9 = e2
% 169.84/26.04 | |
% 169.84/26.04 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 169.84/26.04 | | (14), (15), (17), (20) are inconsistent by sub-proof #451.
% 169.84/26.04 | |
% 169.84/26.04 | End of split
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #392 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) all_58_1 = e2 & op(e3, e2) = e2
% 169.84/26.04 (2) all_58_1 = e0
% 169.84/26.04 (3) ~ (e2 = e0)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | ALPHA: (1) implies:
% 169.84/26.04 | (4) all_58_1 = e2
% 169.84/26.04 |
% 169.84/26.04 | COMBINE_EQS: (2), (4) imply:
% 169.84/26.04 | (5) e2 = e0
% 169.84/26.04 |
% 169.84/26.04 | SIMP: (5) implies:
% 169.84/26.04 | (6) e2 = e0
% 169.84/26.04 |
% 169.84/26.04 | REDUCE: (3), (6) imply:
% 169.84/26.04 | (7) $false
% 169.84/26.04 |
% 169.84/26.04 | CLOSE: (7) is inconsistent.
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #393 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) all_58_0 = e2 & op(e3, e3) = e2
% 169.84/26.04 (2) all_58_0 = e1
% 169.84/26.04 (3) ~ (e2 = e1)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | ALPHA: (1) implies:
% 169.84/26.04 | (4) all_58_0 = e2
% 169.84/26.04 |
% 169.84/26.04 | COMBINE_EQS: (2), (4) imply:
% 169.84/26.04 | (5) e2 = e1
% 169.84/26.04 |
% 169.84/26.04 | SIMP: (5) implies:
% 169.84/26.04 | (6) e2 = e1
% 169.84/26.04 |
% 169.84/26.04 | REDUCE: (3), (6) imply:
% 169.84/26.04 | (7) $false
% 169.84/26.04 |
% 169.84/26.04 | CLOSE: (7) is inconsistent.
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #394 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.84/26.04 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.84/26.04 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/26.04 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/26.04 (3) all_58_2 = e2
% 169.84/26.04 (4) all_58_0 = e1
% 169.84/26.04 (5) ~ (e3 = e1)
% 169.84/26.04 (6) all_58_8 = e2 & op(e1, e1) = e2
% 169.84/26.04 (7) ~ (e1 = e0)
% 169.84/26.04 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.84/26.04 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.84/26.04 (9) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.84/26.04 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.84/26.04 (10) ~ (e3 = e0)
% 169.84/26.04 (11) all_58_4 = e3
% 169.84/26.04 (12) ~ (e2 = e0)
% 169.84/26.04 (13) all_58_13 = e1
% 169.84/26.04 (14) ~ (e2 = e1)
% 169.84/26.04 (15) all_58_15 = e0
% 169.84/26.04 (16) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.84/26.04 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.84/26.04 (17) ~ (e3 = e2)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | ALPHA: (6) implies:
% 169.84/26.04 | (18) all_58_8 = e2
% 169.84/26.04 |
% 169.84/26.04 | BETA: splitting (1) gives:
% 169.84/26.04 |
% 169.84/26.04 | Case 1:
% 169.84/26.04 | |
% 169.84/26.04 | | (19) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 169.84/26.04 | | e2)
% 169.84/26.04 | |
% 169.84/26.04 | | BETA: splitting (19) gives:
% 169.84/26.04 | |
% 169.84/26.04 | | Case 1:
% 169.84/26.04 | | |
% 169.84/26.04 | | | (20) all_58_12 = e2 & op(e0, e3) = e2
% 169.84/26.04 | | |
% 169.84/26.04 | | | ALPHA: (20) implies:
% 169.84/26.04 | | | (21) all_58_12 = e2
% 169.84/26.04 | | |
% 169.84/26.04 | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (12), (17), (21) are
% 169.84/26.04 | | | inconsistent by sub-proof #435.
% 169.84/26.04 | | |
% 169.84/26.04 | | Case 2:
% 169.84/26.04 | | |
% 169.84/26.04 | | | (22) all_58_13 = e2 & op(e0, e2) = e2
% 169.84/26.04 | | |
% 169.84/26.04 | | | ALPHA: (22) implies:
% 169.84/26.04 | | | (23) all_58_13 = e2
% 169.84/26.04 | | |
% 169.84/26.04 | | | REF_CLOSE: (13), (14), (23) are inconsistent by sub-proof #458.
% 169.84/26.04 | | |
% 169.84/26.04 | | End of split
% 169.84/26.04 | |
% 169.84/26.04 | Case 2:
% 169.84/26.04 | |
% 169.84/26.04 | | (24) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 169.84/26.04 | | e2)
% 169.84/26.04 | |
% 169.84/26.04 | | BETA: splitting (24) gives:
% 169.84/26.04 | |
% 169.84/26.04 | | Case 1:
% 169.84/26.04 | | |
% 169.84/26.04 | | | (25) all_58_14 = e2 & op(e0, e1) = e2
% 169.84/26.04 | | |
% 169.84/26.04 | | | ALPHA: (25) implies:
% 169.84/26.04 | | | (26) all_58_14 = e2
% 169.84/26.04 | | |
% 169.84/26.04 | | | REF_CLOSE: (5), (7), (9), (10), (11), (12), (14), (16), (18), (26) are
% 169.84/26.04 | | | inconsistent by sub-proof #395.
% 169.84/26.04 | | |
% 169.84/26.04 | | Case 2:
% 169.84/26.04 | | |
% 169.84/26.04 | | | (27) all_58_15 = e2 & op(e0, e0) = e2
% 169.84/26.04 | | |
% 169.84/26.04 | | | ALPHA: (27) implies:
% 169.84/26.04 | | | (28) all_58_15 = e2
% 169.84/26.04 | | |
% 169.84/26.04 | | | REF_CLOSE: (12), (15), (28) are inconsistent by sub-proof #725.
% 169.84/26.04 | | |
% 169.84/26.04 | | End of split
% 169.84/26.04 | |
% 169.84/26.04 | End of split
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #395 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) all_58_14 = e2
% 169.84/26.04 (2) ~ (e3 = e1)
% 169.84/26.04 (3) ~ (e1 = e0)
% 169.84/26.04 (4) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.84/26.04 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.84/26.04 (5) ~ (e3 = e0)
% 169.84/26.04 (6) all_58_4 = e3
% 169.84/26.04 (7) all_58_8 = e2
% 169.84/26.04 (8) ~ (e2 = e0)
% 169.84/26.04 (9) ~ (e2 = e1)
% 169.84/26.04 (10) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.84/26.04 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | BETA: splitting (10) gives:
% 169.84/26.04 |
% 169.84/26.04 | Case 1:
% 169.84/26.04 | |
% 169.84/26.04 | | (11) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) =
% 169.84/26.04 | | e1)
% 169.84/26.04 | |
% 169.84/26.04 | | BETA: splitting (11) gives:
% 169.84/26.04 | |
% 169.84/26.04 | | Case 1:
% 169.84/26.04 | | |
% 169.84/26.04 | | | (12) all_58_4 = e1 & op(e3, e1) = e1
% 169.84/26.04 | | |
% 169.84/26.04 | | | REF_CLOSE: (2), (6), (12) are inconsistent by sub-proof #702.
% 169.84/26.04 | | |
% 169.84/26.04 | | Case 2:
% 169.84/26.04 | | |
% 169.84/26.04 | | | (13) all_58_5 = e1 & op(e2, e1) = e1
% 169.84/26.04 | | |
% 169.84/26.04 | | | ALPHA: (13) implies:
% 169.84/26.04 | | | (14) all_58_5 = e1
% 169.84/26.04 | | |
% 169.84/26.04 | | | BETA: splitting (4) gives:
% 169.84/26.04 | | |
% 169.84/26.04 | | | Case 1:
% 169.84/26.04 | | | |
% 169.84/26.04 | | | | (15) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1)
% 169.84/26.04 | | | | = e0)
% 169.84/26.04 | | | |
% 169.84/26.04 | | | | BETA: splitting (15) gives:
% 169.84/26.04 | | | |
% 169.84/26.04 | | | | Case 1:
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | | (16) all_58_4 = e0 & op(e3, e1) = e0
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | | REF_CLOSE: (5), (6), (16) are inconsistent by sub-proof #704.
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | Case 2:
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | | (17) all_58_5 = e0 & op(e2, e1) = e0
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | | REF_CLOSE: (3), (14), (17) are inconsistent by sub-proof #781.
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | End of split
% 169.84/26.04 | | | |
% 169.84/26.04 | | | Case 2:
% 169.84/26.04 | | | |
% 169.84/26.04 | | | | (18) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1)
% 169.84/26.04 | | | | = e0)
% 169.84/26.04 | | | |
% 169.84/26.04 | | | | BETA: splitting (18) gives:
% 169.84/26.04 | | | |
% 169.84/26.04 | | | | Case 1:
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | | (19) all_58_8 = e0 & op(e1, e1) = e0
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | | REF_CLOSE: (7), (8), (19) are inconsistent by sub-proof #398.
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | Case 2:
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | | (20) all_58_14 = e0 & op(e0, e1) = e0
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | | ALPHA: (20) implies:
% 169.84/26.04 | | | | | (21) all_58_14 = e0
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | | REF_CLOSE: (1), (8), (21) are inconsistent by sub-proof #806.
% 169.84/26.04 | | | | |
% 169.84/26.04 | | | | End of split
% 169.84/26.04 | | | |
% 169.84/26.04 | | | End of split
% 169.84/26.04 | | |
% 169.84/26.04 | | End of split
% 169.84/26.04 | |
% 169.84/26.04 | Case 2:
% 169.84/26.04 | |
% 169.84/26.04 | | (22) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) =
% 169.84/26.04 | | e1)
% 169.84/26.04 | |
% 169.84/26.04 | | BETA: splitting (22) gives:
% 169.84/26.04 | |
% 169.84/26.04 | | Case 1:
% 169.84/26.04 | | |
% 169.84/26.04 | | | (23) all_58_8 = e1 & op(e1, e1) = e1
% 169.84/26.04 | | |
% 169.84/26.04 | | | REF_CLOSE: (7), (9), (23) are inconsistent by sub-proof #397.
% 169.84/26.04 | | |
% 169.84/26.04 | | Case 2:
% 169.84/26.04 | | |
% 169.84/26.04 | | | (24) all_58_14 = e1 & op(e0, e1) = e1
% 169.84/26.04 | | |
% 169.84/26.04 | | | REF_CLOSE: (1), (9), (24) are inconsistent by sub-proof #396.
% 169.84/26.04 | | |
% 169.84/26.04 | | End of split
% 169.84/26.04 | |
% 169.84/26.04 | End of split
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #396 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) all_58_14 = e1 & op(e0, e1) = e1
% 169.84/26.04 (2) all_58_14 = e2
% 169.84/26.04 (3) ~ (e2 = e1)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | ALPHA: (1) implies:
% 169.84/26.04 | (4) all_58_14 = e1
% 169.84/26.04 |
% 169.84/26.04 | COMBINE_EQS: (2), (4) imply:
% 169.84/26.04 | (5) e2 = e1
% 169.84/26.04 |
% 169.84/26.04 | REDUCE: (3), (5) imply:
% 169.84/26.04 | (6) $false
% 169.84/26.04 |
% 169.84/26.04 | CLOSE: (6) is inconsistent.
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #397 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) all_58_8 = e1 & op(e1, e1) = e1
% 169.84/26.04 (2) all_58_8 = e2
% 169.84/26.04 (3) ~ (e2 = e1)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | ALPHA: (1) implies:
% 169.84/26.04 | (4) all_58_8 = e1
% 169.84/26.04 |
% 169.84/26.04 | COMBINE_EQS: (2), (4) imply:
% 169.84/26.04 | (5) e2 = e1
% 169.84/26.04 |
% 169.84/26.04 | REDUCE: (3), (5) imply:
% 169.84/26.04 | (6) $false
% 169.84/26.04 |
% 169.84/26.04 | CLOSE: (6) is inconsistent.
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #398 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) all_58_8 = e0 & op(e1, e1) = e0
% 169.84/26.04 (2) all_58_8 = e2
% 169.84/26.04 (3) ~ (e2 = e0)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | ALPHA: (1) implies:
% 169.84/26.04 | (4) all_58_8 = e0
% 169.84/26.04 |
% 169.84/26.04 | COMBINE_EQS: (2), (4) imply:
% 169.84/26.04 | (5) e2 = e0
% 169.84/26.04 |
% 169.84/26.04 | REDUCE: (3), (5) imply:
% 169.84/26.04 | (6) $false
% 169.84/26.04 |
% 169.84/26.04 | CLOSE: (6) is inconsistent.
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #399 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.04 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.04 (2) all_58_7 = e2
% 169.84/26.04 (3) all_58_2 = e2
% 169.84/26.04 (4) ~ (e3 = e1)
% 169.84/26.04 (5) ~ (e1 = e0)
% 169.84/26.04 (6) op(e2, e3) = all_52_1
% 169.84/26.04 (7) op(e2, e3) = e2
% 169.84/26.04 (8) ~ (e3 = e0)
% 169.84/26.04 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.04 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.04 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.04 (11) ~ (e2 = e0)
% 169.84/26.04 (12) all_58_3 = e3
% 169.84/26.04 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.04 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.04 (14) ~ (e2 = e1)
% 169.84/26.04 (15) all_58_7 = e3
% 169.84/26.04 (16) ~ (e3 = e2)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | COMBINE_EQS: (2), (15) imply:
% 169.84/26.04 | (17) e3 = e2
% 169.84/26.04 |
% 169.84/26.04 | SIMP: (17) implies:
% 169.84/26.04 | (18) e3 = e2
% 169.84/26.04 |
% 169.84/26.04 | COMBINE_EQS: (12), (18) imply:
% 169.84/26.04 | (19) all_58_3 = e2
% 169.84/26.04 |
% 169.84/26.04 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 169.84/26.04 | (16), (19) are inconsistent by sub-proof #779.
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #400 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.04 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.04 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/26.04 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/26.04 (3) all_58_2 = e2
% 169.84/26.04 (4) all_58_0 = e1
% 169.84/26.04 (5) ~ (e3 = e1)
% 169.84/26.04 (6) ~ (e1 = e0)
% 169.84/26.04 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.84/26.04 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.84/26.04 (8) op(e2, e3) = all_52_1
% 169.84/26.04 (9) all_58_6 = e2
% 169.84/26.04 (10) op(e2, e3) = e2
% 169.84/26.04 (11) ~ (e3 = e0)
% 169.84/26.04 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.04 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.04 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.04 (14) ~ (e2 = e0)
% 169.84/26.04 (15) all_58_3 = e3
% 169.84/26.04 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.04 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.04 (17) ~ (e2 = e1)
% 169.84/26.04 (18) ~ (e3 = e2)
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | BETA: splitting (7) gives:
% 169.84/26.04 |
% 169.84/26.04 | Case 1:
% 169.84/26.04 | |
% 169.84/26.04 | | (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 169.84/26.04 | | e3)
% 169.84/26.04 | |
% 169.84/26.04 | | REF_CLOSE: (4), (5), (8), (10), (13), (18), (19) are inconsistent by
% 169.84/26.04 | | sub-proof #402.
% 169.84/26.04 | |
% 169.84/26.04 | Case 2:
% 169.84/26.04 | |
% 169.84/26.04 | | (20) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 169.84/26.04 | | e3)
% 169.84/26.04 | |
% 169.84/26.04 | | BETA: splitting (20) gives:
% 169.84/26.04 | |
% 169.84/26.04 | | Case 1:
% 169.84/26.04 | | |
% 169.84/26.04 | | | (21) all_58_6 = e3 & op(e1, e3) = e3
% 169.84/26.04 | | |
% 169.84/26.04 | | | ALPHA: (21) implies:
% 169.84/26.04 | | | (22) all_58_6 = e3
% 169.84/26.04 | | |
% 169.84/26.04 | | | COMBINE_EQS: (9), (22) imply:
% 169.84/26.04 | | | (23) e3 = e2
% 169.84/26.04 | | |
% 169.84/26.04 | | | COMBINE_EQS: (15), (23) imply:
% 169.84/26.04 | | | (24) all_58_3 = e2
% 169.84/26.04 | | |
% 169.84/26.04 | | | REF_CLOSE: (1), (3), (5), (6), (8), (10), (11), (12), (13), (14), (16),
% 169.84/26.04 | | | (17), (18), (24) are inconsistent by sub-proof #779.
% 169.84/26.04 | | |
% 169.84/26.04 | | Case 2:
% 169.84/26.04 | | |
% 169.84/26.04 | | | (25) all_58_12 = e3 & op(e0, e3) = e3
% 169.84/26.04 | | |
% 169.84/26.04 | | | ALPHA: (25) implies:
% 169.84/26.04 | | | (26) all_58_12 = e3
% 169.84/26.04 | | |
% 169.84/26.04 | | | REF_CLOSE: (2), (4), (6), (8), (9), (10), (11), (13), (14), (26) are
% 169.84/26.04 | | | inconsistent by sub-proof #401.
% 169.84/26.04 | | |
% 169.84/26.04 | | End of split
% 169.84/26.04 | |
% 169.84/26.04 | End of split
% 169.84/26.04 |
% 169.84/26.04 End of proof
% 169.84/26.04
% 169.84/26.04 Sub-proof #401 shows that the following formulas are inconsistent:
% 169.84/26.04 ----------------------------------------------------------------
% 169.84/26.04 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/26.04 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/26.04 (2) all_58_0 = e1
% 169.84/26.04 (3) ~ (e1 = e0)
% 169.84/26.04 (4) op(e2, e3) = all_52_1
% 169.84/26.04 (5) all_58_6 = e2
% 169.84/26.04 (6) op(e2, e3) = e2
% 169.84/26.04 (7) ~ (e3 = e0)
% 169.84/26.04 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.04 (9) ~ (e2 = e0)
% 169.84/26.04 (10) all_58_12 = e3
% 169.84/26.04
% 169.84/26.04 Begin of proof
% 169.84/26.04 |
% 169.84/26.04 | BETA: splitting (1) gives:
% 169.84/26.04 |
% 169.84/26.04 | Case 1:
% 169.84/26.04 | |
% 169.84/26.05 | | (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.84/26.05 | | e0)
% 169.84/26.05 | |
% 169.84/26.05 | | BETA: splitting (11) gives:
% 169.84/26.05 | |
% 169.84/26.05 | | Case 1:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (12) all_58_0 = e0 & op(e3, e3) = e0
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #903.
% 169.84/26.05 | | |
% 169.84/26.05 | | Case 2:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (13) all_58_2 = e0 & op(e2, e3) = e0
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (4), (6), (8), (9), (13) are inconsistent by sub-proof #782.
% 169.84/26.05 | | |
% 169.84/26.05 | | End of split
% 169.84/26.05 | |
% 169.84/26.05 | Case 2:
% 169.84/26.05 | |
% 169.84/26.05 | | (14) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.84/26.05 | | e0)
% 169.84/26.05 | |
% 169.84/26.05 | | BETA: splitting (14) gives:
% 169.84/26.05 | |
% 169.84/26.05 | | Case 1:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (15) all_58_6 = e0 & op(e1, e3) = e0
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (5), (9), (15) are inconsistent by sub-proof #769.
% 169.84/26.05 | | |
% 169.84/26.05 | | Case 2:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (16) all_58_12 = e0 & op(e0, e3) = e0
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (7), (10), (16) are inconsistent by sub-proof #646.
% 169.84/26.05 | | |
% 169.84/26.05 | | End of split
% 169.84/26.05 | |
% 169.84/26.05 | End of split
% 169.84/26.05 |
% 169.84/26.05 End of proof
% 169.84/26.05
% 169.84/26.05 Sub-proof #402 shows that the following formulas are inconsistent:
% 169.84/26.05 ----------------------------------------------------------------
% 169.84/26.05 (1) all_58_0 = e1
% 169.84/26.05 (2) ~ (e3 = e1)
% 169.84/26.05 (3) op(e2, e3) = all_52_1
% 169.84/26.05 (4) op(e2, e3) = e2
% 169.84/26.05 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.05 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 169.84/26.05 (7) ~ (e3 = e2)
% 169.84/26.05
% 169.84/26.05 Begin of proof
% 169.84/26.05 |
% 169.84/26.05 | BETA: splitting (6) gives:
% 169.84/26.05 |
% 169.84/26.05 | Case 1:
% 169.84/26.05 | |
% 169.84/26.05 | | (8) all_58_0 = e3 & op(e3, e3) = e3
% 169.84/26.05 | |
% 169.84/26.05 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #905.
% 169.84/26.05 | |
% 169.84/26.05 | Case 2:
% 169.84/26.05 | |
% 169.84/26.05 | | (9) all_58_2 = e3 & op(e2, e3) = e3
% 169.84/26.05 | |
% 169.84/26.05 | | ALPHA: (9) implies:
% 169.84/26.05 | | (10) op(e2, e3) = e3
% 169.84/26.05 | |
% 169.84/26.05 | | REF_CLOSE: (3), (4), (5), (7), (10) are inconsistent by sub-proof #462.
% 169.84/26.05 | |
% 169.84/26.05 | End of split
% 169.84/26.05 |
% 169.84/26.05 End of proof
% 169.84/26.05
% 169.84/26.05 Sub-proof #403 shows that the following formulas are inconsistent:
% 169.84/26.05 ----------------------------------------------------------------
% 169.84/26.05 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.05 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.05 (2) all_58_14 = e2
% 169.84/26.05 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/26.05 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/26.05 (4) all_58_2 = e2
% 169.84/26.05 (5) all_58_0 = e1
% 169.84/26.05 (6) ~ (e3 = e1)
% 169.84/26.05 (7) all_58_6 = e3
% 169.84/26.05 (8) ~ (e1 = e0)
% 169.84/26.05 (9) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.84/26.05 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/26.05 (10) op(e2, e3) = all_52_1
% 169.84/26.05 (11) ~ (all_52_7 = e3)
% 169.84/26.05 (12) op(e2, e3) = e2
% 169.84/26.05 (13) ~ (e3 = e0)
% 169.84/26.05 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.05 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.05 (16) ~ (e2 = e0)
% 169.84/26.05 (17) all_58_3 = e3
% 169.84/26.05 (18) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.05 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.05 (19) ~ (e2 = e1)
% 169.84/26.05 (20) all_58_15 = e0
% 169.84/26.05 (21) op(e0, e2) = all_52_7
% 169.84/26.05 (22) ~ (e3 = e2)
% 169.84/26.05
% 169.84/26.05 Begin of proof
% 169.84/26.05 |
% 169.84/26.05 | BETA: splitting (3) gives:
% 169.84/26.05 |
% 169.84/26.05 | Case 1:
% 169.84/26.05 | |
% 169.84/26.05 | | (23) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 169.84/26.05 | | e0)
% 169.84/26.05 | |
% 169.84/26.05 | | BETA: splitting (23) gives:
% 169.84/26.05 | |
% 169.84/26.05 | | Case 1:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (24) all_58_0 = e0 & op(e3, e3) = e0
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (5), (8), (24) are inconsistent by sub-proof #903.
% 169.84/26.05 | | |
% 169.84/26.05 | | Case 2:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (25) all_58_2 = e0 & op(e2, e3) = e0
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (10), (12), (15), (16), (25) are inconsistent by sub-proof
% 169.84/26.05 | | | #782.
% 169.84/26.05 | | |
% 169.84/26.05 | | End of split
% 169.84/26.05 | |
% 169.84/26.05 | Case 2:
% 169.84/26.05 | |
% 169.84/26.05 | | (26) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 169.84/26.05 | | e0)
% 169.84/26.05 | |
% 169.84/26.05 | | BETA: splitting (26) gives:
% 169.84/26.05 | |
% 169.84/26.05 | | Case 1:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (27) all_58_6 = e0 & op(e1, e3) = e0
% 169.84/26.05 | | |
% 169.84/26.05 | | | ALPHA: (27) implies:
% 169.84/26.05 | | | (28) all_58_6 = e0
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (7), (13), (28) are inconsistent by sub-proof #537.
% 169.84/26.05 | | |
% 169.84/26.05 | | Case 2:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (29) all_58_12 = e0 & op(e0, e3) = e0
% 169.84/26.05 | | |
% 169.84/26.05 | | | ALPHA: (29) implies:
% 169.84/26.05 | | | (30) all_58_12 = e0
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (11), (12), (13), (14),
% 169.84/26.05 | | | (15), (16), (17), (18), (19), (20), (21), (22), (30) are
% 169.84/26.05 | | | inconsistent by sub-proof #404.
% 169.84/26.05 | | |
% 169.84/26.05 | | End of split
% 169.84/26.05 | |
% 169.84/26.05 | End of split
% 169.84/26.05 |
% 169.84/26.05 End of proof
% 169.84/26.05
% 169.84/26.05 Sub-proof #404 shows that the following formulas are inconsistent:
% 169.84/26.05 ----------------------------------------------------------------
% 169.84/26.05 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.05 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.05 (2) all_58_14 = e2
% 169.84/26.05 (3) all_58_2 = e2
% 169.84/26.05 (4) ~ (e3 = e1)
% 169.84/26.05 (5) ~ (e1 = e0)
% 169.84/26.05 (6) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 169.84/26.05 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 169.84/26.05 (7) op(e2, e3) = all_52_1
% 169.84/26.05 (8) ~ (all_52_7 = e3)
% 169.84/26.05 (9) op(e2, e3) = e2
% 169.84/26.05 (10) ~ (e3 = e0)
% 169.84/26.05 (11) all_58_12 = e0
% 169.84/26.05 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.05 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.05 (14) ~ (e2 = e0)
% 169.84/26.05 (15) all_58_3 = e3
% 169.84/26.05 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.05 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.05 (17) ~ (e2 = e1)
% 169.84/26.05 (18) all_58_15 = e0
% 169.84/26.05 (19) op(e0, e2) = all_52_7
% 169.84/26.05 (20) ~ (e3 = e2)
% 169.84/26.05
% 169.84/26.05 Begin of proof
% 169.84/26.05 |
% 169.84/26.05 | BETA: splitting (6) gives:
% 169.84/26.05 |
% 169.84/26.05 | Case 1:
% 169.84/26.05 | |
% 169.84/26.05 | | (21) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 169.84/26.05 | | e3)
% 169.84/26.05 | |
% 169.84/26.05 | | REF_CLOSE: (8), (10), (11), (13), (19), (21) are inconsistent by sub-proof
% 169.84/26.05 | | #557.
% 169.84/26.05 | |
% 169.84/26.05 | Case 2:
% 169.84/26.05 | |
% 169.84/26.05 | | (22) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 169.84/26.05 | | e3)
% 169.84/26.05 | |
% 169.84/26.05 | | BETA: splitting (22) gives:
% 169.84/26.05 | |
% 169.84/26.05 | | Case 1:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (23) all_58_14 = e3 & op(e0, e1) = e3
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (12), (13), (14),
% 169.84/26.05 | | | (15), (16), (17), (20), (23) are inconsistent by sub-proof
% 169.84/26.05 | | | #405.
% 169.84/26.05 | | |
% 169.84/26.05 | | Case 2:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (24) all_58_15 = e3 & op(e0, e0) = e3
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (10), (18), (24) are inconsistent by sub-proof #812.
% 169.84/26.05 | | |
% 169.84/26.05 | | End of split
% 169.84/26.05 | |
% 169.84/26.05 | End of split
% 169.84/26.05 |
% 169.84/26.05 End of proof
% 169.84/26.05
% 169.84/26.05 Sub-proof #405 shows that the following formulas are inconsistent:
% 169.84/26.05 ----------------------------------------------------------------
% 169.84/26.05 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.05 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.05 (2) all_58_14 = e2
% 169.84/26.05 (3) all_58_2 = e2
% 169.84/26.05 (4) all_58_14 = e3 & op(e0, e1) = e3
% 169.84/26.05 (5) ~ (e3 = e1)
% 169.84/26.05 (6) ~ (e1 = e0)
% 169.84/26.05 (7) op(e2, e3) = all_52_1
% 169.84/26.05 (8) op(e2, e3) = e2
% 169.84/26.05 (9) ~ (e3 = e0)
% 169.84/26.05 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.05 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.05 (12) ~ (e2 = e0)
% 169.84/26.05 (13) all_58_3 = e3
% 169.84/26.05 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.05 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.05 (15) ~ (e2 = e1)
% 169.84/26.05 (16) ~ (e3 = e2)
% 169.84/26.05
% 169.84/26.05 Begin of proof
% 169.84/26.05 |
% 169.84/26.05 | ALPHA: (4) implies:
% 169.84/26.05 | (17) all_58_14 = e3
% 169.84/26.05 |
% 169.84/26.05 | COMBINE_EQS: (2), (17) imply:
% 169.84/26.05 | (18) e3 = e2
% 169.84/26.05 |
% 169.84/26.05 | COMBINE_EQS: (13), (18) imply:
% 169.84/26.05 | (19) all_58_3 = e2
% 169.84/26.05 |
% 169.84/26.05 | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (14), (15),
% 169.84/26.05 | (16), (19) are inconsistent by sub-proof #779.
% 169.84/26.05 |
% 169.84/26.05 End of proof
% 169.84/26.05
% 169.84/26.05 Sub-proof #406 shows that the following formulas are inconsistent:
% 169.84/26.05 ----------------------------------------------------------------
% 169.84/26.05 (1) op(e2, e1) = all_52_9
% 169.84/26.05 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.05 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.05 (3) ~ (all_52_9 = e3)
% 169.84/26.05 (4) all_58_2 = e2
% 169.84/26.05 (5) all_58_0 = e1
% 169.84/26.05 (6) ~ (all_6_2 = e3)
% 169.84/26.05 (7) ~ (e3 = e1)
% 169.84/26.05 (8) ~ (e1 = e0)
% 169.84/26.05 (9) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.84/26.05 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.84/26.05 (10) op(e2, e3) = all_52_1
% 169.84/26.05 (11) ~ (all_6_2 = e2)
% 169.84/26.05 (12) op(e1, e1) = all_6_2
% 169.84/26.05 (13) op(e2, e3) = e2
% 169.84/26.05 (14) ~ (e3 = e0)
% 169.84/26.05 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.05 (16) all_58_4 = e3
% 169.84/26.05 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.05 (18) ~ (e2 = e0)
% 169.84/26.05 (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 169.84/26.05 (20) all_58_3 = e3
% 169.84/26.05 (21) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.05 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.05 (22) ~ (e2 = e1)
% 169.84/26.05 (23) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.84/26.05 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.84/26.05 (24) ~ (e3 = e2)
% 169.84/26.05
% 169.84/26.05 Begin of proof
% 169.84/26.05 |
% 169.84/26.05 | BETA: splitting (19) gives:
% 169.84/26.05 |
% 169.84/26.05 | Case 1:
% 169.84/26.05 | |
% 169.84/26.05 | | (25) all_58_0 = e3 & op(e3, e3) = e3
% 169.84/26.05 | |
% 169.84/26.05 | | ALPHA: (25) implies:
% 169.84/26.05 | | (26) all_58_0 = e3
% 169.84/26.05 | |
% 169.84/26.05 | | COMBINE_EQS: (5), (26) imply:
% 169.84/26.05 | | (27) e3 = e1
% 169.84/26.05 | |
% 169.84/26.05 | | SIMP: (27) implies:
% 169.84/26.05 | | (28) e3 = e1
% 169.84/26.05 | |
% 169.84/26.05 | | COMBINE_EQS: (16), (28) imply:
% 169.84/26.05 | | (29) all_58_4 = e1
% 169.84/26.05 | |
% 169.84/26.05 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 169.84/26.05 | | (14), (15), (17), (18), (20), (21), (22), (23), (24), (29) are
% 169.84/26.05 | | inconsistent by sub-proof #407.
% 169.84/26.05 | |
% 169.84/26.05 | Case 2:
% 169.84/26.05 | |
% 169.84/26.05 | | (30) all_58_2 = e3 & op(e2, e3) = e3
% 169.84/26.05 | |
% 169.84/26.05 | | ALPHA: (30) implies:
% 169.84/26.05 | | (31) op(e2, e3) = e3
% 169.84/26.05 | |
% 169.84/26.05 | | REF_CLOSE: (10), (13), (17), (24), (31) are inconsistent by sub-proof #462.
% 169.84/26.05 | |
% 169.84/26.05 | End of split
% 169.84/26.05 |
% 169.84/26.05 End of proof
% 169.84/26.05
% 169.84/26.05 Sub-proof #407 shows that the following formulas are inconsistent:
% 169.84/26.05 ----------------------------------------------------------------
% 169.84/26.05 (1) op(e2, e1) = all_52_9
% 169.84/26.05 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.05 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.05 (3) ~ (all_52_9 = e3)
% 169.84/26.05 (4) all_58_2 = e2
% 169.84/26.05 (5) ~ (all_6_2 = e3)
% 169.84/26.05 (6) ~ (e3 = e1)
% 169.84/26.05 (7) ~ (e1 = e0)
% 169.84/26.05 (8) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 169.84/26.05 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 169.84/26.05 (9) op(e2, e3) = all_52_1
% 169.84/26.05 (10) ~ (all_6_2 = e2)
% 169.84/26.05 (11) op(e1, e1) = all_6_2
% 169.84/26.05 (12) op(e2, e3) = e2
% 169.84/26.05 (13) ~ (e3 = e0)
% 169.84/26.05 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.05 (15) all_58_4 = e1
% 169.84/26.05 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.05 (17) ~ (e2 = e0)
% 169.84/26.05 (18) all_58_3 = e3
% 169.84/26.05 (19) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.05 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.05 (20) ~ (e2 = e1)
% 169.84/26.05 (21) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.84/26.05 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.84/26.05 (22) ~ (e3 = e2)
% 169.84/26.05
% 169.84/26.05 Begin of proof
% 169.84/26.05 |
% 169.84/26.05 | BETA: splitting (8) gives:
% 169.84/26.05 |
% 169.84/26.05 | Case 1:
% 169.84/26.05 | |
% 169.84/26.05 | | (23) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 169.84/26.05 | | e3)
% 169.84/26.05 | |
% 169.84/26.05 | | BETA: splitting (23) gives:
% 169.84/26.05 | |
% 169.84/26.05 | | Case 1:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (24) all_58_4 = e3 & op(e3, e1) = e3
% 169.84/26.05 | | |
% 169.84/26.05 | | | ALPHA: (24) implies:
% 169.84/26.05 | | | (25) all_58_4 = e3
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (6), (15), (25) are inconsistent by sub-proof #767.
% 169.84/26.05 | | |
% 169.84/26.05 | | Case 2:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (26) all_58_5 = e3 & op(e2, e1) = e3
% 169.84/26.05 | | |
% 169.84/26.05 | | | ALPHA: (26) implies:
% 169.84/26.05 | | | (27) op(e2, e1) = e3
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (1), (3), (16), (27) are inconsistent by sub-proof #951.
% 169.84/26.05 | | |
% 169.84/26.05 | | End of split
% 169.84/26.05 | |
% 169.84/26.05 | Case 2:
% 169.84/26.05 | |
% 169.84/26.05 | | (28) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 169.84/26.05 | | e3)
% 169.84/26.05 | |
% 169.84/26.05 | | BETA: splitting (28) gives:
% 169.84/26.05 | |
% 169.84/26.05 | | Case 1:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (29) all_58_8 = e3 & op(e1, e1) = e3
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (5), (11), (16), (29) are inconsistent by sub-proof #961.
% 169.84/26.05 | | |
% 169.84/26.05 | | Case 2:
% 169.84/26.05 | | |
% 169.84/26.05 | | | (30) all_58_14 = e3 & op(e0, e1) = e3
% 169.84/26.05 | | |
% 169.84/26.05 | | | ALPHA: (30) implies:
% 169.84/26.05 | | | (31) all_58_14 = e3
% 169.84/26.05 | | |
% 169.84/26.05 | | | REF_CLOSE: (2), (4), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 169.84/26.05 | | | (16), (17), (18), (19), (20), (21), (22), (31) are inconsistent
% 169.84/26.05 | | | by sub-proof #408.
% 169.84/26.05 | | |
% 169.84/26.05 | | End of split
% 169.84/26.05 | |
% 169.84/26.05 | End of split
% 169.84/26.05 |
% 169.84/26.05 End of proof
% 169.84/26.05
% 169.84/26.05 Sub-proof #408 shows that the following formulas are inconsistent:
% 169.84/26.05 ----------------------------------------------------------------
% 169.84/26.05 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.05 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.05 (2) all_58_2 = e2
% 169.84/26.05 (3) ~ (e3 = e1)
% 169.84/26.05 (4) ~ (e1 = e0)
% 169.84/26.05 (5) op(e2, e3) = all_52_1
% 169.84/26.05 (6) ~ (all_6_2 = e2)
% 169.84/26.05 (7) op(e1, e1) = all_6_2
% 169.84/26.05 (8) op(e2, e3) = e2
% 169.84/26.05 (9) ~ (e3 = e0)
% 169.84/26.05 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.05 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.05 (11) all_58_4 = e1
% 169.84/26.05 (12) all_58_14 = e3
% 169.84/26.05 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.05 (14) ~ (e2 = e0)
% 169.84/26.05 (15) all_58_3 = e3
% 169.84/26.05 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.05 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.06 (17) ~ (e2 = e1)
% 169.84/26.06 (18) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.84/26.06 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.84/26.06 (19) ~ (e3 = e2)
% 169.84/26.06
% 169.84/26.06 Begin of proof
% 169.84/26.06 |
% 169.84/26.06 | BETA: splitting (18) gives:
% 169.84/26.06 |
% 169.84/26.06 | Case 1:
% 169.84/26.06 | |
% 169.84/26.06 | | (20) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 169.84/26.06 | | e2)
% 169.84/26.06 | |
% 169.84/26.06 | | BETA: splitting (20) gives:
% 169.84/26.06 | |
% 169.84/26.06 | | Case 1:
% 169.84/26.06 | | |
% 169.84/26.06 | | | (21) all_58_4 = e2 & op(e3, e1) = e2
% 169.84/26.06 | | |
% 169.84/26.06 | | | ALPHA: (21) implies:
% 169.84/26.06 | | | (22) all_58_4 = e2
% 169.84/26.06 | | |
% 169.84/26.06 | | | COMBINE_EQS: (11), (22) imply:
% 169.84/26.06 | | | (23) e2 = e1
% 169.84/26.06 | | |
% 169.84/26.06 | | | REDUCE: (17), (23) imply:
% 169.84/26.06 | | | (24) $false
% 169.84/26.06 | | |
% 169.84/26.06 | | | CLOSE: (24) is inconsistent.
% 169.84/26.06 | | |
% 169.84/26.06 | | Case 2:
% 169.84/26.06 | | |
% 169.84/26.06 | | | (25) all_58_5 = e2 & op(e2, e1) = e2
% 169.84/26.06 | | |
% 169.84/26.06 | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (13), (14), (15), (17),
% 169.84/26.06 | | | (25) are inconsistent by sub-proof #412.
% 169.84/26.06 | | |
% 169.84/26.06 | | End of split
% 169.84/26.06 | |
% 169.84/26.06 | Case 2:
% 169.84/26.06 | |
% 169.84/26.06 | | (26) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 169.84/26.06 | | e2)
% 169.84/26.06 | |
% 169.84/26.06 | | BETA: splitting (26) gives:
% 169.84/26.06 | |
% 169.84/26.06 | | Case 1:
% 169.84/26.06 | | |
% 169.84/26.06 | | | (27) all_58_8 = e2 & op(e1, e1) = e2
% 169.84/26.06 | | |
% 169.84/26.06 | | | REF_CLOSE: (6), (7), (13), (27) are inconsistent by sub-proof #845.
% 169.84/26.06 | | |
% 169.84/26.06 | | Case 2:
% 169.84/26.06 | | |
% 169.84/26.06 | | | (28) all_58_14 = e2 & op(e0, e1) = e2
% 169.84/26.06 | | |
% 169.84/26.06 | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (12), (13), (14),
% 169.84/26.06 | | | (15), (16), (17), (19), (28) are inconsistent by sub-proof
% 169.84/26.06 | | | #411.
% 169.84/26.06 | | |
% 169.84/26.06 | | End of split
% 169.84/26.06 | |
% 169.84/26.06 | End of split
% 169.84/26.06 |
% 169.84/26.06 End of proof
% 169.84/26.06
% 169.84/26.06 Sub-proof #409 shows that the following formulas are inconsistent:
% 169.84/26.06 ----------------------------------------------------------------
% 169.84/26.06 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.06 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.06 (2) all_58_2 = e2
% 169.84/26.06 (3) ~ (e3 = e1)
% 169.84/26.06 (4) ~ (e1 = e0)
% 169.84/26.06 (5) op(e2, e3) = all_52_1
% 169.84/26.06 (6) op(e2, e3) = e2
% 169.84/26.06 (7) ~ (e3 = e0)
% 169.84/26.06 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.06 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.06 (9) all_58_4 = e2 & op(e3, e1) = e2
% 169.84/26.06 (10) all_58_4 = e3
% 169.84/26.06 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.06 (12) ~ (e2 = e0)
% 169.84/26.06 (13) all_58_3 = e3
% 169.84/26.06 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.06 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.06 (15) ~ (e2 = e1)
% 169.84/26.06 (16) ~ (e3 = e2)
% 169.84/26.06
% 169.84/26.06 Begin of proof
% 169.84/26.06 |
% 169.84/26.06 | ALPHA: (9) implies:
% 169.84/26.06 | (17) all_58_4 = e2
% 169.84/26.06 |
% 169.84/26.06 | COMBINE_EQS: (10), (17) imply:
% 169.84/26.06 | (18) e3 = e2
% 169.84/26.06 |
% 169.84/26.06 | COMBINE_EQS: (13), (18) imply:
% 169.84/26.06 | (19) all_58_3 = e2
% 169.84/26.06 |
% 169.84/26.06 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (14), (15),
% 169.84/26.06 | (16), (19) are inconsistent by sub-proof #779.
% 169.84/26.06 |
% 169.84/26.06 End of proof
% 169.84/26.06
% 169.84/26.06 Sub-proof #410 shows that the following formulas are inconsistent:
% 169.84/26.06 ----------------------------------------------------------------
% 169.84/26.06 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 169.84/26.06 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.84/26.06 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.06 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 169.84/26.06 (3) ~ (all_4_2 = e2)
% 169.84/26.06 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 169.84/26.06 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 169.84/26.06 (5) all_58_2 = e2
% 169.84/26.06 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 169.84/26.06 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 169.84/26.06 (7) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 169.84/26.06 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/26.06 (8) ~ (e3 = e1)
% 169.84/26.06 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 169.84/26.06 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 169.84/26.06 (10) ~ (e1 = e0)
% 169.84/26.06 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 169.84/26.06 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 169.84/26.06 (12) op(e1, e2) = all_52_6
% 169.84/26.06 (13) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 169.84/26.06 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 169.84/26.06 (14) op(e2, e3) = all_52_1
% 169.84/26.06 (15) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 169.84/26.06 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 169.84/26.06 (16) ~ (all_6_2 = e2)
% 169.84/26.06 (17) op(e1, e1) = all_6_2
% 169.84/26.06 (18) op(e2, e3) = e2
% 169.84/26.06 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 169.84/26.06 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 169.84/26.06 (20) ~ (e3 = e0)
% 169.84/26.06 (21) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.06 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 169.84/26.06 (22) op(e0, e0) = all_4_2
% 169.84/26.06 (23) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 169.84/26.06 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 169.84/26.06 e2) = all_22_1 & $i(all_22_1))
% 169.84/26.06 (24) all_58_14 = e3
% 169.84/26.06 (25) ~ (all_52_4 = e3)
% 169.84/26.06 (26) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 169.84/26.06 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 169.84/26.06 (27) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 169.84/26.06 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 169.84/26.06 (28) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 169.84/26.06 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 169.84/26.06 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 169.84/26.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 169.84/26.06 (30) ~ (e2 = e0)
% 169.84/26.06 (31) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 169.84/26.06 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 169.84/26.06 (32) all_58_3 = e3
% 169.84/26.06 (33) op(e3, e3) = e3
% 169.84/26.06 (34) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 169.84/26.06 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 169.84/26.06 (35) ~ (e2 = e1)
% 169.84/26.06 (36) op(e3, e2) = all_52_4
% 169.84/26.06 (37) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 169.84/26.06 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 169.84/26.06 (38) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 169.84/26.06 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 169.84/26.06 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 169.84/26.06 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 169.84/26.06 (39) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 169.84/26.06 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 169.84/26.06 (40) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 169.84/26.06 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 169.84/26.06 e2) = all_14_1 & $i(all_14_1))
% 169.84/26.06 (41) ~ (e3 = e2)
% 169.84/26.06
% 169.84/26.06 Begin of proof
% 169.84/26.06 |
% 169.84/26.06 | BETA: splitting (39) gives:
% 169.84/26.06 |
% 169.84/26.06 | Case 1:
% 169.84/26.06 | |
% 169.84/26.06 | | (42) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) =
% 169.84/26.06 | | e2)
% 169.84/26.06 | |
% 169.84/26.06 | | BETA: splitting (42) gives:
% 169.84/26.06 | |
% 169.84/26.06 | | Case 1:
% 169.84/26.06 | | |
% 169.84/26.06 | | | (43) all_58_4 = e2 & op(e3, e1) = e2
% 169.84/26.06 | | |
% 169.84/26.06 | | | ALPHA: (43) implies:
% 169.84/26.06 | | | (44) all_58_4 = e2
% 169.84/26.06 | | |
% 169.84/26.06 | | | BETA: splitting (31) gives:
% 169.84/26.06 | | |
% 169.84/26.06 | | | Case 1:
% 169.84/26.06 | | | |
% 169.84/26.06 | | | | (45) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2)
% 169.84/26.06 | | | | = e3)
% 169.84/26.06 | | | |
% 169.84/26.06 | | | | BETA: splitting (45) gives:
% 169.84/26.06 | | | |
% 169.84/26.06 | | | | Case 1:
% 169.84/26.06 | | | | |
% 169.84/26.06 | | | | | (46) all_58_6 = e3 & op(e1, e3) = e3
% 169.84/26.06 | | | | |
% 169.84/26.06 | | | | | ALPHA: (46) implies:
% 169.84/26.06 | | | | | (47) all_58_6 = e3
% 169.84/26.06 | | | | |
% 169.84/26.06 | | | | | BETA: splitting (1) gives:
% 169.84/26.06 | | | | |
% 169.84/26.06 | | | | | Case 1:
% 169.84/26.06 | | | | | |
% 169.84/26.06 | | | | | | (48) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 169.84/26.06 | | | | | | op(e0, e2) = e2)
% 169.84/26.06 | | | | | |
% 169.84/26.06 | | | | | | BETA: splitting (48) gives:
% 169.84/26.06 | | | | | |
% 169.84/26.06 | | | | | | Case 1:
% 169.84/26.06 | | | | | | |
% 169.84/26.06 | | | | | | | (49) all_58_12 = e2 & op(e0, e3) = e2
% 169.84/26.06 | | | | | | |
% 169.84/26.06 | | | | | | | ALPHA: (49) implies:
% 169.84/26.06 | | | | | | | (50) all_58_12 = e2
% 169.84/26.06 | | | | | | |
% 169.84/26.06 | | | | | | | REF_CLOSE: (4), (8), (10), (14), (18), (19), (20), (29), (30),
% 169.84/26.06 | | | | | | | (35), (47), (50) are inconsistent by sub-proof #461.
% 169.84/26.06 | | | | | | |
% 169.84/26.06 | | | | | | Case 2:
% 169.84/26.06 | | | | | | |
% 169.84/26.06 | | | | | | | (51) all_58_13 = e2 & op(e0, e2) = e2
% 169.84/26.06 | | | | | | |
% 169.84/26.06 | | | | | | | ALPHA: (51) implies:
% 169.84/26.06 | | | | | | | (52) all_58_13 = e2
% 169.84/26.06 | | | | | | |
% 169.84/26.06 | | | | | | | BETA: splitting (4) gives:
% 169.84/26.06 | | | | | | |
% 169.84/26.06 | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | |
% 169.84/26.06 | | | | | | | | (53) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 169.84/26.06 | | | | | | | | op(e2, e3) = e0)
% 169.84/26.06 | | | | | | | |
% 169.84/26.06 | | | | | | | | REF_CLOSE: (14), (18), (20), (29), (30), (33), (53) are
% 169.84/26.06 | | | | | | | | inconsistent by sub-proof #460.
% 169.84/26.06 | | | | | | | |
% 169.84/26.06 | | | | | | | Case 2:
% 169.84/26.06 | | | | | | | |
% 169.84/26.06 | | | | | | | | (54) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 169.84/26.06 | | | | | | | | op(e0, e3) = e0)
% 169.84/26.06 | | | | | | | |
% 169.84/26.06 | | | | | | | | BETA: splitting (54) gives:
% 169.84/26.06 | | | | | | | |
% 169.84/26.06 | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | |
% 169.84/26.06 | | | | | | | | | (55) all_58_6 = e0 & op(e1, e3) = e0
% 169.84/26.06 | | | | | | | | |
% 169.84/26.06 | | | | | | | | | REF_CLOSE: (20), (47), (55) are inconsistent by sub-proof
% 169.84/26.06 | | | | | | | | | #559.
% 169.84/26.06 | | | | | | | | |
% 169.84/26.06 | | | | | | | | Case 2:
% 169.84/26.06 | | | | | | | | |
% 169.84/26.06 | | | | | | | | | (56) all_58_12 = e0 & op(e0, e3) = e0
% 169.84/26.06 | | | | | | | | |
% 169.84/26.06 | | | | | | | | | ALPHA: (56) implies:
% 169.84/26.06 | | | | | | | | | (57) all_58_12 = e0
% 169.84/26.06 | | | | | | | | |
% 169.84/26.06 | | | | | | | | | BETA: splitting (19) gives:
% 169.84/26.06 | | | | | | | | |
% 169.84/26.06 | | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | (58) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 169.84/26.06 | | | | | | | | | | op(e2, e3) = e1)
% 169.84/26.06 | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | BETA: splitting (58) gives:
% 169.84/26.06 | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | (59) all_58_0 = e1 & op(e3, e3) = e1
% 169.84/26.06 | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | ALPHA: (59) implies:
% 169.84/26.06 | | | | | | | | | | | (60) all_58_0 = e1
% 169.84/26.06 | | | | | | | | | | | (61) op(e3, e3) = e1
% 169.84/26.06 | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | BETA: splitting (9) gives:
% 169.84/26.06 | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | (62) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 169.84/26.06 | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 169.84/26.06 | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | BETA: splitting (62) gives:
% 169.84/26.06 | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | (63) all_58_12 = e1 & op(e0, e3) = e1
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | ALPHA: (63) implies:
% 169.84/26.06 | | | | | | | | | | | | | (64) all_58_12 = e1
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | REF_CLOSE: (4), (10), (14), (18), (20), (29), (30), (47),
% 169.84/26.06 | | | | | | | | | | | | | (60), (64) are inconsistent by sub-proof #459.
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | Case 2:
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | (65) all_58_13 = e1 & op(e0, e2) = e1
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | ALPHA: (65) implies:
% 169.84/26.06 | | | | | | | | | | | | | (66) all_58_13 = e1
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | REF_CLOSE: (35), (52), (66) are inconsistent by sub-proof
% 169.84/26.06 | | | | | | | | | | | | | #458.
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | End of split
% 169.84/26.06 | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | Case 2:
% 169.84/26.06 | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | (67) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 169.84/26.06 | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 169.84/26.06 | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | BETA: splitting (67) gives:
% 169.84/26.06 | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | (68) all_58_14 = e1 & op(e0, e1) = e1
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | ALPHA: (68) implies:
% 169.84/26.06 | | | | | | | | | | | | | (69) all_58_14 = e1
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | COMBINE_EQS: (24), (69) imply:
% 169.84/26.06 | | | | | | | | | | | | | (70) e3 = e1
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | COMBINE_EQS: (47), (70) imply:
% 169.84/26.06 | | | | | | | | | | | | | (71) all_58_6 = e1
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (10), (11), (14), (18), (20), (29),
% 169.84/26.06 | | | | | | | | | | | | | (30), (41), (60), (71) are inconsistent by
% 169.84/26.06 | | | | | | | | | | | | | sub-proof #455.
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | Case 2:
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | (72) all_58_15 = e1 & op(e0, e0) = e1
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | ALPHA: (72) implies:
% 169.84/26.06 | | | | | | | | | | | | | (73) all_58_15 = e1
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | BETA: splitting (28) gives:
% 169.84/26.06 | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | (74) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 169.84/26.06 | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 169.84/26.06 | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (10), (11), (14), (18), (19), (20),
% 169.84/26.06 | | | | | | | | | | | | | | (25), (29), (30), (35), (36), (41), (47), (57),
% 169.84/26.06 | | | | | | | | | | | | | | (74) are inconsistent by sub-proof #453.
% 169.84/26.06 | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | Case 2:
% 169.84/26.06 | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | (75) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 169.84/26.06 | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 169.84/26.06 | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | BETA: splitting (75) gives:
% 169.84/26.06 | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | (76) all_58_4 = e3 & op(e3, e1) = e3
% 169.84/26.06 | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | ALPHA: (76) implies:
% 169.84/26.06 | | | | | | | | | | | | | | | (77) all_58_4 = e3
% 169.84/26.06 | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (10), (14), (18), (20), (21), (29),
% 169.84/26.06 | | | | | | | | | | | | | | | (30), (32), (34), (35), (41), (44), (77) are
% 169.84/26.06 | | | | | | | | | | | | | | | inconsistent by sub-proof #452.
% 169.84/26.06 | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | Case 2:
% 169.84/26.06 | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | (78) all_58_9 = e3 & op(e3, e0) = e3
% 169.84/26.06 | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | ALPHA: (78) implies:
% 169.84/26.06 | | | | | | | | | | | | | | | (79) all_58_9 = e3
% 169.84/26.06 | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | BETA: splitting (38) gives:
% 169.84/26.06 | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | (80) all_58_15 = e0 & op(e0, e0) = e0
% 169.84/26.06 | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 169.84/26.06 | | | | | | | | | | | | | | | | (81) all_58_15 = e0
% 169.84/26.06 | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | REF_CLOSE: (10), (73), (81) are inconsistent by sub-proof
% 169.84/26.06 | | | | | | | | | | | | | | | | #881.
% 169.84/26.06 | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | Case 2:
% 169.84/26.06 | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | (82) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 169.84/26.06 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 169.84/26.06 | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 169.84/26.06 | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 169.84/26.06 | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 169.84/26.06 | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | ALPHA: (82) implies:
% 169.84/26.06 | | | | | | | | | | | | | | | | (83) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 169.84/26.06 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 169.84/26.06 | | | | | | | | | | | | | | | | e0) = e0)
% 169.84/26.06 | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 169.84/26.06 | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | | (84) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 169.84/26.06 | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 169.84/26.06 | | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (8), (10), (14), (18), (20), (21), (29),
% 169.84/26.06 | | | | | | | | | | | | | | | | | (30), (32), (34), (35), (41), (79), (84) are
% 169.84/26.06 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #446.
% 169.84/26.06 | | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | Case 2:
% 169.84/26.06 | | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | | (85) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 169.84/26.06 | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 169.84/26.06 | | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 169.84/26.06 | | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | | Case 1:
% 169.84/26.06 | | | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | | | (86) all_58_11 = e2 & op(e1, e0) = e2
% 169.84/26.06 | | | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | | | ALPHA: (86) implies:
% 169.84/26.06 | | | | | | | | | | | | | | | | | | (87) all_58_11 = e2
% 169.84/26.06 | | | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 169.84/26.06 | | | | | | | | | | | | | | | | | |
% 169.84/26.06 | | | | | | | | | | | | | | | | | | Case 1:
% 170.04/26.06 | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | (88) all_58_9 = e0 & op(e3, e0) = e0
% 170.04/26.06 | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (79), (88) are inconsistent by sub-proof
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | #901.
% 170.04/26.06 | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | Case 2:
% 170.04/26.06 | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | (89) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 170.04/26.06 | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 170.04/26.06 | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | Case 1:
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (29) with e1, e3, e3, e3,
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | simplifying with (33), (61) gives:
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | (90) e3 = e1
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (90) imply:
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | (91) all_58_6 = e1
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (10), (11), (14), (18), (20), (29),
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | (30), (41), (60), (91) are inconsistent by
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | sub-proof #455.
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | (92) all_58_11 = e0 & op(e1, e0) = e0
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (87), (92) are inconsistent by sub-proof
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | | #848.
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | Case 2:
% 170.04/26.06 | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | (93) all_58_15 = e2 & op(e0, e0) = e2
% 170.04/26.06 | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 170.04/26.06 | | | | | | | | | | | | | | | | | | (94) all_58_15 = e2
% 170.04/26.06 | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (10), (11), (14), (18),
% 170.04/26.06 | | | | | | | | | | | | | | | | | | (20), (23), (24), (29), (30), (33), (35), (41),
% 170.04/26.06 | | | | | | | | | | | | | | | | | | (44), (47), (60), (79), (94) are inconsistent by
% 170.04/26.06 | | | | | | | | | | | | | | | | | | sub-proof #439.
% 170.04/26.06 | | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | Case 2:
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | (95) all_58_2 = e1 & op(e2, e3) = e1
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | ALPHA: (95) implies:
% 170.04/26.06 | | | | | | | | | | | (96) op(e2, e3) = e1
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | REF_CLOSE: (14), (18), (29), (35), (96) are inconsistent by
% 170.04/26.06 | | | | | | | | | | | sub-proof #784.
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | Case 2:
% 170.04/26.06 | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | (97) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 170.04/26.06 | | | | | | | | | | & op(e0, e3) = e1)
% 170.04/26.06 | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | BETA: splitting (97) gives:
% 170.04/26.06 | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | Case 1:
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | (98) all_58_6 = e1 & op(e1, e3) = e1
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | REF_CLOSE: (8), (47), (98) are inconsistent by sub-proof
% 170.04/26.06 | | | | | | | | | | | #487.
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | Case 2:
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | (99) all_58_12 = e1 & op(e0, e3) = e1
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | | REF_CLOSE: (10), (57), (99) are inconsistent by sub-proof
% 170.04/26.06 | | | | | | | | | | | #773.
% 170.04/26.06 | | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | | |
% 170.04/26.06 | | | | | | | | | End of split
% 170.04/26.06 | | | | | | | | |
% 170.04/26.06 | | | | | | | | End of split
% 170.04/26.06 | | | | | | | |
% 170.04/26.06 | | | | | | | End of split
% 170.04/26.06 | | | | | | |
% 170.04/26.06 | | | | | | End of split
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | Case 2:
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | | (100) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 170.04/26.06 | | | | | | op(e0, e0) = e2)
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | | REF_CLOSE: (2), (3), (5), (8), (10), (14), (18), (20), (21), (22),
% 170.04/26.06 | | | | | | (24), (29), (30), (32), (34), (35), (41), (100) are
% 170.04/26.06 | | | | | | inconsistent by sub-proof #437.
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | End of split
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | Case 2:
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | (101) all_58_7 = e3 & op(e1, e2) = e3
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | ALPHA: (101) implies:
% 170.04/26.06 | | | | | (102) all_58_7 = e3
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | BETA: splitting (1) gives:
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | Case 1:
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | | (103) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 170.04/26.06 | | | | | | op(e0, e2) = e2)
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (10), (11), (12), (14), (18),
% 170.04/26.06 | | | | | | (19), (20), (21), (23), (26), (29), (30), (32), (34),
% 170.04/26.06 | | | | | | (35), (36), (40), (41), (102), (103) are inconsistent by
% 170.04/26.06 | | | | | | sub-proof #424.
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | Case 2:
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | | (104) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 170.04/26.06 | | | | | | op(e0, e0) = e2)
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | | REF_CLOSE: (2), (3), (5), (8), (10), (14), (18), (20), (21), (22),
% 170.04/26.06 | | | | | | (24), (29), (30), (32), (34), (35), (41), (104) are
% 170.04/26.06 | | | | | | inconsistent by sub-proof #437.
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | End of split
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | End of split
% 170.04/26.06 | | | |
% 170.04/26.06 | | | Case 2:
% 170.04/26.06 | | | |
% 170.04/26.06 | | | | (105) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 170.04/26.06 | | | | e0) = e3)
% 170.04/26.06 | | | |
% 170.04/26.06 | | | | BETA: splitting (105) gives:
% 170.04/26.06 | | | |
% 170.04/26.06 | | | | Case 1:
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | (106) all_58_8 = e3 & op(e1, e1) = e3
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | ALPHA: (106) implies:
% 170.04/26.06 | | | | | (107) all_58_8 = e3
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | REF_CLOSE: (8), (10), (15), (20), (24), (30), (35), (37), (44), (107)
% 170.04/26.06 | | | | | are inconsistent by sub-proof #422.
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | Case 2:
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | (108) all_58_11 = e3 & op(e1, e0) = e3
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | ALPHA: (108) implies:
% 170.04/26.06 | | | | | (109) all_58_11 = e3
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | BETA: splitting (11) gives:
% 170.04/26.06 | | | | |
% 170.04/26.06 | | | | | Case 1:
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | | (110) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2,
% 170.04/26.06 | | | | | | e3) = e3)
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | | BETA: splitting (110) gives:
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | | Case 1:
% 170.04/26.06 | | | | | | |
% 170.04/26.06 | | | | | | | (111) all_58_0 = e3 & op(e3, e3) = e3
% 170.04/26.06 | | | | | | |
% 170.04/26.06 | | | | | | | ALPHA: (111) implies:
% 170.04/26.06 | | | | | | | (112) all_58_0 = e3
% 170.04/26.06 | | | | | | |
% 170.04/26.06 | | | | | | | BETA: splitting (13) gives:
% 170.04/26.06 | | | | | | |
% 170.04/26.06 | | | | | | | Case 1:
% 170.04/26.06 | | | | | | | |
% 170.04/26.06 | | | | | | | | (113) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 &
% 170.04/26.06 | | | | | | | | op(e2, e0) = e2)
% 170.04/26.06 | | | | | | | |
% 170.04/26.06 | | | | | | | | BETA: splitting (113) gives:
% 170.04/26.06 | | | | | | | |
% 170.04/26.06 | | | | | | | | Case 1:
% 170.04/26.06 | | | | | | | | |
% 170.04/26.06 | | | | | | | | | (114) all_58_9 = e2 & op(e3, e0) = e2
% 170.04/26.06 | | | | | | | | |
% 170.04/26.06 | | | | | | | | | ALPHA: (114) implies:
% 170.04/26.06 | | | | | | | | | (115) all_58_9 = e2
% 170.04/26.06 | | | | | | | | |
% 170.04/26.06 | | | | | | | | | REF_CLOSE: (7), (8), (10), (20), (27), (29), (30), (33), (35),
% 170.04/26.06 | | | | | | | | | (44), (112), (115) are inconsistent by sub-proof
% 170.04/26.06 | | | | | | | | | #941.
% 170.04/26.06 | | | | | | | | |
% 170.04/26.06 | | | | | | | | Case 2:
% 170.04/26.06 | | | | | | | | |
% 170.04/26.06 | | | | | | | | | (116) all_58_10 = e2 & op(e2, e0) = e2
% 170.04/26.06 | | | | | | | | |
% 170.04/26.06 | | | | | | | | | REF_CLOSE: (2), (8), (10), (14), (18), (20), (21), (29), (30),
% 170.04/26.06 | | | | | | | | | (32), (35), (116) are inconsistent by sub-proof
% 170.04/26.06 | | | | | | | | | #447.
% 170.04/26.06 | | | | | | | | |
% 170.04/26.06 | | | | | | | | End of split
% 170.04/26.06 | | | | | | | |
% 170.04/26.06 | | | | | | | Case 2:
% 170.04/26.06 | | | | | | | |
% 170.04/26.06 | | | | | | | | (117) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 170.04/26.06 | | | | | | | | op(e0, e0) = e2)
% 170.04/26.06 | | | | | | | |
% 170.04/26.06 | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (10), (14), (18), (20), (21),
% 170.04/26.06 | | | | | | | | (22), (29), (30), (32), (34), (35), (41), (109),
% 170.04/26.06 | | | | | | | | (117) are inconsistent by sub-proof #420.
% 170.04/26.06 | | | | | | | |
% 170.04/26.06 | | | | | | | End of split
% 170.04/26.06 | | | | | | |
% 170.04/26.06 | | | | | | Case 2:
% 170.04/26.06 | | | | | | |
% 170.04/26.06 | | | | | | | (118) all_58_2 = e3 & op(e2, e3) = e3
% 170.04/26.06 | | | | | | |
% 170.04/26.06 | | | | | | | ALPHA: (118) implies:
% 170.04/26.06 | | | | | | | (119) op(e2, e3) = e3
% 170.04/26.06 | | | | | | |
% 170.04/26.06 | | | | | | | REF_CLOSE: (14), (18), (29), (41), (119) are inconsistent by
% 170.04/26.06 | | | | | | | sub-proof #462.
% 170.04/26.06 | | | | | | |
% 170.04/26.06 | | | | | | End of split
% 170.04/26.06 | | | | | |
% 170.04/26.06 | | | | | Case 2:
% 170.04/26.06 | | | | | |
% 170.04/26.07 | | | | | | (120) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 170.04/26.07 | | | | | | op(e0, e3) = e3)
% 170.04/26.07 | | | | | |
% 170.04/26.07 | | | | | | BETA: splitting (120) gives:
% 170.04/26.07 | | | | | |
% 170.04/26.07 | | | | | | Case 1:
% 170.04/26.07 | | | | | | |
% 170.04/26.07 | | | | | | | (121) all_58_6 = e3 & op(e1, e3) = e3
% 170.04/26.07 | | | | | | |
% 170.04/26.07 | | | | | | | ALPHA: (121) implies:
% 170.04/26.07 | | | | | | | (122) all_58_6 = e3
% 170.04/26.07 | | | | | | |
% 170.04/26.07 | | | | | | | BETA: splitting (4) gives:
% 170.04/26.07 | | | | | | |
% 170.04/26.07 | | | | | | | Case 1:
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | | (123) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 170.04/26.07 | | | | | | | | op(e2, e3) = e0)
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | | REF_CLOSE: (14), (18), (20), (29), (30), (33), (123) are
% 170.04/26.07 | | | | | | | | inconsistent by sub-proof #460.
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | Case 2:
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | | (124) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 170.04/26.07 | | | | | | | | op(e0, e3) = e0)
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | | BETA: splitting (124) gives:
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | | Case 1:
% 170.04/26.07 | | | | | | | | |
% 170.04/26.07 | | | | | | | | | (125) all_58_6 = e0 & op(e1, e3) = e0
% 170.04/26.07 | | | | | | | | |
% 170.04/26.07 | | | | | | | | | REF_CLOSE: (20), (122), (125) are inconsistent by sub-proof
% 170.04/26.07 | | | | | | | | | #559.
% 170.04/26.07 | | | | | | | | |
% 170.04/26.07 | | | | | | | | Case 2:
% 170.04/26.07 | | | | | | | | |
% 170.04/26.07 | | | | | | | | | (126) all_58_12 = e0 & op(e0, e3) = e0
% 170.04/26.07 | | | | | | | | |
% 170.04/26.07 | | | | | | | | | ALPHA: (126) implies:
% 170.04/26.07 | | | | | | | | | (127) all_58_12 = e0
% 170.04/26.07 | | | | | | | | |
% 170.04/26.07 | | | | | | | | | BETA: splitting (28) gives:
% 170.04/26.07 | | | | | | | | |
% 170.04/26.07 | | | | | | | | | Case 1:
% 170.04/26.07 | | | | | | | | | |
% 170.04/26.07 | | | | | | | | | | (128) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 170.04/26.07 | | | | | | | | | | & op(e3, e2) = e3)
% 170.04/26.07 | | | | | | | | | |
% 170.04/26.07 | | | | | | | | | | REF_CLOSE: (4), (5), (8), (10), (11), (14), (18), (19), (20),
% 170.04/26.07 | | | | | | | | | | (25), (29), (30), (35), (36), (41), (122), (127),
% 170.04/26.07 | | | | | | | | | | (128) are inconsistent by sub-proof #453.
% 170.04/26.07 | | | | | | | | | |
% 170.04/26.07 | | | | | | | | | Case 2:
% 170.04/26.07 | | | | | | | | | |
% 170.04/26.07 | | | | | | | | | | (129) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 170.04/26.07 | | | | | | | | | | & op(e3, e0) = e3)
% 170.04/26.07 | | | | | | | | | |
% 170.04/26.07 | | | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (10), (13), (14), (18), (20),
% 170.04/26.07 | | | | | | | | | | (21), (22), (29), (30), (32), (34), (35), (41),
% 170.04/26.07 | | | | | | | | | | (44), (109), (129) are inconsistent by sub-proof
% 170.04/26.07 | | | | | | | | | | #417.
% 170.04/26.07 | | | | | | | | | |
% 170.04/26.07 | | | | | | | | | End of split
% 170.04/26.07 | | | | | | | | |
% 170.04/26.07 | | | | | | | | End of split
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | End of split
% 170.04/26.07 | | | | | | |
% 170.04/26.07 | | | | | | Case 2:
% 170.04/26.07 | | | | | | |
% 170.04/26.07 | | | | | | | (130) all_58_12 = e3 & op(e0, e3) = e3
% 170.04/26.07 | | | | | | |
% 170.04/26.07 | | | | | | | ALPHA: (130) implies:
% 170.04/26.07 | | | | | | | (131) all_58_12 = e3
% 170.04/26.07 | | | | | | |
% 170.04/26.07 | | | | | | | BETA: splitting (28) gives:
% 170.04/26.07 | | | | | | |
% 170.04/26.07 | | | | | | | Case 1:
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | | (132) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 &
% 170.04/26.07 | | | | | | | | op(e3, e2) = e3)
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | | REF_CLOSE: (4), (8), (10), (14), (18), (19), (20), (25), (29),
% 170.04/26.07 | | | | | | | | (30), (35), (36), (131), (132) are inconsistent by
% 170.04/26.07 | | | | | | | | sub-proof #413.
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | Case 2:
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | | (133) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 &
% 170.04/26.07 | | | | | | | | op(e3, e0) = e3)
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | | REF_CLOSE: (2), (3), (5), (8), (10), (13), (14), (18), (20),
% 170.04/26.07 | | | | | | | | (21), (22), (29), (30), (32), (34), (35), (41), (44),
% 170.04/26.07 | | | | | | | | (109), (133) are inconsistent by sub-proof #417.
% 170.04/26.07 | | | | | | | |
% 170.04/26.07 | | | | | | | End of split
% 170.04/26.07 | | | | | | |
% 170.04/26.07 | | | | | | End of split
% 170.04/26.07 | | | | | |
% 170.04/26.07 | | | | | End of split
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | End of split
% 170.04/26.07 | | | |
% 170.04/26.07 | | | End of split
% 170.04/26.07 | | |
% 170.04/26.07 | | Case 2:
% 170.04/26.07 | | |
% 170.04/26.07 | | | (134) all_58_5 = e2 & op(e2, e1) = e2
% 170.04/26.07 | | |
% 170.04/26.07 | | | REF_CLOSE: (2), (8), (10), (14), (18), (20), (21), (29), (30), (32), (35),
% 170.04/26.07 | | | (134) are inconsistent by sub-proof #412.
% 170.04/26.07 | | |
% 170.04/26.07 | | End of split
% 170.04/26.07 | |
% 170.04/26.07 | Case 2:
% 170.04/26.07 | |
% 170.04/26.07 | | (135) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) =
% 170.04/26.07 | | e2)
% 170.04/26.07 | |
% 170.04/26.07 | | BETA: splitting (135) gives:
% 170.04/26.07 | |
% 170.04/26.07 | | Case 1:
% 170.04/26.07 | | |
% 170.04/26.07 | | | (136) all_58_8 = e2 & op(e1, e1) = e2
% 170.04/26.07 | | |
% 170.04/26.07 | | | REF_CLOSE: (16), (17), (29), (136) are inconsistent by sub-proof #845.
% 170.04/26.07 | | |
% 170.04/26.07 | | Case 2:
% 170.04/26.07 | | |
% 170.04/26.07 | | | (137) all_58_14 = e2 & op(e0, e1) = e2
% 170.04/26.07 | | |
% 170.04/26.07 | | | REF_CLOSE: (2), (5), (8), (10), (14), (18), (20), (21), (24), (29), (30),
% 170.04/26.07 | | | (32), (34), (35), (41), (137) are inconsistent by sub-proof
% 170.04/26.07 | | | #411.
% 170.04/26.07 | | |
% 170.04/26.07 | | End of split
% 170.04/26.07 | |
% 170.04/26.07 | End of split
% 170.04/26.07 |
% 170.04/26.07 End of proof
% 170.04/26.07
% 170.04/26.07 Sub-proof #411 shows that the following formulas are inconsistent:
% 170.04/26.07 ----------------------------------------------------------------
% 170.04/26.07 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.07 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.04/26.07 (2) all_58_2 = e2
% 170.04/26.07 (3) ~ (e3 = e1)
% 170.04/26.07 (4) ~ (e1 = e0)
% 170.04/26.07 (5) op(e2, e3) = all_52_1
% 170.04/26.07 (6) op(e2, e3) = e2
% 170.04/26.07 (7) ~ (e3 = e0)
% 170.04/26.07 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.07 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.04/26.07 (9) all_58_14 = e3
% 170.04/26.07 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.07 (11) ~ (e2 = e0)
% 170.04/26.07 (12) all_58_14 = e2 & op(e0, e1) = e2
% 170.04/26.07 (13) all_58_3 = e3
% 170.04/26.07 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.04/26.07 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.04/26.07 (15) ~ (e2 = e1)
% 170.04/26.07 (16) ~ (e3 = e2)
% 170.04/26.07
% 170.04/26.07 Begin of proof
% 170.04/26.07 |
% 170.04/26.07 | ALPHA: (12) implies:
% 170.04/26.07 | (17) all_58_14 = e2
% 170.04/26.07 |
% 170.04/26.07 | COMBINE_EQS: (9), (17) imply:
% 170.04/26.07 | (18) e3 = e2
% 170.04/26.07 |
% 170.04/26.07 | COMBINE_EQS: (13), (18) imply:
% 170.04/26.07 | (19) all_58_3 = e2
% 170.04/26.07 |
% 170.04/26.07 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (14), (15),
% 170.04/26.07 | (16), (19) are inconsistent by sub-proof #779.
% 170.04/26.07 |
% 170.04/26.07 End of proof
% 170.04/26.07
% 170.04/26.07 Sub-proof #412 shows that the following formulas are inconsistent:
% 170.04/26.07 ----------------------------------------------------------------
% 170.04/26.07 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.07 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.04/26.07 (2) ~ (e3 = e1)
% 170.04/26.07 (3) ~ (e1 = e0)
% 170.04/26.07 (4) op(e2, e3) = all_52_1
% 170.04/26.07 (5) op(e2, e3) = e2
% 170.04/26.07 (6) ~ (e3 = e0)
% 170.04/26.07 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.07 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.04/26.07 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.07 (9) ~ (e2 = e0)
% 170.04/26.07 (10) all_58_3 = e3
% 170.04/26.07 (11) ~ (e2 = e1)
% 170.04/26.07 (12) all_58_5 = e2 & op(e2, e1) = e2
% 170.04/26.07
% 170.04/26.07 Begin of proof
% 170.04/26.07 |
% 170.04/26.07 | ALPHA: (12) implies:
% 170.04/26.07 | (13) all_58_5 = e2
% 170.04/26.07 |
% 170.04/26.07 | BETA: splitting (1) gives:
% 170.04/26.07 |
% 170.04/26.07 | Case 1:
% 170.04/26.07 | |
% 170.04/26.07 | | (14) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 170.04/26.07 | | e1)
% 170.04/26.07 | |
% 170.04/26.07 | | REF_CLOSE: (2), (4), (5), (8), (10), (11), (14) are inconsistent by
% 170.04/26.07 | | sub-proof #450.
% 170.04/26.07 | |
% 170.04/26.07 | Case 2:
% 170.04/26.07 | |
% 170.04/26.07 | | (15) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 170.04/26.07 | | e1)
% 170.04/26.07 | |
% 170.04/26.07 | | BETA: splitting (15) gives:
% 170.04/26.07 | |
% 170.04/26.07 | | Case 1:
% 170.04/26.07 | | |
% 170.04/26.07 | | | (16) all_58_5 = e1 & op(e2, e1) = e1
% 170.04/26.07 | | |
% 170.04/26.07 | | | ALPHA: (16) implies:
% 170.04/26.07 | | | (17) all_58_5 = e1
% 170.04/26.07 | | |
% 170.04/26.07 | | | REF_CLOSE: (11), (13), (17) are inconsistent by sub-proof #522.
% 170.04/26.07 | | |
% 170.04/26.07 | | Case 2:
% 170.04/26.07 | | |
% 170.04/26.07 | | | (18) all_58_10 = e1 & op(e2, e0) = e1
% 170.04/26.07 | | |
% 170.04/26.07 | | | ALPHA: (18) implies:
% 170.04/26.07 | | | (19) all_58_10 = e1
% 170.04/26.07 | | |
% 170.04/26.07 | | | BETA: splitting (7) gives:
% 170.04/26.07 | | |
% 170.04/26.07 | | | Case 1:
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2)
% 170.04/26.07 | | | | = e0)
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | BETA: splitting (20) gives:
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | Case 1:
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | (21) all_58_2 = e0 & op(e2, e3) = e0
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | REF_CLOSE: (4), (5), (8), (9), (21) are inconsistent by sub-proof
% 170.04/26.07 | | | | | #782.
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | Case 2:
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | (22) all_58_3 = e0 & op(e2, e2) = e0
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | REF_CLOSE: (6), (10), (22) are inconsistent by sub-proof #869.
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | End of split
% 170.04/26.07 | | | |
% 170.04/26.07 | | | Case 2:
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | (23) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0)
% 170.04/26.07 | | | | = e0)
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | BETA: splitting (23) gives:
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | Case 1:
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | (24) all_58_5 = e0 & op(e2, e1) = e0
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | REF_CLOSE: (9), (13), (24) are inconsistent by sub-proof #798.
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | Case 2:
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | (25) all_58_10 = e0 & op(e2, e0) = e0
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | REF_CLOSE: (3), (19), (25) are inconsistent by sub-proof #925.
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | End of split
% 170.04/26.07 | | | |
% 170.04/26.07 | | | End of split
% 170.04/26.07 | | |
% 170.04/26.07 | | End of split
% 170.04/26.07 | |
% 170.04/26.07 | End of split
% 170.04/26.07 |
% 170.04/26.07 End of proof
% 170.04/26.07
% 170.04/26.07 Sub-proof #413 shows that the following formulas are inconsistent:
% 170.04/26.07 ----------------------------------------------------------------
% 170.04/26.07 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.04/26.07 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.04/26.07 (2) ~ (e3 = e1)
% 170.04/26.07 (3) ~ (e1 = e0)
% 170.04/26.07 (4) op(e2, e3) = all_52_1
% 170.04/26.07 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 170.04/26.07 (6) op(e2, e3) = e2
% 170.04/26.07 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.04/26.07 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.04/26.07 (8) ~ (e3 = e0)
% 170.04/26.07 (9) ~ (all_52_4 = e3)
% 170.04/26.07 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.07 (11) ~ (e2 = e0)
% 170.04/26.07 (12) all_58_12 = e3
% 170.04/26.07 (13) ~ (e2 = e1)
% 170.04/26.07 (14) op(e3, e2) = all_52_4
% 170.04/26.07
% 170.04/26.07 Begin of proof
% 170.04/26.07 |
% 170.04/26.07 | BETA: splitting (5) gives:
% 170.04/26.07 |
% 170.04/26.07 | Case 1:
% 170.04/26.07 | |
% 170.04/26.07 | | (15) all_58_0 = e3 & op(e3, e3) = e3
% 170.04/26.07 | |
% 170.04/26.07 | | ALPHA: (15) implies:
% 170.04/26.07 | | (16) all_58_0 = e3
% 170.04/26.07 | |
% 170.04/26.07 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (13), (16)
% 170.04/26.07 | | are inconsistent by sub-proof #414.
% 170.04/26.07 | |
% 170.04/26.07 | Case 2:
% 170.04/26.07 | |
% 170.04/26.07 | | (17) all_58_1 = e3 & op(e3, e2) = e3
% 170.04/26.07 | |
% 170.04/26.07 | | ALPHA: (17) implies:
% 170.04/26.07 | | (18) op(e3, e2) = e3
% 170.04/26.07 | |
% 170.04/26.07 | | REF_CLOSE: (9), (10), (14), (18) are inconsistent by sub-proof #974.
% 170.04/26.07 | |
% 170.04/26.07 | End of split
% 170.04/26.07 |
% 170.04/26.07 End of proof
% 170.04/26.07
% 170.04/26.07 Sub-proof #414 shows that the following formulas are inconsistent:
% 170.04/26.07 ----------------------------------------------------------------
% 170.04/26.07 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.04/26.07 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.04/26.07 (2) ~ (e3 = e1)
% 170.04/26.07 (3) ~ (e1 = e0)
% 170.04/26.07 (4) op(e2, e3) = all_52_1
% 170.04/26.07 (5) op(e2, e3) = e2
% 170.04/26.07 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.04/26.07 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.04/26.07 (7) ~ (e3 = e0)
% 170.04/26.07 (8) all_58_0 = e3
% 170.04/26.07 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.07 (10) ~ (e2 = e0)
% 170.04/26.07 (11) all_58_12 = e3
% 170.04/26.07 (12) ~ (e2 = e1)
% 170.04/26.07
% 170.04/26.07 Begin of proof
% 170.04/26.07 |
% 170.04/26.07 | BETA: splitting (6) gives:
% 170.04/26.07 |
% 170.04/26.07 | Case 1:
% 170.04/26.07 | |
% 170.04/26.07 | | (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 170.04/26.07 | | e1)
% 170.04/26.07 | |
% 170.04/26.07 | | REF_CLOSE: (2), (4), (5), (8), (9), (12), (13) are inconsistent by sub-proof
% 170.04/26.07 | | #416.
% 170.04/26.07 | |
% 170.04/26.07 | Case 2:
% 170.04/26.07 | |
% 170.04/26.07 | | (14) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 170.04/26.07 | | e1)
% 170.04/26.07 | |
% 170.04/26.07 | | BETA: splitting (14) gives:
% 170.04/26.07 | |
% 170.04/26.07 | | Case 1:
% 170.04/26.07 | | |
% 170.04/26.07 | | | (15) all_58_6 = e1 & op(e1, e3) = e1
% 170.04/26.07 | | |
% 170.04/26.07 | | | ALPHA: (15) implies:
% 170.04/26.07 | | | (16) all_58_6 = e1
% 170.04/26.07 | | |
% 170.04/26.07 | | | BETA: splitting (1) gives:
% 170.04/26.07 | | |
% 170.04/26.07 | | | Case 1:
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | (17) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 170.04/26.07 | | | | = e0)
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | BETA: splitting (17) gives:
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | Case 1:
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | (18) all_58_0 = e0 & op(e3, e3) = e0
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | REF_CLOSE: (7), (8), (18) are inconsistent by sub-proof #898.
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | Case 2:
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | (19) all_58_2 = e0 & op(e2, e3) = e0
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | REF_CLOSE: (4), (5), (9), (10), (19) are inconsistent by sub-proof
% 170.04/26.07 | | | | | #782.
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | End of split
% 170.04/26.07 | | | |
% 170.04/26.07 | | | Case 2:
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | (20) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 170.04/26.07 | | | | = e0)
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | BETA: splitting (20) gives:
% 170.04/26.07 | | | |
% 170.04/26.07 | | | | Case 1:
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | (21) all_58_6 = e0 & op(e1, e3) = e0
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | REF_CLOSE: (3), (16), (21) are inconsistent by sub-proof #415.
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | Case 2:
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | (22) all_58_12 = e0 & op(e0, e3) = e0
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | ALPHA: (22) implies:
% 170.04/26.07 | | | | | (23) all_58_12 = e0
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | | REF_CLOSE: (7), (11), (23) are inconsistent by sub-proof #608.
% 170.04/26.07 | | | | |
% 170.04/26.07 | | | | End of split
% 170.04/26.07 | | | |
% 170.04/26.07 | | | End of split
% 170.04/26.07 | | |
% 170.04/26.07 | | Case 2:
% 170.04/26.07 | | |
% 170.04/26.07 | | | (24) all_58_12 = e1 & op(e0, e3) = e1
% 170.04/26.07 | | |
% 170.04/26.07 | | | ALPHA: (24) implies:
% 170.04/26.07 | | | (25) all_58_12 = e1
% 170.04/26.07 | | |
% 170.04/26.07 | | | REF_CLOSE: (2), (11), (25) are inconsistent by sub-proof #600.
% 170.04/26.07 | | |
% 170.04/26.07 | | End of split
% 170.04/26.07 | |
% 170.04/26.07 | End of split
% 170.04/26.07 |
% 170.04/26.07 End of proof
% 170.04/26.07
% 170.04/26.07 Sub-proof #415 shows that the following formulas are inconsistent:
% 170.04/26.07 ----------------------------------------------------------------
% 170.04/26.07 (1) all_58_6 = e0 & op(e1, e3) = e0
% 170.04/26.07 (2) all_58_6 = e1
% 170.04/26.07 (3) ~ (e1 = e0)
% 170.04/26.07
% 170.04/26.07 Begin of proof
% 170.04/26.07 |
% 170.04/26.07 | ALPHA: (1) implies:
% 170.04/26.07 | (4) all_58_6 = e0
% 170.04/26.07 |
% 170.04/26.07 | COMBINE_EQS: (2), (4) imply:
% 170.04/26.07 | (5) e1 = e0
% 170.04/26.07 |
% 170.04/26.07 | SIMP: (5) implies:
% 170.04/26.07 | (6) e1 = e0
% 170.04/26.07 |
% 170.04/26.07 | REDUCE: (3), (6) imply:
% 170.04/26.07 | (7) $false
% 170.04/26.07 |
% 170.04/26.07 | CLOSE: (7) is inconsistent.
% 170.04/26.07 |
% 170.04/26.07 End of proof
% 170.04/26.07
% 170.04/26.07 Sub-proof #416 shows that the following formulas are inconsistent:
% 170.04/26.07 ----------------------------------------------------------------
% 170.04/26.07 (1) ~ (e3 = e1)
% 170.04/26.07 (2) op(e2, e3) = all_52_1
% 170.04/26.07 (3) op(e2, e3) = e2
% 170.04/26.07 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 170.04/26.07 (5) all_58_0 = e3
% 170.04/26.07 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.07 (7) ~ (e2 = e1)
% 170.04/26.07
% 170.04/26.07 Begin of proof
% 170.04/26.07 |
% 170.04/26.07 | BETA: splitting (4) gives:
% 170.04/26.07 |
% 170.04/26.07 | Case 1:
% 170.04/26.07 | |
% 170.04/26.07 | | (8) all_58_0 = e1 & op(e3, e3) = e1
% 170.04/26.07 | |
% 170.04/26.07 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #950.
% 170.04/26.07 | |
% 170.04/26.07 | Case 2:
% 170.04/26.07 | |
% 170.04/26.07 | | (9) all_58_2 = e1 & op(e2, e3) = e1
% 170.04/26.07 | |
% 170.04/26.07 | | ALPHA: (9) implies:
% 170.04/26.07 | | (10) op(e2, e3) = e1
% 170.04/26.07 | |
% 170.04/26.07 | | REF_CLOSE: (2), (3), (6), (7), (10) are inconsistent by sub-proof #784.
% 170.04/26.07 | |
% 170.04/26.07 | End of split
% 170.04/26.07 |
% 170.04/26.07 End of proof
% 170.04/26.07
% 170.04/26.07 Sub-proof #417 shows that the following formulas are inconsistent:
% 170.04/26.07 ----------------------------------------------------------------
% 170.04/26.07 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.07 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.04/26.07 (2) ~ (all_4_2 = e2)
% 170.04/26.07 (3) all_58_2 = e2
% 170.04/26.07 (4) ~ (e3 = e1)
% 170.04/26.07 (5) ~ (e1 = e0)
% 170.04/26.07 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 170.04/26.07 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.04/26.07 (7) op(e2, e3) = all_52_1
% 170.04/26.07 (8) op(e2, e3) = e2
% 170.04/26.07 (9) ~ (e3 = e0)
% 170.04/26.07 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.07 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.04/26.07 (11) op(e0, e0) = all_4_2
% 170.04/26.07 (12) all_58_11 = e3
% 170.04/26.07 (13) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.04/26.07 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.07 (15) ~ (e2 = e0)
% 170.04/26.07 (16) all_58_3 = e3
% 170.04/26.07 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.04/26.07 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.04/26.07 (18) ~ (e2 = e1)
% 170.04/26.07 (19) all_58_4 = e2
% 170.04/26.07 (20) ~ (e3 = e2)
% 170.04/26.07
% 170.04/26.07 Begin of proof
% 170.04/26.07 |
% 170.04/26.07 | BETA: splitting (13) gives:
% 170.04/26.07 |
% 170.04/26.07 | Case 1:
% 170.04/26.07 | |
% 170.04/26.07 | | (21) all_58_4 = e3 & op(e3, e1) = e3
% 170.04/26.07 | |
% 170.04/26.07 | | ALPHA: (21) implies:
% 170.04/26.07 | | (22) all_58_4 = e3
% 170.04/26.07 | |
% 170.04/26.07 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (14), (15), (16), (17),
% 170.04/26.07 | | (18), (19), (20), (22) are inconsistent by sub-proof #452.
% 170.04/26.07 | |
% 170.04/26.07 | Case 2:
% 170.04/26.07 | |
% 170.04/26.07 | | (23) all_58_9 = e3 & op(e3, e0) = e3
% 170.04/26.07 | |
% 170.04/26.07 | | ALPHA: (23) implies:
% 170.04/26.07 | | (24) all_58_9 = e3
% 170.04/26.07 | |
% 170.04/26.07 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 170.04/26.07 | | (14), (15), (16), (17), (18), (20), (24) are inconsistent by
% 170.04/26.07 | | sub-proof #418.
% 170.04/26.07 | |
% 170.04/26.07 | End of split
% 170.04/26.07 |
% 170.04/26.07 End of proof
% 170.04/26.07
% 170.04/26.07 Sub-proof #418 shows that the following formulas are inconsistent:
% 170.04/26.07 ----------------------------------------------------------------
% 170.04/26.07 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.07 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.04/26.07 (2) ~ (all_4_2 = e2)
% 170.04/26.07 (3) all_58_2 = e2
% 170.04/26.07 (4) ~ (e3 = e1)
% 170.04/26.07 (5) ~ (e1 = e0)
% 170.04/26.07 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 170.04/26.07 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.04/26.07 (7) op(e2, e3) = all_52_1
% 170.04/26.07 (8) op(e2, e3) = e2
% 170.04/26.07 (9) ~ (e3 = e0)
% 170.04/26.07 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.07 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.04/26.07 (11) op(e0, e0) = all_4_2
% 170.04/26.07 (12) all_58_11 = e3
% 170.04/26.07 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.07 (14) ~ (e2 = e0)
% 170.04/26.07 (15) all_58_3 = e3
% 170.04/26.07 (16) all_58_9 = e3
% 170.04/26.07 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.04/26.07 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.04/26.07 (18) ~ (e2 = e1)
% 170.04/26.07 (19) ~ (e3 = e2)
% 170.04/26.07
% 170.04/26.07 Begin of proof
% 170.04/26.07 |
% 170.04/26.07 | BETA: splitting (6) gives:
% 170.04/26.07 |
% 170.04/26.07 | Case 1:
% 170.04/26.07 | |
% 170.04/26.07 | | (20) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 170.04/26.07 | | e2)
% 170.04/26.07 | |
% 170.04/26.07 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (13), (14), (15), (16),
% 170.04/26.07 | | (17), (18), (19), (20) are inconsistent by sub-proof #446.
% 170.04/26.07 | |
% 170.04/26.07 | Case 2:
% 170.04/26.07 | |
% 170.04/26.07 | | (21) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 170.04/26.07 | | e2)
% 170.04/26.07 | |
% 170.04/26.07 | | BETA: splitting (21) gives:
% 170.04/26.07 | |
% 170.04/26.07 | | Case 1:
% 170.04/26.07 | | |
% 170.04/26.07 | | | (22) all_58_11 = e2 & op(e1, e0) = e2
% 170.04/26.07 | | |
% 170.04/26.07 | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 170.04/26.07 | | | (15), (17), (18), (19), (22) are inconsistent by sub-proof
% 170.04/26.07 | | | #419.
% 170.04/26.07 | | |
% 170.04/26.07 | | Case 2:
% 170.04/26.07 | | |
% 170.04/26.07 | | | (23) all_58_15 = e2 & op(e0, e0) = e2
% 170.04/26.07 | | |
% 170.04/26.07 | | | REF_CLOSE: (2), (11), (13), (23) are inconsistent by sub-proof #854.
% 170.04/26.07 | | |
% 170.04/26.07 | | End of split
% 170.04/26.07 | |
% 170.04/26.07 | End of split
% 170.04/26.07 |
% 170.04/26.07 End of proof
% 170.04/26.07
% 170.04/26.07 Sub-proof #419 shows that the following formulas are inconsistent:
% 170.04/26.07 ----------------------------------------------------------------
% 170.04/26.07 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.07 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.04/26.07 (2) all_58_2 = e2
% 170.04/26.07 (3) ~ (e3 = e1)
% 170.04/26.07 (4) ~ (e1 = e0)
% 170.04/26.07 (5) all_58_11 = e2 & op(e1, e0) = e2
% 170.04/26.07 (6) op(e2, e3) = all_52_1
% 170.04/26.07 (7) op(e2, e3) = e2
% 170.04/26.07 (8) ~ (e3 = e0)
% 170.04/26.07 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.07 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.04/26.07 (10) all_58_11 = e3
% 170.04/26.07 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.07 (12) ~ (e2 = e0)
% 170.04/26.07 (13) all_58_3 = e3
% 170.04/26.07 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.04/26.07 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.04/26.07 (15) ~ (e2 = e1)
% 170.04/26.07 (16) ~ (e3 = e2)
% 170.04/26.07
% 170.04/26.07 Begin of proof
% 170.04/26.07 |
% 170.04/26.07 | ALPHA: (5) implies:
% 170.04/26.07 | (17) all_58_11 = e2
% 170.04/26.07 |
% 170.04/26.07 | COMBINE_EQS: (10), (17) imply:
% 170.04/26.07 | (18) e3 = e2
% 170.04/26.07 |
% 170.04/26.07 | COMBINE_EQS: (13), (18) imply:
% 170.04/26.07 | (19) all_58_3 = e2
% 170.04/26.07 |
% 170.04/26.07 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (14), (15),
% 170.04/26.07 | (16), (19) are inconsistent by sub-proof #779.
% 170.04/26.07 |
% 170.04/26.07 End of proof
% 170.04/26.07
% 170.04/26.07 Sub-proof #420 shows that the following formulas are inconsistent:
% 170.04/26.07 ----------------------------------------------------------------
% 170.04/26.07 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.07 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.04/26.07 (2) ~ (all_4_2 = e2)
% 170.04/26.07 (3) all_58_2 = e2
% 170.04/26.07 (4) ~ (e3 = e1)
% 170.04/26.07 (5) ~ (e1 = e0)
% 170.04/26.07 (6) op(e2, e3) = all_52_1
% 170.04/26.07 (7) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.04/26.07 (8) op(e2, e3) = e2
% 170.04/26.07 (9) ~ (e3 = e0)
% 170.04/26.07 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.07 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.04/26.07 (11) op(e0, e0) = all_4_2
% 170.04/26.07 (12) all_58_11 = e3
% 170.04/26.07 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.07 (14) ~ (e2 = e0)
% 170.04/26.07 (15) all_58_3 = e3
% 170.04/26.08 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.04/26.08 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.04/26.08 (17) ~ (e2 = e1)
% 170.04/26.08 (18) ~ (e3 = e2)
% 170.04/26.08
% 170.04/26.08 Begin of proof
% 170.04/26.08 |
% 170.04/26.08 | BETA: splitting (7) gives:
% 170.04/26.08 |
% 170.04/26.08 | Case 1:
% 170.04/26.08 | |
% 170.04/26.08 | | (19) all_58_11 = e2 & op(e1, e0) = e2
% 170.04/26.08 | |
% 170.04/26.08 | | ALPHA: (19) implies:
% 170.04/26.08 | | (20) all_58_11 = e2
% 170.04/26.08 | |
% 170.04/26.08 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (12), (13), (14), (15),
% 170.04/26.08 | | (16), (17), (18), (20) are inconsistent by sub-proof #421.
% 170.04/26.08 | |
% 170.04/26.08 | Case 2:
% 170.04/26.08 | |
% 170.04/26.08 | | (21) all_58_15 = e2 & op(e0, e0) = e2
% 170.04/26.08 | |
% 170.04/26.08 | | REF_CLOSE: (2), (11), (13), (21) are inconsistent by sub-proof #854.
% 170.04/26.08 | |
% 170.04/26.08 | End of split
% 170.04/26.08 |
% 170.04/26.08 End of proof
% 170.04/26.08
% 170.04/26.08 Sub-proof #421 shows that the following formulas are inconsistent:
% 170.04/26.08 ----------------------------------------------------------------
% 170.04/26.08 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.08 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.04/26.08 (2) all_58_2 = e2
% 170.04/26.08 (3) ~ (e3 = e1)
% 170.04/26.08 (4) ~ (e1 = e0)
% 170.04/26.08 (5) all_58_11 = e2
% 170.04/26.08 (6) op(e2, e3) = all_52_1
% 170.04/26.08 (7) op(e2, e3) = e2
% 170.04/26.08 (8) ~ (e3 = e0)
% 170.04/26.08 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.08 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.04/26.08 (10) all_58_11 = e3
% 170.04/26.08 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.08 (12) ~ (e2 = e0)
% 170.04/26.08 (13) all_58_3 = e3
% 170.04/26.08 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.04/26.08 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.04/26.08 (15) ~ (e2 = e1)
% 170.04/26.08 (16) ~ (e3 = e2)
% 170.04/26.08
% 170.04/26.08 Begin of proof
% 170.04/26.08 |
% 170.04/26.08 | COMBINE_EQS: (5), (10) imply:
% 170.04/26.08 | (17) e3 = e2
% 170.04/26.08 |
% 170.04/26.08 | SIMP: (17) implies:
% 170.04/26.08 | (18) e3 = e2
% 170.04/26.08 |
% 170.04/26.08 | COMBINE_EQS: (13), (18) imply:
% 170.04/26.08 | (19) all_58_3 = e2
% 170.04/26.08 |
% 170.04/26.08 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (14), (15),
% 170.04/26.08 | (16), (19) are inconsistent by sub-proof #779.
% 170.04/26.08 |
% 170.04/26.08 End of proof
% 170.04/26.08
% 170.04/26.08 Sub-proof #422 shows that the following formulas are inconsistent:
% 170.04/26.08 ----------------------------------------------------------------
% 170.04/26.08 (1) ~ (e3 = e1)
% 170.04/26.08 (2) ~ (e1 = e0)
% 170.04/26.08 (3) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 170.04/26.08 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.04/26.08 (4) ~ (e3 = e0)
% 170.04/26.08 (5) all_58_14 = e3
% 170.04/26.08 (6) ~ (e2 = e0)
% 170.04/26.08 (7) all_58_8 = e3
% 170.04/26.08 (8) ~ (e2 = e1)
% 170.04/26.08 (9) all_58_4 = e2
% 170.04/26.08 (10) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 170.04/26.08 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 170.04/26.08
% 170.04/26.08 Begin of proof
% 170.04/26.08 |
% 170.04/26.08 | BETA: splitting (3) gives:
% 170.04/26.08 |
% 170.04/26.08 | Case 1:
% 170.04/26.08 | |
% 170.04/26.08 | | (11) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) =
% 170.04/26.08 | | e0)
% 170.04/26.08 | |
% 170.04/26.08 | | BETA: splitting (11) gives:
% 170.04/26.08 | |
% 170.04/26.08 | | Case 1:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (12) all_58_4 = e0 & op(e3, e1) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (6), (9), (12) are inconsistent by sub-proof #946.
% 170.04/26.08 | | |
% 170.04/26.08 | | Case 2:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (13) all_58_5 = e0 & op(e2, e1) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | ALPHA: (13) implies:
% 170.04/26.08 | | | (14) all_58_5 = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | BETA: splitting (10) gives:
% 170.04/26.08 | | |
% 170.04/26.08 | | | Case 1:
% 170.04/26.08 | | | |
% 170.04/26.08 | | | | (15) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1)
% 170.04/26.08 | | | | = e1)
% 170.04/26.08 | | | |
% 170.04/26.08 | | | | BETA: splitting (15) gives:
% 170.04/26.08 | | | |
% 170.04/26.08 | | | | Case 1:
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | | (16) all_58_4 = e1 & op(e3, e1) = e1
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | | REF_CLOSE: (8), (9), (16) are inconsistent by sub-proof #510.
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | Case 2:
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | | (17) all_58_5 = e1 & op(e2, e1) = e1
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | | ALPHA: (17) implies:
% 170.04/26.08 | | | | | (18) all_58_5 = e1
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | | REF_CLOSE: (2), (14), (18) are inconsistent by sub-proof #449.
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | End of split
% 170.04/26.08 | | | |
% 170.04/26.08 | | | Case 2:
% 170.04/26.08 | | | |
% 170.04/26.08 | | | | (19) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1)
% 170.04/26.08 | | | | = e1)
% 170.04/26.08 | | | |
% 170.04/26.08 | | | | BETA: splitting (19) gives:
% 170.04/26.08 | | | |
% 170.04/26.08 | | | | Case 1:
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | | (20) all_58_8 = e1 & op(e1, e1) = e1
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | | REF_CLOSE: (1), (7), (20) are inconsistent by sub-proof #478.
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | Case 2:
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | | (21) all_58_14 = e1 & op(e0, e1) = e1
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | | ALPHA: (21) implies:
% 170.04/26.08 | | | | | (22) all_58_14 = e1
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | | REF_CLOSE: (1), (5), (22) are inconsistent by sub-proof #626.
% 170.04/26.08 | | | | |
% 170.04/26.08 | | | | End of split
% 170.04/26.08 | | | |
% 170.04/26.08 | | | End of split
% 170.04/26.08 | | |
% 170.04/26.08 | | End of split
% 170.04/26.08 | |
% 170.04/26.08 | Case 2:
% 170.04/26.08 | |
% 170.04/26.08 | | (23) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 170.04/26.08 | | e0)
% 170.04/26.08 | |
% 170.04/26.08 | | BETA: splitting (23) gives:
% 170.04/26.08 | |
% 170.04/26.08 | | Case 1:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (24) all_58_8 = e0 & op(e1, e1) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (4), (7), (24) are inconsistent by sub-proof #496.
% 170.04/26.08 | | |
% 170.04/26.08 | | Case 2:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (25) all_58_14 = e0 & op(e0, e1) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | ALPHA: (25) implies:
% 170.04/26.08 | | | (26) all_58_14 = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (4), (5), (26) are inconsistent by sub-proof #423.
% 170.04/26.08 | | |
% 170.04/26.08 | | End of split
% 170.04/26.08 | |
% 170.04/26.08 | End of split
% 170.04/26.08 |
% 170.04/26.08 End of proof
% 170.04/26.08
% 170.04/26.08 Sub-proof #423 shows that the following formulas are inconsistent:
% 170.04/26.08 ----------------------------------------------------------------
% 170.04/26.08 (1) all_58_14 = e3
% 170.04/26.08 (2) all_58_14 = e0
% 170.04/26.08 (3) ~ (e3 = e0)
% 170.04/26.08
% 170.04/26.08 Begin of proof
% 170.04/26.08 |
% 170.04/26.08 | COMBINE_EQS: (1), (2) imply:
% 170.04/26.08 | (4) e3 = e0
% 170.04/26.08 |
% 170.04/26.08 | SIMP: (4) implies:
% 170.04/26.08 | (5) e3 = e0
% 170.04/26.08 |
% 170.04/26.08 | REDUCE: (3), (5) imply:
% 170.04/26.08 | (6) $false
% 170.04/26.08 |
% 170.04/26.08 | CLOSE: (6) is inconsistent.
% 170.04/26.08 |
% 170.04/26.08 End of proof
% 170.04/26.08
% 170.04/26.08 Sub-proof #424 shows that the following formulas are inconsistent:
% 170.04/26.08 ----------------------------------------------------------------
% 170.04/26.08 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.08 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.04/26.08 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.04/26.08 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.04/26.08 (3) all_58_2 = e2
% 170.04/26.08 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.08 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.04/26.08 (5) ~ (e3 = e1)
% 170.04/26.08 (6) ~ (e1 = e0)
% 170.04/26.08 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.04/26.08 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.04/26.08 (8) op(e1, e2) = all_52_6
% 170.04/26.08 (9) op(e2, e3) = all_52_1
% 170.04/26.08 (10) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 170.04/26.08 (11) op(e2, e3) = e2
% 170.04/26.08 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.04/26.08 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.04/26.08 (13) ~ (e3 = e0)
% 170.04/26.08 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.08 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.04/26.08 (15) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 170.04/26.08 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 170.04/26.08 e2) = all_22_1 & $i(all_22_1))
% 170.04/26.08 (16) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.08 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.04/26.08 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.08 (18) ~ (e2 = e0)
% 170.04/26.08 (19) all_58_3 = e3
% 170.04/26.08 (20) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.04/26.08 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.04/26.08 (21) ~ (e2 = e1)
% 170.04/26.08 (22) op(e3, e2) = all_52_4
% 170.04/26.08 (23) all_58_7 = e3
% 170.04/26.08 (24) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 170.04/26.08 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 170.04/26.08 e2) = all_14_1 & $i(all_14_1))
% 170.04/26.08 (25) ~ (e3 = e2)
% 170.04/26.08
% 170.04/26.08 Begin of proof
% 170.04/26.08 |
% 170.04/26.08 | BETA: splitting (10) gives:
% 170.04/26.08 |
% 170.04/26.08 | Case 1:
% 170.04/26.08 | |
% 170.04/26.08 | | (26) all_58_12 = e2 & op(e0, e3) = e2
% 170.04/26.08 | |
% 170.04/26.08 | | ALPHA: (26) implies:
% 170.04/26.08 | | (27) all_58_12 = e2
% 170.04/26.08 | |
% 170.04/26.08 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (11), (12), (13), (14), (17),
% 170.04/26.08 | | (18), (19), (20), (21), (25), (27) are inconsistent by sub-proof
% 170.04/26.08 | | #433.
% 170.04/26.08 | |
% 170.04/26.08 | Case 2:
% 170.04/26.08 | |
% 170.04/26.08 | | (28) all_58_13 = e2 & op(e0, e2) = e2
% 170.04/26.08 | |
% 170.04/26.08 | | REF_CLOSE: (4), (5), (6), (8), (13), (15), (16), (17), (18), (19), (22),
% 170.04/26.08 | | (23), (24), (28) are inconsistent by sub-proof #425.
% 170.04/26.08 | |
% 170.04/26.08 | End of split
% 170.04/26.08 |
% 170.04/26.08 End of proof
% 170.04/26.08
% 170.04/26.08 Sub-proof #425 shows that the following formulas are inconsistent:
% 170.04/26.08 ----------------------------------------------------------------
% 170.04/26.08 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.08 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.04/26.08 (2) ~ (e3 = e1)
% 170.04/26.08 (3) ~ (e1 = e0)
% 170.04/26.08 (4) op(e1, e2) = all_52_6
% 170.04/26.08 (5) ~ (e3 = e0)
% 170.04/26.08 (6) all_58_13 = e2 & op(e0, e2) = e2
% 170.04/26.08 (7) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) = all_22_1
% 170.04/26.08 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2) =
% 170.04/26.08 all_22_1 & $i(all_22_1))
% 170.04/26.08 (8) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.08 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.04/26.08 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.08 (10) ~ (e2 = e0)
% 170.04/26.08 (11) all_58_3 = e3
% 170.04/26.08 (12) op(e3, e2) = all_52_4
% 170.04/26.08 (13) all_58_7 = e3
% 170.04/26.08 (14) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 170.04/26.08 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 170.04/26.08 e2) = all_14_1 & $i(all_14_1))
% 170.04/26.08
% 170.04/26.08 Begin of proof
% 170.04/26.08 |
% 170.04/26.08 | ALPHA: (6) implies:
% 170.04/26.08 | (15) all_58_13 = e2
% 170.04/26.08 |
% 170.04/26.08 | BETA: splitting (8) gives:
% 170.04/26.08 |
% 170.04/26.08 | Case 1:
% 170.04/26.08 | |
% 170.04/26.08 | | (16) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 170.04/26.08 | | e0)
% 170.04/26.08 | |
% 170.04/26.08 | | BETA: splitting (16) gives:
% 170.04/26.08 | |
% 170.04/26.08 | | Case 1:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (17) all_58_1 = e0 & op(e3, e2) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | ALPHA: (17) implies:
% 170.04/26.08 | | | (18) op(e3, e2) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 170.04/26.08 | | | (14), (15), (18) are inconsistent by sub-proof #428.
% 170.04/26.08 | | |
% 170.04/26.08 | | Case 2:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (19) all_58_3 = e0 & op(e2, e2) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (5), (11), (19) are inconsistent by sub-proof #427.
% 170.04/26.08 | | |
% 170.04/26.08 | | End of split
% 170.04/26.08 | |
% 170.04/26.08 | Case 2:
% 170.04/26.08 | |
% 170.04/26.08 | | (20) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 170.04/26.08 | | e0)
% 170.04/26.08 | |
% 170.04/26.08 | | REF_CLOSE: (5), (10), (13), (15), (20) are inconsistent by sub-proof #426.
% 170.04/26.08 | |
% 170.04/26.08 | End of split
% 170.04/26.08 |
% 170.04/26.08 End of proof
% 170.04/26.08
% 170.04/26.08 Sub-proof #426 shows that the following formulas are inconsistent:
% 170.04/26.08 ----------------------------------------------------------------
% 170.04/26.08 (1) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.04/26.08 (2) ~ (e3 = e0)
% 170.04/26.08 (3) all_58_13 = e2
% 170.04/26.08 (4) ~ (e2 = e0)
% 170.04/26.08 (5) all_58_7 = e3
% 170.04/26.08
% 170.04/26.08 Begin of proof
% 170.04/26.08 |
% 170.04/26.08 | BETA: splitting (1) gives:
% 170.04/26.08 |
% 170.04/26.08 | Case 1:
% 170.04/26.08 | |
% 170.04/26.08 | | (6) all_58_7 = e0 & op(e1, e2) = e0
% 170.04/26.08 | |
% 170.04/26.08 | | ALPHA: (6) implies:
% 170.04/26.08 | | (7) all_58_7 = e0
% 170.04/26.08 | |
% 170.04/26.08 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #748.
% 170.04/26.08 | |
% 170.04/26.08 | Case 2:
% 170.04/26.08 | |
% 170.04/26.08 | | (8) all_58_13 = e0 & op(e0, e2) = e0
% 170.04/26.08 | |
% 170.04/26.08 | | ALPHA: (8) implies:
% 170.04/26.08 | | (9) all_58_13 = e0
% 170.04/26.08 | |
% 170.04/26.08 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #865.
% 170.04/26.08 | |
% 170.04/26.08 | End of split
% 170.04/26.08 |
% 170.04/26.08 End of proof
% 170.04/26.08
% 170.04/26.08 Sub-proof #427 shows that the following formulas are inconsistent:
% 170.04/26.08 ----------------------------------------------------------------
% 170.04/26.08 (1) all_58_3 = e0 & op(e2, e2) = e0
% 170.04/26.08 (2) all_58_3 = e3
% 170.04/26.08 (3) ~ (e3 = e0)
% 170.04/26.08
% 170.04/26.08 Begin of proof
% 170.04/26.08 |
% 170.04/26.08 | ALPHA: (1) implies:
% 170.04/26.08 | (4) all_58_3 = e0
% 170.04/26.08 |
% 170.04/26.08 | COMBINE_EQS: (2), (4) imply:
% 170.04/26.08 | (5) e3 = e0
% 170.04/26.08 |
% 170.04/26.08 | SIMP: (5) implies:
% 170.04/26.08 | (6) e3 = e0
% 170.04/26.08 |
% 170.04/26.08 | REDUCE: (3), (6) imply:
% 170.04/26.08 | (7) $false
% 170.04/26.08 |
% 170.04/26.08 | CLOSE: (7) is inconsistent.
% 170.04/26.08 |
% 170.04/26.08 End of proof
% 170.04/26.08
% 170.04/26.08 Sub-proof #428 shows that the following formulas are inconsistent:
% 170.04/26.08 ----------------------------------------------------------------
% 170.04/26.08 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.08 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.04/26.08 (2) ~ (e3 = e1)
% 170.04/26.08 (3) ~ (e1 = e0)
% 170.04/26.08 (4) op(e1, e2) = all_52_6
% 170.04/26.08 (5) ~ (e3 = e0)
% 170.04/26.08 (6) all_58_13 = e2
% 170.04/26.08 (7) op(e3, e2) = e0
% 170.04/26.08 (8) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) = all_22_1
% 170.04/26.08 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2) =
% 170.04/26.08 all_22_1 & $i(all_22_1))
% 170.04/26.08 (9) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.08 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.04/26.08 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.08 (11) ~ (e2 = e0)
% 170.04/26.08 (12) all_58_3 = e3
% 170.04/26.08 (13) op(e3, e2) = all_52_4
% 170.04/26.08 (14) all_58_7 = e3
% 170.04/26.08 (15) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 170.04/26.08 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 170.04/26.08 e2) = all_14_1 & $i(all_14_1))
% 170.04/26.08
% 170.04/26.08 Begin of proof
% 170.04/26.08 |
% 170.04/26.08 | BETA: splitting (1) gives:
% 170.04/26.08 |
% 170.04/26.08 | Case 1:
% 170.04/26.08 | |
% 170.04/26.08 | | (16) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 170.04/26.08 | | e1)
% 170.04/26.08 | |
% 170.04/26.08 | | BETA: splitting (16) gives:
% 170.04/26.08 | |
% 170.04/26.08 | | Case 1:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (17) all_58_1 = e1 & op(e3, e2) = e1
% 170.04/26.08 | | |
% 170.04/26.08 | | | ALPHA: (17) implies:
% 170.04/26.08 | | | (18) all_58_1 = e1
% 170.04/26.08 | | | (19) op(e3, e2) = e1
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 170.04/26.08 | | | (18), (19) are inconsistent by sub-proof #429.
% 170.04/26.08 | | |
% 170.04/26.08 | | Case 2:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (20) all_58_3 = e1 & op(e2, e2) = e1
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (2), (12), (20) are inconsistent by sub-proof #868.
% 170.04/26.08 | | |
% 170.04/26.08 | | End of split
% 170.04/26.08 | |
% 170.04/26.08 | Case 2:
% 170.04/26.08 | |
% 170.04/26.08 | | (21) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 170.04/26.08 | | e1)
% 170.04/26.08 | |
% 170.04/26.08 | | BETA: splitting (21) gives:
% 170.04/26.08 | |
% 170.04/26.08 | | Case 1:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (22) all_58_7 = e1 & op(e1, e2) = e1
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (2), (14), (22) are inconsistent by sub-proof #757.
% 170.04/26.08 | | |
% 170.04/26.08 | | Case 2:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (23) all_58_13 = e1 & op(e0, e2) = e1
% 170.04/26.08 | | |
% 170.04/26.08 | | | ALPHA: (23) implies:
% 170.04/26.08 | | | (24) op(e0, e2) = e1
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (7), (8), (10), (24) are inconsistent by sub-proof #443.
% 170.04/26.08 | | |
% 170.04/26.08 | | End of split
% 170.04/26.08 | |
% 170.04/26.08 | End of split
% 170.04/26.08 |
% 170.04/26.08 End of proof
% 170.04/26.08
% 170.04/26.08 Sub-proof #429 shows that the following formulas are inconsistent:
% 170.04/26.08 ----------------------------------------------------------------
% 170.04/26.08 (1) all_58_1 = e1
% 170.04/26.08 (2) op(e3, e2) = e1
% 170.04/26.08 (3) ~ (e1 = e0)
% 170.04/26.08 (4) op(e1, e2) = all_52_6
% 170.04/26.08 (5) ~ (e3 = e0)
% 170.04/26.08 (6) all_58_13 = e2
% 170.04/26.08 (7) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) = all_22_1
% 170.04/26.08 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2) =
% 170.04/26.08 all_22_1 & $i(all_22_1))
% 170.04/26.08 (8) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.08 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.04/26.08 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.08 (10) ~ (e2 = e0)
% 170.04/26.08 (11) all_58_3 = e3
% 170.04/26.08 (12) op(e3, e2) = all_52_4
% 170.04/26.08 (13) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 170.04/26.08 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3,
% 170.04/26.08 e2) = all_14_1 & $i(all_14_1))
% 170.04/26.08
% 170.04/26.08 Begin of proof
% 170.04/26.08 |
% 170.04/26.08 | BETA: splitting (8) gives:
% 170.04/26.08 |
% 170.04/26.08 | Case 1:
% 170.04/26.08 | |
% 170.04/26.08 | | (14) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 170.04/26.08 | | e0)
% 170.04/26.08 | |
% 170.04/26.08 | | BETA: splitting (14) gives:
% 170.04/26.08 | |
% 170.04/26.08 | | Case 1:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (15) all_58_1 = e0 & op(e3, e2) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (1), (3), (15) are inconsistent by sub-proof #948.
% 170.04/26.08 | | |
% 170.04/26.08 | | Case 2:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (16) all_58_3 = e0 & op(e2, e2) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (5), (11), (16) are inconsistent by sub-proof #869.
% 170.04/26.08 | | |
% 170.04/26.08 | | End of split
% 170.04/26.08 | |
% 170.04/26.08 | Case 2:
% 170.04/26.08 | |
% 170.04/26.08 | | (17) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 170.04/26.08 | | e0)
% 170.04/26.08 | |
% 170.04/26.08 | | BETA: splitting (17) gives:
% 170.04/26.08 | |
% 170.04/26.08 | | Case 1:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (18) all_58_7 = e0 & op(e1, e2) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | ALPHA: (18) implies:
% 170.04/26.08 | | | (19) op(e1, e2) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (2), (4), (7), (9), (12), (13), (19) are inconsistent by
% 170.04/26.08 | | | sub-proof #430.
% 170.04/26.08 | | |
% 170.04/26.08 | | Case 2:
% 170.04/26.08 | | |
% 170.04/26.08 | | | (20) all_58_13 = e0 & op(e0, e2) = e0
% 170.04/26.08 | | |
% 170.04/26.08 | | | REF_CLOSE: (6), (10), (20) are inconsistent by sub-proof #872.
% 170.04/26.08 | | |
% 170.04/26.08 | | End of split
% 170.04/26.08 | |
% 170.04/26.08 | End of split
% 170.04/26.08 |
% 170.04/26.08 End of proof
% 170.04/26.08
% 170.04/26.08 Sub-proof #430 shows that the following formulas are inconsistent:
% 170.04/26.08 ----------------------------------------------------------------
% 170.04/26.08 (1) op(e3, e2) = e1
% 170.04/26.08 (2) op(e1, e2) = all_52_6
% 170.04/26.08 (3) op(e1, e2) = e0
% 170.04/26.08 (4) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) = all_22_1
% 170.04/26.08 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2) =
% 170.04/26.08 all_22_1 & $i(all_22_1))
% 170.04/26.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.09 (6) op(e3, e2) = all_52_4
% 170.04/26.09 (7) ( ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) = all_14_1
% 170.04/26.09 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) & op(e3, e2) =
% 170.04/26.09 all_14_1 & $i(all_14_1))
% 170.04/26.09
% 170.04/26.09 Begin of proof
% 170.04/26.09 |
% 170.04/26.09 | GROUND_INST: instantiating (5) with all_52_6, e0, e2, e1, simplifying with
% 170.04/26.09 | (2), (3) gives:
% 170.04/26.09 | (8) all_52_6 = e0
% 170.04/26.09 |
% 170.04/26.09 | GROUND_INST: instantiating (5) with all_52_4, e1, e2, e3, simplifying with
% 170.04/26.09 | (1), (6) gives:
% 170.04/26.09 | (9) all_52_4 = e1
% 170.04/26.09 |
% 170.04/26.09 | BETA: splitting (7) gives:
% 170.04/26.09 |
% 170.04/26.09 | Case 1:
% 170.04/26.09 | |
% 170.04/26.09 | | (10) ~ (all_14_0 = e0) & op(all_14_1, e2) = all_14_0 & op(e3, e2) =
% 170.04/26.09 | | all_14_1 & $i(all_14_0) & $i(all_14_1)
% 170.04/26.09 | |
% 170.04/26.09 | | ALPHA: (10) implies:
% 170.04/26.09 | | (11) ~ (all_14_0 = e0)
% 170.04/26.09 | | (12) op(e3, e2) = all_14_1
% 170.04/26.09 | | (13) op(all_14_1, e2) = all_14_0
% 170.04/26.09 | |
% 170.04/26.09 | | BETA: splitting (4) gives:
% 170.04/26.09 | |
% 170.04/26.09 | | Case 1:
% 170.04/26.09 | | |
% 170.04/26.09 | | | (14) ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 170.04/26.09 | | | all_22_1 & $i(all_22_0) & $i(all_22_1)
% 170.04/26.09 | | |
% 170.04/26.09 | | | ALPHA: (14) implies:
% 170.04/26.09 | | | (15) op(e3, e2) = all_22_1
% 170.04/26.09 | | |
% 170.04/26.09 | | | REF_CLOSE: (1), (3), (5), (11), (12), (13), (15) are inconsistent by
% 170.04/26.09 | | | sub-proof #432.
% 170.04/26.09 | | |
% 170.04/26.09 | | Case 2:
% 170.04/26.09 | | |
% 170.04/26.09 | | | (16) ~ (all_22_1 = e0) & op(e3, e2) = all_22_1 & $i(all_22_1)
% 170.04/26.09 | | |
% 170.04/26.09 | | | ALPHA: (16) implies:
% 170.04/26.09 | | | (17) op(e3, e2) = all_22_1
% 170.04/26.09 | | |
% 170.04/26.09 | | | REF_CLOSE: (1), (3), (5), (11), (12), (13), (17) are inconsistent by
% 170.04/26.09 | | | sub-proof #432.
% 170.04/26.09 | | |
% 170.04/26.09 | | End of split
% 170.04/26.09 | |
% 170.04/26.09 | Case 2:
% 170.04/26.09 | |
% 170.04/26.09 | | (18) ~ (all_14_1 = e1) & op(e3, e2) = all_14_1 & $i(all_14_1)
% 170.04/26.09 | |
% 170.04/26.09 | | ALPHA: (18) implies:
% 170.04/26.09 | | (19) ~ (all_14_1 = e1)
% 170.04/26.09 | | (20) op(e3, e2) = all_14_1
% 170.04/26.09 | |
% 170.04/26.09 | | BETA: splitting (4) gives:
% 170.04/26.09 | |
% 170.04/26.09 | | Case 1:
% 170.04/26.09 | | |
% 170.04/26.09 | | | (21) ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 170.04/26.09 | | | all_22_1 & $i(all_22_0) & $i(all_22_1)
% 170.04/26.09 | | |
% 170.04/26.09 | | | ALPHA: (21) implies:
% 170.04/26.09 | | | (22) op(e3, e2) = all_22_1
% 170.04/26.09 | | |
% 170.04/26.09 | | | REF_CLOSE: (1), (5), (19), (20), (22) are inconsistent by sub-proof #431.
% 170.04/26.09 | | |
% 170.04/26.09 | | Case 2:
% 170.04/26.09 | | |
% 170.04/26.09 | | | (23) ~ (all_22_1 = e0) & op(e3, e2) = all_22_1 & $i(all_22_1)
% 170.04/26.09 | | |
% 170.04/26.09 | | | ALPHA: (23) implies:
% 170.04/26.09 | | | (24) op(e3, e2) = all_22_1
% 170.04/26.09 | | |
% 170.04/26.09 | | | REF_CLOSE: (1), (5), (19), (20), (24) are inconsistent by sub-proof #431.
% 170.04/26.09 | | |
% 170.04/26.09 | | End of split
% 170.04/26.09 | |
% 170.04/26.09 | End of split
% 170.04/26.09 |
% 170.04/26.09 End of proof
% 170.04/26.09
% 170.04/26.09 Sub-proof #431 shows that the following formulas are inconsistent:
% 170.04/26.09 ----------------------------------------------------------------
% 170.04/26.09 (1) op(e3, e2) = all_14_1
% 170.04/26.09 (2) op(e3, e2) = e1
% 170.04/26.09 (3) op(e3, e2) = all_22_1
% 170.04/26.09 (4) ~ (all_14_1 = e1)
% 170.04/26.09 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.09
% 170.04/26.09 Begin of proof
% 170.04/26.09 |
% 170.04/26.09 | GROUND_INST: instantiating (5) with e1, all_22_1, e2, e3, simplifying with
% 170.04/26.09 | (2), (3) gives:
% 170.04/26.09 | (6) all_22_1 = e1
% 170.04/26.09 |
% 170.04/26.09 | GROUND_INST: instantiating (5) with all_14_1, all_22_1, e2, e3, simplifying
% 170.04/26.09 | with (1), (3) gives:
% 170.04/26.09 | (7) all_22_1 = all_14_1
% 170.04/26.09 |
% 170.04/26.09 | COMBINE_EQS: (6), (7) imply:
% 170.04/26.09 | (8) all_14_1 = e1
% 170.04/26.09 |
% 170.04/26.09 | REDUCE: (4), (8) imply:
% 170.04/26.09 | (9) $false
% 170.04/26.09 |
% 170.04/26.09 | CLOSE: (9) is inconsistent.
% 170.04/26.09 |
% 170.04/26.09 End of proof
% 170.04/26.09
% 170.04/26.09 Sub-proof #432 shows that the following formulas are inconsistent:
% 170.04/26.09 ----------------------------------------------------------------
% 170.04/26.09 (1) op(all_14_1, e2) = all_14_0
% 170.04/26.09 (2) op(e3, e2) = all_14_1
% 170.04/26.09 (3) op(e3, e2) = e1
% 170.04/26.09 (4) op(e3, e2) = all_22_1
% 170.04/26.09 (5) op(e1, e2) = e0
% 170.04/26.09 (6) ~ (all_14_0 = e0)
% 170.04/26.09 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.09
% 170.04/26.09 Begin of proof
% 170.04/26.09 |
% 170.04/26.09 | GROUND_INST: instantiating (7) with e1, all_22_1, e2, e3, simplifying with
% 170.04/26.09 | (3), (4) gives:
% 170.04/26.09 | (8) all_22_1 = e1
% 170.04/26.09 |
% 170.04/26.09 | GROUND_INST: instantiating (7) with all_14_1, all_22_1, e2, e3, simplifying
% 170.04/26.09 | with (2), (4) gives:
% 170.04/26.09 | (9) all_22_1 = all_14_1
% 170.04/26.09 |
% 170.04/26.09 | COMBINE_EQS: (8), (9) imply:
% 170.04/26.09 | (10) all_14_1 = e1
% 170.04/26.09 |
% 170.04/26.09 | REDUCE: (1), (10) imply:
% 170.04/26.09 | (11) op(e1, e2) = all_14_0
% 170.04/26.09 |
% 170.04/26.09 | GROUND_INST: instantiating (7) with e0, all_14_0, e2, e1, simplifying with
% 170.04/26.09 | (5), (11) gives:
% 170.04/26.09 | (12) all_14_0 = e0
% 170.04/26.09 |
% 170.04/26.09 | REDUCE: (6), (12) imply:
% 170.04/26.09 | (13) $false
% 170.04/26.09 |
% 170.04/26.09 | CLOSE: (13) is inconsistent.
% 170.04/26.09 |
% 170.04/26.09 End of proof
% 170.04/26.09
% 170.04/26.09 Sub-proof #433 shows that the following formulas are inconsistent:
% 170.04/26.09 ----------------------------------------------------------------
% 170.04/26.09 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.04/26.09 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.04/26.09 (2) all_58_12 = e2
% 170.04/26.09 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.04/26.09 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.04/26.09 (4) all_58_2 = e2
% 170.04/26.09 (5) ~ (e3 = e1)
% 170.04/26.09 (6) ~ (e1 = e0)
% 170.04/26.09 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.04/26.09 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.04/26.09 (8) op(e2, e3) = all_52_1
% 170.04/26.09 (9) op(e2, e3) = e2
% 170.04/26.09 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.04/26.09 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.04/26.09 (11) ~ (e3 = e0)
% 170.04/26.09 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.04/26.09 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.04/26.09 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.04/26.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.04/26.09 (14) ~ (e2 = e0)
% 170.04/26.09 (15) all_58_3 = e3
% 170.04/26.09 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.04/26.09 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.04/26.09 (17) ~ (e2 = e1)
% 170.04/26.09 (18) ~ (e3 = e2)
% 170.04/26.09
% 170.04/26.09 Begin of proof
% 170.04/26.09 |
% 170.04/26.09 | BETA: splitting (7) gives:
% 170.04/26.09 |
% 170.04/26.09 | Case 1:
% 170.04/26.09 | |
% 170.04/26.09 | | (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 170.04/26.09 | | e3)
% 170.04/26.09 | |
% 170.04/26.09 | | BETA: splitting (19) gives:
% 170.04/26.09 | |
% 170.04/26.09 | | Case 1:
% 170.04/26.09 | | |
% 170.04/26.09 | | | (20) all_58_0 = e3 & op(e3, e3) = e3
% 170.04/26.09 | | |
% 170.04/26.09 | | | ALPHA: (20) implies:
% 170.04/26.09 | | | (21) all_58_0 = e3
% 170.04/26.09 | | |
% 170.04/26.09 | | | BETA: splitting (10) gives:
% 170.04/26.09 | | |
% 170.04/26.09 | | | Case 1:
% 170.04/26.09 | | | |
% 170.04/26.09 | | | | (22) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 170.04/26.09 | | | | = e1)
% 170.04/26.09 | | | |
% 170.04/26.09 | | | | BETA: splitting (22) gives:
% 170.04/26.09 | | | |
% 170.04/26.09 | | | | Case 1:
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | | (23) all_58_0 = e1 & op(e3, e3) = e1
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | | ALPHA: (23) implies:
% 170.04/26.09 | | | | | (24) all_58_0 = e1
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (11), (14), (18), (24) are
% 170.04/26.09 | | | | | inconsistent by sub-proof #435.
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | Case 2:
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | | (25) all_58_2 = e1 & op(e2, e3) = e1
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | | REF_CLOSE: (4), (17), (25) are inconsistent by sub-proof #829.
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | End of split
% 170.04/26.09 | | | |
% 170.04/26.09 | | | Case 2:
% 170.04/26.09 | | | |
% 170.04/26.09 | | | | (26) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 170.04/26.09 | | | | = e1)
% 170.04/26.09 | | | |
% 170.04/26.09 | | | | BETA: splitting (26) gives:
% 170.04/26.09 | | | |
% 170.04/26.09 | | | | Case 1:
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | | (27) all_58_6 = e1 & op(e1, e3) = e1
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | | ALPHA: (27) implies:
% 170.04/26.09 | | | | | (28) all_58_6 = e1
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | | REF_CLOSE: (2), (3), (4), (6), (11), (14), (21), (28) are inconsistent
% 170.04/26.09 | | | | | by sub-proof #434.
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | Case 2:
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | | (29) all_58_12 = e1 & op(e0, e3) = e1
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | | REF_CLOSE: (2), (17), (29) are inconsistent by sub-proof #891.
% 170.04/26.09 | | | | |
% 170.04/26.09 | | | | End of split
% 170.04/26.09 | | | |
% 170.04/26.09 | | | End of split
% 170.04/26.09 | | |
% 170.04/26.09 | | Case 2:
% 170.04/26.09 | | |
% 170.04/26.09 | | | (30) all_58_2 = e3 & op(e2, e3) = e3
% 170.04/26.09 | | |
% 170.04/26.09 | | | ALPHA: (30) implies:
% 170.04/26.09 | | | (31) op(e2, e3) = e3
% 170.04/26.09 | | |
% 170.04/26.09 | | | REF_CLOSE: (8), (9), (13), (18), (31) are inconsistent by sub-proof #462.
% 170.04/26.09 | | |
% 170.04/26.09 | | End of split
% 170.04/26.09 | |
% 170.04/26.09 | Case 2:
% 170.04/26.09 | |
% 170.04/26.09 | | (32) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 170.04/26.09 | | e3)
% 170.04/26.09 | |
% 170.04/26.09 | | BETA: splitting (32) gives:
% 170.04/26.09 | |
% 170.04/26.09 | | Case 1:
% 170.04/26.09 | | |
% 170.04/26.09 | | | (33) all_58_6 = e3 & op(e1, e3) = e3
% 170.04/26.09 | | |
% 170.04/26.09 | | | ALPHA: (33) implies:
% 170.04/26.09 | | | (34) all_58_6 = e3
% 170.04/26.09 | | |
% 170.04/26.09 | | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (13), (14), (17),
% 170.04/26.09 | | | (34) are inconsistent by sub-proof #461.
% 170.04/26.09 | | |
% 170.04/26.09 | | Case 2:
% 170.04/26.09 | | |
% 170.04/26.09 | | | (35) all_58_12 = e3 & op(e0, e3) = e3
% 170.04/26.09 | | |
% 170.04/26.09 | | | ALPHA: (35) implies:
% 170.04/26.09 | | | (36) all_58_12 = e3
% 170.04/26.09 | | |
% 170.04/26.09 | | | COMBINE_EQS: (2), (36) imply:
% 170.04/26.09 | | | (37) e3 = e2
% 170.04/26.09 | | |
% 170.04/26.09 | | | COMBINE_EQS: (15), (37) imply:
% 170.11/26.09 | | | (38) all_58_3 = e2
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (11), (12), (13), (14), (16),
% 170.11/26.09 | | | (17), (18), (38) are inconsistent by sub-proof #779.
% 170.11/26.09 | | |
% 170.11/26.09 | | End of split
% 170.11/26.09 | |
% 170.11/26.09 | End of split
% 170.11/26.09 |
% 170.11/26.09 End of proof
% 170.11/26.09
% 170.11/26.09 Sub-proof #434 shows that the following formulas are inconsistent:
% 170.11/26.09 ----------------------------------------------------------------
% 170.11/26.09 (1) all_58_12 = e2
% 170.11/26.09 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.09 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.09 (3) all_58_2 = e2
% 170.11/26.09 (4) all_58_6 = e1
% 170.11/26.09 (5) ~ (e1 = e0)
% 170.11/26.09 (6) ~ (e3 = e0)
% 170.11/26.09 (7) all_58_0 = e3
% 170.11/26.09 (8) ~ (e2 = e0)
% 170.11/26.09
% 170.11/26.09 Begin of proof
% 170.11/26.09 |
% 170.11/26.09 | BETA: splitting (2) gives:
% 170.11/26.09 |
% 170.11/26.09 | Case 1:
% 170.11/26.09 | |
% 170.11/26.09 | | (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 170.11/26.09 | |
% 170.11/26.09 | | BETA: splitting (9) gives:
% 170.11/26.09 | |
% 170.11/26.09 | | Case 1:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (10) all_58_0 = e0 & op(e3, e3) = e0
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (6), (7), (10) are inconsistent by sub-proof #898.
% 170.11/26.09 | | |
% 170.11/26.09 | | Case 2:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (11) all_58_2 = e0 & op(e2, e3) = e0
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (3), (8), (11) are inconsistent by sub-proof #928.
% 170.11/26.09 | | |
% 170.11/26.09 | | End of split
% 170.11/26.09 | |
% 170.11/26.09 | Case 2:
% 170.11/26.09 | |
% 170.11/26.09 | | (12) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 170.11/26.09 | | e0)
% 170.11/26.09 | |
% 170.11/26.09 | | BETA: splitting (12) gives:
% 170.11/26.09 | |
% 170.11/26.09 | | Case 1:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (13) all_58_6 = e0 & op(e1, e3) = e0
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #457.
% 170.11/26.09 | | |
% 170.11/26.09 | | Case 2:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (14) all_58_12 = e0 & op(e0, e3) = e0
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #886.
% 170.11/26.09 | | |
% 170.11/26.09 | | End of split
% 170.11/26.09 | |
% 170.11/26.09 | End of split
% 170.11/26.09 |
% 170.11/26.09 End of proof
% 170.11/26.09
% 170.11/26.09 Sub-proof #435 shows that the following formulas are inconsistent:
% 170.11/26.09 ----------------------------------------------------------------
% 170.11/26.09 (1) all_58_12 = e2
% 170.11/26.09 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.09 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.09 (3) all_58_2 = e2
% 170.11/26.09 (4) all_58_0 = e1
% 170.11/26.09 (5) ~ (e3 = e1)
% 170.11/26.09 (6) ~ (e1 = e0)
% 170.11/26.09 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.11/26.09 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.11/26.09 (8) ~ (e3 = e0)
% 170.11/26.09 (9) ~ (e2 = e0)
% 170.11/26.09 (10) ~ (e3 = e2)
% 170.11/26.09
% 170.11/26.09 Begin of proof
% 170.11/26.09 |
% 170.11/26.09 | BETA: splitting (7) gives:
% 170.11/26.09 |
% 170.11/26.09 | Case 1:
% 170.11/26.09 | |
% 170.11/26.09 | | (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 170.11/26.09 | | e3)
% 170.11/26.09 | |
% 170.11/26.09 | | BETA: splitting (11) gives:
% 170.11/26.09 | |
% 170.11/26.09 | | Case 1:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (12) all_58_0 = e3 & op(e3, e3) = e3
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #905.
% 170.11/26.09 | | |
% 170.11/26.09 | | Case 2:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (13) all_58_2 = e3 & op(e2, e3) = e3
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (3), (10), (13) are inconsistent by sub-proof #786.
% 170.11/26.09 | | |
% 170.11/26.09 | | End of split
% 170.11/26.09 | |
% 170.11/26.09 | Case 2:
% 170.11/26.09 | |
% 170.11/26.09 | | (14) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 170.11/26.09 | | e3)
% 170.11/26.09 | |
% 170.11/26.09 | | BETA: splitting (14) gives:
% 170.11/26.09 | |
% 170.11/26.09 | | Case 1:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (15) all_58_6 = e3 & op(e1, e3) = e3
% 170.11/26.09 | | |
% 170.11/26.09 | | | ALPHA: (15) implies:
% 170.11/26.09 | | | (16) all_58_6 = e3
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (16) are inconsistent by
% 170.11/26.09 | | | sub-proof #436.
% 170.11/26.09 | | |
% 170.11/26.09 | | Case 2:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (17) all_58_12 = e3 & op(e0, e3) = e3
% 170.11/26.09 | | |
% 170.11/26.09 | | | ALPHA: (17) implies:
% 170.11/26.09 | | | (18) all_58_12 = e3
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (1), (10), (18) are inconsistent by sub-proof #635.
% 170.11/26.09 | | |
% 170.11/26.09 | | End of split
% 170.11/26.09 | |
% 170.11/26.09 | End of split
% 170.11/26.09 |
% 170.11/26.09 End of proof
% 170.11/26.09
% 170.11/26.09 Sub-proof #436 shows that the following formulas are inconsistent:
% 170.11/26.09 ----------------------------------------------------------------
% 170.11/26.09 (1) all_58_12 = e2
% 170.11/26.09 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.09 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.09 (3) all_58_2 = e2
% 170.11/26.09 (4) all_58_0 = e1
% 170.11/26.09 (5) all_58_6 = e3
% 170.11/26.09 (6) ~ (e1 = e0)
% 170.11/26.09 (7) ~ (e3 = e0)
% 170.11/26.09 (8) ~ (e2 = e0)
% 170.11/26.09
% 170.11/26.09 Begin of proof
% 170.11/26.09 |
% 170.11/26.09 | BETA: splitting (2) gives:
% 170.11/26.09 |
% 170.11/26.09 | Case 1:
% 170.11/26.09 | |
% 170.11/26.09 | | (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 170.11/26.09 | |
% 170.11/26.09 | | BETA: splitting (9) gives:
% 170.11/26.09 | |
% 170.11/26.09 | | Case 1:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (10) all_58_0 = e0 & op(e3, e3) = e0
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #903.
% 170.11/26.09 | | |
% 170.11/26.09 | | Case 2:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (11) all_58_2 = e0 & op(e2, e3) = e0
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (3), (8), (11) are inconsistent by sub-proof #928.
% 170.11/26.09 | | |
% 170.11/26.09 | | End of split
% 170.11/26.09 | |
% 170.11/26.09 | Case 2:
% 170.11/26.09 | |
% 170.11/26.09 | | (12) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 170.11/26.09 | | e0)
% 170.11/26.09 | |
% 170.11/26.09 | | BETA: splitting (12) gives:
% 170.11/26.09 | |
% 170.11/26.09 | | Case 1:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (13) all_58_6 = e0 & op(e1, e3) = e0
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #559.
% 170.11/26.09 | | |
% 170.11/26.09 | | Case 2:
% 170.11/26.09 | | |
% 170.11/26.09 | | | (14) all_58_12 = e0 & op(e0, e3) = e0
% 170.11/26.09 | | |
% 170.11/26.09 | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #886.
% 170.11/26.09 | | |
% 170.11/26.09 | | End of split
% 170.11/26.09 | |
% 170.11/26.09 | End of split
% 170.11/26.09 |
% 170.11/26.09 End of proof
% 170.11/26.09
% 170.11/26.09 Sub-proof #437 shows that the following formulas are inconsistent:
% 170.11/26.09 ----------------------------------------------------------------
% 170.11/26.09 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.11/26.09 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.11/26.09 (2) ~ (all_4_2 = e2)
% 170.11/26.09 (3) all_58_2 = e2
% 170.11/26.09 (4) ~ (e3 = e1)
% 170.11/26.09 (5) ~ (e1 = e0)
% 170.11/26.09 (6) op(e2, e3) = all_52_1
% 170.11/26.09 (7) op(e2, e3) = e2
% 170.11/26.09 (8) ~ (e3 = e0)
% 170.11/26.09 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.11/26.09 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.11/26.09 (10) op(e0, e0) = all_4_2
% 170.11/26.09 (11) all_58_14 = e3
% 170.11/26.09 (12) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.11/26.09 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.10 (14) ~ (e2 = e0)
% 170.11/26.10 (15) all_58_3 = e3
% 170.11/26.10 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.11/26.10 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.11/26.10 (17) ~ (e2 = e1)
% 170.11/26.10 (18) ~ (e3 = e2)
% 170.11/26.10
% 170.11/26.10 Begin of proof
% 170.11/26.10 |
% 170.11/26.10 | BETA: splitting (12) gives:
% 170.11/26.10 |
% 170.11/26.10 | Case 1:
% 170.11/26.10 | |
% 170.11/26.10 | | (19) all_58_14 = e2 & op(e0, e1) = e2
% 170.11/26.10 | |
% 170.11/26.10 | | ALPHA: (19) implies:
% 170.11/26.10 | | (20) all_58_14 = e2
% 170.11/26.10 | |
% 170.11/26.10 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14), (15),
% 170.11/26.10 | | (16), (17), (18), (20) are inconsistent by sub-proof #438.
% 170.11/26.10 | |
% 170.11/26.10 | Case 2:
% 170.11/26.10 | |
% 170.11/26.10 | | (21) all_58_15 = e2 & op(e0, e0) = e2
% 170.11/26.10 | |
% 170.11/26.10 | | REF_CLOSE: (2), (10), (13), (21) are inconsistent by sub-proof #854.
% 170.11/26.10 | |
% 170.11/26.10 | End of split
% 170.11/26.10 |
% 170.11/26.10 End of proof
% 170.11/26.10
% 170.11/26.10 Sub-proof #438 shows that the following formulas are inconsistent:
% 170.11/26.10 ----------------------------------------------------------------
% 170.11/26.10 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.11/26.10 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.11/26.10 (2) all_58_14 = e2
% 170.11/26.10 (3) all_58_2 = e2
% 170.11/26.10 (4) ~ (e3 = e1)
% 170.11/26.10 (5) ~ (e1 = e0)
% 170.11/26.10 (6) op(e2, e3) = all_52_1
% 170.11/26.10 (7) op(e2, e3) = e2
% 170.11/26.10 (8) ~ (e3 = e0)
% 170.11/26.10 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.11/26.10 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.11/26.10 (10) all_58_14 = e3
% 170.11/26.10 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.10 (12) ~ (e2 = e0)
% 170.11/26.10 (13) all_58_3 = e3
% 170.11/26.10 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.11/26.10 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.11/26.10 (15) ~ (e2 = e1)
% 170.11/26.10 (16) ~ (e3 = e2)
% 170.11/26.10
% 170.11/26.10 Begin of proof
% 170.11/26.10 |
% 170.11/26.10 | COMBINE_EQS: (2), (10) imply:
% 170.11/26.10 | (17) e3 = e2
% 170.11/26.10 |
% 170.11/26.10 | SIMP: (17) implies:
% 170.11/26.10 | (18) e3 = e2
% 170.11/26.10 |
% 170.11/26.10 | COMBINE_EQS: (13), (18) imply:
% 170.11/26.10 | (19) all_58_3 = e2
% 170.11/26.10 |
% 170.11/26.10 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15),
% 170.11/26.10 | (16), (19) are inconsistent by sub-proof #779.
% 170.11/26.10 |
% 170.11/26.10 End of proof
% 170.11/26.10
% 170.11/26.10 Sub-proof #439 shows that the following formulas are inconsistent:
% 170.11/26.10 ----------------------------------------------------------------
% 170.11/26.10 (1) all_58_15 = e2
% 170.11/26.10 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.10 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.10 (3) all_58_2 = e2
% 170.11/26.10 (4) all_58_0 = e1
% 170.11/26.10 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.11/26.10 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.11/26.10 (6) ~ (e3 = e1)
% 170.11/26.10 (7) all_58_6 = e3
% 170.11/26.10 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.11/26.10 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.11/26.10 (9) ~ (e1 = e0)
% 170.11/26.10 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.11/26.10 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.11/26.10 (11) op(e2, e3) = all_52_1
% 170.11/26.10 (12) op(e2, e3) = e2
% 170.11/26.10 (13) ~ (e3 = e0)
% 170.11/26.10 (14) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 170.11/26.10 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 170.11/26.10 e2) = all_22_1 & $i(all_22_1))
% 170.11/26.10 (15) all_58_14 = e3
% 170.11/26.10 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.10 (17) ~ (e2 = e0)
% 170.11/26.10 (18) op(e3, e3) = e3
% 170.11/26.10 (19) all_58_9 = e3
% 170.11/26.10 (20) ~ (e2 = e1)
% 170.11/26.10 (21) all_58_4 = e2
% 170.11/26.10 (22) ~ (e3 = e2)
% 170.11/26.10
% 170.11/26.10 Begin of proof
% 170.11/26.10 |
% 170.11/26.10 | BETA: splitting (5) gives:
% 170.11/26.10 |
% 170.11/26.10 | Case 1:
% 170.11/26.10 | |
% 170.11/26.10 | | (23) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 170.11/26.10 | | e0)
% 170.11/26.10 | |
% 170.11/26.10 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 170.11/26.10 | | (14), (15), (16), (17), (18), (20), (22), (23) are inconsistent
% 170.11/26.10 | | by sub-proof #440.
% 170.11/26.10 | |
% 170.11/26.10 | Case 2:
% 170.11/26.10 | |
% 170.11/26.10 | | (24) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 170.11/26.10 | | e0)
% 170.11/26.10 | |
% 170.11/26.10 | | REF_CLOSE: (13), (17), (19), (21), (24) are inconsistent by sub-proof #511.
% 170.11/26.10 | |
% 170.11/26.10 | End of split
% 170.11/26.10 |
% 170.11/26.10 End of proof
% 170.11/26.10
% 170.11/26.10 Sub-proof #440 shows that the following formulas are inconsistent:
% 170.11/26.10 ----------------------------------------------------------------
% 170.11/26.10 (1) all_58_15 = e2
% 170.11/26.10 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.10 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.10 (3) all_58_2 = e2
% 170.11/26.10 (4) all_58_0 = e1
% 170.11/26.10 (5) ~ (e3 = e1)
% 170.11/26.10 (6) all_58_6 = e3
% 170.11/26.10 (7) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.11/26.10 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.11/26.10 (8) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 170.11/26.10 (9) ~ (e1 = e0)
% 170.11/26.10 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.11/26.10 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.11/26.10 (11) op(e2, e3) = all_52_1
% 170.11/26.10 (12) op(e2, e3) = e2
% 170.11/26.10 (13) ~ (e3 = e0)
% 170.11/26.10 (14) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 170.11/26.10 all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 170.11/26.10 e2) = all_22_1 & $i(all_22_1))
% 170.11/26.10 (15) all_58_14 = e3
% 170.11/26.10 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.10 (17) ~ (e2 = e0)
% 170.11/26.10 (18) op(e3, e3) = e3
% 170.11/26.10 (19) ~ (e2 = e1)
% 170.11/26.10 (20) ~ (e3 = e2)
% 170.11/26.10
% 170.11/26.10 Begin of proof
% 170.11/26.10 |
% 170.11/26.10 | BETA: splitting (8) gives:
% 170.11/26.10 |
% 170.11/26.10 | Case 1:
% 170.11/26.10 | |
% 170.11/26.10 | | (21) all_58_0 = e0 & op(e3, e3) = e0
% 170.11/26.10 | |
% 170.11/26.10 | | ALPHA: (21) implies:
% 170.11/26.10 | | (22) op(e3, e3) = e0
% 170.11/26.10 | |
% 170.11/26.10 | | REF_CLOSE: (13), (16), (18), (22) are inconsistent by sub-proof #949.
% 170.11/26.10 | |
% 170.11/26.10 | Case 2:
% 170.11/26.10 | |
% 170.11/26.10 | | (23) all_58_1 = e0 & op(e3, e2) = e0
% 170.11/26.10 | |
% 170.11/26.10 | | ALPHA: (23) implies:
% 170.11/26.10 | | (24) op(e3, e2) = e0
% 170.11/26.10 | |
% 170.11/26.10 | | BETA: splitting (7) gives:
% 170.11/26.10 | |
% 170.11/26.10 | | Case 1:
% 170.11/26.10 | | |
% 170.11/26.10 | | | (25) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2)
% 170.11/26.10 | | | = e1)
% 170.11/26.10 | | |
% 170.11/26.10 | | | REF_CLOSE: (2), (4), (6), (9), (11), (12), (13), (14), (16), (17), (24),
% 170.11/26.10 | | | (25) are inconsistent by sub-proof #442.
% 170.11/26.10 | | |
% 170.11/26.10 | | Case 2:
% 170.11/26.10 | | |
% 170.11/26.10 | | | (26) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0)
% 170.11/26.10 | | | = e1)
% 170.11/26.10 | | |
% 170.11/26.10 | | | BETA: splitting (26) gives:
% 170.11/26.10 | | |
% 170.11/26.10 | | | Case 1:
% 170.11/26.10 | | | |
% 170.11/26.10 | | | | (27) all_58_14 = e1 & op(e0, e1) = e1
% 170.11/26.10 | | | |
% 170.11/26.10 | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (12), (13), (15),
% 170.11/26.10 | | | | (16), (17), (20), (27) are inconsistent by sub-proof #441.
% 170.11/26.10 | | | |
% 170.11/26.10 | | | Case 2:
% 170.11/26.10 | | | |
% 170.11/26.10 | | | | (28) all_58_15 = e1 & op(e0, e0) = e1
% 170.11/26.10 | | | |
% 170.11/26.10 | | | | REF_CLOSE: (1), (19), (28) are inconsistent by sub-proof #720.
% 170.11/26.10 | | | |
% 170.11/26.10 | | | End of split
% 170.11/26.10 | | |
% 170.11/26.10 | | End of split
% 170.11/26.10 | |
% 170.11/26.10 | End of split
% 170.11/26.10 |
% 170.11/26.10 End of proof
% 170.11/26.10
% 170.11/26.10 Sub-proof #441 shows that the following formulas are inconsistent:
% 170.11/26.10 ----------------------------------------------------------------
% 170.11/26.10 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.10 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.10 (2) all_58_2 = e2
% 170.11/26.10 (3) all_58_0 = e1
% 170.11/26.10 (4) all_58_14 = e1 & op(e0, e1) = e1
% 170.11/26.10 (5) ~ (e3 = e1)
% 170.11/26.10 (6) all_58_6 = e3
% 170.11/26.10 (7) ~ (e1 = e0)
% 170.11/26.10 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.11/26.10 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.11/26.10 (9) op(e2, e3) = all_52_1
% 170.11/26.10 (10) op(e2, e3) = e2
% 170.11/26.10 (11) ~ (e3 = e0)
% 170.11/26.10 (12) all_58_14 = e3
% 170.11/26.10 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.10 (14) ~ (e2 = e0)
% 170.11/26.10 (15) ~ (e3 = e2)
% 170.11/26.10
% 170.11/26.10 Begin of proof
% 170.11/26.10 |
% 170.11/26.10 | ALPHA: (4) implies:
% 170.11/26.10 | (16) all_58_14 = e1
% 170.11/26.10 |
% 170.11/26.10 | COMBINE_EQS: (12), (16) imply:
% 170.11/26.10 | (17) e3 = e1
% 170.11/26.10 |
% 170.11/26.10 | SIMP: (17) implies:
% 170.11/26.10 | (18) e3 = e1
% 170.11/26.10 |
% 170.11/26.10 | COMBINE_EQS: (6), (18) imply:
% 170.11/26.10 | (19) all_58_6 = e1
% 170.11/26.10 |
% 170.11/26.10 | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (13), (14), (15),
% 170.11/26.10 | (19) are inconsistent by sub-proof #455.
% 170.11/26.10 |
% 170.11/26.10 End of proof
% 170.11/26.10
% 170.11/26.10 Sub-proof #442 shows that the following formulas are inconsistent:
% 170.11/26.10 ----------------------------------------------------------------
% 170.11/26.10 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.10 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.10 (2) all_58_0 = e1
% 170.11/26.10 (3) all_58_6 = e3
% 170.11/26.10 (4) ~ (e1 = e0)
% 170.11/26.10 (5) op(e2, e3) = all_52_1
% 170.11/26.10 (6) op(e2, e3) = e2
% 170.11/26.10 (7) ~ (e3 = e0)
% 170.11/26.10 (8) op(e3, e2) = e0
% 170.11/26.10 (9) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) = all_22_1
% 170.11/26.10 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2) =
% 170.11/26.10 all_22_1 & $i(all_22_1))
% 170.11/26.10 (10) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.11/26.10 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.10 (12) ~ (e2 = e0)
% 170.11/26.10
% 170.11/26.10 Begin of proof
% 170.11/26.10 |
% 170.11/26.10 | BETA: splitting (10) gives:
% 170.11/26.10 |
% 170.11/26.10 | Case 1:
% 170.11/26.10 | |
% 170.11/26.10 | | (13) all_58_12 = e1 & op(e0, e3) = e1
% 170.11/26.10 | |
% 170.11/26.10 | | ALPHA: (13) implies:
% 170.11/26.10 | | (14) all_58_12 = e1
% 170.11/26.10 | |
% 170.11/26.10 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12), (14) are
% 170.11/26.10 | | inconsistent by sub-proof #459.
% 170.11/26.10 | |
% 170.11/26.10 | Case 2:
% 170.11/26.10 | |
% 170.11/26.10 | | (15) all_58_13 = e1 & op(e0, e2) = e1
% 170.11/26.10 | |
% 170.11/26.10 | | ALPHA: (15) implies:
% 170.11/26.10 | | (16) op(e0, e2) = e1
% 170.11/26.10 | |
% 170.11/26.10 | | REF_CLOSE: (8), (9), (11), (16) are inconsistent by sub-proof #443.
% 170.11/26.10 | |
% 170.11/26.10 | End of split
% 170.11/26.10 |
% 170.11/26.10 End of proof
% 170.11/26.10
% 170.11/26.10 Sub-proof #443 shows that the following formulas are inconsistent:
% 170.11/26.10 ----------------------------------------------------------------
% 170.11/26.10 (1) ( ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) = all_22_1
% 170.11/26.10 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e2) =
% 170.11/26.10 all_22_1 & $i(all_22_1))
% 170.11/26.10 (2) op(e0, e2) = e1
% 170.11/26.10 (3) op(e3, e2) = e0
% 170.11/26.10 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.10
% 170.11/26.10 Begin of proof
% 170.11/26.10 |
% 170.11/26.10 | BETA: splitting (1) gives:
% 170.11/26.10 |
% 170.11/26.10 | Case 1:
% 170.11/26.10 | |
% 170.11/26.10 | | (5) ~ (all_22_0 = e1) & op(all_22_1, e2) = all_22_0 & op(e3, e2) =
% 170.11/26.10 | | all_22_1 & $i(all_22_0) & $i(all_22_1)
% 170.11/26.10 | |
% 170.11/26.10 | | ALPHA: (5) implies:
% 170.11/26.10 | | (6) ~ (all_22_0 = e1)
% 170.11/26.10 | | (7) op(e3, e2) = all_22_1
% 170.11/26.10 | | (8) op(all_22_1, e2) = all_22_0
% 170.11/26.10 | |
% 170.11/26.10 | | REF_CLOSE: (2), (3), (4), (6), (7), (8) are inconsistent by sub-proof #445.
% 170.11/26.10 | |
% 170.11/26.10 | Case 2:
% 170.11/26.10 | |
% 170.11/26.10 | | (9) ~ (all_22_1 = e0) & op(e3, e2) = all_22_1 & $i(all_22_1)
% 170.11/26.10 | |
% 170.11/26.10 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #444.
% 170.11/26.10 | |
% 170.11/26.10 | End of split
% 170.11/26.10 |
% 170.11/26.10 End of proof
% 170.11/26.10
% 170.11/26.10 Sub-proof #444 shows that the following formulas are inconsistent:
% 170.11/26.10 ----------------------------------------------------------------
% 170.11/26.10 (1) ~ (all_22_1 = e0) & op(e3, e2) = all_22_1 & $i(all_22_1)
% 170.11/26.10 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.10 (3) op(e3, e2) = e0
% 170.11/26.10
% 170.11/26.10 Begin of proof
% 170.11/26.10 |
% 170.11/26.10 | ALPHA: (1) implies:
% 170.11/26.10 | (4) ~ (all_22_1 = e0)
% 170.11/26.10 | (5) op(e3, e2) = all_22_1
% 170.11/26.10 |
% 170.11/26.10 | GROUND_INST: instantiating (2) with e0, all_22_1, e2, e3, simplifying with
% 170.11/26.10 | (3), (5) gives:
% 170.11/26.10 | (6) all_22_1 = e0
% 170.11/26.10 |
% 170.11/26.10 | REDUCE: (4), (6) imply:
% 170.11/26.10 | (7) $false
% 170.11/26.10 |
% 170.11/26.10 | CLOSE: (7) is inconsistent.
% 170.11/26.10 |
% 170.11/26.10 End of proof
% 170.11/26.10
% 170.11/26.10 Sub-proof #445 shows that the following formulas are inconsistent:
% 170.11/26.10 ----------------------------------------------------------------
% 170.11/26.10 (1) op(e3, e2) = all_22_1
% 170.11/26.10 (2) op(all_22_1, e2) = all_22_0
% 170.11/26.10 (3) op(e0, e2) = e1
% 170.11/26.10 (4) op(e3, e2) = e0
% 170.11/26.10 (5) ~ (all_22_0 = e1)
% 170.11/26.10 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.10
% 170.11/26.10 Begin of proof
% 170.11/26.10 |
% 170.11/26.10 | GROUND_INST: instantiating (6) with e0, all_22_1, e2, e3, simplifying with
% 170.11/26.10 | (1), (4) gives:
% 170.11/26.10 | (7) all_22_1 = e0
% 170.11/26.10 |
% 170.11/26.10 | REDUCE: (2), (7) imply:
% 170.11/26.10 | (8) op(e0, e2) = all_22_0
% 170.11/26.10 |
% 170.11/26.10 | GROUND_INST: instantiating (6) with e1, all_22_0, e2, e0, simplifying with
% 170.11/26.10 | (3), (8) gives:
% 170.11/26.10 | (9) all_22_0 = e1
% 170.11/26.10 |
% 170.11/26.10 | REDUCE: (5), (9) imply:
% 170.11/26.10 | (10) $false
% 170.11/26.10 |
% 170.11/26.10 | CLOSE: (10) is inconsistent.
% 170.11/26.10 |
% 170.11/26.10 End of proof
% 170.11/26.10
% 170.11/26.10 Sub-proof #446 shows that the following formulas are inconsistent:
% 170.11/26.10 ----------------------------------------------------------------
% 170.11/26.10 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.11/26.10 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.11/26.10 (2) all_58_2 = e2
% 170.11/26.10 (3) ~ (e3 = e1)
% 170.11/26.10 (4) ~ (e1 = e0)
% 170.11/26.10 (5) op(e2, e3) = all_52_1
% 170.11/26.10 (6) op(e2, e3) = e2
% 170.11/26.10 (7) ~ (e3 = e0)
% 170.11/26.10 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.11/26.10 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.11/26.10 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.10 (10) ~ (e2 = e0)
% 170.11/26.10 (11) all_58_3 = e3
% 170.11/26.10 (12) all_58_9 = e3
% 170.11/26.10 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.11/26.10 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.11/26.10 (14) ~ (e2 = e1)
% 170.11/26.11 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.11/26.11 (16) ~ (e3 = e2)
% 170.11/26.11
% 170.11/26.11 Begin of proof
% 170.11/26.11 |
% 170.11/26.11 | BETA: splitting (15) gives:
% 170.11/26.11 |
% 170.11/26.11 | Case 1:
% 170.11/26.11 | |
% 170.11/26.11 | | (17) all_58_9 = e2 & op(e3, e0) = e2
% 170.11/26.11 | |
% 170.11/26.11 | | ALPHA: (17) implies:
% 170.11/26.11 | | (18) all_58_9 = e2
% 170.11/26.11 | |
% 170.11/26.11 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 170.11/26.11 | | (13), (14), (16), (18) are inconsistent by sub-proof #451.
% 170.11/26.11 | |
% 170.11/26.11 | Case 2:
% 170.11/26.11 | |
% 170.11/26.11 | | (19) all_58_10 = e2 & op(e2, e0) = e2
% 170.11/26.11 | |
% 170.11/26.11 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), (19)
% 170.11/26.11 | | are inconsistent by sub-proof #447.
% 170.11/26.11 | |
% 170.11/26.11 | End of split
% 170.11/26.11 |
% 170.11/26.11 End of proof
% 170.11/26.11
% 170.11/26.11 Sub-proof #447 shows that the following formulas are inconsistent:
% 170.11/26.11 ----------------------------------------------------------------
% 170.11/26.11 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.11/26.11 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.11/26.11 (2) ~ (e3 = e1)
% 170.11/26.11 (3) all_58_10 = e2 & op(e2, e0) = e2
% 170.11/26.11 (4) ~ (e1 = e0)
% 170.11/26.11 (5) op(e2, e3) = all_52_1
% 170.11/26.11 (6) op(e2, e3) = e2
% 170.11/26.11 (7) ~ (e3 = e0)
% 170.11/26.11 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.11/26.11 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.11/26.11 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.11 (10) ~ (e2 = e0)
% 170.11/26.11 (11) all_58_3 = e3
% 170.11/26.11 (12) ~ (e2 = e1)
% 170.11/26.11
% 170.11/26.11 Begin of proof
% 170.11/26.11 |
% 170.11/26.11 | ALPHA: (3) implies:
% 170.11/26.11 | (13) all_58_10 = e2
% 170.11/26.11 |
% 170.11/26.11 | BETA: splitting (1) gives:
% 170.11/26.11 |
% 170.11/26.11 | Case 1:
% 170.11/26.11 | |
% 170.11/26.11 | | (14) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 170.11/26.11 | | e1)
% 170.11/26.11 | |
% 170.11/26.11 | | REF_CLOSE: (2), (5), (6), (9), (11), (12), (14) are inconsistent by
% 170.11/26.11 | | sub-proof #450.
% 170.11/26.11 | |
% 170.11/26.11 | Case 2:
% 170.11/26.11 | |
% 170.11/26.11 | | (15) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 170.11/26.11 | | e1)
% 170.11/26.11 | |
% 170.11/26.11 | | BETA: splitting (15) gives:
% 170.11/26.11 | |
% 170.11/26.11 | | Case 1:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (16) all_58_5 = e1 & op(e2, e1) = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | ALPHA: (16) implies:
% 170.11/26.11 | | | (17) all_58_5 = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (10), (11), (13), (17) are
% 170.11/26.11 | | | inconsistent by sub-proof #448.
% 170.11/26.11 | | |
% 170.11/26.11 | | Case 2:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (18) all_58_10 = e1 & op(e2, e0) = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | ALPHA: (18) implies:
% 170.11/26.11 | | | (19) all_58_10 = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (12), (13), (19) are inconsistent by sub-proof #922.
% 170.11/26.11 | | |
% 170.11/26.11 | | End of split
% 170.11/26.11 | |
% 170.11/26.11 | End of split
% 170.11/26.11 |
% 170.11/26.11 End of proof
% 170.11/26.11
% 170.11/26.11 Sub-proof #448 shows that the following formulas are inconsistent:
% 170.11/26.11 ----------------------------------------------------------------
% 170.11/26.11 (1) ~ (e1 = e0)
% 170.11/26.11 (2) op(e2, e3) = all_52_1
% 170.11/26.11 (3) all_58_10 = e2
% 170.11/26.11 (4) op(e2, e3) = e2
% 170.11/26.11 (5) ~ (e3 = e0)
% 170.11/26.11 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.11/26.11 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.11/26.11 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.11 (8) ~ (e2 = e0)
% 170.11/26.11 (9) all_58_5 = e1
% 170.11/26.11 (10) all_58_3 = e3
% 170.11/26.11
% 170.11/26.11 Begin of proof
% 170.11/26.11 |
% 170.11/26.11 | BETA: splitting (6) gives:
% 170.11/26.11 |
% 170.11/26.11 | Case 1:
% 170.11/26.11 | |
% 170.11/26.11 | | (11) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 170.11/26.11 | | e0)
% 170.11/26.11 | |
% 170.11/26.11 | | BETA: splitting (11) gives:
% 170.11/26.11 | |
% 170.11/26.11 | | Case 1:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (12) all_58_2 = e0 & op(e2, e3) = e0
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (2), (4), (7), (8), (12) are inconsistent by sub-proof #782.
% 170.11/26.11 | | |
% 170.11/26.11 | | Case 2:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (13) all_58_3 = e0 & op(e2, e2) = e0
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (5), (10), (13) are inconsistent by sub-proof #869.
% 170.11/26.11 | | |
% 170.11/26.11 | | End of split
% 170.11/26.11 | |
% 170.11/26.11 | Case 2:
% 170.11/26.11 | |
% 170.11/26.11 | | (14) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.11/26.11 | | e0)
% 170.11/26.11 | |
% 170.11/26.11 | | BETA: splitting (14) gives:
% 170.11/26.11 | |
% 170.11/26.11 | | Case 1:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (15) all_58_5 = e0 & op(e2, e1) = e0
% 170.11/26.11 | | |
% 170.11/26.11 | | | ALPHA: (15) implies:
% 170.11/26.11 | | | (16) all_58_5 = e0
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (1), (9), (16) are inconsistent by sub-proof #449.
% 170.11/26.11 | | |
% 170.11/26.11 | | Case 2:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (17) all_58_10 = e0 & op(e2, e0) = e0
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (3), (8), (17) are inconsistent by sub-proof #918.
% 170.11/26.11 | | |
% 170.11/26.11 | | End of split
% 170.11/26.11 | |
% 170.11/26.11 | End of split
% 170.11/26.11 |
% 170.11/26.11 End of proof
% 170.11/26.11
% 170.11/26.11 Sub-proof #449 shows that the following formulas are inconsistent:
% 170.11/26.11 ----------------------------------------------------------------
% 170.11/26.11 (1) all_58_5 = e1
% 170.11/26.11 (2) all_58_5 = e0
% 170.11/26.11 (3) ~ (e1 = e0)
% 170.11/26.11
% 170.11/26.11 Begin of proof
% 170.11/26.11 |
% 170.11/26.11 | COMBINE_EQS: (1), (2) imply:
% 170.11/26.11 | (4) e1 = e0
% 170.11/26.11 |
% 170.11/26.11 | SIMP: (4) implies:
% 170.11/26.11 | (5) e1 = e0
% 170.11/26.11 |
% 170.11/26.11 | REDUCE: (3), (5) imply:
% 170.11/26.11 | (6) $false
% 170.11/26.11 |
% 170.11/26.11 | CLOSE: (6) is inconsistent.
% 170.11/26.11 |
% 170.11/26.11 End of proof
% 170.11/26.11
% 170.11/26.11 Sub-proof #450 shows that the following formulas are inconsistent:
% 170.11/26.11 ----------------------------------------------------------------
% 170.11/26.11 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 170.11/26.11 (2) ~ (e3 = e1)
% 170.11/26.11 (3) op(e2, e3) = all_52_1
% 170.11/26.11 (4) op(e2, e3) = e2
% 170.11/26.11 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.11 (6) all_58_3 = e3
% 170.11/26.11 (7) ~ (e2 = e1)
% 170.11/26.11
% 170.11/26.11 Begin of proof
% 170.11/26.11 |
% 170.11/26.11 | BETA: splitting (1) gives:
% 170.11/26.11 |
% 170.11/26.11 | Case 1:
% 170.11/26.11 | |
% 170.11/26.11 | | (8) all_58_2 = e1 & op(e2, e3) = e1
% 170.11/26.11 | |
% 170.11/26.11 | | ALPHA: (8) implies:
% 170.11/26.11 | | (9) op(e2, e3) = e1
% 170.11/26.11 | |
% 170.11/26.11 | | REF_CLOSE: (3), (4), (5), (7), (9) are inconsistent by sub-proof #784.
% 170.11/26.11 | |
% 170.11/26.11 | Case 2:
% 170.11/26.11 | |
% 170.11/26.11 | | (10) all_58_3 = e1 & op(e2, e2) = e1
% 170.11/26.11 | |
% 170.11/26.11 | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #868.
% 170.11/26.11 | |
% 170.11/26.11 | End of split
% 170.11/26.11 |
% 170.11/26.11 End of proof
% 170.11/26.11
% 170.11/26.11 Sub-proof #451 shows that the following formulas are inconsistent:
% 170.11/26.11 ----------------------------------------------------------------
% 170.11/26.11 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.11/26.11 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.11/26.11 (2) all_58_9 = e2
% 170.11/26.11 (3) all_58_2 = e2
% 170.11/26.11 (4) ~ (e3 = e1)
% 170.11/26.11 (5) ~ (e1 = e0)
% 170.11/26.11 (6) op(e2, e3) = all_52_1
% 170.11/26.11 (7) op(e2, e3) = e2
% 170.11/26.11 (8) ~ (e3 = e0)
% 170.11/26.11 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.11/26.11 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.11/26.11 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.11 (11) ~ (e2 = e0)
% 170.11/26.11 (12) all_58_3 = e3
% 170.11/26.11 (13) all_58_9 = e3
% 170.11/26.11 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.11/26.11 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.11/26.11 (15) ~ (e2 = e1)
% 170.11/26.11 (16) ~ (e3 = e2)
% 170.11/26.11
% 170.11/26.11 Begin of proof
% 170.11/26.11 |
% 170.11/26.11 | COMBINE_EQS: (2), (13) imply:
% 170.11/26.11 | (17) e3 = e2
% 170.11/26.11 |
% 170.11/26.11 | SIMP: (17) implies:
% 170.11/26.11 | (18) e3 = e2
% 170.11/26.11 |
% 170.11/26.11 | COMBINE_EQS: (12), (18) imply:
% 170.11/26.11 | (19) all_58_3 = e2
% 170.11/26.11 |
% 170.11/26.11 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14), (15),
% 170.11/26.11 | (16), (19) are inconsistent by sub-proof #779.
% 170.11/26.11 |
% 170.11/26.11 End of proof
% 170.11/26.11
% 170.11/26.11 Sub-proof #452 shows that the following formulas are inconsistent:
% 170.11/26.11 ----------------------------------------------------------------
% 170.11/26.11 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.11/26.11 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.11/26.11 (2) all_58_2 = e2
% 170.11/26.11 (3) ~ (e3 = e1)
% 170.11/26.11 (4) ~ (e1 = e0)
% 170.11/26.11 (5) op(e2, e3) = all_52_1
% 170.11/26.11 (6) op(e2, e3) = e2
% 170.11/26.11 (7) ~ (e3 = e0)
% 170.11/26.11 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.11/26.11 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.11/26.11 (9) all_58_4 = e3
% 170.11/26.11 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.11 (11) ~ (e2 = e0)
% 170.11/26.11 (12) all_58_3 = e3
% 170.11/26.11 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.11/26.11 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.11/26.11 (14) ~ (e2 = e1)
% 170.11/26.11 (15) all_58_4 = e2
% 170.11/26.11 (16) ~ (e3 = e2)
% 170.11/26.11
% 170.11/26.11 Begin of proof
% 170.11/26.11 |
% 170.11/26.11 | COMBINE_EQS: (9), (15) imply:
% 170.11/26.11 | (17) e3 = e2
% 170.11/26.11 |
% 170.11/26.11 | SIMP: (17) implies:
% 170.11/26.11 | (18) e3 = e2
% 170.11/26.11 |
% 170.11/26.11 | COMBINE_EQS: (12), (18) imply:
% 170.11/26.11 | (19) all_58_3 = e2
% 170.11/26.11 |
% 170.11/26.11 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (13), (14),
% 170.11/26.11 | (16), (19) are inconsistent by sub-proof #779.
% 170.11/26.11 |
% 170.11/26.11 End of proof
% 170.11/26.11
% 170.11/26.11 Sub-proof #453 shows that the following formulas are inconsistent:
% 170.11/26.11 ----------------------------------------------------------------
% 170.11/26.11 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.11 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.11 (2) all_58_2 = e2
% 170.11/26.11 (3) ~ (e3 = e1)
% 170.11/26.11 (4) all_58_6 = e3
% 170.11/26.11 (5) ~ (e1 = e0)
% 170.11/26.11 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.11/26.11 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.11/26.11 (7) op(e2, e3) = all_52_1
% 170.11/26.11 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3)
% 170.11/26.11 (9) op(e2, e3) = e2
% 170.11/26.11 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.11/26.11 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.11/26.11 (11) ~ (e3 = e0)
% 170.11/26.11 (12) all_58_12 = e0
% 170.11/26.11 (13) ~ (all_52_4 = e3)
% 170.11/26.11 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.11 (15) ~ (e2 = e0)
% 170.11/26.11 (16) ~ (e2 = e1)
% 170.11/26.11 (17) op(e3, e2) = all_52_4
% 170.11/26.11 (18) ~ (e3 = e2)
% 170.11/26.11
% 170.11/26.11 Begin of proof
% 170.11/26.11 |
% 170.11/26.11 | BETA: splitting (8) gives:
% 170.11/26.11 |
% 170.11/26.11 | Case 1:
% 170.11/26.11 | |
% 170.11/26.11 | | (19) all_58_0 = e3 & op(e3, e3) = e3
% 170.11/26.11 | |
% 170.11/26.11 | | ALPHA: (19) implies:
% 170.11/26.11 | | (20) all_58_0 = e3
% 170.11/26.11 | |
% 170.11/26.11 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14),
% 170.11/26.11 | | (15), (16), (18), (20) are inconsistent by sub-proof #454.
% 170.11/26.11 | |
% 170.11/26.11 | Case 2:
% 170.11/26.11 | |
% 170.11/26.11 | | (21) all_58_1 = e3 & op(e3, e2) = e3
% 170.11/26.11 | |
% 170.11/26.11 | | ALPHA: (21) implies:
% 170.11/26.11 | | (22) op(e3, e2) = e3
% 170.11/26.11 | |
% 170.11/26.11 | | REF_CLOSE: (13), (14), (17), (22) are inconsistent by sub-proof #974.
% 170.11/26.11 | |
% 170.11/26.11 | End of split
% 170.11/26.11 |
% 170.11/26.11 End of proof
% 170.11/26.11
% 170.11/26.11 Sub-proof #454 shows that the following formulas are inconsistent:
% 170.11/26.11 ----------------------------------------------------------------
% 170.11/26.11 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.11 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.11 (2) all_58_2 = e2
% 170.11/26.11 (3) ~ (e3 = e1)
% 170.11/26.11 (4) all_58_6 = e3
% 170.11/26.11 (5) ~ (e1 = e0)
% 170.11/26.11 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.11/26.11 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.11/26.11 (7) op(e2, e3) = all_52_1
% 170.11/26.11 (8) op(e2, e3) = e2
% 170.11/26.11 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.11/26.11 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.11/26.11 (10) ~ (e3 = e0)
% 170.11/26.11 (11) all_58_12 = e0
% 170.11/26.11 (12) all_58_0 = e3
% 170.11/26.11 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.11 (14) ~ (e2 = e0)
% 170.11/26.11 (15) ~ (e2 = e1)
% 170.11/26.11 (16) ~ (e3 = e2)
% 170.11/26.11
% 170.11/26.11 Begin of proof
% 170.11/26.11 |
% 170.11/26.11 | BETA: splitting (9) gives:
% 170.11/26.11 |
% 170.11/26.11 | Case 1:
% 170.11/26.11 | |
% 170.11/26.11 | | (17) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 170.11/26.11 | | e1)
% 170.11/26.11 | |
% 170.11/26.11 | | BETA: splitting (17) gives:
% 170.11/26.11 | |
% 170.11/26.11 | | Case 1:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (18) all_58_0 = e1 & op(e3, e3) = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | ALPHA: (18) implies:
% 170.11/26.11 | | | (19) all_58_0 = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | COMBINE_EQS: (12), (19) imply:
% 170.11/26.11 | | | (20) e3 = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | COMBINE_EQS: (4), (20) imply:
% 170.11/26.11 | | | (21) all_58_6 = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (13), (14), (16),
% 170.11/26.11 | | | (19), (21) are inconsistent by sub-proof #455.
% 170.11/26.11 | | |
% 170.11/26.11 | | Case 2:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (22) all_58_2 = e1 & op(e2, e3) = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | ALPHA: (22) implies:
% 170.11/26.11 | | | (23) op(e2, e3) = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (7), (8), (13), (15), (23) are inconsistent by sub-proof #784.
% 170.11/26.11 | | |
% 170.11/26.11 | | End of split
% 170.11/26.11 | |
% 170.11/26.11 | Case 2:
% 170.11/26.11 | |
% 170.11/26.11 | | (24) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 170.11/26.11 | | e1)
% 170.11/26.11 | |
% 170.11/26.11 | | BETA: splitting (24) gives:
% 170.11/26.11 | |
% 170.11/26.11 | | Case 1:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (25) all_58_6 = e1 & op(e1, e3) = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | ALPHA: (25) implies:
% 170.11/26.11 | | | (26) all_58_6 = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | COMBINE_EQS: (4), (26) imply:
% 170.11/26.11 | | | (27) e3 = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | COMBINE_EQS: (12), (27) imply:
% 170.11/26.11 | | | (28) all_58_0 = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (2), (3), (6), (10), (11), (16), (26), (28) are inconsistent by
% 170.11/26.11 | | | sub-proof #456.
% 170.11/26.11 | | |
% 170.11/26.11 | | Case 2:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (29) all_58_12 = e1 & op(e0, e3) = e1
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (5), (11), (29) are inconsistent by sub-proof #773.
% 170.11/26.11 | | |
% 170.11/26.11 | | End of split
% 170.11/26.11 | |
% 170.11/26.11 | End of split
% 170.11/26.11 |
% 170.11/26.11 End of proof
% 170.11/26.11
% 170.11/26.11 Sub-proof #455 shows that the following formulas are inconsistent:
% 170.11/26.11 ----------------------------------------------------------------
% 170.11/26.11 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.11 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.11 (2) all_58_2 = e2
% 170.11/26.11 (3) all_58_0 = e1
% 170.11/26.11 (4) all_58_6 = e1
% 170.11/26.11 (5) ~ (e3 = e1)
% 170.11/26.11 (6) ~ (e1 = e0)
% 170.11/26.11 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.11/26.11 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.11/26.11 (8) op(e2, e3) = all_52_1
% 170.11/26.11 (9) op(e2, e3) = e2
% 170.11/26.11 (10) ~ (e3 = e0)
% 170.11/26.11 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.11 (12) ~ (e2 = e0)
% 170.11/26.11 (13) ~ (e3 = e2)
% 170.11/26.11
% 170.11/26.11 Begin of proof
% 170.11/26.11 |
% 170.11/26.11 | BETA: splitting (1) gives:
% 170.11/26.11 |
% 170.11/26.11 | Case 1:
% 170.11/26.11 | |
% 170.11/26.11 | | (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 170.11/26.11 | | e0)
% 170.11/26.11 | |
% 170.11/26.11 | | BETA: splitting (14) gives:
% 170.11/26.11 | |
% 170.11/26.11 | | Case 1:
% 170.11/26.11 | | |
% 170.11/26.11 | | | (15) all_58_0 = e0 & op(e3, e3) = e0
% 170.11/26.11 | | |
% 170.11/26.11 | | | REF_CLOSE: (3), (6), (15) are inconsistent by sub-proof #903.
% 170.11/26.12 | | |
% 170.11/26.12 | | Case 2:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (16) all_58_2 = e0 & op(e2, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (8), (9), (11), (12), (16) are inconsistent by sub-proof #782.
% 170.11/26.12 | | |
% 170.11/26.12 | | End of split
% 170.11/26.12 | |
% 170.11/26.12 | Case 2:
% 170.11/26.12 | |
% 170.11/26.12 | | (17) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 170.11/26.12 | | e0)
% 170.11/26.12 | |
% 170.11/26.12 | | BETA: splitting (17) gives:
% 170.11/26.12 | |
% 170.11/26.12 | | Case 1:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (18) all_58_6 = e0 & op(e1, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (4), (6), (18) are inconsistent by sub-proof #457.
% 170.11/26.12 | | |
% 170.11/26.12 | | Case 2:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (19) all_58_12 = e0 & op(e0, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | ALPHA: (19) implies:
% 170.11/26.12 | | | (20) all_58_12 = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (2), (3), (4), (5), (7), (10), (13), (20) are inconsistent by
% 170.11/26.12 | | | sub-proof #456.
% 170.11/26.12 | | |
% 170.11/26.12 | | End of split
% 170.11/26.12 | |
% 170.11/26.12 | End of split
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #456 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) all_58_2 = e2
% 170.11/26.12 (2) all_58_0 = e1
% 170.11/26.12 (3) all_58_6 = e1
% 170.11/26.12 (4) ~ (e3 = e1)
% 170.11/26.12 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.11/26.12 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.11/26.12 (6) ~ (e3 = e0)
% 170.11/26.12 (7) all_58_12 = e0
% 170.11/26.12 (8) ~ (e3 = e2)
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | BETA: splitting (5) gives:
% 170.11/26.12 |
% 170.11/26.12 | Case 1:
% 170.11/26.12 | |
% 170.11/26.12 | | (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 170.11/26.12 | |
% 170.11/26.12 | | BETA: splitting (9) gives:
% 170.11/26.12 | |
% 170.11/26.12 | | Case 1:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (10) all_58_0 = e3 & op(e3, e3) = e3
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #905.
% 170.11/26.12 | | |
% 170.11/26.12 | | Case 2:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (11) all_58_2 = e3 & op(e2, e3) = e3
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (1), (8), (11) are inconsistent by sub-proof #786.
% 170.11/26.12 | | |
% 170.11/26.12 | | End of split
% 170.11/26.12 | |
% 170.11/26.12 | Case 2:
% 170.11/26.12 | |
% 170.11/26.12 | | (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 170.11/26.12 | | e3)
% 170.11/26.12 | |
% 170.11/26.12 | | BETA: splitting (12) gives:
% 170.11/26.12 | |
% 170.11/26.12 | | Case 1:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (13) all_58_6 = e3 & op(e1, e3) = e3
% 170.11/26.12 | | |
% 170.11/26.12 | | | ALPHA: (13) implies:
% 170.11/26.12 | | | (14) all_58_6 = e3
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (3), (4), (14) are inconsistent by sub-proof #476.
% 170.11/26.12 | | |
% 170.11/26.12 | | Case 2:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (15) all_58_12 = e3 & op(e0, e3) = e3
% 170.11/26.12 | | |
% 170.11/26.12 | | | ALPHA: (15) implies:
% 170.11/26.12 | | | (16) all_58_12 = e3
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (6), (7), (16) are inconsistent by sub-proof #608.
% 170.11/26.12 | | |
% 170.11/26.12 | | End of split
% 170.11/26.12 | |
% 170.11/26.12 | End of split
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #457 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) all_58_6 = e0 & op(e1, e3) = e0
% 170.11/26.12 (2) all_58_6 = e1
% 170.11/26.12 (3) ~ (e1 = e0)
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | ALPHA: (1) implies:
% 170.11/26.12 | (4) all_58_6 = e0
% 170.11/26.12 |
% 170.11/26.12 | COMBINE_EQS: (2), (4) imply:
% 170.11/26.12 | (5) e1 = e0
% 170.11/26.12 |
% 170.11/26.12 | REDUCE: (3), (5) imply:
% 170.11/26.12 | (6) $false
% 170.11/26.12 |
% 170.11/26.12 | CLOSE: (6) is inconsistent.
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #458 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) all_58_13 = e2
% 170.11/26.12 (2) all_58_13 = e1
% 170.11/26.12 (3) ~ (e2 = e1)
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | COMBINE_EQS: (1), (2) imply:
% 170.11/26.12 | (4) e2 = e1
% 170.11/26.12 |
% 170.11/26.12 | SIMP: (4) implies:
% 170.11/26.12 | (5) e2 = e1
% 170.11/26.12 |
% 170.11/26.12 | REDUCE: (3), (5) imply:
% 170.11/26.12 | (6) $false
% 170.11/26.12 |
% 170.11/26.12 | CLOSE: (6) is inconsistent.
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #459 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) all_58_12 = e1
% 170.11/26.12 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.12 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.12 (3) all_58_0 = e1
% 170.11/26.12 (4) all_58_6 = e3
% 170.11/26.12 (5) ~ (e1 = e0)
% 170.11/26.12 (6) op(e2, e3) = all_52_1
% 170.11/26.12 (7) op(e2, e3) = e2
% 170.11/26.12 (8) ~ (e3 = e0)
% 170.11/26.12 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.12 (10) ~ (e2 = e0)
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | BETA: splitting (2) gives:
% 170.11/26.12 |
% 170.11/26.12 | Case 1:
% 170.11/26.12 | |
% 170.11/26.12 | | (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 170.11/26.12 | | e0)
% 170.11/26.12 | |
% 170.11/26.12 | | BETA: splitting (11) gives:
% 170.11/26.12 | |
% 170.11/26.12 | | Case 1:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (12) all_58_0 = e0 & op(e3, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (3), (5), (12) are inconsistent by sub-proof #903.
% 170.11/26.12 | | |
% 170.11/26.12 | | Case 2:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (13) all_58_2 = e0 & op(e2, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (6), (7), (9), (10), (13) are inconsistent by sub-proof #782.
% 170.11/26.12 | | |
% 170.11/26.12 | | End of split
% 170.11/26.12 | |
% 170.11/26.12 | Case 2:
% 170.11/26.12 | |
% 170.11/26.12 | | (14) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 170.11/26.12 | | e0)
% 170.11/26.12 | |
% 170.11/26.12 | | BETA: splitting (14) gives:
% 170.11/26.12 | |
% 170.11/26.12 | | Case 1:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (15) all_58_6 = e0 & op(e1, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | ALPHA: (15) implies:
% 170.11/26.12 | | | (16) all_58_6 = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (4), (8), (16) are inconsistent by sub-proof #537.
% 170.11/26.12 | | |
% 170.11/26.12 | | Case 2:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (17) all_58_12 = e0 & op(e0, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (1), (5), (17) are inconsistent by sub-proof #859.
% 170.11/26.12 | | |
% 170.11/26.12 | | End of split
% 170.11/26.12 | |
% 170.11/26.12 | End of split
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #460 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 170.11/26.12 (2) op(e2, e3) = all_52_1
% 170.11/26.12 (3) op(e2, e3) = e2
% 170.11/26.12 (4) ~ (e3 = e0)
% 170.11/26.12 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.12 (6) ~ (e2 = e0)
% 170.11/26.12 (7) op(e3, e3) = e3
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | BETA: splitting (1) gives:
% 170.11/26.12 |
% 170.11/26.12 | Case 1:
% 170.11/26.12 | |
% 170.11/26.12 | | (8) all_58_0 = e0 & op(e3, e3) = e0
% 170.11/26.12 | |
% 170.11/26.12 | | ALPHA: (8) implies:
% 170.11/26.12 | | (9) op(e3, e3) = e0
% 170.11/26.12 | |
% 170.11/26.12 | | REF_CLOSE: (4), (5), (7), (9) are inconsistent by sub-proof #949.
% 170.11/26.12 | |
% 170.11/26.12 | Case 2:
% 170.11/26.12 | |
% 170.11/26.12 | | (10) all_58_2 = e0 & op(e2, e3) = e0
% 170.11/26.12 | |
% 170.11/26.12 | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #782.
% 170.11/26.12 | |
% 170.11/26.12 | End of split
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #461 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) all_58_12 = e2
% 170.11/26.12 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.11/26.12 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.11/26.12 (3) ~ (e3 = e1)
% 170.11/26.12 (4) all_58_6 = e3
% 170.11/26.12 (5) ~ (e1 = e0)
% 170.11/26.12 (6) op(e2, e3) = all_52_1
% 170.11/26.12 (7) op(e2, e3) = e2
% 170.11/26.12 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.11/26.12 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.11/26.12 (9) ~ (e3 = e0)
% 170.11/26.12 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.12 (11) ~ (e2 = e0)
% 170.11/26.12 (12) ~ (e2 = e1)
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | BETA: splitting (2) gives:
% 170.11/26.12 |
% 170.11/26.12 | Case 1:
% 170.11/26.12 | |
% 170.11/26.12 | | (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 170.11/26.12 | | e0)
% 170.11/26.12 | |
% 170.11/26.12 | | BETA: splitting (13) gives:
% 170.11/26.12 | |
% 170.11/26.12 | | Case 1:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (14) all_58_0 = e0 & op(e3, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | ALPHA: (14) implies:
% 170.11/26.12 | | | (15) all_58_0 = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | BETA: splitting (8) gives:
% 170.11/26.12 | | |
% 170.11/26.12 | | | Case 1:
% 170.11/26.12 | | | |
% 170.11/26.12 | | | | (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3)
% 170.11/26.12 | | | | = e1)
% 170.11/26.12 | | | |
% 170.11/26.12 | | | | BETA: splitting (16) gives:
% 170.11/26.12 | | | |
% 170.11/26.12 | | | | Case 1:
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | (17) all_58_0 = e1 & op(e3, e3) = e1
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | ALPHA: (17) implies:
% 170.11/26.12 | | | | | (18) all_58_0 = e1
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | COMBINE_EQS: (15), (18) imply:
% 170.11/26.12 | | | | | (19) e1 = e0
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | SIMP: (19) implies:
% 170.11/26.12 | | | | | (20) e1 = e0
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | REDUCE: (5), (20) imply:
% 170.11/26.12 | | | | | (21) $false
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | CLOSE: (21) is inconsistent.
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | Case 2:
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | (22) all_58_2 = e1 & op(e2, e3) = e1
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | ALPHA: (22) implies:
% 170.11/26.12 | | | | | (23) op(e2, e3) = e1
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | REF_CLOSE: (6), (7), (10), (12), (23) are inconsistent by sub-proof
% 170.11/26.12 | | | | | #784.
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | End of split
% 170.11/26.12 | | | |
% 170.11/26.12 | | | Case 2:
% 170.11/26.12 | | | |
% 170.11/26.12 | | | | (24) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3)
% 170.11/26.12 | | | | = e1)
% 170.11/26.12 | | | |
% 170.11/26.12 | | | | BETA: splitting (24) gives:
% 170.11/26.12 | | | |
% 170.11/26.12 | | | | Case 1:
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | (25) all_58_6 = e1 & op(e1, e3) = e1
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | REF_CLOSE: (3), (4), (25) are inconsistent by sub-proof #487.
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | Case 2:
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | (26) all_58_12 = e1 & op(e0, e3) = e1
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | | REF_CLOSE: (1), (12), (26) are inconsistent by sub-proof #891.
% 170.11/26.12 | | | | |
% 170.11/26.12 | | | | End of split
% 170.11/26.12 | | | |
% 170.11/26.12 | | | End of split
% 170.11/26.12 | | |
% 170.11/26.12 | | Case 2:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (27) all_58_2 = e0 & op(e2, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (6), (7), (10), (11), (27) are inconsistent by sub-proof #782.
% 170.11/26.12 | | |
% 170.11/26.12 | | End of split
% 170.11/26.12 | |
% 170.11/26.12 | Case 2:
% 170.11/26.12 | |
% 170.11/26.12 | | (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 170.11/26.12 | | e0)
% 170.11/26.12 | |
% 170.11/26.12 | | BETA: splitting (28) gives:
% 170.11/26.12 | |
% 170.11/26.12 | | Case 1:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (29) all_58_6 = e0 & op(e1, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (4), (9), (29) are inconsistent by sub-proof #559.
% 170.11/26.12 | | |
% 170.11/26.12 | | Case 2:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (30) all_58_12 = e0 & op(e0, e3) = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (1), (11), (30) are inconsistent by sub-proof #886.
% 170.11/26.12 | | |
% 170.11/26.12 | | End of split
% 170.11/26.12 | |
% 170.11/26.12 | End of split
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #462 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) op(e2, e3) = e3
% 170.11/26.12 (2) op(e2, e3) = all_52_1
% 170.11/26.12 (3) op(e2, e3) = e2
% 170.11/26.12 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.12 (5) ~ (e3 = e2)
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | GROUND_INST: instantiating (4) with all_52_1, e2, e3, e2, simplifying with
% 170.11/26.12 | (2), (3) gives:
% 170.11/26.12 | (6) all_52_1 = e2
% 170.11/26.12 |
% 170.11/26.12 | GROUND_INST: instantiating (4) with all_52_1, e3, e3, e2, simplifying with
% 170.11/26.12 | (1), (2) gives:
% 170.11/26.12 | (7) all_52_1 = e3
% 170.11/26.12 |
% 170.11/26.12 | COMBINE_EQS: (6), (7) imply:
% 170.11/26.12 | (8) e3 = e2
% 170.11/26.12 |
% 170.11/26.12 | REDUCE: (5), (8) imply:
% 170.11/26.12 | (9) $false
% 170.11/26.12 |
% 170.11/26.12 | CLOSE: (9) is inconsistent.
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #463 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.11/26.12 (2) op(e1, e2) = all_52_6
% 170.11/26.12 (3) ~ (all_52_7 = e3)
% 170.11/26.12 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.12 (5) ~ (all_52_6 = e3)
% 170.11/26.12 (6) op(e0, e2) = all_52_7
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | BETA: splitting (1) gives:
% 170.11/26.12 |
% 170.11/26.12 | Case 1:
% 170.11/26.12 | |
% 170.11/26.12 | | (7) all_58_7 = e3 & op(e1, e2) = e3
% 170.11/26.12 | |
% 170.11/26.12 | | ALPHA: (7) implies:
% 170.11/26.12 | | (8) op(e1, e2) = e3
% 170.11/26.12 | |
% 170.11/26.12 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #668.
% 170.11/26.12 | |
% 170.11/26.12 | Case 2:
% 170.11/26.12 | |
% 170.11/26.12 | | (9) all_58_13 = e3 & op(e0, e2) = e3
% 170.11/26.12 | |
% 170.11/26.12 | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #962.
% 170.11/26.12 | |
% 170.11/26.12 | End of split
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #464 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) all_58_15 = e3 & op(e0, e0) = e3
% 170.11/26.12 (2) all_58_15 = e2
% 170.11/26.12 (3) ~ (e3 = e2)
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | ALPHA: (1) implies:
% 170.11/26.12 | (4) all_58_15 = e3
% 170.11/26.12 |
% 170.11/26.12 | COMBINE_EQS: (2), (4) imply:
% 170.11/26.12 | (5) e3 = e2
% 170.11/26.12 |
% 170.11/26.12 | REDUCE: (3), (5) imply:
% 170.11/26.12 | (6) $false
% 170.11/26.12 |
% 170.11/26.12 | CLOSE: (6) is inconsistent.
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #465 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.11/26.12 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.11/26.12 (2) ~ (all_8_2 = e3)
% 170.11/26.12 (3) ~ (e3 = e1)
% 170.11/26.12 (4) op(e3, e0) = all_52_12
% 170.11/26.12 (5) ~ (e1 = e0)
% 170.11/26.12 (6) ~ (all_52_12 = e2)
% 170.11/26.12 (7) op(e2, e2) = all_8_2
% 170.11/26.12 (8) ~ (e3 = e0)
% 170.11/26.12 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.11/26.12 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.11/26.12 (10) all_58_3 = e2
% 170.11/26.12 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.12 (12) ~ (e2 = e0)
% 170.11/26.12 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.11/26.12 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.11/26.12 (14) ~ (e2 = e1)
% 170.11/26.12 (15) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.11/26.12 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.11/26.12 (16) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.11/26.12 (17) ~ (e3 = e2)
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | BETA: splitting (16) gives:
% 170.11/26.12 |
% 170.11/26.12 | Case 1:
% 170.11/26.12 | |
% 170.11/26.12 | | (18) all_58_9 = e2 & op(e3, e0) = e2
% 170.11/26.12 | |
% 170.11/26.12 | | REF_CLOSE: (4), (6), (11), (18) are inconsistent by sub-proof #663.
% 170.11/26.12 | |
% 170.11/26.12 | Case 2:
% 170.11/26.12 | |
% 170.11/26.12 | | (19) all_58_10 = e2 & op(e2, e0) = e2
% 170.11/26.12 | |
% 170.11/26.12 | | ALPHA: (19) implies:
% 170.11/26.12 | | (20) all_58_10 = e2
% 170.11/26.12 | |
% 170.11/26.12 | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 170.11/26.12 | | (15), (17), (20) are inconsistent by sub-proof #908.
% 170.11/26.12 | |
% 170.11/26.12 | End of split
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #466 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) op(e2, e1) = all_52_9
% 170.11/26.12 (2) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 170.11/26.12 (3) ~ (all_8_2 = e3)
% 170.11/26.12 (4) ~ (all_56_12 = e0) | (all_56_11 = e2 & op(e2, e0) = e2)
% 170.11/26.12 (5) all_56_12 = all_8_2
% 170.11/26.12 (6) ~ (all_52_13 = e2)
% 170.11/26.12 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.12 (8) op(e2, e1) = e2
% 170.11/26.12 (9) ~ (all_52_9 = all_8_2)
% 170.11/26.12 (10) all_54_5 = all_8_2
% 170.11/26.12 (11) ~ (all_8_2 = e1)
% 170.11/26.12 (12) op(e2, e0) = all_52_13
% 170.11/26.12
% 170.11/26.12 Begin of proof
% 170.11/26.12 |
% 170.11/26.12 | BETA: splitting (4) gives:
% 170.11/26.12 |
% 170.11/26.12 | Case 1:
% 170.11/26.12 | |
% 170.11/26.12 | | (13) ~ (all_56_12 = e0)
% 170.11/26.12 | |
% 170.11/26.12 | | REDUCE: (5), (13) imply:
% 170.11/26.12 | | (14) ~ (all_8_2 = e0)
% 170.11/26.12 | |
% 170.11/26.12 | | BETA: splitting (2) gives:
% 170.11/26.12 | |
% 170.11/26.12 | | Case 1:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (15) all_54_5 = e3
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (3), (10), (15) are inconsistent by sub-proof #667.
% 170.11/26.12 | | |
% 170.11/26.12 | | Case 2:
% 170.11/26.12 | | |
% 170.11/26.12 | | | (16) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 170.11/26.12 | | |
% 170.11/26.12 | | | REF_CLOSE: (1), (7), (8), (9), (10), (11), (14), (16) are inconsistent by
% 170.11/26.12 | | | sub-proof #467.
% 170.11/26.12 | | |
% 170.11/26.12 | | End of split
% 170.11/26.12 | |
% 170.11/26.12 | Case 2:
% 170.11/26.12 | |
% 170.11/26.12 | | (17) all_56_11 = e2 & op(e2, e0) = e2
% 170.11/26.12 | |
% 170.11/26.12 | | ALPHA: (17) implies:
% 170.11/26.12 | | (18) op(e2, e0) = e2
% 170.11/26.12 | |
% 170.11/26.12 | | REF_CLOSE: (6), (7), (12), (18) are inconsistent by sub-proof #662.
% 170.11/26.12 | |
% 170.11/26.12 | End of split
% 170.11/26.12 |
% 170.11/26.12 End of proof
% 170.11/26.12
% 170.11/26.12 Sub-proof #467 shows that the following formulas are inconsistent:
% 170.11/26.12 ----------------------------------------------------------------
% 170.11/26.12 (1) op(e2, e1) = all_52_9
% 170.11/26.12 (2) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 170.11/26.12 (3) ~ (all_8_2 = e0)
% 170.11/26.12 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.11/26.12 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.11/26.13 (5) op(e2, e1) = e2
% 170.11/26.13 (6) ~ (all_52_9 = all_8_2)
% 170.11/26.13 (7) all_54_5 = all_8_2
% 170.11/26.13 (8) ~ (all_8_2 = e1)
% 170.11/26.13
% 170.11/26.13 Begin of proof
% 170.11/26.13 |
% 170.11/26.13 | BETA: splitting (2) gives:
% 170.11/26.13 |
% 170.11/26.13 | Case 1:
% 170.11/26.13 | |
% 170.11/26.13 | | (9) all_54_5 = e2
% 170.11/26.13 | |
% 170.11/26.13 | | COMBINE_EQS: (7), (9) imply:
% 170.11/26.13 | | (10) all_8_2 = e2
% 170.11/26.13 | |
% 170.11/26.13 | | SIMP: (10) implies:
% 170.11/26.13 | | (11) all_8_2 = e2
% 170.11/26.13 | |
% 170.11/26.13 | | REDUCE: (6), (11) imply:
% 170.11/26.13 | | (12) ~ (all_52_9 = e2)
% 170.21/26.13 | |
% 170.21/26.13 | | REF_CLOSE: (1), (4), (5), (12) are inconsistent by sub-proof #571.
% 170.21/26.13 | |
% 170.21/26.13 | Case 2:
% 170.21/26.13 | |
% 170.21/26.13 | | (13) all_54_5 = e1 | all_54_5 = e0
% 170.21/26.13 | |
% 170.21/26.13 | | REF_CLOSE: (3), (7), (8), (13) are inconsistent by sub-proof #735.
% 170.21/26.13 | |
% 170.21/26.13 | End of split
% 170.21/26.13 |
% 170.21/26.13 End of proof
% 170.21/26.13
% 170.21/26.13 Sub-proof #468 shows that the following formulas are inconsistent:
% 170.21/26.13 ----------------------------------------------------------------
% 170.21/26.13 (1) all_58_7 = e2 & op(e1, e2) = e2
% 170.21/26.13 (2) all_58_7 = e0
% 170.21/26.13 (3) ~ (e2 = e0)
% 170.21/26.13
% 170.21/26.13 Begin of proof
% 170.21/26.13 |
% 170.21/26.13 | ALPHA: (1) implies:
% 170.21/26.13 | (4) all_58_7 = e2
% 170.21/26.13 |
% 170.21/26.13 | COMBINE_EQS: (2), (4) imply:
% 170.21/26.13 | (5) e2 = e0
% 170.21/26.13 |
% 170.21/26.13 | REDUCE: (3), (5) imply:
% 170.21/26.13 | (6) $false
% 170.21/26.13 |
% 170.21/26.13 | CLOSE: (6) is inconsistent.
% 170.21/26.13 |
% 170.21/26.13 End of proof
% 170.21/26.13
% 170.21/26.13 Sub-proof #469 shows that the following formulas are inconsistent:
% 170.21/26.13 ----------------------------------------------------------------
% 170.21/26.13 (1) all_58_12 = e1
% 170.21/26.13 (2) op(e0, e1) = all_52_11
% 170.21/26.13 (3) ~ (e3 = e1)
% 170.21/26.13 (4) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 170.21/26.13 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.21/26.13 (5) ~ (all_52_7 = e3)
% 170.21/26.13 (6) ~ (e3 = e0)
% 170.21/26.13 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.21/26.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.21/26.13 (8) all_58_15 = e0
% 170.21/26.13 (9) ~ (all_52_11 = e3)
% 170.21/26.13 (10) op(e0, e2) = all_52_7
% 170.21/26.13
% 170.21/26.13 Begin of proof
% 170.21/26.13 |
% 170.21/26.13 | BETA: splitting (4) gives:
% 170.21/26.13 |
% 170.21/26.13 | Case 1:
% 170.21/26.13 | |
% 170.21/26.13 | | (11) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 170.21/26.13 | | e3)
% 170.21/26.13 | |
% 170.21/26.13 | | REF_CLOSE: (1), (3), (5), (7), (10), (11) are inconsistent by sub-proof
% 170.21/26.13 | | #470.
% 170.21/26.13 | |
% 170.21/26.13 | Case 2:
% 170.21/26.13 | |
% 170.21/26.13 | | (12) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.21/26.13 | | e3)
% 170.21/26.13 | |
% 170.21/26.13 | | BETA: splitting (12) gives:
% 170.21/26.13 | |
% 170.21/26.13 | | Case 1:
% 170.21/26.13 | | |
% 170.21/26.13 | | | (13) all_58_14 = e3 & op(e0, e1) = e3
% 170.21/26.13 | | |
% 170.21/26.13 | | | REF_CLOSE: (2), (7), (9), (13) are inconsistent by sub-proof #960.
% 170.21/26.13 | | |
% 170.21/26.13 | | Case 2:
% 170.21/26.13 | | |
% 170.21/26.13 | | | (14) all_58_15 = e3 & op(e0, e0) = e3
% 170.21/26.13 | | |
% 170.21/26.13 | | | REF_CLOSE: (6), (8), (14) are inconsistent by sub-proof #812.
% 170.21/26.13 | | |
% 170.21/26.13 | | End of split
% 170.21/26.13 | |
% 170.21/26.13 | End of split
% 170.21/26.13 |
% 170.21/26.13 End of proof
% 170.21/26.13
% 170.21/26.13 Sub-proof #470 shows that the following formulas are inconsistent:
% 170.21/26.13 ----------------------------------------------------------------
% 170.21/26.13 (1) all_58_12 = e1
% 170.21/26.13 (2) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.21/26.13 (3) ~ (e3 = e1)
% 170.21/26.13 (4) ~ (all_52_7 = e3)
% 170.21/26.13 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.21/26.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.21/26.13 (6) op(e0, e2) = all_52_7
% 170.21/26.13
% 170.21/26.13 Begin of proof
% 170.21/26.13 |
% 170.21/26.13 | BETA: splitting (2) gives:
% 170.21/26.13 |
% 170.21/26.13 | Case 1:
% 170.21/26.13 | |
% 170.21/26.13 | | (7) all_58_12 = e3 & op(e0, e3) = e3
% 170.21/26.13 | |
% 170.21/26.13 | | ALPHA: (7) implies:
% 170.21/26.13 | | (8) all_58_12 = e3
% 170.21/26.13 | |
% 170.21/26.13 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #600.
% 170.21/26.13 | |
% 170.21/26.13 | Case 2:
% 170.21/26.13 | |
% 170.21/26.13 | | (9) all_58_13 = e3 & op(e0, e2) = e3
% 170.21/26.13 | |
% 170.21/26.13 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #962.
% 170.21/26.13 | |
% 170.21/26.13 | End of split
% 170.21/26.13 |
% 170.21/26.13 End of proof
% 170.21/26.13
% 170.21/26.13 Sub-proof #471 shows that the following formulas are inconsistent:
% 170.21/26.13 ----------------------------------------------------------------
% 170.21/26.13 (1) all_58_11 = e2 & op(e1, e0) = e2
% 170.21/26.13 (2) all_58_11 = e1
% 170.21/26.13 (3) ~ (e2 = e1)
% 170.21/26.13
% 170.21/26.13 Begin of proof
% 170.21/26.13 |
% 170.21/26.13 | ALPHA: (1) implies:
% 170.21/26.13 | (4) all_58_11 = e2
% 170.21/26.13 |
% 170.21/26.13 | COMBINE_EQS: (2), (4) imply:
% 170.21/26.13 | (5) e2 = e1
% 170.21/26.13 |
% 170.21/26.13 | REDUCE: (3), (5) imply:
% 170.21/26.13 | (6) $false
% 170.21/26.13 |
% 170.21/26.13 | CLOSE: (6) is inconsistent.
% 170.21/26.13 |
% 170.21/26.13 End of proof
% 170.21/26.13
% 170.21/26.13 Sub-proof #472 shows that the following formulas are inconsistent:
% 170.21/26.13 ----------------------------------------------------------------
% 170.21/26.13 (1) op(e2, e1) = all_52_9
% 170.21/26.13 (2) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 170.21/26.13 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 170.21/26.13 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.21/26.13 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.21/26.13 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.21/26.13 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 170.21/26.13 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.21/26.13 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.21/26.13 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.21/26.13 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 170.21/26.13 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 170.21/26.13 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.21/26.13 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.21/26.13 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.21/26.13 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.21/26.13 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 170.21/26.13 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.21/26.13 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.21/26.13 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.21/26.13 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 170.21/26.13 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 170.21/26.13 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.21/26.13 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.21/26.13 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.21/26.13 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 170.21/26.13 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 170.21/26.13 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.21/26.13 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.21/26.13 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.21/26.13 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.21/26.13 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 170.21/26.13 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.21/26.13 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.21/26.13 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.21/26.13 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 170.21/26.13 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 170.21/26.13 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.21/26.13 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.21/26.13 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.21/26.13 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.21/26.13 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 170.21/26.13 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.21/26.13 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.21/26.13 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.21/26.13 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 170.21/26.13 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.21/26.13 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 170.21/26.13 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 170.21/26.13 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 170.21/26.13 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 170.21/26.13 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.21/26.13 (3) op(e0, e1) = all_52_11
% 170.21/26.13 (4) all_58_14 = e2
% 170.21/26.13 (5) all_56_1 = e3
% 170.21/26.13 (6) all_56_10 = e2
% 170.21/26.13 (7) all_56_2 = e1
% 170.21/26.13 (8) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.21/26.13 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.21/26.13 (9) all_54_12 = all_52_3
% 170.21/26.13 (10) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 170.21/26.13 (11) ~ (all_52_11 = all_4_2)
% 170.21/26.13 (12) ~ (all_52_1 = all_8_2)
% 170.21/26.13 (13) ~ (all_8_2 = e3)
% 170.21/26.13 (14) all_58_6 = e1
% 170.21/26.13 (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.21/26.13 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.21/26.13 (16) ~ (all_56_15 = e3) | (all_56_6 = e0 & op(e0, e3) = e0)
% 170.21/26.13 (17) all_56_14 = e3
% 170.21/26.13 (18) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.21/26.13 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.21/26.13 (19) ~ (all_52_1 = all_52_3)
% 170.21/26.13 (20) op(e1, e3) = all_52_2
% 170.21/26.13 (21) ~ (all_52_6 = all_8_2)
% 170.21/26.13 (22) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.21/26.13 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.21/26.13 e3)
% 170.21/26.13 (23) ~ (all_56_12 = e0) | (all_56_11 = e2 & op(e2, e0) = e2)
% 170.21/26.13 (24) ~ (all_52_1 = e2)
% 170.21/26.13 (25) op(e1, e2) = all_52_6
% 170.21/26.13 (26) op(e0, e2) = e1
% 170.21/26.13 (27) ~ (all_52_3 = all_4_2)
% 170.21/26.13 (28) op(e2, e3) = all_52_1
% 170.21/26.13 (29) ~ (all_52_7 = all_4_2)
% 170.21/26.13 (30) ~ (all_52_3 = all_52_7)
% 170.21/26.13 (31) ~ (all_52_7 = e3)
% 170.21/26.13 (32) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 170.21/26.13 (33) all_54_15 = all_4_2
% 170.21/26.13 (34) ~ (all_6_2 = e2)
% 170.21/26.13 (35) all_56_12 = all_8_2
% 170.21/26.13 (36) op(e1, e1) = all_6_2
% 170.21/26.13 (37) all_54_4 = all_52_1
% 170.21/26.13 (38) all_56_15 = all_4_2
% 170.21/26.13 (39) ~ (all_52_7 = all_8_2)
% 170.21/26.13 (40) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.21/26.13 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.21/26.13 (41) ~ (all_52_1 = e1)
% 170.21/26.13 (42) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.21/26.13 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.21/26.13 (43) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 170.21/26.13 (44) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.21/26.13 (45) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.21/26.13 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 170.21/26.13 (46) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 170.21/26.13 (47) all_58_1 = e3
% 170.22/26.13 (48) ~ (all_52_3 = all_52_11)
% 170.22/26.13 (49) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.22/26.13 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.22/26.13 (50) ~ (all_52_7 = all_52_11)
% 170.22/26.13 (51) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.13 (52) ~ (e2 = e0)
% 170.22/26.13 (53) all_58_8 = e3
% 170.22/26.13 (54) ~ (all_52_9 = all_8_2)
% 170.22/26.13 (55) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.22/26.13 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.22/26.13 (56) all_58_0 = e2
% 170.22/26.13 (57) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.22/26.13 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.22/26.13 (58) op(e3, e3) = e2
% 170.22/26.13 (59) all_54_5 = all_8_2
% 170.22/26.13 (60) ~ (all_52_4 = e2)
% 170.22/26.13 (61) op(e3, e2) = all_52_4
% 170.22/26.13 (62) all_30_2 = all_8_2
% 170.22/26.13 (63) op(e0, e1) = e2
% 170.22/26.13 (64) ~ (all_52_11 = e3)
% 170.22/26.13 (65) op(e0, e2) = all_52_7
% 170.22/26.13 (66) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.22/26.13 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.22/26.13 (67) ~ (all_30_2 = e0) | ( ~ (all_30_0 = e1) & op(all_30_1, e2) = all_30_0 &
% 170.22/26.13 op(e0, e2) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 170.22/26.13 e3) & op(e0, e2) = all_30_1 & $i(all_30_1))
% 170.22/26.13 (68) op(e1, e3) = e1
% 170.22/26.13 (69) op(e2, e0) = all_52_13
% 170.22/26.13
% 170.22/26.13 Begin of proof
% 170.22/26.13 |
% 170.22/26.13 | GROUND_INST: instantiating (51) with all_52_11, e2, e1, e0, simplifying with
% 170.22/26.13 | (3), (63) gives:
% 170.22/26.13 | (70) all_52_11 = e2
% 170.22/26.13 |
% 170.22/26.13 | GROUND_INST: instantiating (51) with all_52_7, e1, e2, e0, simplifying with
% 170.22/26.13 | (26), (65) gives:
% 170.22/26.13 | (71) all_52_7 = e1
% 170.22/26.13 |
% 170.22/26.13 | REDUCE: (30), (71) imply:
% 170.22/26.13 | (72) ~ (all_52_3 = e1)
% 170.22/26.13 |
% 170.22/26.13 | REDUCE: (48), (70) imply:
% 170.22/26.13 | (73) ~ (all_52_3 = e2)
% 170.22/26.13 |
% 170.22/26.13 | REDUCE: (50), (70), (71) imply:
% 170.22/26.13 | (74) ~ (e2 = e1)
% 170.22/26.13 |
% 170.22/26.13 | SIMP: (74) implies:
% 170.22/26.13 | (75) ~ (e2 = e1)
% 170.22/26.13 |
% 170.22/26.13 | REDUCE: (39), (71) imply:
% 170.22/26.13 | (76) ~ (all_8_2 = e1)
% 170.22/26.13 |
% 170.22/26.13 | SIMP: (76) implies:
% 170.22/26.13 | (77) ~ (all_8_2 = e1)
% 170.22/26.13 |
% 170.22/26.13 | REDUCE: (29), (71) imply:
% 170.22/26.13 | (78) ~ (all_4_2 = e1)
% 170.22/26.13 |
% 170.22/26.13 | SIMP: (78) implies:
% 170.22/26.13 | (79) ~ (all_4_2 = e1)
% 170.22/26.13 |
% 170.22/26.13 | REDUCE: (31), (71) imply:
% 170.22/26.13 | (80) ~ (e3 = e1)
% 170.22/26.13 |
% 170.22/26.13 | SIMP: (80) implies:
% 170.22/26.13 | (81) ~ (e3 = e1)
% 170.22/26.13 |
% 170.22/26.13 | REDUCE: (11), (70) imply:
% 170.22/26.13 | (82) ~ (all_4_2 = e2)
% 170.22/26.13 |
% 170.22/26.13 | SIMP: (82) implies:
% 170.22/26.13 | (83) ~ (all_4_2 = e2)
% 170.22/26.13 |
% 170.22/26.13 | REDUCE: (64), (70) imply:
% 170.22/26.13 | (84) ~ (e3 = e2)
% 170.22/26.13 |
% 170.22/26.13 | SIMP: (84) implies:
% 170.22/26.13 | (85) ~ (e3 = e2)
% 170.22/26.13 |
% 170.22/26.13 | BETA: splitting (67) gives:
% 170.22/26.13 |
% 170.22/26.13 | Case 1:
% 170.22/26.13 | |
% 170.22/26.13 | | (86) ~ (all_30_2 = e0)
% 170.22/26.13 | |
% 170.22/26.13 | | REDUCE: (62), (86) imply:
% 170.22/26.13 | | (87) ~ (all_8_2 = e0)
% 170.22/26.13 | |
% 170.22/26.13 | | BETA: splitting (10) gives:
% 170.22/26.13 | |
% 170.22/26.13 | | Case 1:
% 170.22/26.13 | | |
% 170.22/26.13 | | | (88) all_54_5 = e3
% 170.22/26.13 | | |
% 170.22/26.13 | | | REF_CLOSE: (13), (59), (88) are inconsistent by sub-proof #667.
% 170.22/26.13 | | |
% 170.22/26.13 | | Case 2:
% 170.22/26.13 | | |
% 170.22/26.13 | | | (89) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 170.22/26.13 | | |
% 170.22/26.13 | | | BETA: splitting (89) gives:
% 170.22/26.13 | | |
% 170.22/26.13 | | | Case 1:
% 170.22/26.13 | | | |
% 170.22/26.13 | | | | (90) all_54_5 = e2
% 170.22/26.13 | | | |
% 170.22/26.13 | | | | COMBINE_EQS: (59), (90) imply:
% 170.22/26.13 | | | | (91) all_8_2 = e2
% 170.22/26.13 | | | |
% 170.22/26.13 | | | | SIMP: (91) implies:
% 170.22/26.13 | | | | (92) all_8_2 = e2
% 170.22/26.13 | | | |
% 170.22/26.13 | | | | REDUCE: (21), (92) imply:
% 170.22/26.13 | | | | (93) ~ (all_52_6 = e2)
% 170.22/26.13 | | | |
% 170.22/26.13 | | | | BETA: splitting (15) gives:
% 170.22/26.13 | | | |
% 170.22/26.13 | | | | Case 1:
% 170.22/26.13 | | | | |
% 170.22/26.13 | | | | | (94) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1,
% 170.22/26.13 | | | | | e2) = e2)
% 170.22/26.13 | | | | |
% 170.22/26.13 | | | | | BETA: splitting (94) gives:
% 170.22/26.13 | | | | |
% 170.22/26.13 | | | | | Case 1:
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | (95) all_58_6 = e2 & op(e1, e3) = e2
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | ALPHA: (95) implies:
% 170.22/26.13 | | | | | | (96) all_58_6 = e2
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | REF_CLOSE: (14), (75), (96) are inconsistent by sub-proof #823.
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | Case 2:
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | (97) all_58_7 = e2 & op(e1, e2) = e2
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | ALPHA: (97) implies:
% 170.22/26.13 | | | | | | (98) op(e1, e2) = e2
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | REF_CLOSE: (25), (51), (93), (98) are inconsistent by sub-proof
% 170.22/26.13 | | | | | | #986.
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | End of split
% 170.22/26.13 | | | | |
% 170.22/26.13 | | | | Case 2:
% 170.22/26.13 | | | | |
% 170.22/26.13 | | | | | (99) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1,
% 170.22/26.13 | | | | | e0) = e2)
% 170.22/26.13 | | | | |
% 170.22/26.13 | | | | | BETA: splitting (99) gives:
% 170.22/26.13 | | | | |
% 170.22/26.13 | | | | | Case 1:
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | (100) all_58_8 = e2 & op(e1, e1) = e2
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | REF_CLOSE: (34), (36), (51), (100) are inconsistent by sub-proof
% 170.22/26.13 | | | | | | #845.
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | Case 2:
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | (101) all_58_11 = e2 & op(e1, e0) = e2
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | ALPHA: (101) implies:
% 170.22/26.13 | | | | | | (102) op(e1, e0) = e2
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | BETA: splitting (2) gives:
% 170.22/26.13 | | | | | |
% 170.22/26.13 | | | | | | Case 1:
% 170.22/26.13 | | | | | | |
% 170.22/26.13 | | | | | | | (103) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 &
% 170.22/26.13 | | | | | | | ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2)
% 170.22/26.13 | | | | | | | = all_56_1 & $i(all_56_1))) & ( ~ (all_56_14 = e2)
% 170.22/26.13 | | | | | | | | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.13 | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.22/26.13 | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.22/26.13 | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~ (all_56_10 =
% 170.22/26.13 | | | | | | | e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 170.22/26.13 | | | | | | | (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 170.22/26.13 | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.22/26.13 | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.13 | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.22/26.13 | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.22/26.13 | | | | | | | $i(all_56_6)))) | (all_56_2 = e3 & ~ (all_56_14 =
% 170.22/26.13 | | | | | | | e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 170.22/26.13 | | | | | | | (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 170.22/26.13 | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.22/26.13 | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.13 | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.22/26.13 | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.22/26.13 | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~ (all_56_14 =
% 170.22/26.13 | | | | | | | e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 170.22/26.13 | | | | | | | (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 170.22/26.13 | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.22/26.13 | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.13 | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.22/26.13 | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.22/26.13 | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~ (all_56_10 =
% 170.22/26.13 | | | | | | | e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 170.22/26.13 | | | | | | | (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 170.22/26.13 | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.22/26.13 | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.13 | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.22/26.13 | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.22/26.13 | | | | | | | $i(all_56_6))))
% 170.22/26.13 | | | | | | |
% 170.22/26.13 | | | | | | | BETA: splitting (103) gives:
% 170.22/26.13 | | | | | | |
% 170.22/26.13 | | | | | | | Case 1:
% 170.22/26.13 | | | | | | | |
% 170.22/26.13 | | | | | | | | (104) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3
% 170.22/26.13 | | | | | | | | & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 170.22/26.13 | | | | | | | | e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.22/26.13 | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2)
% 170.22/26.13 | | | | | | | | = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 =
% 170.22/26.13 | | | | | | | | e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 170.22/26.13 | | | | | | | | & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.22/26.13 | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 =
% 170.22/26.13 | | | | | | | | e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0
% 170.22/26.13 | | | | | | | | & $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.22/26.13 | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.13 | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.22/26.13 | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.22/26.13 | | | | | | | | $i(all_56_6))))
% 170.22/26.13 | | | | | | | |
% 170.22/26.13 | | | | | | | | BETA: splitting (104) gives:
% 170.22/26.13 | | | | | | | |
% 170.22/26.13 | | | | | | | | Case 1:
% 170.22/26.13 | | | | | | | | |
% 170.22/26.13 | | | | | | | | | (105) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3
% 170.22/26.13 | | | | | | | | | & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 170.22/26.13 | | | | | | | | | e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.22/26.13 | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2)
% 170.22/26.13 | | | | | | | | | = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 =
% 170.22/26.13 | | | | | | | | | e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 170.22/26.13 | | | | | | | | | & $i(all_56_7)))
% 170.22/26.13 | | | | | | | | |
% 170.22/26.13 | | | | | | | | | ALPHA: (105) implies:
% 170.22/26.13 | | | | | | | | | (106) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 170.22/26.13 | | | | | | | | | e2) = all_56_1 & $i(all_56_1))
% 170.22/26.13 | | | | | | | | |
% 170.22/26.13 | | | | | | | | | REF_CLOSE: (5), (6), (106) are inconsistent by sub-proof #554.
% 170.22/26.13 | | | | | | | | |
% 170.22/26.13 | | | | | | | | Case 2:
% 170.22/26.13 | | | | | | | | |
% 170.22/26.13 | | | | | | | | | (107) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2
% 170.22/26.13 | | | | | | | | | & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2,
% 170.22/26.13 | | | | | | | | | e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.13 | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3)
% 170.22/26.13 | | | | | | | | | = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 =
% 170.22/26.13 | | | | | | | | | e3) | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6
% 170.22/26.13 | | | | | | | | | & $i(all_56_6)))
% 170.22/26.13 | | | | | | | | |
% 170.22/26.13 | | | | | | | | | ALPHA: (107) implies:
% 170.22/26.13 | | | | | | | | | (108) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 170.22/26.13 | | | | | | | | | e3) = all_56_2 & $i(all_56_2))
% 170.22/26.13 | | | | | | | | |
% 170.22/26.13 | | | | | | | | | REF_CLOSE: (7), (17), (108) are inconsistent by sub-proof
% 170.22/26.13 | | | | | | | | | #485.
% 170.22/26.13 | | | | | | | | |
% 170.22/26.13 | | | | | | | | End of split
% 170.22/26.13 | | | | | | | |
% 170.22/26.13 | | | | | | | Case 2:
% 170.22/26.13 | | | | | | | |
% 170.22/26.13 | | | | | | | | (109) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3
% 170.22/26.13 | | | | | | | | & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 170.22/26.13 | | | | | | | | e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.13 | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1)
% 170.22/26.13 | | | | | | | | = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 =
% 170.22/26.13 | | | | | | | | e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8
% 170.22/26.13 | | | | | | | | & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.22/26.13 | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 =
% 170.22/26.13 | | | | | | | | e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4
% 170.22/26.13 | | | | | | | | & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.22/26.13 | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.13 | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.22/26.13 | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.22/26.13 | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~ (all_56_10
% 170.22/26.13 | | | | | | | | = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | (
% 170.22/26.13 | | | | | | | | ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 170.22/26.13 | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.22/26.13 | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.13 | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.22/26.13 | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.22/26.13 | | | | | | | | $i(all_56_6))))
% 170.22/26.13 | | | | | | | |
% 170.22/26.13 | | | | | | | | BETA: splitting (109) gives:
% 170.22/26.13 | | | | | | | |
% 170.22/26.13 | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | (110) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3
% 170.22/26.14 | | | | | | | | | & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3,
% 170.22/26.14 | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1)
% 170.22/26.14 | | | | | | | | | = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 =
% 170.22/26.14 | | | | | | | | | e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8
% 170.22/26.14 | | | | | | | | | & $i(all_56_8)))
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | ALPHA: (110) implies:
% 170.22/26.14 | | | | | | | | | (111) op(e1, e3) = e3
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | REF_CLOSE: (20), (51), (68), (81), (111) are inconsistent by
% 170.22/26.14 | | | | | | | | | sub-proof #750.
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | (112) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 170.22/26.14 | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.22/26.14 | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.22/26.14 | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.22/26.14 | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) | (all_56_4
% 170.22/26.14 | | | | | | | | | = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2,
% 170.22/26.14 | | | | | | | | | e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 170.22/26.14 | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 170.22/26.14 | | | | | | | | | e3) = all_56_6 & $i(all_56_6))))
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | BETA: splitting (112) gives:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | (113) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 170.22/26.14 | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.22/26.14 | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.14 | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.22/26.14 | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.14 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.22/26.14 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | ALPHA: (113) implies:
% 170.22/26.14 | | | | | | | | | | (114) op(e1, e2) = e2
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | REF_CLOSE: (25), (51), (93), (114) are inconsistent by
% 170.22/26.14 | | | | | | | | | | sub-proof #986.
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | (115) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 170.22/26.14 | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.22/26.14 | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.14 | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 170.22/26.14 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.22/26.14 | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 170.22/26.14 | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | ALPHA: (115) implies:
% 170.22/26.14 | | | | | | | | | | (116) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 170.22/26.14 | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | REF_CLOSE: (7), (17), (116) are inconsistent by sub-proof
% 170.22/26.14 | | | | | | | | | | #485.
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | End of split
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | End of split
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | End of split
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | Case 2:
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | (117) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 &
% 170.22/26.14 | | | | | | | ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2)
% 170.22/26.14 | | | | | | | = all_56_1 & $i(all_56_1))) & ( ~ (all_56_14 = e2)
% 170.22/26.14 | | | | | | | | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.14 | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.22/26.14 | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.22/26.14 | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~ (all_56_10 =
% 170.22/26.14 | | | | | | | e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 170.22/26.14 | | | | | | | (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 170.22/26.14 | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.22/26.14 | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.14 | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.22/26.14 | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.22/26.14 | | | | | | | $i(all_56_6)))) | (all_56_11 = e0 & ~ (all_56_12 =
% 170.22/26.14 | | | | | | | e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 170.22/26.14 | | | | | | | (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 170.22/26.14 | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.22/26.14 | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.14 | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.22/26.14 | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.22/26.14 | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~ (all_56_14 =
% 170.22/26.14 | | | | | | | e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 170.22/26.14 | | | | | | | (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 170.22/26.14 | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.22/26.14 | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.14 | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.22/26.14 | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.22/26.14 | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 170.22/26.14 | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) =
% 170.22/26.14 | | | | | | | all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) |
% 170.22/26.14 | | | | | | | ( ~ (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.22/26.14 | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.22/26.14 | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.22/26.14 | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) =
% 170.22/26.14 | | | | | | | e3) | (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8
% 170.22/26.14 | | | | | | | = e1 & op(e0, e1) = e1)))
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | BETA: splitting (117) gives:
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | (118) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1
% 170.22/26.14 | | | | | | | | & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 170.22/26.14 | | | | | | | | e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.22/26.14 | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2)
% 170.22/26.14 | | | | | | | | = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 =
% 170.22/26.14 | | | | | | | | e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 170.22/26.14 | | | | | | | | & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.22/26.14 | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 =
% 170.22/26.14 | | | | | | | | e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0
% 170.22/26.14 | | | | | | | | & $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.22/26.14 | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.14 | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.22/26.14 | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.22/26.14 | | | | | | | | $i(all_56_6))))
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | BETA: splitting (118) gives:
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | (119) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1
% 170.22/26.14 | | | | | | | | | & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 170.22/26.14 | | | | | | | | | e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2)
% 170.22/26.14 | | | | | | | | | = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 =
% 170.22/26.14 | | | | | | | | | e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 170.22/26.14 | | | | | | | | | & $i(all_56_7)))
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | ALPHA: (119) implies:
% 170.22/26.14 | | | | | | | | | (120) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 170.22/26.14 | | | | | | | | | e2) = all_56_1 & $i(all_56_1))
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | REF_CLOSE: (5), (6), (120) are inconsistent by sub-proof #554.
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | (121) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0
% 170.22/26.14 | | | | | | | | | & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2,
% 170.22/26.14 | | | | | | | | | e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3)
% 170.22/26.14 | | | | | | | | | = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 =
% 170.22/26.14 | | | | | | | | | e3) | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6
% 170.22/26.14 | | | | | | | | | & $i(all_56_6)))
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | ALPHA: (121) implies:
% 170.22/26.14 | | | | | | | | | (122) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 170.22/26.14 | | | | | | | | | e3) = all_56_2 & $i(all_56_2))
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | REF_CLOSE: (7), (17), (122) are inconsistent by sub-proof
% 170.22/26.14 | | | | | | | | | #485.
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | End of split
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | (123) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) = e0
% 170.22/26.14 | | | | | | | | & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 170.22/26.14 | | | | | | | | e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.22/26.14 | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2)
% 170.22/26.14 | | | | | | | | = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 =
% 170.22/26.14 | | | | | | | | e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 170.22/26.14 | | | | | | | | & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.22/26.14 | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 =
% 170.22/26.14 | | | | | | | | e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4
% 170.22/26.14 | | | | | | | | & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.22/26.14 | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.14 | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.22/26.14 | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.22/26.14 | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 170.22/26.14 | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0)
% 170.22/26.14 | | | | | | | | = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 =
% 170.22/26.14 | | | | | | | | e0) | ( ~ (all_56_11 = e2) & op(e2, e0) =
% 170.22/26.14 | | | | | | | | all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 =
% 170.22/26.14 | | | | | | | | e0) | ( ~ (all_56_13 = e1) & op(e1, e0) =
% 170.22/26.14 | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_6 = e3 &
% 170.22/26.14 | | | | | | | | op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 170.22/26.14 | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | BETA: splitting (123) gives:
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | (124) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0) =
% 170.22/26.14 | | | | | | | | | e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) &
% 170.22/26.14 | | | | | | | | | op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2)
% 170.22/26.14 | | | | | | | | | = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 =
% 170.22/26.14 | | | | | | | | | e2) | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7
% 170.22/26.14 | | | | | | | | | & $i(all_56_7)))
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | ALPHA: (124) implies:
% 170.22/26.14 | | | | | | | | | (125) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 170.22/26.14 | | | | | | | | | e2) = all_56_1 & $i(all_56_1))
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | REF_CLOSE: (5), (6), (125) are inconsistent by sub-proof #554.
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | (126) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) =
% 170.22/26.14 | | | | | | | | | e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.22/26.14 | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.22/26.14 | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.14 | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.22/26.14 | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))) | ( ~
% 170.22/26.14 | | | | | | | | | (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.22/26.14 | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.22/26.14 | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.22/26.14 | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.22/26.14 | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.22/26.14 | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.22/26.14 | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 170.22/26.14 | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 170.22/26.14 | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | BETA: splitting (126) gives:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | (127) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0) =
% 170.22/26.14 | | | | | | | | | | e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.22/26.14 | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.14 | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.22/26.14 | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.14 | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.22/26.14 | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | ALPHA: (127) implies:
% 170.22/26.14 | | | | | | | | | | (128) op(e1, e0) = e0
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | GROUND_INST: instantiating (51) with e0, e2, e0, e1,
% 170.22/26.14 | | | | | | | | | | simplifying with (102), (128) gives:
% 170.22/26.14 | | | | | | | | | | (129) e2 = e0
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | REDUCE: (52), (129) imply:
% 170.22/26.14 | | | | | | | | | | (130) $false
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | CLOSE: (130) is inconsistent.
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | (131) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.22/26.14 | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.22/26.14 | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.22/26.14 | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.22/26.14 | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.22/26.14 | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.22/26.14 | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 170.22/26.14 | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 170.22/26.14 | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | ALPHA: (131) implies:
% 170.22/26.14 | | | | | | | | | | (132) ~ (all_56_15 = e0)
% 170.22/26.14 | | | | | | | | | | (133) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 170.22/26.14 | | | | | | | | | | & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1)
% 170.22/26.14 | | | | | | | | | | = e1)
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | REDUCE: (38), (132) imply:
% 170.22/26.14 | | | | | | | | | | (134) ~ (all_4_2 = e0)
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | BETA: splitting (32) gives:
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | (135) all_54_15 = e3
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | COMBINE_EQS: (33), (135) imply:
% 170.22/26.14 | | | | | | | | | | | (136) all_4_2 = e3
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | SIMP: (136) implies:
% 170.22/26.14 | | | | | | | | | | | (137) all_4_2 = e3
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | COMBINE_EQS: (38), (137) imply:
% 170.22/26.14 | | | | | | | | | | | (138) all_56_15 = e3
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | REDUCE: (134), (137) imply:
% 170.22/26.14 | | | | | | | | | | | (139) ~ (e3 = e0)
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | BETA: splitting (16) gives:
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | (140) ~ (all_56_15 = e3)
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | REDUCE: (138), (140) imply:
% 170.22/26.14 | | | | | | | | | | | | (141) $false
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | CLOSE: (141) is inconsistent.
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | (142) all_56_6 = e0 & op(e0, e3) = e0
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | ALPHA: (142) implies:
% 170.22/26.14 | | | | | | | | | | | | (143) all_56_6 = e0
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | REF_CLOSE: (26), (51), (63), (75), (133), (139), (143) are
% 170.22/26.14 | | | | | | | | | | | | inconsistent by sub-proof #966.
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | End of split
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | (144) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | REF_CLOSE: (33), (79), (83), (134), (144) are inconsistent by
% 170.22/26.14 | | | | | | | | | | | sub-proof #697.
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | End of split
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | End of split
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | End of split
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | End of split
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | End of split
% 170.22/26.14 | | | | | |
% 170.22/26.14 | | | | | End of split
% 170.22/26.14 | | | | |
% 170.22/26.14 | | | | End of split
% 170.22/26.14 | | | |
% 170.22/26.14 | | | Case 2:
% 170.22/26.14 | | | |
% 170.22/26.14 | | | | (145) all_54_5 = e1 | all_54_5 = e0
% 170.22/26.14 | | | |
% 170.22/26.14 | | | | REF_CLOSE: (59), (77), (87), (145) are inconsistent by sub-proof #735.
% 170.22/26.14 | | | |
% 170.22/26.14 | | | End of split
% 170.22/26.14 | | |
% 170.22/26.14 | | End of split
% 170.22/26.14 | |
% 170.22/26.14 | Case 2:
% 170.22/26.14 | |
% 170.22/26.14 | | (146) all_30_2 = e0
% 170.22/26.14 | |
% 170.22/26.14 | | COMBINE_EQS: (62), (146) imply:
% 170.22/26.14 | | (147) all_8_2 = e0
% 170.22/26.14 | |
% 170.22/26.14 | | SIMP: (147) implies:
% 170.22/26.14 | | (148) all_8_2 = e0
% 170.22/26.14 | |
% 170.22/26.14 | | COMBINE_EQS: (35), (148) imply:
% 170.22/26.14 | | (149) all_56_12 = e0
% 170.22/26.14 | |
% 170.22/26.14 | | REDUCE: (12), (148) imply:
% 170.22/26.14 | | (150) ~ (all_52_1 = e0)
% 170.22/26.14 | |
% 170.22/26.14 | | REDUCE: (54), (148) imply:
% 170.22/26.14 | | (151) ~ (all_52_9 = e0)
% 170.22/26.14 | |
% 170.22/26.14 | | REDUCE: (13), (148) imply:
% 170.22/26.14 | | (152) ~ (e3 = e0)
% 170.22/26.14 | |
% 170.22/26.14 | | SIMP: (152) implies:
% 170.22/26.14 | | (153) ~ (e3 = e0)
% 170.22/26.14 | |
% 170.22/26.14 | | REDUCE: (77), (148) imply:
% 170.22/26.14 | | (154) ~ (e1 = e0)
% 170.22/26.14 | |
% 170.22/26.14 | | SIMP: (154) implies:
% 170.22/26.14 | | (155) ~ (e1 = e0)
% 170.22/26.14 | |
% 170.22/26.14 | | BETA: splitting (23) gives:
% 170.22/26.14 | |
% 170.22/26.14 | | Case 1:
% 170.22/26.14 | | |
% 170.22/26.14 | | | (156) ~ (all_56_12 = e0)
% 170.22/26.14 | | |
% 170.22/26.14 | | | REDUCE: (149), (156) imply:
% 170.22/26.14 | | | (157) $false
% 170.22/26.14 | | |
% 170.22/26.14 | | | CLOSE: (157) is inconsistent.
% 170.22/26.14 | | |
% 170.22/26.14 | | Case 2:
% 170.22/26.14 | | |
% 170.22/26.14 | | | (158) all_56_11 = e2 & op(e2, e0) = e2
% 170.22/26.14 | | |
% 170.22/26.14 | | | ALPHA: (158) implies:
% 170.22/26.14 | | | (159) op(e2, e0) = e2
% 170.22/26.14 | | |
% 170.22/26.14 | | | BETA: splitting (45) gives:
% 170.22/26.14 | | |
% 170.22/26.14 | | | Case 1:
% 170.22/26.14 | | | |
% 170.22/26.14 | | | | (160) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2)
% 170.22/26.14 | | | | = e2)
% 170.22/26.14 | | | |
% 170.22/26.14 | | | | REF_CLOSE: (1), (28), (40), (51), (52), (60), (61), (69), (150), (151),
% 170.22/26.14 | | | | (159), (160) are inconsistent by sub-proof #483.
% 170.22/26.14 | | | |
% 170.22/26.14 | | | Case 2:
% 170.22/26.14 | | | |
% 170.22/26.14 | | | | (161) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0,
% 170.22/26.14 | | | | e2) = e2)
% 170.22/26.14 | | | |
% 170.22/26.14 | | | | BETA: splitting (161) gives:
% 170.22/26.14 | | | |
% 170.22/26.14 | | | | Case 1:
% 170.22/26.14 | | | | |
% 170.22/26.14 | | | | | (162) all_58_7 = e2 & op(e1, e2) = e2
% 170.22/26.14 | | | | |
% 170.22/26.14 | | | | | ALPHA: (162) implies:
% 170.22/26.14 | | | | | (163) all_58_7 = e2
% 170.22/26.14 | | | | |
% 170.22/26.14 | | | | | BETA: splitting (42) gives:
% 170.22/26.14 | | | | |
% 170.22/26.14 | | | | | Case 1:
% 170.22/26.14 | | | | | |
% 170.22/26.14 | | | | | | (164) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1,
% 170.22/26.14 | | | | | | e2) = e0)
% 170.22/26.14 | | | | | |
% 170.22/26.14 | | | | | | BETA: splitting (164) gives:
% 170.22/26.14 | | | | | |
% 170.22/26.14 | | | | | | Case 1:
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | (165) all_58_6 = e0 & op(e1, e3) = e0
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | ALPHA: (165) implies:
% 170.22/26.14 | | | | | | | (166) op(e1, e3) = e0
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | REF_CLOSE: (20), (51), (68), (155), (166) are inconsistent by
% 170.22/26.14 | | | | | | | sub-proof #749.
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | Case 2:
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | (167) all_58_7 = e0 & op(e1, e2) = e0
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | ALPHA: (167) implies:
% 170.22/26.14 | | | | | | | (168) all_58_7 = e0
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | REF_CLOSE: (1), (26), (28), (40), (45), (51), (52), (60), (61),
% 170.22/26.14 | | | | | | | (69), (75), (150), (151), (159), (168) are inconsistent
% 170.22/26.14 | | | | | | | by sub-proof #481.
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | End of split
% 170.22/26.14 | | | | | |
% 170.22/26.14 | | | | | Case 2:
% 170.22/26.14 | | | | | |
% 170.22/26.14 | | | | | | (169) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 &
% 170.22/26.14 | | | | | | op(e1, e0) = e0)
% 170.22/26.14 | | | | | |
% 170.22/26.14 | | | | | | BETA: splitting (169) gives:
% 170.22/26.14 | | | | | |
% 170.22/26.14 | | | | | | Case 1:
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | (170) all_58_8 = e0 & op(e1, e1) = e0
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | ALPHA: (170) implies:
% 170.22/26.14 | | | | | | | (171) all_58_8 = e0
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | REF_CLOSE: (53), (153), (171) are inconsistent by sub-proof #480.
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | Case 2:
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | (172) all_58_11 = e0 & op(e1, e0) = e0
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | ALPHA: (172) implies:
% 170.22/26.14 | | | | | | | (173) all_58_11 = e0
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | BETA: splitting (66) gives:
% 170.22/26.14 | | | | | | |
% 170.22/26.14 | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | (174) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 &
% 170.22/26.14 | | | | | | | | op(e2, e0) = e3)
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | BETA: splitting (174) gives:
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | (175) all_58_9 = e3 & op(e3, e0) = e3
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | ALPHA: (175) implies:
% 170.22/26.14 | | | | | | | | | (176) all_58_9 = e3
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | BETA: splitting (49) gives:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | (177) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1
% 170.22/26.14 | | | | | | | | | | & op(e3, e2) = e1)
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | REF_CLOSE: (47), (51), (58), (75), (81), (177) are
% 170.22/26.14 | | | | | | | | | | inconsistent by sub-proof #565.
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | (178) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1
% 170.22/26.14 | | | | | | | | | | & op(e3, e0) = e1)
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | BETA: splitting (178) gives:
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | (179) all_58_4 = e1 & op(e3, e1) = e1
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | ALPHA: (179) implies:
% 170.22/26.14 | | | | | | | | | | | (180) op(e3, e1) = e1
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | BETA: splitting (18) gives:
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | (181) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 170.22/26.14 | | | | | | | | | | | | & op(e3, e2) = e0)
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | BETA: splitting (181) gives:
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | (182) all_58_0 = e0 & op(e3, e3) = e0
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | REF_CLOSE: (1), (26), (28), (40), (45), (51), (52), (56),
% 170.22/26.14 | | | | | | | | | | | | | (60), (61), (69), (75), (150), (151), (159),
% 170.22/26.14 | | | | | | | | | | | | | (163), (182) are inconsistent by sub-proof #479.
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | (183) all_58_1 = e0 & op(e3, e2) = e0
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | REF_CLOSE: (47), (153), (183) are inconsistent by sub-proof
% 170.22/26.14 | | | | | | | | | | | | | #794.
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | End of split
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | (184) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 170.22/26.14 | | | | | | | | | | | | & op(e3, e0) = e0)
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | BETA: splitting (184) gives:
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | (185) all_58_4 = e0 & op(e3, e1) = e0
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | ALPHA: (185) implies:
% 170.22/26.14 | | | | | | | | | | | | | (186) op(e3, e1) = e0
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | REF_CLOSE: (51), (155), (180), (186) are inconsistent by
% 170.22/26.14 | | | | | | | | | | | | | sub-proof #569.
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | (187) all_58_9 = e0 & op(e3, e0) = e0
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | REF_CLOSE: (153), (176), (187) are inconsistent by sub-proof
% 170.22/26.14 | | | | | | | | | | | | | #901.
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | End of split
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | End of split
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | (188) all_58_9 = e1 & op(e3, e0) = e1
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | ALPHA: (188) implies:
% 170.22/26.14 | | | | | | | | | | | (189) all_58_9 = e1
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | REF_CLOSE: (81), (176), (189) are inconsistent by sub-proof
% 170.22/26.14 | | | | | | | | | | | #896.
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | End of split
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | End of split
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | (190) all_58_10 = e3 & op(e2, e0) = e3
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | ALPHA: (190) implies:
% 170.22/26.14 | | | | | | | | | (191) op(e2, e0) = e3
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | REF_CLOSE: (51), (85), (159), (191) are inconsistent by
% 170.22/26.14 | | | | | | | | | sub-proof #682.
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | End of split
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | (192) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 &
% 170.22/26.14 | | | | | | | | op(e0, e0) = e3)
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | BETA: splitting (192) gives:
% 170.22/26.14 | | | | | | | |
% 170.22/26.14 | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | (193) all_58_11 = e3 & op(e1, e0) = e3
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | REF_CLOSE: (20), (42), (51), (52), (53), (55), (75), (81),
% 170.22/26.14 | | | | | | | | | (153), (155), (163), (193) are inconsistent by
% 170.22/26.14 | | | | | | | | | sub-proof #477.
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | (194) all_58_15 = e3 & op(e0, e0) = e3
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | ALPHA: (194) implies:
% 170.22/26.14 | | | | | | | | | (195) all_58_15 = e3
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | BETA: splitting (46) gives:
% 170.22/26.14 | | | | | | | | |
% 170.22/26.14 | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | (196) all_54_4 = e3
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | COMBINE_EQS: (37), (196) imply:
% 170.22/26.14 | | | | | | | | | | (197) all_52_1 = e3
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | SIMP: (197) implies:
% 170.22/26.14 | | | | | | | | | | (198) all_52_1 = e3
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | REDUCE: (19), (198) imply:
% 170.22/26.14 | | | | | | | | | | (199) ~ (all_52_3 = e3)
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | SIMP: (199) implies:
% 170.22/26.14 | | | | | | | | | | (200) ~ (all_52_3 = e3)
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | BETA: splitting (43) gives:
% 170.22/26.14 | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | (201) all_56_10 = e3
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | COMBINE_EQS: (6), (201) imply:
% 170.22/26.14 | | | | | | | | | | | (202) e3 = e2
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | REF_CLOSE: (14), (53), (57), (81), (85), (153), (163), (173),
% 170.22/26.14 | | | | | | | | | | | (202) are inconsistent by sub-proof #473.
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | (203) ~ (all_56_10 = e3)
% 170.22/26.14 | | | | | | | | | | | (204) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | BETA: splitting (8) gives:
% 170.22/26.14 | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | (205) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0
% 170.22/26.14 | | | | | | | | | | | | & op(e2, e3) = e0)
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | BETA: splitting (205) gives:
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | (206) all_58_0 = e0 & op(e3, e3) = e0
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | REF_CLOSE: (1), (26), (28), (40), (45), (51), (52), (56),
% 170.22/26.14 | | | | | | | | | | | | | (60), (61), (69), (75), (150), (151), (159),
% 170.22/26.14 | | | | | | | | | | | | | (163), (206) are inconsistent by sub-proof #479.
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | (207) all_58_2 = e0 & op(e2, e3) = e0
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | REF_CLOSE: (28), (51), (150), (207) are inconsistent by
% 170.22/26.14 | | | | | | | | | | | | | sub-proof #693.
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | End of split
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | (208) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 =
% 170.22/26.14 | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | BETA: splitting (208) gives:
% 170.22/26.14 | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | Case 1:
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | (209) all_58_6 = e0 & op(e1, e3) = e0
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | ALPHA: (209) implies:
% 170.22/26.14 | | | | | | | | | | | | | (210) op(e1, e3) = e0
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | | REF_CLOSE: (20), (51), (68), (155), (210) are inconsistent by
% 170.22/26.14 | | | | | | | | | | | | | sub-proof #749.
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.14 | | | | | | | | | | | | Case 2:
% 170.22/26.14 | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | (211) all_58_12 = e0 & op(e0, e3) = e0
% 170.22/26.15 | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | ALPHA: (211) implies:
% 170.22/26.15 | | | | | | | | | | | | | (212) all_58_12 = e0
% 170.22/26.15 | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | BETA: splitting (204) gives:
% 170.22/26.15 | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | Case 1:
% 170.22/26.15 | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | (213) all_56_12 = e2
% 170.22/26.15 | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | COMBINE_EQS: (149), (213) imply:
% 170.22/26.15 | | | | | | | | | | | | | | (214) e2 = e0
% 170.22/26.15 | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | COMBINE_EQS: (163), (214) imply:
% 170.22/26.15 | | | | | | | | | | | | | | (215) all_58_7 = e0
% 170.22/26.15 | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | REF_CLOSE: (1), (26), (28), (40), (45), (51), (52), (60),
% 170.22/26.15 | | | | | | | | | | | | | | (61), (69), (75), (150), (151), (159), (215) are
% 170.22/26.15 | | | | | | | | | | | | | | inconsistent by sub-proof #481.
% 170.22/26.15 | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | Case 2:
% 170.22/26.15 | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | (216) all_56_14 = e1 | all_56_15 = e0
% 170.22/26.15 | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 170.22/26.15 | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | Case 1:
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | | (217) all_56_14 = e1
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | | COMBINE_EQS: (17), (217) imply:
% 170.22/26.15 | | | | | | | | | | | | | | | (218) e3 = e1
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | | SIMP: (218) implies:
% 170.22/26.15 | | | | | | | | | | | | | | | (219) e3 = e1
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | | COMBINE_EQS: (195), (219) imply:
% 170.22/26.15 | | | | | | | | | | | | | | | (220) all_58_15 = e1
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | | REF_CLOSE: (4), (22), (31), (51), (65), (81), (85), (153),
% 170.22/26.15 | | | | | | | | | | | | | | | (212), (220) are inconsistent by sub-proof #555.
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | Case 2:
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | | (221) all_56_15 = e0
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | | COMBINE_EQS: (38), (221) imply:
% 170.22/26.15 | | | | | | | | | | | | | | | (222) all_4_2 = e0
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | | SIMP: (222) implies:
% 170.22/26.15 | | | | | | | | | | | | | | | (223) all_4_2 = e0
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | | REDUCE: (27), (223) imply:
% 170.22/26.15 | | | | | | | | | | | | | | | (224) ~ (all_52_3 = e0)
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | | REF_CLOSE: (9), (44), (72), (73), (200), (224) are
% 170.22/26.15 | | | | | | | | | | | | | | | inconsistent by sub-proof #674.
% 170.22/26.15 | | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | | End of split
% 170.22/26.15 | | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | | End of split
% 170.22/26.15 | | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | | End of split
% 170.22/26.15 | | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | | End of split
% 170.22/26.15 | | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | End of split
% 170.22/26.15 | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | Case 2:
% 170.22/26.15 | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | (225) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 170.22/26.15 | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | | REF_CLOSE: (24), (37), (41), (150), (225) are inconsistent by
% 170.22/26.15 | | | | | | | | | | sub-proof #671.
% 170.22/26.15 | | | | | | | | | |
% 170.22/26.15 | | | | | | | | | End of split
% 170.22/26.15 | | | | | | | | |
% 170.22/26.15 | | | | | | | | End of split
% 170.22/26.15 | | | | | | | |
% 170.22/26.15 | | | | | | | End of split
% 170.22/26.15 | | | | | | |
% 170.22/26.15 | | | | | | End of split
% 170.22/26.15 | | | | | |
% 170.22/26.15 | | | | | End of split
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | Case 2:
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | (226) all_58_13 = e2 & op(e0, e2) = e2
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | ALPHA: (226) implies:
% 170.22/26.15 | | | | | (227) op(e0, e2) = e2
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | REF_CLOSE: (26), (51), (75), (227) are inconsistent by sub-proof #968.
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | End of split
% 170.22/26.15 | | | |
% 170.22/26.15 | | | End of split
% 170.22/26.15 | | |
% 170.22/26.15 | | End of split
% 170.22/26.15 | |
% 170.22/26.15 | End of split
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #473 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) all_58_7 = e2
% 170.22/26.15 (2) all_58_6 = e1
% 170.22/26.15 (3) ~ (e3 = e1)
% 170.22/26.15 (4) all_58_11 = e0
% 170.22/26.15 (5) ~ (e3 = e0)
% 170.22/26.15 (6) all_58_8 = e3
% 170.22/26.15 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.22/26.15 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.22/26.15 (8) ~ (e3 = e2)
% 170.22/26.15 (9) e3 = e2
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | COMBINE_EQS: (6), (9) imply:
% 170.22/26.15 | (10) all_58_8 = e2
% 170.22/26.15 |
% 170.22/26.15 | BETA: splitting (7) gives:
% 170.22/26.15 |
% 170.22/26.15 | Case 1:
% 170.22/26.15 | |
% 170.22/26.15 | | (11) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 170.22/26.15 | | e3)
% 170.22/26.15 | |
% 170.22/26.15 | | BETA: splitting (11) gives:
% 170.22/26.15 | |
% 170.22/26.15 | | Case 1:
% 170.22/26.15 | | |
% 170.22/26.15 | | | (12) all_58_6 = e3 & op(e1, e3) = e3
% 170.22/26.15 | | |
% 170.22/26.15 | | | ALPHA: (12) implies:
% 170.22/26.15 | | | (13) all_58_6 = e3
% 170.22/26.15 | | |
% 170.22/26.15 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #476.
% 170.22/26.15 | | |
% 170.22/26.15 | | Case 2:
% 170.22/26.15 | | |
% 170.22/26.15 | | | (14) all_58_7 = e3 & op(e1, e2) = e3
% 170.22/26.15 | | |
% 170.22/26.15 | | | ALPHA: (14) implies:
% 170.22/26.15 | | | (15) all_58_7 = e3
% 170.22/26.15 | | |
% 170.22/26.15 | | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #825.
% 170.22/26.15 | | |
% 170.22/26.15 | | End of split
% 170.22/26.15 | |
% 170.22/26.15 | Case 2:
% 170.22/26.15 | |
% 170.22/26.15 | | (16) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 170.22/26.15 | | e3)
% 170.22/26.15 | |
% 170.22/26.15 | | BETA: splitting (16) gives:
% 170.22/26.15 | |
% 170.22/26.15 | | Case 1:
% 170.22/26.15 | | |
% 170.22/26.15 | | | (17) all_58_8 = e3 & op(e1, e1) = e3
% 170.22/26.15 | | |
% 170.22/26.15 | | | REF_CLOSE: (8), (10), (17) are inconsistent by sub-proof #475.
% 170.22/26.15 | | |
% 170.22/26.15 | | Case 2:
% 170.22/26.15 | | |
% 170.22/26.15 | | | (18) all_58_11 = e3 & op(e1, e0) = e3
% 170.22/26.15 | | |
% 170.22/26.15 | | | ALPHA: (18) implies:
% 170.22/26.15 | | | (19) all_58_11 = e3
% 170.22/26.15 | | |
% 170.22/26.15 | | | REF_CLOSE: (4), (5), (19) are inconsistent by sub-proof #474.
% 170.22/26.15 | | |
% 170.22/26.15 | | End of split
% 170.22/26.15 | |
% 170.22/26.15 | End of split
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #474 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) all_58_11 = e3
% 170.22/26.15 (2) all_58_11 = e0
% 170.22/26.15 (3) ~ (e3 = e0)
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | COMBINE_EQS: (1), (2) imply:
% 170.22/26.15 | (4) e3 = e0
% 170.22/26.15 |
% 170.22/26.15 | SIMP: (4) implies:
% 170.22/26.15 | (5) e3 = e0
% 170.22/26.15 |
% 170.22/26.15 | REDUCE: (3), (5) imply:
% 170.22/26.15 | (6) $false
% 170.22/26.15 |
% 170.22/26.15 | CLOSE: (6) is inconsistent.
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #475 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) all_58_8 = e3 & op(e1, e1) = e3
% 170.22/26.15 (2) all_58_8 = e2
% 170.22/26.15 (3) ~ (e3 = e2)
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | ALPHA: (1) implies:
% 170.22/26.15 | (4) all_58_8 = e3
% 170.22/26.15 |
% 170.22/26.15 | COMBINE_EQS: (2), (4) imply:
% 170.22/26.15 | (5) e3 = e2
% 170.22/26.15 |
% 170.22/26.15 | SIMP: (5) implies:
% 170.22/26.15 | (6) e3 = e2
% 170.22/26.15 |
% 170.22/26.15 | REDUCE: (3), (6) imply:
% 170.22/26.15 | (7) $false
% 170.22/26.15 |
% 170.22/26.15 | CLOSE: (7) is inconsistent.
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #476 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) all_58_6 = e3
% 170.22/26.15 (2) all_58_6 = e1
% 170.22/26.15 (3) ~ (e3 = e1)
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | COMBINE_EQS: (1), (2) imply:
% 170.22/26.15 | (4) e3 = e1
% 170.22/26.15 |
% 170.22/26.15 | SIMP: (4) implies:
% 170.22/26.15 | (5) e3 = e1
% 170.22/26.15 |
% 170.22/26.15 | REDUCE: (3), (5) imply:
% 170.22/26.15 | (6) $false
% 170.22/26.15 |
% 170.22/26.15 | CLOSE: (6) is inconsistent.
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #477 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) all_58_7 = e2
% 170.22/26.15 (2) ~ (e3 = e1)
% 170.22/26.15 (3) op(e1, e3) = all_52_2
% 170.22/26.15 (4) ~ (e1 = e0)
% 170.22/26.15 (5) all_58_11 = e3 & op(e1, e0) = e3
% 170.22/26.15 (6) ~ (e3 = e0)
% 170.22/26.15 (7) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.22/26.15 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.22/26.15 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.15 (9) ~ (e2 = e0)
% 170.22/26.15 (10) all_58_8 = e3
% 170.22/26.15 (11) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.22/26.15 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.22/26.15 (12) ~ (e2 = e1)
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | ALPHA: (5) implies:
% 170.22/26.15 | (13) all_58_11 = e3
% 170.22/26.15 |
% 170.22/26.15 | BETA: splitting (7) gives:
% 170.22/26.15 |
% 170.22/26.15 | Case 1:
% 170.22/26.15 | |
% 170.22/26.15 | | (14) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 170.22/26.15 | | e0)
% 170.22/26.15 | |
% 170.22/26.15 | | BETA: splitting (14) gives:
% 170.22/26.15 | |
% 170.22/26.15 | | Case 1:
% 170.22/26.15 | | |
% 170.22/26.15 | | | (15) all_58_6 = e0 & op(e1, e3) = e0
% 170.22/26.15 | | |
% 170.22/26.15 | | | ALPHA: (15) implies:
% 170.22/26.15 | | | (16) op(e1, e3) = e0
% 170.22/26.15 | | |
% 170.22/26.15 | | | BETA: splitting (11) gives:
% 170.22/26.15 | | |
% 170.22/26.15 | | | Case 1:
% 170.22/26.15 | | | |
% 170.22/26.15 | | | | (17) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 170.22/26.15 | | | | = e1)
% 170.22/26.15 | | | |
% 170.22/26.15 | | | | BETA: splitting (17) gives:
% 170.22/26.15 | | | |
% 170.22/26.15 | | | | Case 1:
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | (18) all_58_6 = e1 & op(e1, e3) = e1
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | ALPHA: (18) implies:
% 170.22/26.15 | | | | | (19) op(e1, e3) = e1
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | REF_CLOSE: (3), (4), (8), (16), (19) are inconsistent by sub-proof
% 170.22/26.15 | | | | | #749.
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | Case 2:
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | (20) all_58_7 = e1 & op(e1, e2) = e1
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | ALPHA: (20) implies:
% 170.22/26.15 | | | | | (21) all_58_7 = e1
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | REF_CLOSE: (1), (12), (21) are inconsistent by sub-proof #494.
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | End of split
% 170.22/26.15 | | | |
% 170.22/26.15 | | | Case 2:
% 170.22/26.15 | | | |
% 170.22/26.15 | | | | (22) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0)
% 170.22/26.15 | | | | = e1)
% 170.22/26.15 | | | |
% 170.22/26.15 | | | | BETA: splitting (22) gives:
% 170.22/26.15 | | | |
% 170.22/26.15 | | | | Case 1:
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | (23) all_58_8 = e1 & op(e1, e1) = e1
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | REF_CLOSE: (2), (10), (23) are inconsistent by sub-proof #478.
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | Case 2:
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | (24) all_58_11 = e1 & op(e1, e0) = e1
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | ALPHA: (24) implies:
% 170.22/26.15 | | | | | (25) all_58_11 = e1
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | | REF_CLOSE: (2), (13), (25) are inconsistent by sub-proof #755.
% 170.22/26.15 | | | | |
% 170.22/26.15 | | | | End of split
% 170.22/26.15 | | | |
% 170.22/26.15 | | | End of split
% 170.22/26.15 | | |
% 170.22/26.15 | | Case 2:
% 170.22/26.15 | | |
% 170.22/26.15 | | | (26) all_58_7 = e0 & op(e1, e2) = e0
% 170.22/26.15 | | |
% 170.22/26.15 | | | ALPHA: (26) implies:
% 170.22/26.15 | | | (27) all_58_7 = e0
% 170.22/26.15 | | |
% 170.22/26.15 | | | REF_CLOSE: (1), (9), (27) are inconsistent by sub-proof #482.
% 170.22/26.15 | | |
% 170.22/26.15 | | End of split
% 170.22/26.15 | |
% 170.22/26.15 | Case 2:
% 170.22/26.15 | |
% 170.22/26.15 | | (28) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 170.22/26.15 | | e0)
% 170.22/26.15 | |
% 170.22/26.15 | | BETA: splitting (28) gives:
% 170.22/26.15 | |
% 170.22/26.15 | | Case 1:
% 170.22/26.15 | | |
% 170.22/26.15 | | | (29) all_58_8 = e0 & op(e1, e1) = e0
% 170.22/26.15 | | |
% 170.22/26.15 | | | ALPHA: (29) implies:
% 170.22/26.15 | | | (30) all_58_8 = e0
% 170.22/26.15 | | |
% 170.22/26.15 | | | REF_CLOSE: (6), (10), (30) are inconsistent by sub-proof #480.
% 170.22/26.15 | | |
% 170.22/26.15 | | Case 2:
% 170.22/26.15 | | |
% 170.22/26.15 | | | (31) all_58_11 = e0 & op(e1, e0) = e0
% 170.22/26.15 | | |
% 170.22/26.15 | | | REF_CLOSE: (6), (13), (31) are inconsistent by sub-proof #724.
% 170.22/26.15 | | |
% 170.22/26.15 | | End of split
% 170.22/26.15 | |
% 170.22/26.15 | End of split
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #478 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) all_58_8 = e1 & op(e1, e1) = e1
% 170.22/26.15 (2) all_58_8 = e3
% 170.22/26.15 (3) ~ (e3 = e1)
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | ALPHA: (1) implies:
% 170.22/26.15 | (4) all_58_8 = e1
% 170.22/26.15 |
% 170.22/26.15 | COMBINE_EQS: (2), (4) imply:
% 170.22/26.15 | (5) e3 = e1
% 170.22/26.15 |
% 170.22/26.15 | SIMP: (5) implies:
% 170.22/26.15 | (6) e3 = e1
% 170.22/26.15 |
% 170.22/26.15 | REDUCE: (3), (6) imply:
% 170.22/26.15 | (7) $false
% 170.22/26.15 |
% 170.22/26.15 | CLOSE: (7) is inconsistent.
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #479 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) op(e2, e1) = all_52_9
% 170.22/26.15 (2) all_58_7 = e2
% 170.22/26.15 (3) ~ (all_52_1 = e0)
% 170.22/26.15 (4) all_58_0 = e0 & op(e3, e3) = e0
% 170.22/26.15 (5) op(e0, e2) = e1
% 170.22/26.15 (6) op(e2, e3) = all_52_1
% 170.22/26.15 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.22/26.15 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.22/26.15 (8) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.22/26.15 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 170.22/26.15 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.15 (10) ~ (e2 = e0)
% 170.22/26.15 (11) all_58_0 = e2
% 170.22/26.15 (12) ~ (all_52_9 = e0)
% 170.22/26.15 (13) ~ (e2 = e1)
% 170.22/26.15 (14) ~ (all_52_4 = e2)
% 170.22/26.15 (15) op(e3, e2) = all_52_4
% 170.22/26.15 (16) op(e2, e0) = e2
% 170.22/26.15 (17) op(e2, e0) = all_52_13
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | ALPHA: (4) implies:
% 170.22/26.15 | (18) all_58_0 = e0
% 170.22/26.15 |
% 170.22/26.15 | COMBINE_EQS: (11), (18) imply:
% 170.22/26.15 | (19) e2 = e0
% 170.22/26.15 |
% 170.22/26.15 | COMBINE_EQS: (2), (19) imply:
% 170.22/26.15 | (20) all_58_7 = e0
% 170.22/26.15 |
% 170.22/26.15 | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (12), (13), (14), (15),
% 170.22/26.15 | (16), (17), (20) are inconsistent by sub-proof #481.
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #480 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) all_58_8 = e3
% 170.22/26.15 (2) all_58_8 = e0
% 170.22/26.15 (3) ~ (e3 = e0)
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | COMBINE_EQS: (1), (2) imply:
% 170.22/26.15 | (4) e3 = e0
% 170.22/26.15 |
% 170.22/26.15 | SIMP: (4) implies:
% 170.22/26.15 | (5) e3 = e0
% 170.22/26.15 |
% 170.22/26.15 | REDUCE: (3), (5) imply:
% 170.22/26.15 | (6) $false
% 170.22/26.15 |
% 170.22/26.15 | CLOSE: (6) is inconsistent.
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #481 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) op(e2, e1) = all_52_9
% 170.22/26.15 (2) ~ (all_52_1 = e0)
% 170.22/26.15 (3) op(e0, e2) = e1
% 170.22/26.15 (4) op(e2, e3) = all_52_1
% 170.22/26.15 (5) all_58_7 = e0
% 170.22/26.15 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.22/26.15 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.22/26.15 (7) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.22/26.15 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 170.22/26.15 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.15 (9) ~ (e2 = e0)
% 170.22/26.15 (10) ~ (all_52_9 = e0)
% 170.22/26.15 (11) ~ (e2 = e1)
% 170.22/26.15 (12) ~ (all_52_4 = e2)
% 170.22/26.15 (13) op(e3, e2) = all_52_4
% 170.22/26.15 (14) op(e2, e0) = e2
% 170.22/26.15 (15) op(e2, e0) = all_52_13
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | BETA: splitting (7) gives:
% 170.22/26.15 |
% 170.22/26.15 | Case 1:
% 170.22/26.15 | |
% 170.22/26.15 | | (16) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 170.22/26.15 | | e2)
% 170.22/26.15 | |
% 170.22/26.15 | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (10), (12), (13), (14), (15), (16)
% 170.22/26.15 | | are inconsistent by sub-proof #483.
% 170.22/26.15 | |
% 170.22/26.15 | Case 2:
% 170.22/26.15 | |
% 170.22/26.15 | | (17) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 170.22/26.15 | | e2)
% 170.22/26.15 | |
% 170.22/26.15 | | BETA: splitting (17) gives:
% 170.22/26.15 | |
% 170.22/26.15 | | Case 1:
% 170.22/26.15 | | |
% 170.22/26.15 | | | (18) all_58_7 = e2 & op(e1, e2) = e2
% 170.22/26.15 | | |
% 170.22/26.15 | | | ALPHA: (18) implies:
% 170.22/26.15 | | | (19) all_58_7 = e2
% 170.22/26.15 | | |
% 170.22/26.15 | | | REF_CLOSE: (5), (9), (19) are inconsistent by sub-proof #482.
% 170.22/26.15 | | |
% 170.22/26.15 | | Case 2:
% 170.22/26.15 | | |
% 170.22/26.15 | | | (20) all_58_13 = e2 & op(e0, e2) = e2
% 170.22/26.15 | | |
% 170.22/26.15 | | | ALPHA: (20) implies:
% 170.22/26.15 | | | (21) op(e0, e2) = e2
% 170.22/26.15 | | |
% 170.22/26.15 | | | REF_CLOSE: (3), (8), (11), (21) are inconsistent by sub-proof #968.
% 170.22/26.15 | | |
% 170.22/26.15 | | End of split
% 170.22/26.15 | |
% 170.22/26.15 | End of split
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #482 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) all_58_7 = e2
% 170.22/26.15 (2) all_58_7 = e0
% 170.22/26.15 (3) ~ (e2 = e0)
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | COMBINE_EQS: (1), (2) imply:
% 170.22/26.15 | (4) e2 = e0
% 170.22/26.15 |
% 170.22/26.15 | SIMP: (4) implies:
% 170.22/26.15 | (5) e2 = e0
% 170.22/26.15 |
% 170.22/26.15 | REDUCE: (3), (5) imply:
% 170.22/26.15 | (6) $false
% 170.22/26.15 |
% 170.22/26.15 | CLOSE: (6) is inconsistent.
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #483 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) op(e2, e1) = all_52_9
% 170.22/26.15 (2) ~ (all_52_1 = e0)
% 170.22/26.15 (3) op(e2, e3) = all_52_1
% 170.22/26.15 (4) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.22/26.15 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.22/26.15 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.15 (6) ~ (e2 = e0)
% 170.22/26.15 (7) ~ (all_52_9 = e0)
% 170.22/26.15 (8) ~ (all_52_4 = e2)
% 170.22/26.15 (9) op(e3, e2) = all_52_4
% 170.22/26.15 (10) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2)
% 170.22/26.15 (11) op(e2, e0) = e2
% 170.22/26.15 (12) op(e2, e0) = all_52_13
% 170.22/26.15
% 170.22/26.15 Begin of proof
% 170.22/26.15 |
% 170.22/26.15 | BETA: splitting (10) gives:
% 170.22/26.15 |
% 170.22/26.15 | Case 1:
% 170.22/26.15 | |
% 170.22/26.15 | | (13) all_58_1 = e2 & op(e3, e2) = e2
% 170.22/26.15 | |
% 170.22/26.15 | | ALPHA: (13) implies:
% 170.22/26.15 | | (14) op(e3, e2) = e2
% 170.22/26.15 | |
% 170.22/26.15 | | REF_CLOSE: (5), (8), (9), (14) are inconsistent by sub-proof #993.
% 170.22/26.15 | |
% 170.22/26.15 | Case 2:
% 170.22/26.15 | |
% 170.22/26.15 | | (15) all_58_3 = e2 & op(e2, e2) = e2
% 170.22/26.15 | |
% 170.22/26.15 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (11), (12), (15) are
% 170.22/26.15 | | inconsistent by sub-proof #484.
% 170.22/26.15 | |
% 170.22/26.15 | End of split
% 170.22/26.15 |
% 170.22/26.15 End of proof
% 170.22/26.15
% 170.22/26.15 Sub-proof #484 shows that the following formulas are inconsistent:
% 170.22/26.15 ----------------------------------------------------------------
% 170.22/26.15 (1) op(e2, e1) = all_52_9
% 170.22/26.15 (2) ~ (all_52_1 = e0)
% 170.22/26.15 (3) all_58_3 = e2 & op(e2, e2) = e2
% 170.22/26.15 (4) op(e2, e3) = all_52_1
% 170.22/26.16 (5) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.22/26.16 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.22/26.16 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.16 (7) ~ (e2 = e0)
% 170.22/26.16 (8) ~ (all_52_9 = e0)
% 170.22/26.16 (9) op(e2, e0) = e2
% 170.22/26.16 (10) op(e2, e0) = all_52_13
% 170.22/26.16
% 170.22/26.16 Begin of proof
% 170.22/26.16 |
% 170.22/26.16 | ALPHA: (3) implies:
% 170.22/26.16 | (11) all_58_3 = e2
% 170.22/26.16 |
% 170.22/26.16 | BETA: splitting (5) gives:
% 170.22/26.16 |
% 170.22/26.16 | Case 1:
% 170.22/26.16 | |
% 170.22/26.16 | | (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 170.22/26.16 | | e0)
% 170.22/26.16 | |
% 170.22/26.16 | | BETA: splitting (12) gives:
% 170.22/26.16 | |
% 170.22/26.16 | | Case 1:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (13) all_58_2 = e0 & op(e2, e3) = e0
% 170.22/26.16 | | |
% 170.22/26.16 | | | REF_CLOSE: (2), (4), (6), (13) are inconsistent by sub-proof #693.
% 170.22/26.16 | | |
% 170.22/26.16 | | Case 2:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (14) all_58_3 = e0 & op(e2, e2) = e0
% 170.22/26.16 | | |
% 170.22/26.16 | | | ALPHA: (14) implies:
% 170.22/26.16 | | | (15) all_58_3 = e0
% 170.22/26.16 | | |
% 170.22/26.16 | | | REF_CLOSE: (7), (11), (15) are inconsistent by sub-proof #843.
% 170.22/26.16 | | |
% 170.22/26.16 | | End of split
% 170.22/26.16 | |
% 170.22/26.16 | Case 2:
% 170.22/26.16 | |
% 170.22/26.16 | | (16) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.22/26.16 | | e0)
% 170.22/26.16 | |
% 170.22/26.16 | | REF_CLOSE: (1), (6), (7), (8), (9), (10), (16) are inconsistent by sub-proof
% 170.22/26.16 | | #669.
% 170.22/26.16 | |
% 170.22/26.16 | End of split
% 170.22/26.16 |
% 170.22/26.16 End of proof
% 170.22/26.16
% 170.22/26.16 Sub-proof #485 shows that the following formulas are inconsistent:
% 170.22/26.16 ----------------------------------------------------------------
% 170.22/26.16 (1) ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.16 $i(all_56_2))
% 170.22/26.16 (2) all_56_14 = e3
% 170.22/26.16 (3) all_56_2 = e1
% 170.22/26.16
% 170.22/26.16 Begin of proof
% 170.22/26.16 |
% 170.22/26.16 | BETA: splitting (1) gives:
% 170.22/26.16 |
% 170.22/26.16 | Case 1:
% 170.22/26.16 | |
% 170.22/26.16 | | (4) ~ (all_56_14 = e3)
% 170.22/26.16 | |
% 170.22/26.16 | | REDUCE: (2), (4) imply:
% 170.22/26.16 | | (5) $false
% 170.22/26.16 | |
% 170.22/26.16 | | CLOSE: (5) is inconsistent.
% 170.22/26.16 | |
% 170.22/26.16 | Case 2:
% 170.22/26.16 | |
% 170.22/26.16 | | (6) ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 & $i(all_56_2)
% 170.22/26.16 | |
% 170.22/26.16 | | ALPHA: (6) implies:
% 170.22/26.16 | | (7) ~ (all_56_2 = e1)
% 170.22/26.16 | |
% 170.22/26.16 | | REDUCE: (3), (7) imply:
% 170.22/26.16 | | (8) $false
% 170.22/26.16 | |
% 170.22/26.16 | | CLOSE: (8) is inconsistent.
% 170.22/26.16 | |
% 170.22/26.16 | End of split
% 170.22/26.16 |
% 170.22/26.16 End of proof
% 170.22/26.16
% 170.22/26.16 Sub-proof #486 shows that the following formulas are inconsistent:
% 170.22/26.16 ----------------------------------------------------------------
% 170.22/26.16 (1) all_58_12 = e2
% 170.22/26.16 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.22/26.16 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.22/26.16 (3) ~ (e3 = e1)
% 170.22/26.16 (4) op(e1, e3) = all_52_2
% 170.22/26.16 (5) ~ (e1 = e0)
% 170.22/26.16 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.22/26.16 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.22/26.16 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.22/26.16 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.22/26.16 (8) ~ (e3 = e0)
% 170.22/26.16 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.16 (10) ~ (e2 = e0)
% 170.22/26.16 (11) all_58_0 = e2
% 170.22/26.16 (12) op(e3, e3) = e2
% 170.22/26.16 (13) ~ (e2 = e1)
% 170.22/26.16 (14) op(e1, e3) = e1
% 170.22/26.16 (15) ~ (e3 = e2)
% 170.22/26.16
% 170.22/26.16 Begin of proof
% 170.22/26.16 |
% 170.22/26.16 | BETA: splitting (2) gives:
% 170.22/26.16 |
% 170.22/26.16 | Case 1:
% 170.22/26.16 | |
% 170.22/26.16 | | (16) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 170.22/26.16 | | e0)
% 170.22/26.16 | |
% 170.22/26.16 | | BETA: splitting (16) gives:
% 170.22/26.16 | |
% 170.22/26.16 | | Case 1:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (17) all_58_0 = e0 & op(e3, e3) = e0
% 170.22/26.16 | | |
% 170.22/26.16 | | | REF_CLOSE: (10), (11), (17) are inconsistent by sub-proof #705.
% 170.22/26.16 | | |
% 170.22/26.16 | | Case 2:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (18) all_58_2 = e0 & op(e2, e3) = e0
% 170.22/26.16 | | |
% 170.22/26.16 | | | ALPHA: (18) implies:
% 170.22/26.16 | | | (19) all_58_2 = e0
% 170.22/26.16 | | |
% 170.22/26.16 | | | BETA: splitting (6) gives:
% 170.22/26.16 | | |
% 170.22/26.16 | | | Case 1:
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 170.22/26.16 | | | | = e3)
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | BETA: splitting (20) gives:
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | Case 1:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | (21) all_58_0 = e3 & op(e3, e3) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | ALPHA: (21) implies:
% 170.22/26.16 | | | | | (22) op(e3, e3) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | REF_CLOSE: (9), (12), (15), (22) are inconsistent by sub-proof #838.
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | Case 2:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | (23) all_58_2 = e3 & op(e2, e3) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | ALPHA: (23) implies:
% 170.22/26.16 | | | | | (24) all_58_2 = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | REF_CLOSE: (8), (19), (24) are inconsistent by sub-proof #913.
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | End of split
% 170.22/26.16 | | | |
% 170.22/26.16 | | | Case 2:
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | (25) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 170.22/26.16 | | | | = e3)
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | BETA: splitting (25) gives:
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | Case 1:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | (26) all_58_6 = e3 & op(e1, e3) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | ALPHA: (26) implies:
% 170.22/26.16 | | | | | (27) all_58_6 = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | BETA: splitting (7) gives:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | Case 1:
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 170.22/26.16 | | | | | | e3) = e1)
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | BETA: splitting (28) gives:
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | Case 1:
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | (29) all_58_0 = e1 & op(e3, e3) = e1
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | REF_CLOSE: (11), (13), (29) are inconsistent by sub-proof #706.
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | Case 2:
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | (30) all_58_2 = e1 & op(e2, e3) = e1
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | ALPHA: (30) implies:
% 170.22/26.16 | | | | | | | (31) all_58_2 = e1
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | REF_CLOSE: (1), (2), (5), (8), (10), (11), (27), (31) are
% 170.22/26.16 | | | | | | | inconsistent by sub-proof #488.
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | End of split
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | Case 2:
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | (32) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 170.22/26.16 | | | | | | e3) = e1)
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | BETA: splitting (32) gives:
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | Case 1:
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | (33) all_58_6 = e1 & op(e1, e3) = e1
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | REF_CLOSE: (3), (27), (33) are inconsistent by sub-proof #487.
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | Case 2:
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | (34) all_58_12 = e1 & op(e0, e3) = e1
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | REF_CLOSE: (1), (13), (34) are inconsistent by sub-proof #891.
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | End of split
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | End of split
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | Case 2:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | (35) all_58_12 = e3 & op(e0, e3) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | ALPHA: (35) implies:
% 170.22/26.16 | | | | | (36) all_58_12 = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | REF_CLOSE: (1), (15), (36) are inconsistent by sub-proof #635.
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | End of split
% 170.22/26.16 | | | |
% 170.22/26.16 | | | End of split
% 170.22/26.16 | | |
% 170.22/26.16 | | End of split
% 170.22/26.16 | |
% 170.22/26.16 | Case 2:
% 170.22/26.16 | |
% 170.22/26.16 | | (37) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 170.22/26.16 | | e0)
% 170.22/26.16 | |
% 170.22/26.16 | | REF_CLOSE: (1), (4), (5), (9), (10), (14), (37) are inconsistent by
% 170.22/26.16 | | sub-proof #713.
% 170.22/26.16 | |
% 170.22/26.16 | End of split
% 170.22/26.16 |
% 170.22/26.16 End of proof
% 170.22/26.16
% 170.22/26.16 Sub-proof #487 shows that the following formulas are inconsistent:
% 170.22/26.16 ----------------------------------------------------------------
% 170.22/26.16 (1) all_58_6 = e1 & op(e1, e3) = e1
% 170.22/26.16 (2) all_58_6 = e3
% 170.22/26.16 (3) ~ (e3 = e1)
% 170.22/26.16
% 170.22/26.16 Begin of proof
% 170.22/26.16 |
% 170.22/26.16 | ALPHA: (1) implies:
% 170.22/26.16 | (4) all_58_6 = e1
% 170.22/26.16 |
% 170.22/26.16 | COMBINE_EQS: (2), (4) imply:
% 170.22/26.16 | (5) e3 = e1
% 170.22/26.16 |
% 170.22/26.16 | REDUCE: (3), (5) imply:
% 170.22/26.16 | (6) $false
% 170.22/26.16 |
% 170.22/26.16 | CLOSE: (6) is inconsistent.
% 170.22/26.16 |
% 170.22/26.16 End of proof
% 170.22/26.16
% 170.22/26.16 Sub-proof #488 shows that the following formulas are inconsistent:
% 170.22/26.16 ----------------------------------------------------------------
% 170.22/26.16 (1) all_58_12 = e2
% 170.22/26.16 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.22/26.16 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.22/26.16 (3) all_58_6 = e3
% 170.22/26.16 (4) ~ (e1 = e0)
% 170.22/26.16 (5) ~ (e3 = e0)
% 170.22/26.16 (6) ~ (e2 = e0)
% 170.22/26.16 (7) all_58_0 = e2
% 170.22/26.16 (8) all_58_2 = e1
% 170.22/26.16
% 170.22/26.16 Begin of proof
% 170.22/26.16 |
% 170.22/26.16 | BETA: splitting (2) gives:
% 170.22/26.16 |
% 170.22/26.16 | Case 1:
% 170.22/26.16 | |
% 170.22/26.16 | | (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 170.22/26.16 | |
% 170.22/26.16 | | BETA: splitting (9) gives:
% 170.22/26.16 | |
% 170.22/26.16 | | Case 1:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (10) all_58_0 = e0 & op(e3, e3) = e0
% 170.22/26.16 | | |
% 170.22/26.16 | | | REF_CLOSE: (6), (7), (10) are inconsistent by sub-proof #705.
% 170.22/26.16 | | |
% 170.22/26.16 | | Case 2:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (11) all_58_2 = e0 & op(e2, e3) = e0
% 170.22/26.16 | | |
% 170.22/26.16 | | | REF_CLOSE: (4), (8), (11) are inconsistent by sub-proof #935.
% 170.22/26.16 | | |
% 170.22/26.16 | | End of split
% 170.22/26.16 | |
% 170.22/26.16 | Case 2:
% 170.22/26.16 | |
% 170.22/26.16 | | (12) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 170.22/26.16 | | e0)
% 170.22/26.16 | |
% 170.22/26.16 | | BETA: splitting (12) gives:
% 170.22/26.16 | |
% 170.22/26.16 | | Case 1:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (13) all_58_6 = e0 & op(e1, e3) = e0
% 170.22/26.16 | | |
% 170.22/26.16 | | | REF_CLOSE: (3), (5), (13) are inconsistent by sub-proof #559.
% 170.22/26.16 | | |
% 170.22/26.16 | | Case 2:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (14) all_58_12 = e0 & op(e0, e3) = e0
% 170.22/26.16 | | |
% 170.22/26.16 | | | REF_CLOSE: (1), (6), (14) are inconsistent by sub-proof #886.
% 170.22/26.16 | | |
% 170.22/26.16 | | End of split
% 170.22/26.16 | |
% 170.22/26.16 | End of split
% 170.22/26.16 |
% 170.22/26.16 End of proof
% 170.22/26.16
% 170.22/26.16 Sub-proof #489 shows that the following formulas are inconsistent:
% 170.22/26.16 ----------------------------------------------------------------
% 170.22/26.16 (1) op(e2, e1) = all_52_9
% 170.22/26.16 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.22/26.16 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.22/26.16 (3) all_58_7 = e1 & op(e1, e2) = e1
% 170.22/26.16 (4) ~ (all_52_9 = e3)
% 170.22/26.16 (5) ~ (all_4_2 = e2)
% 170.22/26.16 (6) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.22/26.16 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.22/26.16 (7) ~ (all_8_2 = e3)
% 170.22/26.16 (8) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.22/26.16 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.22/26.16 (9) ~ (e3 = e1)
% 170.22/26.16 (10) op(e3, e0) = all_52_12
% 170.22/26.16 (11) op(e1, e3) = all_52_2
% 170.22/26.16 (12) ~ (e1 = e0)
% 170.22/26.16 (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.22/26.16 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.22/26.16 (14) ~ (all_52_12 = e2)
% 170.22/26.16 (15) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 170.22/26.16 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.22/26.16 (16) op(e2, e2) = all_8_2
% 170.22/26.16 (17) ~ (all_6_2 = e2)
% 170.22/26.16 (18) op(e1, e1) = all_6_2
% 170.22/26.16 (19) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.22/26.16 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.22/26.16 (20) ~ (e3 = e0)
% 170.22/26.16 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.22/26.16 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.22/26.16 (22) op(e0, e0) = all_4_2
% 170.22/26.16 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.16 (24) ~ (e2 = e0)
% 170.22/26.16 (25) all_58_8 = e3
% 170.22/26.16 (26) all_58_0 = e2
% 170.22/26.16 (27) op(e3, e3) = e2
% 170.22/26.16 (28) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.22/26.16 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.22/26.16 (29) ~ (e2 = e1)
% 170.22/26.16 (30) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.22/26.16 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.22/26.16 (31) op(e1, e3) = e1
% 170.22/26.16 (32) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.22/26.16 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.22/26.16 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.22/26.16 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.22/26.16 (33) op(e2, e0) = all_52_13
% 170.22/26.16 (34) ~ (e3 = e2)
% 170.22/26.16
% 170.22/26.16 Begin of proof
% 170.22/26.16 |
% 170.22/26.16 | ALPHA: (3) implies:
% 170.22/26.16 | (35) all_58_7 = e1
% 170.22/26.16 |
% 170.22/26.16 | BETA: splitting (19) gives:
% 170.22/26.16 |
% 170.22/26.16 | Case 1:
% 170.22/26.16 | |
% 170.22/26.16 | | (36) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) =
% 170.22/26.16 | | e1)
% 170.22/26.16 | |
% 170.22/26.16 | | BETA: splitting (36) gives:
% 170.22/26.16 | |
% 170.22/26.16 | | Case 1:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (37) all_58_0 = e1 & op(e3, e3) = e1
% 170.22/26.16 | | |
% 170.22/26.16 | | | ALPHA: (37) implies:
% 170.22/26.16 | | | (38) op(e3, e3) = e1
% 170.22/26.16 | | |
% 170.22/26.16 | | | REF_CLOSE: (23), (27), (29), (38) are inconsistent by sub-proof #957.
% 170.22/26.16 | | |
% 170.22/26.16 | | Case 2:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (39) all_58_2 = e1 & op(e2, e3) = e1
% 170.22/26.16 | | |
% 170.22/26.16 | | | ALPHA: (39) implies:
% 170.22/26.16 | | | (40) all_58_2 = e1
% 170.22/26.16 | | |
% 170.22/26.16 | | | BETA: splitting (28) gives:
% 170.22/26.16 | | |
% 170.22/26.16 | | | Case 1:
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | (41) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2)
% 170.22/26.16 | | | | = e3)
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | BETA: splitting (41) gives:
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | Case 1:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | (42) all_58_2 = e3 & op(e2, e3) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | REF_CLOSE: (9), (40), (42) are inconsistent by sub-proof #679.
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | Case 2:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | (43) all_58_3 = e3 & op(e2, e2) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | REF_CLOSE: (7), (16), (23), (43) are inconsistent by sub-proof #973.
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | End of split
% 170.22/26.16 | | | |
% 170.22/26.16 | | | Case 2:
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | (44) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0)
% 170.22/26.16 | | | | = e3)
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | BETA: splitting (44) gives:
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | Case 1:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | (45) all_58_5 = e3 & op(e2, e1) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | ALPHA: (45) implies:
% 170.22/26.16 | | | | | (46) op(e2, e1) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | REF_CLOSE: (1), (4), (23), (46) are inconsistent by sub-proof #951.
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | Case 2:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | (47) all_58_10 = e3 & op(e2, e0) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | ALPHA: (47) implies:
% 170.22/26.16 | | | | | (48) op(e2, e0) = e3
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | BETA: splitting (15) gives:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | Case 1:
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | (49) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 170.22/26.16 | | | | | | e0) = e2)
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | BETA: splitting (49) gives:
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | Case 1:
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | (50) all_58_9 = e2 & op(e3, e0) = e2
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | REF_CLOSE: (10), (14), (23), (50) are inconsistent by sub-proof
% 170.22/26.16 | | | | | | | #663.
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | Case 2:
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | (51) all_58_10 = e2 & op(e2, e0) = e2
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | ALPHA: (51) implies:
% 170.22/26.16 | | | | | | | (52) op(e2, e0) = e2
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | REF_CLOSE: (23), (34), (48), (52) are inconsistent by sub-proof
% 170.22/26.16 | | | | | | | #682.
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | End of split
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | Case 2:
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | (53) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 170.22/26.16 | | | | | | op(e0, e0) = e2)
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | BETA: splitting (53) gives:
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | | Case 1:
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | (54) all_58_11 = e2 & op(e1, e0) = e2
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | REF_CLOSE: (11), (12), (20), (21), (23), (24), (25), (31), (35),
% 170.22/26.16 | | | | | | | (54) are inconsistent by sub-proof #495.
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | Case 2:
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | (55) all_58_15 = e2 & op(e0, e0) = e2
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | | REF_CLOSE: (5), (22), (23), (55) are inconsistent by sub-proof
% 170.22/26.16 | | | | | | | #854.
% 170.22/26.16 | | | | | | |
% 170.22/26.16 | | | | | | End of split
% 170.22/26.16 | | | | | |
% 170.22/26.16 | | | | | End of split
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | End of split
% 170.22/26.16 | | | |
% 170.22/26.16 | | | End of split
% 170.22/26.16 | | |
% 170.22/26.16 | | End of split
% 170.22/26.16 | |
% 170.22/26.16 | Case 2:
% 170.22/26.16 | |
% 170.22/26.16 | | (56) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 170.22/26.16 | | e1)
% 170.22/26.16 | |
% 170.22/26.16 | | BETA: splitting (56) gives:
% 170.22/26.16 | |
% 170.22/26.16 | | Case 1:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (57) all_58_6 = e1 & op(e1, e3) = e1
% 170.22/26.16 | | |
% 170.22/26.16 | | | ALPHA: (57) implies:
% 170.22/26.16 | | | (58) all_58_6 = e1
% 170.22/26.16 | | |
% 170.22/26.16 | | | REF_CLOSE: (8), (11), (12), (17), (18), (20), (21), (23), (24), (25),
% 170.22/26.16 | | | (29), (31), (35), (58) are inconsistent by sub-proof #493.
% 170.22/26.16 | | |
% 170.22/26.16 | | Case 2:
% 170.22/26.16 | | |
% 170.22/26.16 | | | (59) all_58_12 = e1 & op(e0, e3) = e1
% 170.22/26.16 | | |
% 170.22/26.16 | | | ALPHA: (59) implies:
% 170.22/26.16 | | | (60) all_58_12 = e1
% 170.22/26.16 | | |
% 170.22/26.16 | | | BETA: splitting (13) gives:
% 170.22/26.16 | | |
% 170.22/26.16 | | | Case 1:
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | (61) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 170.22/26.16 | | | | = e3)
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | BETA: splitting (61) gives:
% 170.22/26.16 | | | |
% 170.22/26.16 | | | | Case 1:
% 170.22/26.16 | | | | |
% 170.22/26.16 | | | | | (62) all_58_0 = e3 & op(e3, e3) = e3
% 170.22/26.16 | | | | |
% 170.22/26.17 | | | | | ALPHA: (62) implies:
% 170.22/26.17 | | | | | (63) op(e3, e3) = e3
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | REF_CLOSE: (23), (27), (34), (63) are inconsistent by sub-proof #838.
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | Case 2:
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | (64) all_58_2 = e3 & op(e2, e3) = e3
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | ALPHA: (64) implies:
% 170.22/26.17 | | | | | (65) all_58_2 = e3
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | BETA: splitting (15) gives:
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | Case 1:
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | (66) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2,
% 170.22/26.17 | | | | | | e0) = e2)
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | BETA: splitting (66) gives:
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | Case 1:
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | | (67) all_58_9 = e2 & op(e3, e0) = e2
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | | REF_CLOSE: (10), (14), (23), (67) are inconsistent by sub-proof
% 170.22/26.17 | | | | | | | #663.
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | Case 2:
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | | (68) all_58_10 = e2 & op(e2, e0) = e2
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | | ALPHA: (68) implies:
% 170.22/26.17 | | | | | | | (69) op(e2, e0) = e2
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | | BETA: splitting (2) gives:
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | | Case 1:
% 170.22/26.17 | | | | | | | |
% 170.22/26.17 | | | | | | | | (70) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 &
% 170.22/26.17 | | | | | | | | op(e2, e0) = e1)
% 170.22/26.17 | | | | | | | |
% 170.22/26.17 | | | | | | | | BETA: splitting (70) gives:
% 170.22/26.17 | | | | | | | |
% 170.22/26.17 | | | | | | | | Case 1:
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | (71) all_58_9 = e1 & op(e3, e0) = e1
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | ALPHA: (71) implies:
% 170.22/26.17 | | | | | | | | | (72) all_58_9 = e1
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | BETA: splitting (8) gives:
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | Case 1:
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | (73) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 170.22/26.17 | | | | | | | | | | op(e1, e2) = e2)
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | REF_CLOSE: (6), (9), (12), (19), (20), (24), (26), (29),
% 170.22/26.17 | | | | | | | | | | (35), (65), (73) are inconsistent by sub-proof
% 170.22/26.17 | | | | | | | | | | #492.
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | Case 2:
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | (74) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2
% 170.22/26.17 | | | | | | | | | | & op(e1, e0) = e2)
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | BETA: splitting (74) gives:
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | Case 1:
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | (75) all_58_8 = e2 & op(e1, e1) = e2
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | REF_CLOSE: (17), (18), (23), (75) are inconsistent by
% 170.22/26.17 | | | | | | | | | | | sub-proof #845.
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | Case 2:
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | (76) all_58_11 = e2 & op(e1, e0) = e2
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | ALPHA: (76) implies:
% 170.22/26.17 | | | | | | | | | | | (77) all_58_11 = e2
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | REF_CLOSE: (9), (12), (20), (23), (24), (30), (32), (33),
% 170.22/26.17 | | | | | | | | | | | (34), (69), (72), (77) are inconsistent by
% 170.22/26.17 | | | | | | | | | | | sub-proof #527.
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | End of split
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | End of split
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | Case 2:
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | (78) all_58_10 = e1 & op(e2, e0) = e1
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | ALPHA: (78) implies:
% 170.22/26.17 | | | | | | | | | (79) op(e2, e0) = e1
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | REF_CLOSE: (23), (29), (69), (79) are inconsistent by
% 170.22/26.17 | | | | | | | | | sub-proof #526.
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | End of split
% 170.22/26.17 | | | | | | | |
% 170.22/26.17 | | | | | | | Case 2:
% 170.22/26.17 | | | | | | | |
% 170.22/26.17 | | | | | | | | (80) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 &
% 170.22/26.17 | | | | | | | | op(e0, e0) = e1)
% 170.22/26.17 | | | | | | | |
% 170.22/26.17 | | | | | | | | BETA: splitting (80) gives:
% 170.22/26.17 | | | | | | | |
% 170.22/26.17 | | | | | | | | Case 1:
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | (81) all_58_11 = e1 & op(e1, e0) = e1
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | ALPHA: (81) implies:
% 170.22/26.17 | | | | | | | | | (82) all_58_11 = e1
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | BETA: splitting (21) gives:
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | Case 1:
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | (83) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 &
% 170.22/26.17 | | | | | | | | | | op(e1, e2) = e0)
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | BETA: splitting (83) gives:
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | Case 1:
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | (84) all_58_6 = e0 & op(e1, e3) = e0
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | ALPHA: (84) implies:
% 170.22/26.17 | | | | | | | | | | | (85) op(e1, e3) = e0
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | REF_CLOSE: (11), (12), (23), (31), (85) are inconsistent by
% 170.22/26.17 | | | | | | | | | | | sub-proof #749.
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | Case 2:
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | (86) all_58_7 = e0 & op(e1, e2) = e0
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | ALPHA: (86) implies:
% 170.22/26.17 | | | | | | | | | | | (87) all_58_7 = e0
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | REF_CLOSE: (12), (35), (87) are inconsistent by sub-proof
% 170.22/26.17 | | | | | | | | | | | #710.
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | End of split
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | Case 2:
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | (88) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0
% 170.22/26.17 | | | | | | | | | | & op(e1, e0) = e0)
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | BETA: splitting (88) gives:
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | Case 1:
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | (89) all_58_8 = e0 & op(e1, e1) = e0
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | REF_CLOSE: (20), (25), (89) are inconsistent by sub-proof
% 170.22/26.17 | | | | | | | | | | | #496.
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | Case 2:
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | (90) all_58_11 = e0 & op(e1, e0) = e0
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | ALPHA: (90) implies:
% 170.22/26.17 | | | | | | | | | | | (91) all_58_11 = e0
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | REF_CLOSE: (12), (82), (91) are inconsistent by sub-proof
% 170.22/26.17 | | | | | | | | | | | #491.
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | End of split
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | End of split
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | Case 2:
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | (92) all_58_15 = e1 & op(e0, e0) = e1
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | ALPHA: (92) implies:
% 170.22/26.17 | | | | | | | | | (93) all_58_15 = e1
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | BETA: splitting (8) gives:
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | | Case 1:
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | (94) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 &
% 170.22/26.17 | | | | | | | | | | op(e1, e2) = e2)
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | REF_CLOSE: (6), (9), (12), (19), (20), (24), (26), (29),
% 170.22/26.17 | | | | | | | | | | (35), (65), (94) are inconsistent by sub-proof
% 170.22/26.17 | | | | | | | | | | #492.
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | Case 2:
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | (95) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2
% 170.22/26.17 | | | | | | | | | | & op(e1, e0) = e2)
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | BETA: splitting (95) gives:
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | Case 1:
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | (96) all_58_8 = e2 & op(e1, e1) = e2
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | REF_CLOSE: (17), (18), (23), (96) are inconsistent by
% 170.22/26.17 | | | | | | | | | | | sub-proof #845.
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | Case 2:
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | (97) all_58_11 = e2 & op(e1, e0) = e2
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | ALPHA: (97) implies:
% 170.22/26.17 | | | | | | | | | | | (98) all_58_11 = e2
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | | REF_CLOSE: (9), (12), (20), (23), (24), (30), (32), (33),
% 170.22/26.17 | | | | | | | | | | | (34), (69), (93), (98) are inconsistent by
% 170.22/26.17 | | | | | | | | | | | sub-proof #539.
% 170.22/26.17 | | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | | End of split
% 170.22/26.17 | | | | | | | | | |
% 170.22/26.17 | | | | | | | | | End of split
% 170.22/26.17 | | | | | | | | |
% 170.22/26.17 | | | | | | | | End of split
% 170.22/26.17 | | | | | | | |
% 170.22/26.17 | | | | | | | End of split
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | End of split
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | Case 2:
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | (99) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 &
% 170.22/26.17 | | | | | | op(e0, e0) = e2)
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | BETA: splitting (99) gives:
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | Case 1:
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | | (100) all_58_11 = e2 & op(e1, e0) = e2
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | | REF_CLOSE: (11), (12), (20), (21), (23), (24), (25), (31), (35),
% 170.22/26.17 | | | | | | | (100) are inconsistent by sub-proof #495.
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | Case 2:
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | | (101) all_58_15 = e2 & op(e0, e0) = e2
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | | REF_CLOSE: (5), (22), (23), (101) are inconsistent by sub-proof
% 170.22/26.17 | | | | | | | #854.
% 170.22/26.17 | | | | | | |
% 170.22/26.17 | | | | | | End of split
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | End of split
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | End of split
% 170.22/26.17 | | | |
% 170.22/26.17 | | | Case 2:
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | (102) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0,
% 170.22/26.17 | | | | e3) = e3)
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | BETA: splitting (102) gives:
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | Case 1:
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | (103) all_58_6 = e3 & op(e1, e3) = e3
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | ALPHA: (103) implies:
% 170.22/26.17 | | | | | (104) op(e1, e3) = e3
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | REF_CLOSE: (9), (11), (23), (31), (104) are inconsistent by sub-proof
% 170.22/26.17 | | | | | #750.
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | Case 2:
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | (105) all_58_12 = e3 & op(e0, e3) = e3
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | REF_CLOSE: (9), (60), (105) are inconsistent by sub-proof #490.
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | End of split
% 170.22/26.17 | | | |
% 170.22/26.17 | | | End of split
% 170.22/26.17 | | |
% 170.22/26.17 | | End of split
% 170.22/26.17 | |
% 170.22/26.17 | End of split
% 170.22/26.17 |
% 170.22/26.17 End of proof
% 170.22/26.17
% 170.22/26.17 Sub-proof #490 shows that the following formulas are inconsistent:
% 170.22/26.17 ----------------------------------------------------------------
% 170.22/26.17 (1) all_58_12 = e3 & op(e0, e3) = e3
% 170.22/26.17 (2) all_58_12 = e1
% 170.22/26.17 (3) ~ (e3 = e1)
% 170.22/26.17
% 170.22/26.17 Begin of proof
% 170.22/26.17 |
% 170.22/26.17 | ALPHA: (1) implies:
% 170.22/26.17 | (4) all_58_12 = e3
% 170.22/26.17 |
% 170.22/26.17 | COMBINE_EQS: (2), (4) imply:
% 170.22/26.17 | (5) e3 = e1
% 170.22/26.17 |
% 170.22/26.17 | REDUCE: (3), (5) imply:
% 170.22/26.17 | (6) $false
% 170.22/26.17 |
% 170.22/26.17 | CLOSE: (6) is inconsistent.
% 170.22/26.17 |
% 170.22/26.17 End of proof
% 170.22/26.17
% 170.22/26.17 Sub-proof #491 shows that the following formulas are inconsistent:
% 170.22/26.17 ----------------------------------------------------------------
% 170.22/26.17 (1) all_58_11 = e1
% 170.22/26.17 (2) all_58_11 = e0
% 170.22/26.17 (3) ~ (e1 = e0)
% 170.22/26.17
% 170.22/26.17 Begin of proof
% 170.22/26.17 |
% 170.22/26.17 | COMBINE_EQS: (1), (2) imply:
% 170.22/26.17 | (4) e1 = e0
% 170.22/26.17 |
% 170.22/26.17 | SIMP: (4) implies:
% 170.22/26.17 | (5) e1 = e0
% 170.22/26.17 |
% 170.22/26.17 | REDUCE: (3), (5) imply:
% 170.22/26.17 | (6) $false
% 170.22/26.17 |
% 170.22/26.17 | CLOSE: (6) is inconsistent.
% 170.22/26.17 |
% 170.22/26.17 End of proof
% 170.22/26.17
% 170.22/26.17 Sub-proof #492 shows that the following formulas are inconsistent:
% 170.22/26.17 ----------------------------------------------------------------
% 170.22/26.17 (1) all_58_2 = e3
% 170.22/26.17 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.22/26.17 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.22/26.17 (3) all_58_7 = e1
% 170.22/26.17 (4) ~ (e3 = e1)
% 170.22/26.17 (5) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2)
% 170.22/26.17 (6) ~ (e1 = e0)
% 170.22/26.17 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.22/26.17 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.22/26.17 (8) ~ (e3 = e0)
% 170.22/26.17 (9) ~ (e2 = e0)
% 170.22/26.17 (10) all_58_0 = e2
% 170.22/26.17 (11) ~ (e2 = e1)
% 170.22/26.17
% 170.22/26.17 Begin of proof
% 170.22/26.17 |
% 170.22/26.17 | BETA: splitting (5) gives:
% 170.22/26.17 |
% 170.22/26.17 | Case 1:
% 170.22/26.17 | |
% 170.22/26.17 | | (12) all_58_6 = e2 & op(e1, e3) = e2
% 170.22/26.17 | |
% 170.22/26.17 | | ALPHA: (12) implies:
% 170.22/26.17 | | (13) all_58_6 = e2
% 170.22/26.17 | |
% 170.22/26.17 | | BETA: splitting (2) gives:
% 170.22/26.17 | |
% 170.22/26.17 | | Case 1:
% 170.22/26.17 | | |
% 170.22/26.17 | | | (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 170.22/26.17 | | | e0)
% 170.22/26.17 | | |
% 170.22/26.17 | | | BETA: splitting (14) gives:
% 170.22/26.17 | | |
% 170.22/26.17 | | | Case 1:
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | (15) all_58_0 = e0 & op(e3, e3) = e0
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | REF_CLOSE: (9), (10), (15) are inconsistent by sub-proof #705.
% 170.22/26.17 | | | |
% 170.22/26.17 | | | Case 2:
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | (16) all_58_2 = e0 & op(e2, e3) = e0
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | REF_CLOSE: (1), (8), (16) are inconsistent by sub-proof #621.
% 170.22/26.17 | | | |
% 170.22/26.17 | | | End of split
% 170.22/26.17 | | |
% 170.22/26.17 | | Case 2:
% 170.22/26.17 | | |
% 170.22/26.17 | | | (17) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 170.22/26.17 | | | e0)
% 170.22/26.17 | | |
% 170.22/26.17 | | | BETA: splitting (17) gives:
% 170.22/26.17 | | |
% 170.22/26.17 | | | Case 1:
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | (18) all_58_6 = e0 & op(e1, e3) = e0
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | REF_CLOSE: (9), (13), (18) are inconsistent by sub-proof #769.
% 170.22/26.17 | | | |
% 170.22/26.17 | | | Case 2:
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | (19) all_58_12 = e0 & op(e0, e3) = e0
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | ALPHA: (19) implies:
% 170.22/26.17 | | | | (20) all_58_12 = e0
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | BETA: splitting (7) gives:
% 170.22/26.17 | | | |
% 170.22/26.17 | | | | Case 1:
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | (21) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 170.22/26.17 | | | | | e3) = e1)
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | BETA: splitting (21) gives:
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | Case 1:
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | (22) all_58_0 = e1 & op(e3, e3) = e1
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | REF_CLOSE: (10), (11), (22) are inconsistent by sub-proof #706.
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | Case 2:
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | (23) all_58_2 = e1 & op(e2, e3) = e1
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | ALPHA: (23) implies:
% 170.22/26.17 | | | | | | (24) all_58_2 = e1
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | COMBINE_EQS: (1), (24) imply:
% 170.22/26.17 | | | | | | (25) e3 = e1
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | REDUCE: (4), (25) imply:
% 170.22/26.17 | | | | | | (26) $false
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | CLOSE: (26) is inconsistent.
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | End of split
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | Case 2:
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | (27) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 170.22/26.17 | | | | | e3) = e1)
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | BETA: splitting (27) gives:
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | | Case 1:
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | (28) all_58_6 = e1 & op(e1, e3) = e1
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | REF_CLOSE: (11), (13), (28) are inconsistent by sub-proof #774.
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | Case 2:
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | (29) all_58_12 = e1 & op(e0, e3) = e1
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | ALPHA: (29) implies:
% 170.22/26.17 | | | | | | (30) all_58_12 = e1
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | | REF_CLOSE: (6), (20), (30) are inconsistent by sub-proof #873.
% 170.22/26.17 | | | | | |
% 170.22/26.17 | | | | | End of split
% 170.22/26.17 | | | | |
% 170.22/26.17 | | | | End of split
% 170.22/26.17 | | | |
% 170.22/26.17 | | | End of split
% 170.22/26.17 | | |
% 170.22/26.17 | | End of split
% 170.22/26.17 | |
% 170.22/26.17 | Case 2:
% 170.22/26.17 | |
% 170.22/26.17 | | (31) all_58_7 = e2 & op(e1, e2) = e2
% 170.22/26.17 | |
% 170.22/26.17 | | ALPHA: (31) implies:
% 170.22/26.17 | | (32) all_58_7 = e2
% 170.22/26.17 | |
% 170.22/26.17 | | REF_CLOSE: (3), (11), (32) are inconsistent by sub-proof #494.
% 170.22/26.17 | |
% 170.22/26.17 | End of split
% 170.22/26.17 |
% 170.22/26.17 End of proof
% 170.22/26.17
% 170.22/26.17 Sub-proof #493 shows that the following formulas are inconsistent:
% 170.22/26.17 ----------------------------------------------------------------
% 170.22/26.17 (1) all_58_6 = e1
% 170.22/26.17 (2) all_58_7 = e1
% 170.22/26.17 (3) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.22/26.17 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.22/26.17 (4) op(e1, e3) = all_52_2
% 170.22/26.17 (5) ~ (e1 = e0)
% 170.22/26.17 (6) ~ (all_6_2 = e2)
% 170.22/26.17 (7) op(e1, e1) = all_6_2
% 170.22/26.17 (8) ~ (e3 = e0)
% 170.22/26.17 (9) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.22/26.17 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.22/26.17 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.17 (11) ~ (e2 = e0)
% 170.22/26.17 (12) all_58_8 = e3
% 170.22/26.17 (13) ~ (e2 = e1)
% 170.22/26.17 (14) op(e1, e3) = e1
% 170.22/26.17
% 170.22/26.17 Begin of proof
% 170.22/26.17 |
% 170.22/26.17 | BETA: splitting (3) gives:
% 170.22/26.17 |
% 170.22/26.17 | Case 1:
% 170.22/26.17 | |
% 170.22/26.17 | | (15) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 170.22/26.17 | | e2)
% 170.22/26.17 | |
% 170.22/26.17 | | BETA: splitting (15) gives:
% 170.22/26.17 | |
% 170.22/26.17 | | Case 1:
% 170.22/26.17 | | |
% 170.22/26.17 | | | (16) all_58_6 = e2 & op(e1, e3) = e2
% 170.22/26.17 | | |
% 170.22/26.17 | | | REF_CLOSE: (1), (13), (16) are inconsistent by sub-proof #715.
% 170.22/26.17 | | |
% 170.22/26.17 | | Case 2:
% 170.22/26.17 | | |
% 170.22/26.17 | | | (17) all_58_7 = e2 & op(e1, e2) = e2
% 170.22/26.17 | | |
% 170.22/26.17 | | | ALPHA: (17) implies:
% 170.22/26.17 | | | (18) all_58_7 = e2
% 170.22/26.17 | | |
% 170.22/26.17 | | | REF_CLOSE: (2), (13), (18) are inconsistent by sub-proof #494.
% 170.22/26.17 | | |
% 170.22/26.17 | | End of split
% 170.22/26.17 | |
% 170.22/26.17 | Case 2:
% 170.22/26.17 | |
% 170.22/26.17 | | (19) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 170.22/26.17 | | e2)
% 170.22/26.17 | |
% 170.22/26.17 | | BETA: splitting (19) gives:
% 170.22/26.17 | |
% 170.22/26.17 | | Case 1:
% 170.22/26.17 | | |
% 170.22/26.17 | | | (20) all_58_8 = e2 & op(e1, e1) = e2
% 170.22/26.17 | | |
% 170.22/26.17 | | | REF_CLOSE: (6), (7), (10), (20) are inconsistent by sub-proof #845.
% 170.22/26.17 | | |
% 170.22/26.17 | | Case 2:
% 170.22/26.17 | | |
% 170.22/26.17 | | | (21) all_58_11 = e2 & op(e1, e0) = e2
% 170.22/26.17 | | |
% 170.22/26.17 | | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (11), (12), (14), (21) are
% 170.22/26.17 | | | inconsistent by sub-proof #495.
% 170.22/26.17 | | |
% 170.22/26.17 | | End of split
% 170.22/26.17 | |
% 170.22/26.17 | End of split
% 170.22/26.17 |
% 170.22/26.17 End of proof
% 170.22/26.17
% 170.22/26.17 Sub-proof #494 shows that the following formulas are inconsistent:
% 170.22/26.17 ----------------------------------------------------------------
% 170.22/26.17 (1) all_58_7 = e2
% 170.22/26.17 (2) all_58_7 = e1
% 170.22/26.17 (3) ~ (e2 = e1)
% 170.22/26.17
% 170.22/26.17 Begin of proof
% 170.22/26.17 |
% 170.22/26.17 | COMBINE_EQS: (1), (2) imply:
% 170.22/26.17 | (4) e2 = e1
% 170.22/26.17 |
% 170.22/26.17 | SIMP: (4) implies:
% 170.22/26.17 | (5) e2 = e1
% 170.22/26.17 |
% 170.22/26.17 | REDUCE: (3), (5) imply:
% 170.22/26.17 | (6) $false
% 170.22/26.17 |
% 170.22/26.17 | CLOSE: (6) is inconsistent.
% 170.22/26.17 |
% 170.22/26.17 End of proof
% 170.22/26.17
% 170.22/26.17 Sub-proof #495 shows that the following formulas are inconsistent:
% 170.22/26.17 ----------------------------------------------------------------
% 170.22/26.17 (1) all_58_7 = e1
% 170.22/26.17 (2) op(e1, e3) = all_52_2
% 170.22/26.17 (3) ~ (e1 = e0)
% 170.22/26.17 (4) all_58_11 = e2 & op(e1, e0) = e2
% 170.22/26.17 (5) ~ (e3 = e0)
% 170.22/26.17 (6) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.22/26.17 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.22/26.17 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.17 (8) ~ (e2 = e0)
% 170.22/26.17 (9) all_58_8 = e3
% 170.22/26.17 (10) op(e1, e3) = e1
% 170.22/26.17
% 170.22/26.17 Begin of proof
% 170.22/26.17 |
% 170.22/26.17 | ALPHA: (4) implies:
% 170.22/26.17 | (11) all_58_11 = e2
% 170.22/26.17 |
% 170.22/26.17 | BETA: splitting (6) gives:
% 170.22/26.17 |
% 170.22/26.17 | Case 1:
% 170.22/26.17 | |
% 170.22/26.17 | | (12) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 170.22/26.17 | | e0)
% 170.22/26.17 | |
% 170.22/26.17 | | REF_CLOSE: (1), (2), (3), (7), (10), (12) are inconsistent by sub-proof
% 170.22/26.17 | | #497.
% 170.22/26.17 | |
% 170.22/26.17 | Case 2:
% 170.22/26.17 | |
% 170.22/26.17 | | (13) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 170.22/26.17 | | e0)
% 170.22/26.17 | |
% 170.22/26.17 | | BETA: splitting (13) gives:
% 170.22/26.17 | |
% 170.22/26.17 | | Case 1:
% 170.22/26.17 | | |
% 170.22/26.17 | | | (14) all_58_8 = e0 & op(e1, e1) = e0
% 170.22/26.17 | | |
% 170.22/26.17 | | | REF_CLOSE: (5), (9), (14) are inconsistent by sub-proof #496.
% 170.22/26.17 | | |
% 170.22/26.17 | | Case 2:
% 170.22/26.17 | | |
% 170.22/26.17 | | | (15) all_58_11 = e0 & op(e1, e0) = e0
% 170.22/26.17 | | |
% 170.22/26.17 | | | REF_CLOSE: (8), (11), (15) are inconsistent by sub-proof #848.
% 170.22/26.17 | | |
% 170.22/26.17 | | End of split
% 170.22/26.17 | |
% 170.22/26.17 | End of split
% 170.22/26.17 |
% 170.22/26.17 End of proof
% 170.22/26.17
% 170.22/26.17 Sub-proof #496 shows that the following formulas are inconsistent:
% 170.22/26.17 ----------------------------------------------------------------
% 170.22/26.17 (1) all_58_8 = e0 & op(e1, e1) = e0
% 170.22/26.17 (2) all_58_8 = e3
% 170.22/26.17 (3) ~ (e3 = e0)
% 170.22/26.17
% 170.22/26.17 Begin of proof
% 170.22/26.17 |
% 170.22/26.17 | ALPHA: (1) implies:
% 170.22/26.17 | (4) all_58_8 = e0
% 170.22/26.17 |
% 170.22/26.17 | COMBINE_EQS: (2), (4) imply:
% 170.22/26.17 | (5) e3 = e0
% 170.22/26.17 |
% 170.22/26.17 | REDUCE: (3), (5) imply:
% 170.22/26.17 | (6) $false
% 170.22/26.17 |
% 170.22/26.17 | CLOSE: (6) is inconsistent.
% 170.22/26.17 |
% 170.22/26.17 End of proof
% 170.22/26.17
% 170.22/26.17 Sub-proof #497 shows that the following formulas are inconsistent:
% 170.22/26.17 ----------------------------------------------------------------
% 170.22/26.18 (1) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 170.22/26.18 (2) all_58_7 = e1
% 170.22/26.18 (3) op(e1, e3) = all_52_2
% 170.22/26.18 (4) ~ (e1 = e0)
% 170.22/26.18 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.18 (6) op(e1, e3) = e1
% 170.22/26.18
% 170.22/26.18 Begin of proof
% 170.22/26.18 |
% 170.22/26.18 | BETA: splitting (1) gives:
% 170.22/26.18 |
% 170.22/26.18 | Case 1:
% 170.22/26.18 | |
% 170.22/26.18 | | (7) all_58_6 = e0 & op(e1, e3) = e0
% 170.22/26.18 | |
% 170.22/26.18 | | ALPHA: (7) implies:
% 170.22/26.18 | | (8) op(e1, e3) = e0
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (3), (4), (5), (6), (8) are inconsistent by sub-proof #749.
% 170.22/26.18 | |
% 170.22/26.18 | Case 2:
% 170.22/26.18 | |
% 170.22/26.18 | | (9) all_58_7 = e0 & op(e1, e2) = e0
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #727.
% 170.22/26.18 | |
% 170.22/26.18 | End of split
% 170.22/26.18 |
% 170.22/26.18 End of proof
% 170.22/26.18
% 170.22/26.18 Sub-proof #498 shows that the following formulas are inconsistent:
% 170.22/26.18 ----------------------------------------------------------------
% 170.22/26.18 (1) all_58_3 = e1 & op(e2, e2) = e1
% 170.22/26.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.18 (3) op(e2, e2) = all_8_2
% 170.22/26.18 (4) ~ (all_8_2 = e1)
% 170.22/26.18
% 170.22/26.18 Begin of proof
% 170.22/26.18 |
% 170.22/26.18 | ALPHA: (1) implies:
% 170.22/26.18 | (5) op(e2, e2) = e1
% 170.22/26.18 |
% 170.22/26.18 | GROUND_INST: instantiating (2) with all_8_2, e1, e2, e2, simplifying with (3),
% 170.22/26.18 | (5) gives:
% 170.22/26.18 | (6) all_8_2 = e1
% 170.22/26.18 |
% 170.22/26.18 | REDUCE: (4), (6) imply:
% 170.22/26.18 | (7) $false
% 170.22/26.18 |
% 170.22/26.18 | CLOSE: (7) is inconsistent.
% 170.22/26.18 |
% 170.22/26.18 End of proof
% 170.22/26.18
% 170.22/26.18 Sub-proof #499 shows that the following formulas are inconsistent:
% 170.22/26.18 ----------------------------------------------------------------
% 170.22/26.18 (1) op(e2, e1) = all_52_9
% 170.22/26.18 (2) ~ (all_52_9 = e3)
% 170.22/26.18 (3) op(e3, e1) = all_52_8
% 170.22/26.18 (4) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 170.22/26.18 (5) ~ (all_52_8 = e3)
% 170.22/26.18 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.18
% 170.22/26.18 Begin of proof
% 170.22/26.18 |
% 170.22/26.18 | BETA: splitting (4) gives:
% 170.22/26.18 |
% 170.22/26.18 | Case 1:
% 170.22/26.18 | |
% 170.22/26.18 | | (7) all_58_4 = e3 & op(e3, e1) = e3
% 170.22/26.18 | |
% 170.22/26.18 | | ALPHA: (7) implies:
% 170.22/26.18 | | (8) op(e3, e1) = e3
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #975.
% 170.22/26.18 | |
% 170.22/26.18 | Case 2:
% 170.22/26.18 | |
% 170.22/26.18 | | (9) all_58_5 = e3 & op(e2, e1) = e3
% 170.22/26.18 | |
% 170.22/26.18 | | ALPHA: (9) implies:
% 170.22/26.18 | | (10) op(e2, e1) = e3
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #951.
% 170.22/26.18 | |
% 170.22/26.18 | End of split
% 170.22/26.18 |
% 170.22/26.18 End of proof
% 170.22/26.18
% 170.22/26.18 Sub-proof #500 shows that the following formulas are inconsistent:
% 170.22/26.18 ----------------------------------------------------------------
% 170.22/26.18 (1) op(e2, e1) = all_52_9
% 170.22/26.18 (2) all_56_12 = e0
% 170.22/26.18 (3) ~ (all_56_12 = e0) | (all_56_11 = e2 & op(e2, e0) = e2)
% 170.22/26.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.18 (5) ~ (e2 = e0)
% 170.22/26.18 (6) ~ (all_52_9 = e0)
% 170.22/26.18 (7) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.22/26.18 (8) op(e2, e0) = all_52_13
% 170.22/26.18
% 170.22/26.18 Begin of proof
% 170.22/26.18 |
% 170.22/26.18 | BETA: splitting (7) gives:
% 170.22/26.18 |
% 170.22/26.18 | Case 1:
% 170.22/26.18 | |
% 170.22/26.18 | | (9) all_58_5 = e0 & op(e2, e1) = e0
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #670.
% 170.22/26.18 | |
% 170.22/26.18 | Case 2:
% 170.22/26.18 | |
% 170.22/26.18 | | (10) all_58_10 = e0 & op(e2, e0) = e0
% 170.22/26.18 | |
% 170.22/26.18 | | ALPHA: (10) implies:
% 170.22/26.18 | | (11) op(e2, e0) = e0
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (2), (3), (4), (5), (8), (11) are inconsistent by sub-proof #501.
% 170.22/26.18 | |
% 170.22/26.18 | End of split
% 170.22/26.18 |
% 170.22/26.18 End of proof
% 170.22/26.18
% 170.22/26.18 Sub-proof #501 shows that the following formulas are inconsistent:
% 170.22/26.18 ----------------------------------------------------------------
% 170.22/26.18 (1) all_56_12 = e0
% 170.22/26.18 (2) ~ (all_56_12 = e0) | (all_56_11 = e2 & op(e2, e0) = e2)
% 170.22/26.18 (3) op(e2, e0) = e0
% 170.22/26.18 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.18 (5) ~ (e2 = e0)
% 170.22/26.18 (6) op(e2, e0) = all_52_13
% 170.22/26.18
% 170.22/26.18 Begin of proof
% 170.22/26.18 |
% 170.22/26.18 | BETA: splitting (2) gives:
% 170.22/26.18 |
% 170.22/26.18 | Case 1:
% 170.22/26.18 | |
% 170.22/26.18 | | (7) ~ (all_56_12 = e0)
% 170.22/26.18 | |
% 170.22/26.18 | | REDUCE: (1), (7) imply:
% 170.22/26.18 | | (8) $false
% 170.22/26.18 | |
% 170.22/26.18 | | CLOSE: (8) is inconsistent.
% 170.22/26.18 | |
% 170.22/26.18 | Case 2:
% 170.22/26.18 | |
% 170.22/26.18 | | (9) all_56_11 = e2 & op(e2, e0) = e2
% 170.22/26.18 | |
% 170.22/26.18 | | ALPHA: (9) implies:
% 170.22/26.18 | | (10) op(e2, e0) = e2
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #684.
% 170.22/26.18 | |
% 170.22/26.18 | End of split
% 170.22/26.18 |
% 170.22/26.18 End of proof
% 170.22/26.18
% 170.22/26.18 Sub-proof #502 shows that the following formulas are inconsistent:
% 170.22/26.18 ----------------------------------------------------------------
% 170.22/26.18 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.22/26.18 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.22/26.18 (2) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.22/26.18 (3) ~ (e3 = e1)
% 170.22/26.18 (4) ~ (e1 = e0)
% 170.22/26.18 (5) ~ (all_6_2 = e2)
% 170.22/26.18 (6) op(e1, e1) = all_6_2
% 170.22/26.18 (7) ~ (e3 = e0)
% 170.22/26.18 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.18 (9) ~ (e2 = e0)
% 170.22/26.18 (10) ~ (e2 = e1)
% 170.22/26.18 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.22/26.18 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.22/26.18 (12) op(e2, e0) = e2
% 170.22/26.18 (13) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.22/26.18 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.22/26.18 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.22/26.18 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.22/26.18 (14) op(e2, e0) = all_52_13
% 170.22/26.18 (15) ~ (e3 = e2)
% 170.22/26.18
% 170.22/26.18 Begin of proof
% 170.22/26.18 |
% 170.22/26.18 | BETA: splitting (2) gives:
% 170.22/26.18 |
% 170.22/26.18 | Case 1:
% 170.22/26.18 | |
% 170.22/26.18 | | (16) all_58_8 = e2 & op(e1, e1) = e2
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (5), (6), (8), (16) are inconsistent by sub-proof #845.
% 170.22/26.18 | |
% 170.22/26.18 | Case 2:
% 170.22/26.18 | |
% 170.22/26.18 | | (17) all_58_11 = e2 & op(e1, e0) = e2
% 170.22/26.18 | |
% 170.22/26.18 | | ALPHA: (17) implies:
% 170.22/26.18 | | (18) all_58_11 = e2
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 170.22/26.18 | | (18) are inconsistent by sub-proof #525.
% 170.22/26.18 | |
% 170.22/26.18 | End of split
% 170.22/26.18 |
% 170.22/26.18 End of proof
% 170.22/26.18
% 170.22/26.18 Sub-proof #503 shows that the following formulas are inconsistent:
% 170.22/26.18 ----------------------------------------------------------------
% 170.22/26.18 (1) all_58_7 = e1 & op(e1, e2) = e1
% 170.22/26.18 (2) all_58_7 = e2
% 170.22/26.18 (3) ~ (e2 = e1)
% 170.22/26.18
% 170.22/26.18 Begin of proof
% 170.22/26.18 |
% 170.22/26.18 | ALPHA: (1) implies:
% 170.22/26.18 | (4) all_58_7 = e1
% 170.22/26.18 |
% 170.22/26.18 | COMBINE_EQS: (2), (4) imply:
% 170.22/26.18 | (5) e2 = e1
% 170.22/26.18 |
% 170.22/26.18 | REDUCE: (3), (5) imply:
% 170.22/26.18 | (6) $false
% 170.22/26.18 |
% 170.22/26.18 | CLOSE: (6) is inconsistent.
% 170.22/26.18 |
% 170.22/26.18 End of proof
% 170.22/26.18
% 170.22/26.18 Sub-proof #504 shows that the following formulas are inconsistent:
% 170.22/26.18 ----------------------------------------------------------------
% 170.22/26.18 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.22/26.18 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.22/26.18 (2) ~ (all_4_2 = e2)
% 170.22/26.18 (3) ~ (e3 = e1)
% 170.22/26.18 (4) ~ (e1 = e0)
% 170.22/26.18 (5) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.22/26.18 (6) ~ (e3 = e0)
% 170.22/26.18 (7) op(e0, e0) = all_4_2
% 170.22/26.18 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.18 (9) ~ (e2 = e0)
% 170.22/26.18 (10) ~ (e2 = e1)
% 170.22/26.18 (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.22/26.18 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.22/26.18 (12) op(e2, e0) = e2
% 170.22/26.18 (13) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.22/26.18 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.22/26.18 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.22/26.18 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.22/26.18 (14) op(e2, e0) = all_52_13
% 170.22/26.18 (15) ~ (e3 = e2)
% 170.22/26.18
% 170.22/26.18 Begin of proof
% 170.22/26.18 |
% 170.22/26.18 | BETA: splitting (5) gives:
% 170.22/26.18 |
% 170.22/26.18 | Case 1:
% 170.22/26.18 | |
% 170.22/26.18 | | (16) all_58_11 = e2 & op(e1, e0) = e2
% 170.22/26.18 | |
% 170.22/26.18 | | ALPHA: (16) implies:
% 170.22/26.18 | | (17) all_58_11 = e2
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (11), (12), (13), (14), (15),
% 170.22/26.18 | | (17) are inconsistent by sub-proof #525.
% 170.22/26.18 | |
% 170.22/26.18 | Case 2:
% 170.22/26.18 | |
% 170.22/26.18 | | (18) all_58_15 = e2 & op(e0, e0) = e2
% 170.22/26.18 | |
% 170.22/26.18 | | REF_CLOSE: (2), (7), (8), (18) are inconsistent by sub-proof #854.
% 170.22/26.18 | |
% 170.22/26.18 | End of split
% 170.22/26.18 |
% 170.22/26.18 End of proof
% 170.22/26.18
% 170.22/26.18 Sub-proof #505 shows that the following formulas are inconsistent:
% 170.22/26.18 ----------------------------------------------------------------
% 170.22/26.18 (1) op(e2, e1) = all_52_9
% 170.22/26.18 (2) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 170.22/26.18 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 170.22/26.18 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.18 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.22/26.18 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.22/26.18 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 170.22/26.18 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.18 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.18 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.22/26.18 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 170.22/26.18 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 170.22/26.18 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.18 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.18 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.22/26.18 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.22/26.18 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 170.22/26.18 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.18 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.18 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.22/26.18 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 170.22/26.18 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 170.22/26.18 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.18 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.18 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.22/26.18 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 170.22/26.18 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 170.22/26.18 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.22/26.18 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.18 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.22/26.18 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.22/26.18 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 170.22/26.18 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.18 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.18 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.22/26.18 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 170.22/26.18 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 170.22/26.18 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.22/26.18 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.18 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.22/26.18 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.22/26.18 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 170.22/26.18 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.18 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.18 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.22/26.18 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 170.22/26.18 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.22/26.18 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 170.22/26.18 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 170.22/26.18 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 170.22/26.18 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 170.22/26.18 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.22/26.18 (3) all_54_2 = all_52_8
% 170.22/26.18 (4) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.22/26.18 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.22/26.18 (5) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.22/26.18 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.22/26.18 (6) op(e0, e1) = all_52_11
% 170.22/26.18 (7) all_58_14 = e2
% 170.22/26.18 (8) all_56_1 = e3
% 170.22/26.18 (9) all_56_10 = e2
% 170.22/26.18 (10) ~ (all_52_1 = all_52_2)
% 170.22/26.18 (11) ~ (all_52_1 = e0)
% 170.22/26.18 (12) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.22/26.18 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.22/26.18 (13) all_54_8 = all_52_2
% 170.22/26.18 (14) all_54_12 = all_52_3
% 170.22/26.18 (15) ~ (all_52_8 = all_52_11)
% 170.22/26.18 (16) ~ (all_52_11 = all_4_2)
% 170.22/26.18 (17) ~ (all_8_2 = e3)
% 170.22/26.18 (18) ~ (all_6_2 = e3)
% 170.22/26.18 (19) all_54_10 = all_6_2
% 170.22/26.18 (20) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 170.22/26.18 (21) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.22/26.18 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.22/26.18 (22) ~ (e3 = e1)
% 170.22/26.18 (23) all_56_14 = all_6_2
% 170.22/26.18 (24) ~ (all_46_2 = e0) | ( ~ (all_46_0 = e3) & op(all_46_1, e1) = all_46_0 &
% 170.22/26.18 op(e0, e1) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 170.22/26.18 e2) & op(e0, e1) = all_46_1 & $i(all_46_1))
% 170.22/26.18 (25) all_56_12 = e0
% 170.22/26.18 (26) op(e3, e1) = all_52_8
% 170.22/26.18 (27) ~ (all_52_2 = all_52_6)
% 170.22/26.18 (28) ~ (e1 = e0)
% 170.22/26.18 (29) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.22/26.18 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.22/26.18 e3)
% 170.22/26.18 (30) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.22/26.18 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.22/26.18 (31) op(e1, e2) = all_52_6
% 170.22/26.18 (32) op(e0, e2) = e1
% 170.22/26.18 (33) ~ (all_52_3 = all_4_2)
% 170.22/26.18 (34) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 170.22/26.18 (35) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.22/26.18 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.22/26.18 (36) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 170.22/26.18 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.22/26.18 (37) op(e2, e3) = all_52_1
% 170.22/26.18 (38) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 170.22/26.18 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.22/26.18 (39) ~ (all_52_3 = all_52_7)
% 170.22/26.18 (40) ~ (all_52_7 = e3)
% 170.22/26.18 (41) all_58_10 = e2
% 170.22/26.18 (42) all_56_11 = e2
% 170.22/26.18 (43) ~ (all_52_2 = all_6_2)
% 170.22/26.18 (44) op(e2, e2) = all_8_2
% 170.22/26.18 (45) all_58_7 = e2 & op(e1, e2) = e2
% 170.22/26.18 (46) op(e1, e1) = all_6_2
% 170.22/26.18 (47) all_56_15 = all_4_2
% 170.22/26.19 (48) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.22/26.19 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.22/26.19 (49) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.22/26.19 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.22/26.19 (50) op(e0, e0) = all_4_2
% 170.22/26.19 (51) ~ (all_52_9 = all_6_2)
% 170.22/26.19 (52) all_56_10 = e3 | all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 170.22/26.19 (53) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.22/26.19 (54) ~ (all_52_8 = e3)
% 170.22/26.19 (55) ~ (all_52_8 = all_52_9)
% 170.22/26.19 (56) all_58_1 = e3
% 170.22/26.19 (57) ~ (all_52_3 = all_52_11)
% 170.22/26.19 (58) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.22/26.19 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.22/26.19 (59) ~ (all_52_7 = e0)
% 170.22/26.19 (60) ~ (all_52_11 = all_6_2)
% 170.22/26.19 (61) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.22/26.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.22/26.19 (62) ~ (all_52_6 = e0)
% 170.22/26.19 (63) ~ (all_52_8 = all_6_2)
% 170.22/26.19 (64) ~ (e2 = e0)
% 170.22/26.19 (65) all_58_13 = e1
% 170.22/26.19 (66) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 170.22/26.19 (67) all_58_0 = e2
% 170.22/26.19 (68) ~ (all_52_9 = e0)
% 170.22/26.19 (69) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.22/26.19 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.22/26.19 (70) op(e3, e3) = e2
% 170.22/26.19 (71) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.22/26.19 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.22/26.19 (72) ~ (e2 = e1)
% 170.22/26.19 (73) ~ (all_52_4 = e2)
% 170.22/26.19 (74) op(e3, e2) = all_52_4
% 170.22/26.19 (75) all_46_2 = all_6_2
% 170.22/26.19 (76) ~ (all_52_6 = e3)
% 170.22/26.19 (77) op(e0, e1) = e2
% 170.22/26.19 (78) op(e0, e2) = all_52_7
% 170.22/26.19 (79) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.22/26.19 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.22/26.19 (80) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 170.22/26.19 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 170.22/26.19 (81) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1) |
% 170.22/26.19 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 170.22/26.19 (82) op(e2, e0) = e2
% 170.22/26.19 (83) ~ (all_52_9 = e2)
% 170.22/26.19 (84) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.22/26.19 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.22/26.19 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.22/26.19 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.22/26.19 (85) ~ (all_52_2 = all_52_3)
% 170.22/26.19 (86) op(e2, e0) = all_52_13
% 170.22/26.19 (87) ~ (e3 = e2)
% 170.22/26.19
% 170.22/26.19 Begin of proof
% 170.22/26.19 |
% 170.22/26.19 | BETA: splitting (35) gives:
% 170.22/26.19 |
% 170.22/26.19 | Case 1:
% 170.22/26.19 | |
% 170.22/26.19 | | (88) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 170.22/26.19 | | e3)
% 170.22/26.19 | |
% 170.22/26.19 | | BETA: splitting (88) gives:
% 170.22/26.19 | |
% 170.22/26.19 | | Case 1:
% 170.22/26.19 | | |
% 170.22/26.19 | | | (89) all_58_4 = e3 & op(e3, e1) = e3
% 170.22/26.19 | | |
% 170.22/26.19 | | | ALPHA: (89) implies:
% 170.22/26.19 | | | (90) op(e3, e1) = e3
% 170.22/26.19 | | |
% 170.22/26.19 | | | REF_CLOSE: (26), (54), (61), (90) are inconsistent by sub-proof #975.
% 170.22/26.19 | | |
% 170.22/26.19 | | Case 2:
% 170.22/26.19 | | |
% 170.22/26.19 | | | (91) all_58_5 = e3 & op(e2, e1) = e3
% 170.22/26.19 | | |
% 170.22/26.19 | | | ALPHA: (91) implies:
% 170.22/26.19 | | | (92) op(e2, e1) = e3
% 170.22/26.19 | | |
% 170.22/26.19 | | | BETA: splitting (5) gives:
% 170.22/26.19 | | |
% 170.22/26.19 | | | Case 1:
% 170.22/26.19 | | | |
% 170.22/26.19 | | | | (93) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 170.22/26.19 | | | | = e1)
% 170.22/26.19 | | | |
% 170.22/26.19 | | | | BETA: splitting (93) gives:
% 170.22/26.19 | | | |
% 170.22/26.19 | | | | Case 1:
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | (94) all_58_2 = e1 & op(e2, e3) = e1
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | ALPHA: (94) implies:
% 170.22/26.19 | | | | | (95) all_58_2 = e1
% 170.22/26.19 | | | | | (96) op(e2, e3) = e1
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | ALPHA: (45) implies:
% 170.22/26.19 | | | | | (97) all_58_7 = e2
% 170.22/26.19 | | | | | (98) op(e1, e2) = e2
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | ALPHA: (91) implies:
% 170.22/26.19 | | | | | (99) all_58_5 = e3
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | GROUND_INST: instantiating (61) with all_52_11, e2, e1, e0,
% 170.22/26.19 | | | | | simplifying with (6), (77) gives:
% 170.22/26.19 | | | | | (100) all_52_11 = e2
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | GROUND_INST: instantiating (61) with all_52_7, e1, e2, e0, simplifying
% 170.22/26.19 | | | | | with (32), (78) gives:
% 170.22/26.19 | | | | | (101) all_52_7 = e1
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | GROUND_INST: instantiating (61) with all_52_6, e2, e2, e1, simplifying
% 170.22/26.19 | | | | | with (31), (98) gives:
% 170.22/26.19 | | | | | (102) all_52_6 = e2
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | GROUND_INST: instantiating (61) with all_52_9, e3, e1, e2, simplifying
% 170.22/26.19 | | | | | with (1), (92) gives:
% 170.22/26.19 | | | | | (103) all_52_9 = e3
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | GROUND_INST: instantiating (61) with all_52_1, e1, e3, e2, simplifying
% 170.22/26.19 | | | | | with (37), (96) gives:
% 170.22/26.19 | | | | | (104) all_52_1 = e1
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | REDUCE: (10), (104) imply:
% 170.22/26.19 | | | | | (105) ~ (all_52_2 = e1)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | SIMP: (105) implies:
% 170.22/26.19 | | | | | (106) ~ (all_52_2 = e1)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | REDUCE: (27), (102) imply:
% 170.22/26.19 | | | | | (107) ~ (all_52_2 = e2)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | REDUCE: (39), (101) imply:
% 170.22/26.19 | | | | | (108) ~ (all_52_3 = e1)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | REDUCE: (57), (100) imply:
% 170.22/26.19 | | | | | (109) ~ (all_52_3 = e2)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | REDUCE: (15), (100) imply:
% 170.22/26.19 | | | | | (110) ~ (all_52_8 = e2)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | REDUCE: (51), (103) imply:
% 170.22/26.19 | | | | | (111) ~ (all_6_2 = e3)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | REDUCE: (68), (103) imply:
% 170.22/26.19 | | | | | (112) ~ (e3 = e0)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | REDUCE: (60), (100) imply:
% 170.22/26.19 | | | | | (113) ~ (all_6_2 = e2)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | SIMP: (113) implies:
% 170.22/26.19 | | | | | (114) ~ (all_6_2 = e2)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | REDUCE: (16), (100) imply:
% 170.22/26.19 | | | | | (115) ~ (all_4_2 = e2)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | SIMP: (115) implies:
% 170.22/26.19 | | | | | (116) ~ (all_4_2 = e2)
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | BETA: splitting (24) gives:
% 170.22/26.19 | | | | |
% 170.22/26.19 | | | | | Case 1:
% 170.22/26.19 | | | | | |
% 170.22/26.19 | | | | | | (117) ~ (all_46_2 = e0)
% 170.22/26.19 | | | | | |
% 170.22/26.19 | | | | | | REDUCE: (75), (117) imply:
% 170.22/26.19 | | | | | | (118) ~ (all_6_2 = e0)
% 170.22/26.19 | | | | | |
% 170.22/26.19 | | | | | | BETA: splitting (20) gives:
% 170.22/26.19 | | | | | |
% 170.22/26.19 | | | | | | Case 1:
% 170.22/26.19 | | | | | | |
% 170.22/26.19 | | | | | | | (119) all_54_10 = e3
% 170.22/26.19 | | | | | | |
% 170.22/26.19 | | | | | | | REF_CLOSE: (18), (19), (119) are inconsistent by sub-proof #982.
% 170.22/26.19 | | | | | | |
% 170.22/26.19 | | | | | | Case 2:
% 170.22/26.19 | | | | | | |
% 170.22/26.19 | | | | | | | (120) ~ (all_54_10 = e3)
% 170.22/26.19 | | | | | | | (121) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 170.22/26.19 | | | | | | |
% 170.22/26.19 | | | | | | | BETA: splitting (121) gives:
% 170.22/26.19 | | | | | | |
% 170.22/26.19 | | | | | | | Case 1:
% 170.22/26.19 | | | | | | | |
% 170.22/26.19 | | | | | | | | (122) all_54_10 = e2
% 170.22/26.19 | | | | | | | |
% 170.22/26.19 | | | | | | | | REF_CLOSE: (19), (114), (122) are inconsistent by sub-proof
% 170.22/26.19 | | | | | | | | #981.
% 170.22/26.19 | | | | | | | |
% 170.22/26.19 | | | | | | | Case 2:
% 170.22/26.19 | | | | | | | |
% 170.22/26.19 | | | | | | | | (123) ~ (all_54_10 = e2)
% 170.22/26.19 | | | | | | | | (124) all_54_10 = e1 | all_54_10 = e0
% 170.22/26.19 | | | | | | | |
% 170.22/26.19 | | | | | | | | BETA: splitting (124) gives:
% 170.22/26.19 | | | | | | | |
% 170.22/26.19 | | | | | | | | Case 1:
% 170.22/26.19 | | | | | | | | |
% 170.22/26.19 | | | | | | | | | (125) all_54_10 = e1
% 170.22/26.19 | | | | | | | | |
% 170.22/26.19 | | | | | | | | | COMBINE_EQS: (19), (125) imply:
% 170.22/26.19 | | | | | | | | | (126) all_6_2 = e1
% 170.22/26.19 | | | | | | | | |
% 170.22/26.19 | | | | | | | | | SIMP: (126) implies:
% 170.22/26.19 | | | | | | | | | (127) all_6_2 = e1
% 170.22/26.19 | | | | | | | | |
% 170.22/26.19 | | | | | | | | | COMBINE_EQS: (23), (127) imply:
% 170.22/26.19 | | | | | | | | | (128) all_56_14 = e1
% 170.22/26.19 | | | | | | | | |
% 170.22/26.19 | | | | | | | | | REDUCE: (63), (127) imply:
% 170.22/26.19 | | | | | | | | | (129) ~ (all_52_8 = e1)
% 170.22/26.19 | | | | | | | | |
% 170.22/26.19 | | | | | | | | | REDUCE: (18), (127) imply:
% 170.22/26.19 | | | | | | | | | (130) ~ (e3 = e1)
% 170.22/26.19 | | | | | | | | |
% 170.22/26.19 | | | | | | | | | REDUCE: (114), (127) imply:
% 170.22/26.19 | | | | | | | | | (131) ~ (e2 = e1)
% 170.22/26.19 | | | | | | | | |
% 170.22/26.19 | | | | | | | | | BETA: splitting (4) gives:
% 170.22/26.19 | | | | | | | | |
% 170.22/26.19 | | | | | | | | | Case 1:
% 170.22/26.19 | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | (132) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1
% 170.22/26.19 | | | | | | | | | | & op(e2, e0) = e1)
% 170.22/26.19 | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | BETA: splitting (132) gives:
% 170.22/26.19 | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | Case 1:
% 170.22/26.19 | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | (133) all_58_9 = e1 & op(e3, e0) = e1
% 170.22/26.19 | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | ALPHA: (133) implies:
% 170.22/26.19 | | | | | | | | | | | (134) op(e3, e0) = e1
% 170.22/26.19 | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | BETA: splitting (2) gives:
% 170.22/26.19 | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | Case 1:
% 170.22/26.19 | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | (135) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 170.22/26.19 | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.22/26.19 | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.22/26.19 | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.19 | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.22/26.19 | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.22/26.19 | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.22/26.19 | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.22/26.19 | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 170.22/26.19 | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 170.22/26.19 | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.22/26.19 | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.22/26.19 | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.19 | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.22/26.19 | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.22/26.19 | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.22/26.19 | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.22/26.19 | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 170.22/26.19 | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 170.22/26.19 | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 170.22/26.19 | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 170.22/26.19 | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.19 | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.22/26.19 | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.22/26.19 | | | | | | | | | | | | $i(all_56_6))))
% 170.22/26.19 | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | BETA: splitting (135) gives:
% 170.22/26.19 | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | Case 1:
% 170.22/26.19 | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | (136) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 170.22/26.19 | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.22/26.19 | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.22/26.19 | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.19 | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.22/26.19 | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.22/26.19 | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.22/26.19 | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.22/26.19 | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.22/26.19 | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | REF_CLOSE: (8), (9), (61), (73), (74), (136) are inconsistent
% 170.22/26.19 | | | | | | | | | | | | | by sub-proof #520.
% 170.22/26.19 | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | Case 2:
% 170.22/26.19 | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | (137) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 170.22/26.19 | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.22/26.19 | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.22/26.19 | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.19 | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.22/26.19 | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.22/26.19 | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.22/26.19 | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.22/26.19 | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 170.22/26.19 | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 170.22/26.19 | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 170.22/26.19 | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 170.22/26.19 | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.22/26.19 | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.22/26.19 | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.22/26.19 | | | | | | | | | | | | | $i(all_56_6))))
% 170.22/26.19 | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | BETA: splitting (137) gives:
% 170.22/26.19 | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | Case 1:
% 170.22/26.19 | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | (138) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 170.22/26.19 | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.22/26.19 | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.22/26.19 | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.22/26.19 | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 170.22/26.19 | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | ALPHA: (138) implies:
% 170.22/26.19 | | | | | | | | | | | | | | (139) ~ (all_56_14 = e1)
% 170.22/26.19 | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | REDUCE: (128), (139) imply:
% 170.22/26.19 | | | | | | | | | | | | | | (140) $false
% 170.22/26.19 | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | CLOSE: (140) is inconsistent.
% 170.22/26.19 | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | Case 2:
% 170.22/26.19 | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | (141) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 170.22/26.19 | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.22/26.19 | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.22/26.19 | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.22/26.19 | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.19 | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.22/26.19 | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.22/26.19 | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 170.22/26.19 | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 170.22/26.19 | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.22/26.19 | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.22/26.19 | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.22/26.19 | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.22/26.19 | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 170.22/26.19 | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | Case 1:
% 170.22/26.19 | | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | | (142) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 170.22/26.19 | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.22/26.19 | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.22/26.19 | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.22/26.19 | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 170.22/26.19 | | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 170.22/26.19 | | | | | | | | | | | | | | | (143) ~ (all_56_14 = e1)
% 170.22/26.19 | | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | | REDUCE: (128), (143) imply:
% 170.22/26.19 | | | | | | | | | | | | | | | (144) $false
% 170.22/26.19 | | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | | CLOSE: (144) is inconsistent.
% 170.22/26.19 | | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | Case 2:
% 170.22/26.19 | | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | | (145) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 170.22/26.19 | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.22/26.19 | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 170.22/26.19 | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.22/26.19 | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 170.22/26.19 | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 170.22/26.19 | | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 170.22/26.19 | | | | | | | | | | | | | | | (146) op(e3, e1) = e1
% 170.22/26.19 | | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | | REF_CLOSE: (3), (26), (54), (61), (66), (110), (129), (146)
% 170.22/26.19 | | | | | | | | | | | | | | | are inconsistent by sub-proof #567.
% 170.22/26.19 | | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | | End of split
% 170.22/26.19 | | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | | End of split
% 170.22/26.19 | | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | | End of split
% 170.22/26.19 | | | | | | | | | | | |
% 170.22/26.19 | | | | | | | | | | | Case 2:
% 170.22/26.19 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | (147) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 170.22/26.20 | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.22/26.20 | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.22/26.20 | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.20 | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.22/26.20 | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.22/26.20 | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.22/26.20 | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.22/26.20 | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 170.22/26.20 | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 170.22/26.20 | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.22/26.20 | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.22/26.20 | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.20 | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.22/26.20 | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.22/26.20 | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.22/26.20 | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.22/26.20 | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 170.22/26.20 | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.22/26.20 | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.22/26.20 | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.22/26.20 | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.22/26.20 | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 170.22/26.20 | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 170.22/26.20 | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.22/26.20 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | BETA: splitting (147) gives:
% 170.22/26.20 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | (148) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 170.22/26.20 | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.22/26.20 | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.22/26.20 | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.20 | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.22/26.20 | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.22/26.20 | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.22/26.20 | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.22/26.20 | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | REF_CLOSE: (8), (9), (28), (61), (134), (148) are
% 170.22/26.20 | | | | | | | | | | | | | inconsistent by sub-proof #552.
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | (149) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 170.22/26.20 | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.22/26.20 | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.22/26.20 | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.22/26.20 | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.22/26.20 | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.22/26.20 | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.22/26.20 | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.22/26.20 | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 170.22/26.20 | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.22/26.20 | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.22/26.20 | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.22/26.20 | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 170.22/26.20 | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 170.22/26.20 | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | BETA: splitting (149) gives:
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | (150) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 170.22/26.20 | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 170.22/26.20 | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 170.22/26.20 | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 170.22/26.20 | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | ALPHA: (150) implies:
% 170.22/26.20 | | | | | | | | | | | | | | (151) op(e2, e0) = e0
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | REF_CLOSE: (61), (64), (82), (86), (151) are inconsistent by
% 170.22/26.20 | | | | | | | | | | | | | | sub-proof #684.
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | (152) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 170.22/26.20 | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.22/26.20 | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.22/26.20 | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.22/26.20 | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.22/26.20 | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 170.22/26.20 | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 170.22/26.20 | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 170.22/26.20 | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 170.22/26.20 | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 170.22/26.20 | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 170.22/26.20 | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 170.22/26.20 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 170.22/26.20 | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | (153) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 170.22/26.20 | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 170.22/26.20 | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.22/26.20 | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.22/26.20 | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.22/26.20 | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | (154) ~ (all_56_14 = e1)
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | REDUCE: (128), (154) imply:
% 170.22/26.20 | | | | | | | | | | | | | | | (155) $false
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | (156) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.22/26.20 | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.22/26.20 | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.22/26.20 | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.22/26.20 | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 170.22/26.20 | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 170.22/26.20 | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | REF_CLOSE: (25), (42), (156) are inconsistent by sub-proof
% 170.22/26.20 | | | | | | | | | | | | | | | #683.
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | (157) all_58_10 = e1 & op(e2, e0) = e1
% 170.22/26.20 | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | ALPHA: (157) implies:
% 170.22/26.20 | | | | | | | | | | | (158) op(e2, e0) = e1
% 170.22/26.20 | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | REF_CLOSE: (61), (72), (82), (158) are inconsistent by
% 170.22/26.20 | | | | | | | | | | | sub-proof #526.
% 170.22/26.20 | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | (159) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 170.22/26.20 | | | | | | | | | | e1 & op(e0, e0) = e1)
% 170.22/26.20 | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | BETA: splitting (159) gives:
% 170.22/26.20 | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | (160) all_58_11 = e1 & op(e1, e0) = e1
% 170.22/26.20 | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | ALPHA: (160) implies:
% 170.22/26.20 | | | | | | | | | | | (161) all_58_11 = e1
% 170.22/26.20 | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | BETA: splitting (79) gives:
% 170.22/26.20 | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | (162) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 170.22/26.20 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 170.22/26.20 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | BETA: splitting (162) gives:
% 170.22/26.20 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | (163) all_58_9 = e3 & op(e3, e0) = e3
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | ALPHA: (163) implies:
% 170.22/26.20 | | | | | | | | | | | | | (164) all_58_9 = e3
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | BETA: splitting (81) gives:
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | (165) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 170.22/26.20 | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | (166) all_58_4 = e1 & op(e3, e1) = e1
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | (167) all_58_4 = e1
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | (168) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | (169) all_58_6 = e3 & op(e1, e3) = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | | | (170) all_58_6 = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (12), (17), (21), (22), (28), (29),
% 170.22/26.20 | | | | | | | | | | | | | | | | | (37), (40), (44), (56), (61), (64), (65), (67),
% 170.22/26.20 | | | | | | | | | | | | | | | | | (71), (78), (82), (84), (87), (95), (99), (112),
% 170.22/26.20 | | | | | | | | | | | | | | | | | (164), (167), (170) are inconsistent by sub-proof
% 170.22/26.20 | | | | | | | | | | | | | | | | | #516.
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | (171) all_58_7 = e3 & op(e1, e2) = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | | | (172) op(e1, e2) = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (61), (76), (172) are inconsistent by
% 170.22/26.20 | | | | | | | | | | | | | | | | | sub-proof #668.
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | (173) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 170.22/26.20 | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | BETA: splitting (173) gives:
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | (174) all_58_8 = e3 & op(e1, e1) = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (46), (61), (174) are inconsistent by
% 170.22/26.20 | | | | | | | | | | | | | | | | | sub-proof #961.
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | (175) all_58_11 = e3 & op(e1, e0) = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | | | (176) all_58_11 = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (161), (176) are inconsistent by sub-proof
% 170.22/26.20 | | | | | | | | | | | | | | | | | #755.
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | (177) all_58_5 = e1 & op(e2, e1) = e1
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | (178) op(e2, e1) = e1
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | REF_CLOSE: (22), (61), (92), (178) are inconsistent by
% 170.22/26.20 | | | | | | | | | | | | | | | sub-proof #686.
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | (179) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 170.22/26.20 | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | REF_CLOSE: (7), (22), (28), (38), (56), (58), (61), (64),
% 170.22/26.20 | | | | | | | | | | | | | | (70), (72), (77), (99), (112), (164), (179) are
% 170.22/26.20 | | | | | | | | | | | | | | inconsistent by sub-proof #563.
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | (180) all_58_10 = e3 & op(e2, e0) = e3
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | ALPHA: (180) implies:
% 170.22/26.20 | | | | | | | | | | | | | (181) op(e2, e0) = e3
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | REF_CLOSE: (61), (82), (87), (181) are inconsistent by
% 170.22/26.20 | | | | | | | | | | | | | sub-proof #682.
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | (182) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 170.22/26.20 | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 170.22/26.20 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | BETA: splitting (182) gives:
% 170.22/26.20 | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | (183) all_58_11 = e3 & op(e1, e0) = e3
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | ALPHA: (183) implies:
% 170.22/26.20 | | | | | | | | | | | | | (184) all_58_11 = e3
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | REF_CLOSE: (22), (161), (184) are inconsistent by sub-proof
% 170.22/26.20 | | | | | | | | | | | | | #755.
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | (185) all_58_15 = e3 & op(e0, e0) = e3
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | ALPHA: (185) implies:
% 170.22/26.20 | | | | | | | | | | | | | (186) all_58_15 = e3
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | BETA: splitting (66) gives:
% 170.22/26.20 | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | (187) all_54_2 = e3
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | COMBINE_EQS: (3), (187) imply:
% 170.22/26.20 | | | | | | | | | | | | | | (188) all_52_8 = e3
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | REDUCE: (54), (188) imply:
% 170.22/26.20 | | | | | | | | | | | | | | (189) $false
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | (190) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 170.22/26.20 | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | (191) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 170.22/26.20 | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | (192) all_58_4 = e1 & op(e3, e1) = e1
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | | (193) op(e3, e1) = e1
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (26), (61), (110), (129), (190), (193) are
% 170.22/26.20 | | | | | | | | | | | | | | | | inconsistent by sub-proof #568.
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | (194) all_58_5 = e1 & op(e2, e1) = e1
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | | (195) op(e2, e1) = e1
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | REF_CLOSE: (22), (61), (92), (195) are inconsistent by
% 170.22/26.20 | | | | | | | | | | | | | | | | sub-proof #686.
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | End of split
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | (196) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 170.22/26.20 | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 170.22/26.20 | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | (197) all_58_8 = e1 & op(e1, e1) = e1
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | | (198) all_58_8 = e1
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 170.22/26.20 | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | (199) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 170.22/26.20 | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | (200) all_58_6 = e3 & op(e1, e3) = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | | | | (201) all_58_6 = e3
% 170.22/26.20 | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 170.22/26.20 | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | (202) all_58_15 = e0 & op(e0, e0) = e0
% 170.22/26.20 | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | (203) all_58_15 = e0
% 170.22/26.20 | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (12), (17), (22), (29), (37), (40),
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | (44), (61), (64), (67), (71), (78), (82), (87),
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | (95), (99), (112), (201), (203) are inconsistent
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | by sub-proof #518.
% 170.22/26.20 | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | Case 2:
% 170.22/26.20 | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | (204) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.22/26.20 | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | (205) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | e0) = e0)
% 170.22/26.20 | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 170.22/26.20 | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | | (206) all_58_9 = e0 & op(e3, e0) = e0
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | | (207) all_58_9 = e0
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | |
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.22/26.20 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | (208) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (209) all_58_6 = e0 & op(e1, e3) = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (210) all_58_6 = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (201), (210) imply:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (211) e3 = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | SIMP: (211) implies:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (212) e3 = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (212) imply:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (213) all_58_15 = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (12), (17), (22), (29), (37), (40),
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (44), (61), (64), (67), (71), (78), (82), (87),
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (95), (99), (112), (201), (213) are inconsistent
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #518.
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (214) all_58_7 = e0 & op(e1, e2) = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (215) all_58_7 = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (97), (215) imply:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (216) e2 = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (41), (216) imply:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (217) all_58_10 = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | (218) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | | (219) all_58_9 = e2 & op(e3, e0) = e2
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (207), (219) are inconsistent by sub-proof
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | | #515.
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | | (220) all_58_10 = e2 & op(e2, e0) = e2
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (64), (217), (220) are inconsistent by sub-proof
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | | #760.
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | (221) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (50), (61), (72), (116), (161), (221) are
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #514.
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | (222) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (223) all_58_8 = e0 & op(e1, e1) = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (198), (223) are inconsistent by sub-proof
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | #718.
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | (224) all_58_11 = e0 & op(e1, e0) = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (161), (224) are inconsistent by sub-proof
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | | #513.
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | (225) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | | (226) all_58_10 = e0 & op(e2, e0) = e0
% 170.47/26.20 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | | (227) op(e2, e0) = e0
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (64), (82), (86), (227) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | | sub-proof #684.
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | | (228) all_58_11 = e0 & op(e1, e0) = e0
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (161), (228) are inconsistent by sub-proof
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | | #513.
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | (229) all_58_7 = e3 & op(e1, e2) = e3
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | | | | (230) op(e1, e2) = e3
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (61), (76), (230) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | | | | | | sub-proof #668.
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | (231) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 =
% 170.47/26.21 | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | (232) all_58_8 = e3 & op(e1, e1) = e3
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (46), (61), (232) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | | | | | | sub-proof #961.
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | (233) all_58_11 = e3 & op(e1, e0) = e3
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | | | | (234) all_58_11 = e3
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (22), (28), (61), (64), (72), (82), (84),
% 170.47/26.21 | | | | | | | | | | | | | | | | | | (86), (112), (186), (234) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | | | | | | sub-proof #512.
% 170.47/26.21 | | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | (235) all_58_14 = e1 & op(e0, e1) = e1
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | ALPHA: (235) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | | (236) op(e0, e1) = e1
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | REF_CLOSE: (61), (72), (77), (236) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | | | | sub-proof #967.
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | (237) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.21 | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | ALPHA: (237) implies:
% 170.47/26.21 | | | | | | | | | | | (238) all_58_15 = e1
% 170.47/26.21 | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | BETA: splitting (79) gives:
% 170.47/26.21 | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | (239) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 170.47/26.21 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 170.47/26.21 | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | BETA: splitting (239) gives:
% 170.47/26.21 | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | (240) all_58_9 = e3 & op(e3, e0) = e3
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | ALPHA: (240) implies:
% 170.47/26.21 | | | | | | | | | | | | | (241) all_58_9 = e3
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | BETA: splitting (30) gives:
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | (242) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 170.47/26.21 | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | (243) all_58_0 = e3 & op(e3, e3) = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | (244) all_58_0 = e3
% 170.47/26.21 | | | | | | | | | | | | | | | (245) op(e3, e3) = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | (246) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2
% 170.47/26.21 | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | (247) all_58_0 = e2 & op(e3, e3) = e2
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (70), (87), (245) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | | | | | sub-proof #838.
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | (248) all_58_1 = e2 & op(e3, e2) = e2
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | | | (249) op(e3, e2) = e2
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (61), (73), (74), (249) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | | | | | sub-proof #993.
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | (250) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2
% 170.47/26.21 | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | (251) all_58_4 = e2 & op(e3, e1) = e2
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | | | (252) all_58_4 = e2
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (22), (28), (58), (64), (72), (112), (241),
% 170.47/26.21 | | | | | | | | | | | | | | | | | (244), (252) are inconsistent by sub-proof #509.
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | (253) all_58_9 = e2 & op(e3, e0) = e2
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | | | (254) all_58_9 = e2
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | COMBINE_EQS: (241), (254) imply:
% 170.47/26.21 | | | | | | | | | | | | | | | | | (255) e3 = e2
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (22), (44), (61), (71), (82), (87), (95),
% 170.47/26.21 | | | | | | | | | | | | | | | | | (99), (255) are inconsistent by sub-proof #508.
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | (256) all_58_2 = e3 & op(e2, e3) = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | (257) all_58_2 = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | REF_CLOSE: (22), (95), (257) are inconsistent by sub-proof
% 170.47/26.21 | | | | | | | | | | | | | | | #938.
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | (258) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 170.47/26.21 | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | (259) all_58_6 = e3 & op(e1, e3) = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | (260) all_58_6 = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | (261) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1
% 170.47/26.21 | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | BETA: splitting (261) gives:
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | (262) all_58_4 = e1 & op(e3, e1) = e1
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | ALPHA: (262) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | | | (263) all_58_4 = e1
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (12), (17), (21), (22), (28), (29),
% 170.47/26.21 | | | | | | | | | | | | | | | | | (37), (40), (44), (56), (61), (64), (65), (67),
% 170.47/26.21 | | | | | | | | | | | | | | | | | (71), (78), (82), (84), (87), (95), (99), (112),
% 170.47/26.21 | | | | | | | | | | | | | | | | | (241), (260), (263) are inconsistent by sub-proof
% 170.47/26.21 | | | | | | | | | | | | | | | | | #516.
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | (264) all_58_5 = e1 & op(e2, e1) = e1
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | | | (265) op(e2, e1) = e1
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (61), (92), (265) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | | | | | sub-proof #686.
% 170.47/26.21 | | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | (266) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 =
% 170.47/26.21 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (22), (28), (38), (56), (58), (61), (64),
% 170.47/26.21 | | | | | | | | | | | | | | | | (70), (72), (77), (99), (112), (241), (266) are
% 170.47/26.21 | | | | | | | | | | | | | | | | inconsistent by sub-proof #563.
% 170.47/26.21 | | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | (267) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | ALPHA: (267) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | (268) all_58_12 = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | REF_CLOSE: (7), (28), (64), (65), (84), (112), (238), (268)
% 170.47/26.21 | | | | | | | | | | | | | | | are inconsistent by sub-proof #544.
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | (269) all_58_10 = e3 & op(e2, e0) = e3
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | ALPHA: (269) implies:
% 170.47/26.21 | | | | | | | | | | | | | (270) op(e2, e0) = e3
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | REF_CLOSE: (61), (82), (87), (270) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | sub-proof #682.
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | (271) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 170.47/26.21 | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 170.47/26.21 | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | BETA: splitting (271) gives:
% 170.47/26.21 | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | (272) all_58_11 = e3 & op(e1, e0) = e3
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | ALPHA: (272) implies:
% 170.47/26.21 | | | | | | | | | | | | | (273) all_58_11 = e3
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | BETA: splitting (29) gives:
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | (274) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 170.47/26.21 | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | (275) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | (276) all_58_12 = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | REF_CLOSE: (7), (28), (64), (65), (84), (112), (238), (276)
% 170.47/26.21 | | | | | | | | | | | | | | | are inconsistent by sub-proof #544.
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | (277) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | REF_CLOSE: (40), (61), (78), (277) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | | | sub-proof #962.
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | (278) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 170.47/26.21 | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | BETA: splitting (278) gives:
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | (279) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (22), (44), (61), (71), (82), (87),
% 170.47/26.21 | | | | | | | | | | | | | | | (95), (99), (279) are inconsistent by sub-proof
% 170.47/26.21 | | | | | | | | | | | | | | | #519.
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | (280) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | ALPHA: (280) implies:
% 170.47/26.21 | | | | | | | | | | | | | | | (281) all_58_15 = e3
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | | REF_CLOSE: (4), (22), (28), (61), (64), (72), (82), (84),
% 170.47/26.21 | | | | | | | | | | | | | | | (86), (112), (273), (281) are inconsistent by
% 170.47/26.21 | | | | | | | | | | | | | | | sub-proof #512.
% 170.47/26.21 | | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | (282) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | ALPHA: (282) implies:
% 170.47/26.21 | | | | | | | | | | | | | (283) all_58_15 = e3
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | | REF_CLOSE: (22), (238), (283) are inconsistent by sub-proof
% 170.47/26.21 | | | | | | | | | | | | | #556.
% 170.47/26.21 | | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | | (284) all_54_10 = e0
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | | REF_CLOSE: (19), (118), (284) are inconsistent by sub-proof
% 170.47/26.21 | | | | | | | | | #979.
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | End of split
% 170.47/26.21 | | | | | | | |
% 170.47/26.21 | | | | | | | End of split
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | End of split
% 170.47/26.21 | | | | | |
% 170.47/26.21 | | | | | Case 2:
% 170.47/26.21 | | | | | |
% 170.47/26.21 | | | | | | (285) all_46_2 = e0
% 170.47/26.21 | | | | | |
% 170.47/26.21 | | | | | | COMBINE_EQS: (75), (285) imply:
% 170.47/26.21 | | | | | | (286) all_6_2 = e0
% 170.47/26.21 | | | | | |
% 170.47/26.21 | | | | | | COMBINE_EQS: (23), (286) imply:
% 170.47/26.21 | | | | | | (287) all_56_14 = e0
% 170.47/26.21 | | | | | |
% 170.47/26.21 | | | | | | REDUCE: (43), (286) imply:
% 170.47/26.21 | | | | | | (288) ~ (all_52_2 = e0)
% 170.47/26.21 | | | | | |
% 170.47/26.21 | | | | | | REDUCE: (114), (286) imply:
% 170.47/26.21 | | | | | | (289) ~ (e2 = e0)
% 170.47/26.21 | | | | | |
% 170.47/26.21 | | | | | | BETA: splitting (34) gives:
% 170.47/26.21 | | | | | |
% 170.47/26.21 | | | | | | Case 1:
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | | (290) all_54_8 = e3
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | | COMBINE_EQS: (13), (290) imply:
% 170.47/26.21 | | | | | | | (291) all_52_2 = e3
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | | SIMP: (291) implies:
% 170.47/26.21 | | | | | | | (292) all_52_2 = e3
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | | REDUCE: (85), (292) imply:
% 170.47/26.21 | | | | | | | (293) ~ (all_52_3 = e3)
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | | SIMP: (293) implies:
% 170.47/26.21 | | | | | | | (294) ~ (all_52_3 = e3)
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | | BETA: splitting (52) gives:
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | |
% 170.47/26.21 | | | | | | | | (295) all_56_10 = e3
% 170.47/26.21 | | | | | | | |
% 170.47/26.21 | | | | | | | | COMBINE_EQS: (9), (295) imply:
% 170.47/26.21 | | | | | | | | (296) e3 = e2
% 170.47/26.21 | | | | | | | |
% 170.47/26.21 | | | | | | | | REF_CLOSE: (17), (22), (44), (61), (71), (82), (87), (95), (99),
% 170.47/26.21 | | | | | | | | (296) are inconsistent by sub-proof #508.
% 170.47/26.21 | | | | | | | |
% 170.47/26.21 | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | |
% 170.47/26.21 | | | | | | | | (297) all_56_12 = e2 | all_56_14 = e1 | all_56_15 = e0
% 170.47/26.21 | | | | | | | |
% 170.47/26.21 | | | | | | | | BETA: splitting (297) gives:
% 170.47/26.21 | | | | | | | |
% 170.47/26.21 | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | | (298) all_56_12 = e2
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | | COMBINE_EQS: (25), (298) imply:
% 170.47/26.21 | | | | | | | | | (299) e2 = e0
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | | SIMP: (299) implies:
% 170.47/26.21 | | | | | | | | | (300) e2 = e0
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | | REDUCE: (64), (300) imply:
% 170.47/26.21 | | | | | | | | | (301) $false
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | | CLOSE: (301) is inconsistent.
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | | (302) all_56_14 = e1 | all_56_15 = e0
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | | BETA: splitting (302) gives:
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | | Case 1:
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | (303) all_56_14 = e1
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | COMBINE_EQS: (287), (303) imply:
% 170.47/26.21 | | | | | | | | | | (304) e1 = e0
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | SIMP: (304) implies:
% 170.47/26.21 | | | | | | | | | | (305) e1 = e0
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | REDUCE: (28), (305) imply:
% 170.47/26.21 | | | | | | | | | | (306) $false
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | CLOSE: (306) is inconsistent.
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | Case 2:
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | (307) all_56_15 = e0
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | COMBINE_EQS: (47), (307) imply:
% 170.47/26.21 | | | | | | | | | | (308) all_4_2 = e0
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | REDUCE: (33), (308) imply:
% 170.47/26.21 | | | | | | | | | | (309) ~ (all_52_3 = e0)
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | | REF_CLOSE: (14), (53), (108), (109), (294), (309) are
% 170.47/26.21 | | | | | | | | | | inconsistent by sub-proof #674.
% 170.47/26.21 | | | | | | | | | |
% 170.47/26.21 | | | | | | | | | End of split
% 170.47/26.21 | | | | | | | | |
% 170.47/26.21 | | | | | | | | End of split
% 170.47/26.21 | | | | | | | |
% 170.47/26.21 | | | | | | | End of split
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | Case 2:
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | | (310) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | | REF_CLOSE: (13), (27), (31), (61), (98), (106), (288), (310) are
% 170.47/26.21 | | | | | | | inconsistent by sub-proof #687.
% 170.47/26.21 | | | | | | |
% 170.47/26.21 | | | | | | End of split
% 170.47/26.21 | | | | | |
% 170.47/26.21 | | | | | End of split
% 170.47/26.21 | | | | |
% 170.47/26.21 | | | | Case 2:
% 170.47/26.21 | | | | |
% 170.47/26.21 | | | | | (311) all_58_3 = e1 & op(e2, e2) = e1
% 170.47/26.21 | | | | |
% 170.47/26.21 | | | | | REF_CLOSE: (1), (11), (28), (37), (48), (61), (64), (68), (82), (86),
% 170.47/26.21 | | | | | (311) are inconsistent by sub-proof #507.
% 170.47/26.21 | | | | |
% 170.47/26.21 | | | | End of split
% 170.47/26.21 | | | |
% 170.47/26.21 | | | Case 2:
% 170.47/26.21 | | | |
% 170.47/26.21 | | | | (312) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2,
% 170.47/26.21 | | | | e0) = e1)
% 170.47/26.21 | | | |
% 170.47/26.21 | | | | REF_CLOSE: (22), (61), (72), (82), (92), (312) are inconsistent by
% 170.47/26.21 | | | | sub-proof #506.
% 170.47/26.21 | | | |
% 170.47/26.21 | | | End of split
% 170.47/26.21 | | |
% 170.47/26.21 | | End of split
% 170.47/26.21 | |
% 170.47/26.21 | Case 2:
% 170.47/26.21 | |
% 170.47/26.21 | | (313) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 170.47/26.21 | | e3)
% 170.47/26.21 | |
% 170.47/26.21 | | BETA: splitting (313) gives:
% 170.47/26.21 | |
% 170.47/26.21 | | Case 1:
% 170.47/26.21 | | |
% 170.47/26.21 | | | (314) all_58_8 = e3 & op(e1, e1) = e3
% 170.47/26.21 | | |
% 170.47/26.21 | | | REF_CLOSE: (18), (46), (61), (314) are inconsistent by sub-proof #961.
% 170.47/26.21 | | |
% 170.47/26.21 | | Case 2:
% 170.47/26.21 | | |
% 170.47/26.21 | | | (315) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.21 | | |
% 170.47/26.21 | | | REF_CLOSE: (7), (87), (315) are inconsistent by sub-proof #809.
% 170.47/26.21 | | |
% 170.47/26.21 | | End of split
% 170.47/26.21 | |
% 170.47/26.21 | End of split
% 170.47/26.21 |
% 170.47/26.21 End of proof
% 170.47/26.21
% 170.47/26.21 Sub-proof #506 shows that the following formulas are inconsistent:
% 170.47/26.21 ----------------------------------------------------------------
% 170.47/26.21 (1) ~ (e3 = e1)
% 170.47/26.21 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.21 (3) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.21 (4) op(e2, e1) = e3
% 170.47/26.21 (5) ~ (e2 = e1)
% 170.47/26.21 (6) op(e2, e0) = e2
% 170.47/26.21
% 170.47/26.21 Begin of proof
% 170.47/26.21 |
% 170.47/26.21 | BETA: splitting (3) gives:
% 170.47/26.21 |
% 170.47/26.21 | Case 1:
% 170.47/26.21 | |
% 170.47/26.21 | | (7) all_58_5 = e1 & op(e2, e1) = e1
% 170.47/26.21 | |
% 170.47/26.21 | | ALPHA: (7) implies:
% 170.47/26.21 | | (8) op(e2, e1) = e1
% 170.47/26.21 | |
% 170.47/26.21 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #686.
% 170.47/26.21 | |
% 170.47/26.21 | Case 2:
% 170.47/26.21 | |
% 170.47/26.21 | | (9) all_58_10 = e1 & op(e2, e0) = e1
% 170.47/26.21 | |
% 170.47/26.21 | | ALPHA: (9) implies:
% 170.47/26.21 | | (10) op(e2, e0) = e1
% 170.47/26.21 | |
% 170.47/26.21 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #526.
% 170.47/26.21 | |
% 170.47/26.21 | End of split
% 170.47/26.21 |
% 170.47/26.21 End of proof
% 170.47/26.21
% 170.47/26.21 Sub-proof #507 shows that the following formulas are inconsistent:
% 170.47/26.21 ----------------------------------------------------------------
% 170.47/26.21 (1) op(e2, e1) = all_52_9
% 170.47/26.21 (2) ~ (all_52_1 = e0)
% 170.47/26.21 (3) ~ (e1 = e0)
% 170.47/26.21 (4) op(e2, e3) = all_52_1
% 170.47/26.21 (5) all_58_3 = e1 & op(e2, e2) = e1
% 170.47/26.21 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.21 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.21 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.21 (8) ~ (e2 = e0)
% 170.47/26.21 (9) ~ (all_52_9 = e0)
% 170.47/26.21 (10) op(e2, e0) = e2
% 170.47/26.21 (11) op(e2, e0) = all_52_13
% 170.47/26.21
% 170.47/26.21 Begin of proof
% 170.47/26.21 |
% 170.47/26.21 | ALPHA: (5) implies:
% 170.47/26.21 | (12) all_58_3 = e1
% 170.47/26.21 |
% 170.47/26.21 | BETA: splitting (6) gives:
% 170.47/26.21 |
% 170.47/26.21 | Case 1:
% 170.47/26.21 | |
% 170.47/26.22 | | (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 170.47/26.22 | | e0)
% 170.47/26.22 | |
% 170.47/26.22 | | BETA: splitting (13) gives:
% 170.47/26.22 | |
% 170.47/26.22 | | Case 1:
% 170.47/26.22 | | |
% 170.47/26.22 | | | (14) all_58_2 = e0 & op(e2, e3) = e0
% 170.47/26.22 | | |
% 170.47/26.22 | | | REF_CLOSE: (2), (4), (7), (14) are inconsistent by sub-proof #693.
% 170.47/26.22 | | |
% 170.47/26.22 | | Case 2:
% 170.47/26.22 | | |
% 170.47/26.22 | | | (15) all_58_3 = e0 & op(e2, e2) = e0
% 170.47/26.22 | | |
% 170.47/26.22 | | | ALPHA: (15) implies:
% 170.47/26.22 | | | (16) all_58_3 = e0
% 170.47/26.22 | | |
% 170.47/26.22 | | | REF_CLOSE: (3), (12), (16) are inconsistent by sub-proof #523.
% 170.47/26.22 | | |
% 170.47/26.22 | | End of split
% 170.47/26.22 | |
% 170.47/26.22 | Case 2:
% 170.47/26.22 | |
% 170.47/26.22 | | (17) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.22 | | e0)
% 170.47/26.22 | |
% 170.47/26.22 | | REF_CLOSE: (1), (7), (8), (9), (10), (11), (17) are inconsistent by
% 170.47/26.22 | | sub-proof #669.
% 170.47/26.22 | |
% 170.47/26.22 | End of split
% 170.47/26.22 |
% 170.47/26.22 End of proof
% 170.47/26.22
% 170.47/26.22 Sub-proof #508 shows that the following formulas are inconsistent:
% 170.47/26.22 ----------------------------------------------------------------
% 170.47/26.22 (1) ~ (all_8_2 = e3)
% 170.47/26.22 (2) ~ (e3 = e1)
% 170.47/26.22 (3) e3 = e2
% 170.47/26.22 (4) all_58_5 = e3
% 170.47/26.22 (5) op(e2, e2) = all_8_2
% 170.47/26.22 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.22 (7) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.22 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.22 (8) all_58_2 = e1
% 170.47/26.22 (9) op(e2, e0) = e2
% 170.47/26.22 (10) ~ (e3 = e2)
% 170.47/26.22
% 170.47/26.22 Begin of proof
% 170.47/26.22 |
% 170.47/26.22 | SIMP: (3) implies:
% 170.47/26.22 | (11) e3 = e2
% 170.47/26.22 |
% 170.47/26.22 | COMBINE_EQS: (4), (11) imply:
% 170.47/26.22 | (12) all_58_5 = e2
% 170.47/26.22 |
% 170.47/26.22 | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (12) are inconsistent by
% 170.47/26.22 | sub-proof #524.
% 170.47/26.22 |
% 170.47/26.22 End of proof
% 170.47/26.22
% 170.47/26.22 Sub-proof #509 shows that the following formulas are inconsistent:
% 170.47/26.22 ----------------------------------------------------------------
% 170.47/26.22 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.22 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.22 (2) ~ (e3 = e1)
% 170.47/26.22 (3) ~ (e1 = e0)
% 170.47/26.22 (4) ~ (e3 = e0)
% 170.47/26.22 (5) all_58_0 = e3
% 170.47/26.22 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.22 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.22 (7) ~ (e2 = e0)
% 170.47/26.22 (8) all_58_9 = e3
% 170.47/26.22 (9) ~ (e2 = e1)
% 170.47/26.22 (10) all_58_4 = e2
% 170.47/26.22
% 170.47/26.22 Begin of proof
% 170.47/26.22 |
% 170.47/26.22 | BETA: splitting (6) gives:
% 170.47/26.22 |
% 170.47/26.22 | Case 1:
% 170.47/26.22 | |
% 170.47/26.22 | | (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 170.47/26.22 | | e1)
% 170.47/26.22 | |
% 170.47/26.22 | | BETA: splitting (11) gives:
% 170.47/26.22 | |
% 170.47/26.22 | | Case 1:
% 170.47/26.22 | | |
% 170.47/26.22 | | | (12) all_58_0 = e1 & op(e3, e3) = e1
% 170.47/26.22 | | |
% 170.47/26.22 | | | REF_CLOSE: (2), (5), (12) are inconsistent by sub-proof #950.
% 170.47/26.22 | | |
% 170.47/26.22 | | Case 2:
% 170.47/26.22 | | |
% 170.47/26.22 | | | (13) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.22 | | |
% 170.47/26.22 | | | ALPHA: (13) implies:
% 170.47/26.22 | | | (14) all_58_1 = e1
% 170.47/26.22 | | |
% 170.47/26.22 | | | BETA: splitting (1) gives:
% 170.47/26.22 | | |
% 170.47/26.22 | | | Case 1:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | (15) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 170.47/26.22 | | | | = e0)
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | BETA: splitting (15) gives:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | Case 1:
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | (16) all_58_0 = e0 & op(e3, e3) = e0
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | REF_CLOSE: (4), (5), (16) are inconsistent by sub-proof #898.
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | Case 2:
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | (17) all_58_1 = e0 & op(e3, e2) = e0
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | REF_CLOSE: (3), (14), (17) are inconsistent by sub-proof #948.
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | End of split
% 170.47/26.22 | | | |
% 170.47/26.22 | | | Case 2:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | (18) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 170.47/26.22 | | | | = e0)
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | REF_CLOSE: (4), (7), (8), (10), (18) are inconsistent by sub-proof #511.
% 170.47/26.22 | | | |
% 170.47/26.22 | | | End of split
% 170.47/26.22 | | |
% 170.47/26.22 | | End of split
% 170.47/26.22 | |
% 170.47/26.22 | Case 2:
% 170.47/26.22 | |
% 170.47/26.22 | | (19) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 170.47/26.22 | | e1)
% 170.47/26.22 | |
% 170.47/26.22 | | BETA: splitting (19) gives:
% 170.47/26.22 | |
% 170.47/26.22 | | Case 1:
% 170.47/26.22 | | |
% 170.47/26.22 | | | (20) all_58_4 = e1 & op(e3, e1) = e1
% 170.47/26.22 | | |
% 170.47/26.22 | | | REF_CLOSE: (9), (10), (20) are inconsistent by sub-proof #510.
% 170.47/26.22 | | |
% 170.47/26.22 | | Case 2:
% 170.47/26.22 | | |
% 170.47/26.22 | | | (21) all_58_9 = e1 & op(e3, e0) = e1
% 170.47/26.22 | | |
% 170.47/26.22 | | | REF_CLOSE: (2), (8), (21) are inconsistent by sub-proof #836.
% 170.47/26.22 | | |
% 170.47/26.22 | | End of split
% 170.47/26.22 | |
% 170.47/26.22 | End of split
% 170.47/26.22 |
% 170.47/26.22 End of proof
% 170.47/26.22
% 170.47/26.22 Sub-proof #510 shows that the following formulas are inconsistent:
% 170.47/26.22 ----------------------------------------------------------------
% 170.47/26.22 (1) all_58_4 = e1 & op(e3, e1) = e1
% 170.47/26.22 (2) all_58_4 = e2
% 170.47/26.22 (3) ~ (e2 = e1)
% 170.47/26.22
% 170.47/26.22 Begin of proof
% 170.47/26.22 |
% 170.47/26.22 | ALPHA: (1) implies:
% 170.47/26.22 | (4) all_58_4 = e1
% 170.47/26.22 |
% 170.47/26.22 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.22 | (5) e2 = e1
% 170.47/26.22 |
% 170.47/26.22 | SIMP: (5) implies:
% 170.47/26.22 | (6) e2 = e1
% 170.47/26.22 |
% 170.47/26.22 | REDUCE: (3), (6) imply:
% 170.47/26.22 | (7) $false
% 170.47/26.22 |
% 170.47/26.22 | CLOSE: (7) is inconsistent.
% 170.47/26.22 |
% 170.47/26.22 End of proof
% 170.47/26.22
% 170.47/26.22 Sub-proof #511 shows that the following formulas are inconsistent:
% 170.47/26.22 ----------------------------------------------------------------
% 170.47/26.22 (1) ~ (e3 = e0)
% 170.47/26.22 (2) ~ (e2 = e0)
% 170.47/26.22 (3) all_58_9 = e3
% 170.47/26.22 (4) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.22 (5) all_58_4 = e2
% 170.47/26.22
% 170.47/26.22 Begin of proof
% 170.47/26.22 |
% 170.47/26.22 | BETA: splitting (4) gives:
% 170.47/26.22 |
% 170.47/26.22 | Case 1:
% 170.47/26.22 | |
% 170.47/26.22 | | (6) all_58_4 = e0 & op(e3, e1) = e0
% 170.47/26.22 | |
% 170.47/26.22 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #902.
% 170.47/26.22 | |
% 170.47/26.22 | Case 2:
% 170.47/26.22 | |
% 170.47/26.22 | | (7) all_58_9 = e0 & op(e3, e0) = e0
% 170.47/26.22 | |
% 170.47/26.22 | | ALPHA: (7) implies:
% 170.47/26.22 | | (8) all_58_9 = e0
% 170.47/26.22 | |
% 170.47/26.22 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #835.
% 170.47/26.22 | |
% 170.47/26.22 | End of split
% 170.47/26.22 |
% 170.47/26.22 End of proof
% 170.47/26.22
% 170.47/26.22 Sub-proof #512 shows that the following formulas are inconsistent:
% 170.47/26.22 ----------------------------------------------------------------
% 170.47/26.22 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.47/26.22 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.22 (2) ~ (e3 = e1)
% 170.47/26.22 (3) ~ (e1 = e0)
% 170.47/26.22 (4) ~ (e3 = e0)
% 170.47/26.22 (5) all_58_11 = e3
% 170.47/26.22 (6) all_58_15 = e3
% 170.47/26.22 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.22 (8) ~ (e2 = e0)
% 170.47/26.22 (9) ~ (e2 = e1)
% 170.47/26.22 (10) op(e2, e0) = e2
% 170.47/26.22 (11) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.22 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.22 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.22 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.22 (12) op(e2, e0) = all_52_13
% 170.47/26.22
% 170.47/26.22 Begin of proof
% 170.47/26.22 |
% 170.47/26.22 | BETA: splitting (11) gives:
% 170.47/26.22 |
% 170.47/26.22 | Case 1:
% 170.47/26.22 | |
% 170.47/26.22 | | (13) all_58_15 = e0 & op(e0, e0) = e0
% 170.47/26.22 | |
% 170.47/26.22 | | REF_CLOSE: (4), (6), (13) are inconsistent by sub-proof #887.
% 170.47/26.22 | |
% 170.47/26.22 | Case 2:
% 170.47/26.22 | |
% 170.47/26.22 | | (14) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.22 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 170.47/26.22 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 170.47/26.22 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.47/26.22 | |
% 170.47/26.22 | | ALPHA: (14) implies:
% 170.47/26.22 | | (15) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.22 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.47/26.22 | |
% 170.47/26.22 | | BETA: splitting (1) gives:
% 170.47/26.22 | |
% 170.47/26.22 | | Case 1:
% 170.47/26.22 | | |
% 170.47/26.22 | | | (16) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 170.47/26.22 | | | e1)
% 170.47/26.22 | | |
% 170.47/26.22 | | | BETA: splitting (16) gives:
% 170.47/26.22 | | |
% 170.47/26.22 | | | Case 1:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | (17) all_58_9 = e1 & op(e3, e0) = e1
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | ALPHA: (17) implies:
% 170.47/26.22 | | | | (18) all_58_9 = e1
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | BETA: splitting (15) gives:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | Case 1:
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | (19) all_58_9 = e0 & op(e3, e0) = e0
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | REF_CLOSE: (3), (18), (19) are inconsistent by sub-proof #880.
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | Case 2:
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | (20) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 170.47/26.22 | | | | | e0) = e0)
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | BETA: splitting (20) gives:
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | Case 1:
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | (21) all_58_10 = e0 & op(e2, e0) = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | ALPHA: (21) implies:
% 170.47/26.22 | | | | | | (22) op(e2, e0) = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | REF_CLOSE: (7), (8), (10), (12), (22) are inconsistent by sub-proof
% 170.47/26.22 | | | | | | #684.
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | Case 2:
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | (23) all_58_11 = e0 & op(e1, e0) = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | REF_CLOSE: (4), (5), (23) are inconsistent by sub-proof #724.
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | End of split
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | End of split
% 170.47/26.22 | | | |
% 170.47/26.22 | | | Case 2:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | (24) all_58_10 = e1 & op(e2, e0) = e1
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | ALPHA: (24) implies:
% 170.47/26.22 | | | | (25) op(e2, e0) = e1
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | REF_CLOSE: (7), (9), (10), (25) are inconsistent by sub-proof #526.
% 170.47/26.22 | | | |
% 170.47/26.22 | | | End of split
% 170.47/26.22 | | |
% 170.47/26.22 | | Case 2:
% 170.47/26.22 | | |
% 170.47/26.22 | | | (26) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0)
% 170.47/26.22 | | | = e1)
% 170.47/26.22 | | |
% 170.47/26.22 | | | BETA: splitting (26) gives:
% 170.47/26.22 | | |
% 170.47/26.22 | | | Case 1:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | (27) all_58_11 = e1 & op(e1, e0) = e1
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | REF_CLOSE: (2), (5), (27) are inconsistent by sub-proof #721.
% 170.47/26.22 | | | |
% 170.47/26.22 | | | Case 2:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | (28) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | REF_CLOSE: (2), (6), (28) are inconsistent by sub-proof #831.
% 170.47/26.22 | | | |
% 170.47/26.22 | | | End of split
% 170.47/26.22 | | |
% 170.47/26.22 | | End of split
% 170.47/26.22 | |
% 170.47/26.22 | End of split
% 170.47/26.22 |
% 170.47/26.22 End of proof
% 170.47/26.22
% 170.47/26.22 Sub-proof #513 shows that the following formulas are inconsistent:
% 170.47/26.22 ----------------------------------------------------------------
% 170.47/26.22 (1) all_58_11 = e0 & op(e1, e0) = e0
% 170.47/26.22 (2) all_58_11 = e1
% 170.47/26.22 (3) ~ (e1 = e0)
% 170.47/26.22
% 170.47/26.22 Begin of proof
% 170.47/26.22 |
% 170.47/26.22 | ALPHA: (1) implies:
% 170.47/26.22 | (4) all_58_11 = e0
% 170.47/26.22 |
% 170.47/26.22 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.22 | (5) e1 = e0
% 170.47/26.22 |
% 170.47/26.22 | REDUCE: (3), (5) imply:
% 170.47/26.22 | (6) $false
% 170.47/26.22 |
% 170.47/26.22 | CLOSE: (6) is inconsistent.
% 170.47/26.22 |
% 170.47/26.22 End of proof
% 170.47/26.22
% 170.47/26.22 Sub-proof #514 shows that the following formulas are inconsistent:
% 170.47/26.22 ----------------------------------------------------------------
% 170.47/26.22 (1) ~ (all_4_2 = e2)
% 170.47/26.22 (2) all_58_11 = e1
% 170.47/26.22 (3) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.22 (4) op(e0, e0) = all_4_2
% 170.47/26.22 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.22 (6) ~ (e2 = e1)
% 170.47/26.22
% 170.47/26.22 Begin of proof
% 170.47/26.22 |
% 170.47/26.22 | BETA: splitting (3) gives:
% 170.47/26.22 |
% 170.47/26.22 | Case 1:
% 170.47/26.22 | |
% 170.47/26.22 | | (7) all_58_11 = e2 & op(e1, e0) = e2
% 170.47/26.22 | |
% 170.47/26.22 | | ALPHA: (7) implies:
% 170.47/26.22 | | (8) all_58_11 = e2
% 170.47/26.22 | |
% 170.47/26.22 | | REF_CLOSE: (2), (6), (8) are inconsistent by sub-proof #832.
% 170.47/26.22 | |
% 170.47/26.22 | Case 2:
% 170.47/26.22 | |
% 170.47/26.22 | | (9) all_58_15 = e2 & op(e0, e0) = e2
% 170.47/26.22 | |
% 170.47/26.22 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #854.
% 170.47/26.22 | |
% 170.47/26.22 | End of split
% 170.47/26.22 |
% 170.47/26.22 End of proof
% 170.47/26.22
% 170.47/26.22 Sub-proof #515 shows that the following formulas are inconsistent:
% 170.47/26.22 ----------------------------------------------------------------
% 170.47/26.22 (1) all_58_9 = e2 & op(e3, e0) = e2
% 170.47/26.22 (2) all_58_9 = e0
% 170.47/26.22 (3) ~ (e2 = e0)
% 170.47/26.22
% 170.47/26.22 Begin of proof
% 170.47/26.22 |
% 170.47/26.22 | ALPHA: (1) implies:
% 170.47/26.22 | (4) all_58_9 = e2
% 170.47/26.22 |
% 170.47/26.22 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.22 | (5) e2 = e0
% 170.47/26.22 |
% 170.47/26.22 | REDUCE: (3), (5) imply:
% 170.47/26.22 | (6) $false
% 170.47/26.22 |
% 170.47/26.22 | CLOSE: (6) is inconsistent.
% 170.47/26.22 |
% 170.47/26.22 End of proof
% 170.47/26.22
% 170.47/26.22 Sub-proof #516 shows that the following formulas are inconsistent:
% 170.47/26.22 ----------------------------------------------------------------
% 170.47/26.22 (1) all_58_14 = e2
% 170.47/26.22 (2) ~ (all_52_1 = e0)
% 170.47/26.22 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.47/26.22 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.47/26.22 (4) ~ (all_8_2 = e3)
% 170.47/26.22 (5) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.22 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.22 (6) ~ (e3 = e1)
% 170.47/26.22 (7) all_58_6 = e3
% 170.47/26.22 (8) ~ (e1 = e0)
% 170.47/26.22 (9) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 170.47/26.22 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.47/26.22 (10) op(e2, e3) = all_52_1
% 170.47/26.22 (11) all_58_5 = e3
% 170.47/26.22 (12) ~ (all_52_7 = e3)
% 170.47/26.22 (13) op(e2, e2) = all_8_2
% 170.47/26.22 (14) ~ (e3 = e0)
% 170.47/26.22 (15) all_58_4 = e1
% 170.47/26.22 (16) all_58_1 = e3
% 170.47/26.22 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.22 (18) ~ (e2 = e0)
% 170.47/26.22 (19) all_58_13 = e1
% 170.47/26.22 (20) all_58_0 = e2
% 170.47/26.22 (21) all_58_9 = e3
% 170.47/26.22 (22) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.22 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.22 (23) all_58_2 = e1
% 170.47/26.22 (24) op(e0, e2) = all_52_7
% 170.47/26.22 (25) op(e2, e0) = e2
% 170.47/26.22 (26) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.22 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.22 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.22 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.22 (27) ~ (e3 = e2)
% 170.47/26.22
% 170.47/26.22 Begin of proof
% 170.47/26.22 |
% 170.47/26.22 | BETA: splitting (26) gives:
% 170.47/26.22 |
% 170.47/26.22 | Case 1:
% 170.47/26.22 | |
% 170.47/26.22 | | (28) all_58_15 = e0 & op(e0, e0) = e0
% 170.47/26.22 | |
% 170.47/26.22 | | ALPHA: (28) implies:
% 170.47/26.22 | | (29) all_58_15 = e0
% 170.47/26.22 | |
% 170.47/26.22 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (13), (14),
% 170.47/26.22 | | (17), (18), (20), (22), (23), (24), (25), (27), (29) are
% 170.47/26.22 | | inconsistent by sub-proof #518.
% 170.47/26.22 | |
% 170.47/26.22 | Case 2:
% 170.47/26.22 | |
% 170.47/26.22 | | (30) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.22 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 170.47/26.22 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 170.47/26.22 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.47/26.22 | |
% 170.47/26.22 | | ALPHA: (30) implies:
% 170.47/26.22 | | (31) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 170.47/26.22 | | e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.22 | |
% 170.47/26.22 | | BETA: splitting (9) gives:
% 170.47/26.22 | |
% 170.47/26.22 | | Case 1:
% 170.47/26.22 | | |
% 170.47/26.22 | | | (32) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2)
% 170.47/26.22 | | | = e3)
% 170.47/26.22 | | |
% 170.47/26.22 | | | REF_CLOSE: (1), (8), (12), (14), (17), (18), (19), (24), (31), (32) are
% 170.47/26.22 | | | inconsistent by sub-proof #517.
% 170.47/26.22 | | |
% 170.47/26.22 | | Case 2:
% 170.47/26.22 | | |
% 170.47/26.22 | | | (33) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0)
% 170.47/26.22 | | | = e3)
% 170.47/26.22 | | |
% 170.47/26.22 | | | BETA: splitting (33) gives:
% 170.47/26.22 | | |
% 170.47/26.22 | | | Case 1:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | (34) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | REF_CLOSE: (1), (4), (6), (11), (13), (17), (22), (23), (25), (27), (34)
% 170.47/26.22 | | | | are inconsistent by sub-proof #519.
% 170.47/26.22 | | | |
% 170.47/26.22 | | | Case 2:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | (35) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | ALPHA: (35) implies:
% 170.47/26.22 | | | | (36) all_58_15 = e3
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | BETA: splitting (5) gives:
% 170.47/26.22 | | | |
% 170.47/26.22 | | | | Case 1:
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | (37) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 170.47/26.22 | | | | | e2) = e0)
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | BETA: splitting (37) gives:
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | Case 1:
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | (38) all_58_0 = e0 & op(e3, e3) = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | REF_CLOSE: (18), (20), (38) are inconsistent by sub-proof #705.
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | Case 2:
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | (39) all_58_1 = e0 & op(e3, e2) = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | ALPHA: (39) implies:
% 170.47/26.22 | | | | | | (40) all_58_1 = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | COMBINE_EQS: (16), (40) imply:
% 170.47/26.22 | | | | | | (41) e3 = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | COMBINE_EQS: (36), (41) imply:
% 170.47/26.22 | | | | | | (42) all_58_15 = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12),
% 170.47/26.22 | | | | | | (13), (14), (17), (18), (20), (22), (23), (24), (25),
% 170.47/26.22 | | | | | | (27), (42) are inconsistent by sub-proof #518.
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | End of split
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | Case 2:
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | (43) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 170.47/26.22 | | | | | e0) = e0)
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | BETA: splitting (43) gives:
% 170.47/26.22 | | | | |
% 170.47/26.22 | | | | | Case 1:
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | (44) all_58_4 = e0 & op(e3, e1) = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | REF_CLOSE: (8), (15), (44) are inconsistent by sub-proof #793.
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | Case 2:
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | (45) all_58_9 = e0 & op(e3, e0) = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | ALPHA: (45) implies:
% 170.47/26.22 | | | | | | (46) all_58_9 = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | COMBINE_EQS: (21), (46) imply:
% 170.47/26.22 | | | | | | (47) e3 = e0
% 170.47/26.22 | | | | | |
% 170.47/26.22 | | | | | | COMBINE_EQS: (36), (47) imply:
% 170.47/26.22 | | | | | | (48) all_58_15 = e0
% 170.47/26.22 | | | | | |
% 170.47/26.23 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12),
% 170.47/26.23 | | | | | | (13), (14), (17), (18), (20), (22), (23), (24), (25),
% 170.47/26.23 | | | | | | (27), (48) are inconsistent by sub-proof #518.
% 170.47/26.23 | | | | | |
% 170.47/26.23 | | | | | End of split
% 170.47/26.23 | | | | |
% 170.47/26.23 | | | | End of split
% 170.47/26.23 | | | |
% 170.47/26.23 | | | End of split
% 170.47/26.23 | | |
% 170.47/26.23 | | End of split
% 170.47/26.23 | |
% 170.47/26.23 | End of split
% 170.47/26.23 |
% 170.47/26.23 End of proof
% 170.47/26.23
% 170.47/26.23 Sub-proof #517 shows that the following formulas are inconsistent:
% 170.47/26.23 ----------------------------------------------------------------
% 170.47/26.23 (1) all_58_14 = e2
% 170.47/26.23 (2) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.23 (3) ~ (e1 = e0)
% 170.47/26.23 (4) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 170.47/26.23 (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.23 (5) ~ (all_52_7 = e3)
% 170.47/26.23 (6) ~ (e3 = e0)
% 170.47/26.23 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.23 (8) ~ (e2 = e0)
% 170.47/26.23 (9) all_58_13 = e1
% 170.47/26.23 (10) op(e0, e2) = all_52_7
% 170.47/26.23
% 170.47/26.23 Begin of proof
% 170.47/26.23 |
% 170.47/26.23 | BETA: splitting (2) gives:
% 170.47/26.23 |
% 170.47/26.23 | Case 1:
% 170.47/26.23 | |
% 170.47/26.23 | | (11) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.23 | |
% 170.47/26.23 | | ALPHA: (11) implies:
% 170.47/26.23 | | (12) all_58_12 = e3
% 170.47/26.23 | |
% 170.47/26.23 | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (12) are inconsistent by sub-proof
% 170.47/26.23 | | #545.
% 170.47/26.23 | |
% 170.47/26.23 | Case 2:
% 170.47/26.23 | |
% 170.47/26.23 | | (13) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.23 | |
% 170.47/26.23 | | REF_CLOSE: (5), (7), (10), (13) are inconsistent by sub-proof #962.
% 170.47/26.23 | |
% 170.47/26.23 | End of split
% 170.47/26.23 |
% 170.47/26.23 End of proof
% 170.47/26.23
% 170.47/26.23 Sub-proof #518 shows that the following formulas are inconsistent:
% 170.47/26.23 ----------------------------------------------------------------
% 170.47/26.23 (1) all_58_14 = e2
% 170.47/26.23 (2) ~ (all_52_1 = e0)
% 170.47/26.23 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.47/26.23 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.47/26.23 (4) ~ (all_8_2 = e3)
% 170.47/26.23 (5) ~ (e3 = e1)
% 170.47/26.23 (6) all_58_6 = e3
% 170.47/26.23 (7) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 170.47/26.23 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.47/26.23 (8) op(e2, e3) = all_52_1
% 170.47/26.23 (9) all_58_5 = e3
% 170.47/26.23 (10) ~ (all_52_7 = e3)
% 170.47/26.23 (11) op(e2, e2) = all_8_2
% 170.47/26.23 (12) ~ (e3 = e0)
% 170.47/26.23 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.23 (14) ~ (e2 = e0)
% 170.47/26.23 (15) all_58_0 = e2
% 170.47/26.23 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.23 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.23 (17) all_58_15 = e0
% 170.47/26.23 (18) all_58_2 = e1
% 170.47/26.23 (19) op(e0, e2) = all_52_7
% 170.47/26.23 (20) op(e2, e0) = e2
% 170.47/26.23 (21) ~ (e3 = e2)
% 170.47/26.23
% 170.47/26.23 Begin of proof
% 170.47/26.23 |
% 170.47/26.23 | BETA: splitting (7) gives:
% 170.47/26.23 |
% 170.47/26.23 | Case 1:
% 170.47/26.23 | |
% 170.47/26.23 | | (22) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 170.47/26.23 | | e3)
% 170.47/26.23 | |
% 170.47/26.23 | | BETA: splitting (22) gives:
% 170.47/26.23 | |
% 170.47/26.23 | | Case 1:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (23) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.23 | | |
% 170.47/26.23 | | | ALPHA: (23) implies:
% 170.47/26.23 | | | (24) all_58_12 = e3
% 170.47/26.23 | | |
% 170.47/26.23 | | | BETA: splitting (3) gives:
% 170.47/26.23 | | |
% 170.47/26.23 | | | Case 1:
% 170.47/26.23 | | | |
% 170.47/26.23 | | | | (25) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3)
% 170.47/26.23 | | | | = e0)
% 170.47/26.23 | | | |
% 170.47/26.23 | | | | BETA: splitting (25) gives:
% 170.47/26.23 | | | |
% 170.47/26.23 | | | | Case 1:
% 170.47/26.23 | | | | |
% 170.47/26.23 | | | | | (26) all_58_0 = e0 & op(e3, e3) = e0
% 170.47/26.23 | | | | |
% 170.47/26.23 | | | | | REF_CLOSE: (14), (15), (26) are inconsistent by sub-proof #705.
% 170.47/26.23 | | | | |
% 170.47/26.23 | | | | Case 2:
% 170.47/26.23 | | | | |
% 170.47/26.23 | | | | | (27) all_58_2 = e0 & op(e2, e3) = e0
% 170.47/26.23 | | | | |
% 170.47/26.23 | | | | | REF_CLOSE: (2), (8), (13), (27) are inconsistent by sub-proof #693.
% 170.47/26.23 | | | | |
% 170.47/26.23 | | | | End of split
% 170.47/26.23 | | | |
% 170.47/26.23 | | | Case 2:
% 170.47/26.23 | | | |
% 170.47/26.23 | | | | (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3)
% 170.47/26.23 | | | | = e0)
% 170.47/26.23 | | | |
% 170.47/26.23 | | | | REF_CLOSE: (6), (12), (24), (28) are inconsistent by sub-proof #536.
% 170.47/26.23 | | | |
% 170.47/26.23 | | | End of split
% 170.47/26.23 | | |
% 170.47/26.23 | | Case 2:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (29) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (10), (13), (19), (29) are inconsistent by sub-proof #962.
% 170.47/26.23 | | |
% 170.47/26.23 | | End of split
% 170.47/26.23 | |
% 170.47/26.23 | Case 2:
% 170.47/26.23 | |
% 170.47/26.23 | | (30) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.47/26.23 | | e3)
% 170.47/26.23 | |
% 170.47/26.23 | | BETA: splitting (30) gives:
% 170.47/26.23 | |
% 170.47/26.23 | | Case 1:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (31) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (1), (4), (5), (9), (11), (13), (16), (18), (20), (21), (31)
% 170.47/26.23 | | | are inconsistent by sub-proof #519.
% 170.47/26.23 | | |
% 170.47/26.23 | | Case 2:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (32) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (12), (17), (32) are inconsistent by sub-proof #812.
% 170.47/26.23 | | |
% 170.47/26.23 | | End of split
% 170.47/26.23 | |
% 170.47/26.23 | End of split
% 170.47/26.23 |
% 170.47/26.23 End of proof
% 170.47/26.23
% 170.47/26.23 Sub-proof #519 shows that the following formulas are inconsistent:
% 170.47/26.23 ----------------------------------------------------------------
% 170.47/26.23 (1) all_58_14 = e2
% 170.47/26.23 (2) ~ (all_8_2 = e3)
% 170.47/26.23 (3) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.23 (4) ~ (e3 = e1)
% 170.47/26.23 (5) all_58_5 = e3
% 170.47/26.23 (6) op(e2, e2) = all_8_2
% 170.47/26.23 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.23 (8) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.23 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.23 (9) all_58_2 = e1
% 170.47/26.23 (10) op(e2, e0) = e2
% 170.47/26.23 (11) ~ (e3 = e2)
% 170.47/26.23
% 170.47/26.23 Begin of proof
% 170.47/26.23 |
% 170.47/26.23 | ALPHA: (3) implies:
% 170.47/26.23 | (12) all_58_14 = e3
% 170.47/26.23 |
% 170.47/26.23 | COMBINE_EQS: (1), (12) imply:
% 170.47/26.23 | (13) e3 = e2
% 170.47/26.23 |
% 170.47/26.23 | COMBINE_EQS: (5), (13) imply:
% 170.47/26.23 | (14) all_58_5 = e2
% 170.47/26.23 |
% 170.47/26.23 | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (11), (14) are inconsistent by
% 170.47/26.23 | sub-proof #524.
% 170.47/26.23 |
% 170.47/26.23 End of proof
% 170.47/26.23
% 170.47/26.23 Sub-proof #520 shows that the following formulas are inconsistent:
% 170.47/26.23 ----------------------------------------------------------------
% 170.47/26.23 (1) all_56_1 = e3
% 170.47/26.23 (2) all_56_10 = e2
% 170.47/26.23 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.23 (4) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 170.47/26.23 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 170.47/26.23 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.23 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.23 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.47/26.23 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.23 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.23 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.23 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.23 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.47/26.23 (5) ~ (all_52_4 = e2)
% 170.47/26.23 (6) op(e3, e2) = all_52_4
% 170.47/26.23
% 170.47/26.23 Begin of proof
% 170.47/26.23 |
% 170.47/26.23 | BETA: splitting (4) gives:
% 170.47/26.23 |
% 170.47/26.23 | Case 1:
% 170.47/26.23 | |
% 170.47/26.23 | | (7) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 170.47/26.23 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 170.47/26.23 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 170.47/26.23 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 170.47/26.23 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 170.47/26.23 | |
% 170.47/26.23 | | ALPHA: (7) implies:
% 170.47/26.23 | | (8) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 170.47/26.23 | | $i(all_56_1))
% 170.47/26.23 | |
% 170.47/26.23 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #554.
% 170.47/26.23 | |
% 170.47/26.23 | Case 2:
% 170.47/26.23 | |
% 170.47/26.23 | | (9) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 170.47/26.23 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 170.47/26.23 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.23 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 170.47/26.23 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 170.47/26.23 | |
% 170.47/26.23 | | ALPHA: (9) implies:
% 170.47/26.23 | | (10) op(e3, e2) = e2
% 170.47/26.23 | |
% 170.47/26.23 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #993.
% 170.47/26.23 | |
% 170.47/26.23 | End of split
% 170.47/26.23 |
% 170.47/26.23 End of proof
% 170.47/26.23
% 170.47/26.23 Sub-proof #521 shows that the following formulas are inconsistent:
% 170.47/26.23 ----------------------------------------------------------------
% 170.47/26.23 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.23 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.23 (2) ~ (all_8_2 = e3)
% 170.47/26.23 (3) ~ (e3 = e1)
% 170.47/26.23 (4) ~ (e1 = e0)
% 170.47/26.23 (5) op(e2, e2) = all_8_2
% 170.47/26.23 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.23 (7) all_58_3 = e0
% 170.47/26.23 (8) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.23 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.23 (9) ~ (e2 = e1)
% 170.47/26.23 (10) op(e2, e0) = e2
% 170.47/26.23 (11) all_58_5 = e2 & op(e2, e1) = e2
% 170.47/26.23 (12) ~ (e3 = e2)
% 170.47/26.23
% 170.47/26.23 Begin of proof
% 170.47/26.23 |
% 170.47/26.23 | ALPHA: (11) implies:
% 170.47/26.23 | (13) all_58_5 = e2
% 170.47/26.23 |
% 170.47/26.23 | BETA: splitting (1) gives:
% 170.47/26.23 |
% 170.47/26.23 | Case 1:
% 170.47/26.23 | |
% 170.47/26.23 | | (14) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 170.47/26.23 | | e1)
% 170.47/26.23 | |
% 170.47/26.23 | | BETA: splitting (14) gives:
% 170.47/26.23 | |
% 170.47/26.23 | | Case 1:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (15) all_58_2 = e1 & op(e2, e3) = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | ALPHA: (15) implies:
% 170.47/26.23 | | | (16) all_58_2 = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (2), (3), (5), (6), (8), (10), (12), (13), (16) are
% 170.47/26.23 | | | inconsistent by sub-proof #524.
% 170.47/26.23 | | |
% 170.47/26.23 | | Case 2:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (17) all_58_3 = e1 & op(e2, e2) = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | ALPHA: (17) implies:
% 170.47/26.23 | | | (18) all_58_3 = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (4), (7), (18) are inconsistent by sub-proof #523.
% 170.47/26.23 | | |
% 170.47/26.23 | | End of split
% 170.47/26.23 | |
% 170.47/26.23 | Case 2:
% 170.47/26.23 | |
% 170.47/26.23 | | (19) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 170.47/26.23 | | e1)
% 170.47/26.23 | |
% 170.47/26.23 | | BETA: splitting (19) gives:
% 170.47/26.23 | |
% 170.47/26.23 | | Case 1:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (20) all_58_5 = e1 & op(e2, e1) = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | ALPHA: (20) implies:
% 170.47/26.23 | | | (21) all_58_5 = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (9), (13), (21) are inconsistent by sub-proof #522.
% 170.47/26.23 | | |
% 170.47/26.23 | | Case 2:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (22) all_58_10 = e1 & op(e2, e0) = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | ALPHA: (22) implies:
% 170.47/26.23 | | | (23) op(e2, e0) = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (6), (9), (10), (23) are inconsistent by sub-proof #526.
% 170.47/26.23 | | |
% 170.47/26.23 | | End of split
% 170.47/26.23 | |
% 170.47/26.23 | End of split
% 170.47/26.23 |
% 170.47/26.23 End of proof
% 170.47/26.23
% 170.47/26.23 Sub-proof #522 shows that the following formulas are inconsistent:
% 170.47/26.23 ----------------------------------------------------------------
% 170.47/26.23 (1) all_58_5 = e2
% 170.47/26.23 (2) all_58_5 = e1
% 170.47/26.23 (3) ~ (e2 = e1)
% 170.47/26.23
% 170.47/26.23 Begin of proof
% 170.47/26.23 |
% 170.47/26.23 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.23 | (4) e2 = e1
% 170.47/26.23 |
% 170.47/26.23 | SIMP: (4) implies:
% 170.47/26.23 | (5) e2 = e1
% 170.47/26.23 |
% 170.47/26.23 | REDUCE: (3), (5) imply:
% 170.47/26.23 | (6) $false
% 170.47/26.23 |
% 170.47/26.23 | CLOSE: (6) is inconsistent.
% 170.47/26.23 |
% 170.47/26.23 End of proof
% 170.47/26.23
% 170.47/26.23 Sub-proof #523 shows that the following formulas are inconsistent:
% 170.47/26.23 ----------------------------------------------------------------
% 170.47/26.23 (1) all_58_3 = e1
% 170.47/26.23 (2) all_58_3 = e0
% 170.47/26.23 (3) ~ (e1 = e0)
% 170.47/26.23
% 170.47/26.23 Begin of proof
% 170.47/26.23 |
% 170.47/26.23 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.23 | (4) e1 = e0
% 170.47/26.23 |
% 170.47/26.23 | SIMP: (4) implies:
% 170.47/26.23 | (5) e1 = e0
% 170.47/26.23 |
% 170.47/26.23 | REDUCE: (3), (5) imply:
% 170.47/26.23 | (6) $false
% 170.47/26.23 |
% 170.47/26.23 | CLOSE: (6) is inconsistent.
% 170.47/26.23 |
% 170.47/26.23 End of proof
% 170.47/26.23
% 170.47/26.23 Sub-proof #524 shows that the following formulas are inconsistent:
% 170.47/26.23 ----------------------------------------------------------------
% 170.47/26.23 (1) ~ (all_8_2 = e3)
% 170.47/26.23 (2) ~ (e3 = e1)
% 170.47/26.23 (3) op(e2, e2) = all_8_2
% 170.47/26.23 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.23 (5) all_58_5 = e2
% 170.47/26.23 (6) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.23 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.23 (7) all_58_2 = e1
% 170.47/26.23 (8) op(e2, e0) = e2
% 170.47/26.23 (9) ~ (e3 = e2)
% 170.47/26.23
% 170.47/26.23 Begin of proof
% 170.47/26.23 |
% 170.47/26.23 | BETA: splitting (6) gives:
% 170.47/26.23 |
% 170.47/26.23 | Case 1:
% 170.47/26.23 | |
% 170.47/26.23 | | (10) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.47/26.23 | | e3)
% 170.47/26.23 | |
% 170.47/26.23 | | REF_CLOSE: (1), (2), (3), (4), (7), (10) are inconsistent by sub-proof #937.
% 170.47/26.23 | |
% 170.47/26.23 | Case 2:
% 170.47/26.23 | |
% 170.47/26.23 | | (11) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 170.47/26.23 | | e3)
% 170.47/26.23 | |
% 170.47/26.23 | | BETA: splitting (11) gives:
% 170.47/26.23 | |
% 170.47/26.23 | | Case 1:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (12) all_58_5 = e3 & op(e2, e1) = e3
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (5), (9), (12) are inconsistent by sub-proof #561.
% 170.47/26.23 | | |
% 170.47/26.23 | | Case 2:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (13) all_58_10 = e3 & op(e2, e0) = e3
% 170.47/26.23 | | |
% 170.47/26.23 | | | ALPHA: (13) implies:
% 170.47/26.23 | | | (14) op(e2, e0) = e3
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (4), (8), (9), (14) are inconsistent by sub-proof #682.
% 170.47/26.23 | | |
% 170.47/26.23 | | End of split
% 170.47/26.23 | |
% 170.47/26.23 | End of split
% 170.47/26.23 |
% 170.47/26.23 End of proof
% 170.47/26.23
% 170.47/26.23 Sub-proof #525 shows that the following formulas are inconsistent:
% 170.47/26.23 ----------------------------------------------------------------
% 170.47/26.23 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.47/26.23 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.23 (2) ~ (e3 = e1)
% 170.47/26.23 (3) ~ (e1 = e0)
% 170.47/26.23 (4) all_58_11 = e2
% 170.47/26.23 (5) ~ (e3 = e0)
% 170.47/26.23 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.23 (7) ~ (e2 = e0)
% 170.47/26.23 (8) ~ (e2 = e1)
% 170.47/26.23 (9) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.47/26.23 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.47/26.23 (10) op(e2, e0) = e2
% 170.47/26.23 (11) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.23 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.23 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.23 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.23 (12) op(e2, e0) = all_52_13
% 170.47/26.23 (13) ~ (e3 = e2)
% 170.47/26.23
% 170.47/26.23 Begin of proof
% 170.47/26.23 |
% 170.47/26.23 | BETA: splitting (1) gives:
% 170.47/26.23 |
% 170.47/26.23 | Case 1:
% 170.47/26.23 | |
% 170.47/26.23 | | (14) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 170.47/26.23 | | e1)
% 170.47/26.23 | |
% 170.47/26.23 | | BETA: splitting (14) gives:
% 170.47/26.23 | |
% 170.47/26.23 | | Case 1:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (15) all_58_9 = e1 & op(e3, e0) = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | ALPHA: (15) implies:
% 170.47/26.23 | | | (16) all_58_9 = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (16)
% 170.47/26.23 | | | are inconsistent by sub-proof #527.
% 170.47/26.23 | | |
% 170.47/26.23 | | Case 2:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (17) all_58_10 = e1 & op(e2, e0) = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | ALPHA: (17) implies:
% 170.47/26.23 | | | (18) op(e2, e0) = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (6), (8), (10), (18) are inconsistent by sub-proof #526.
% 170.47/26.23 | | |
% 170.47/26.23 | | End of split
% 170.47/26.23 | |
% 170.47/26.23 | Case 2:
% 170.47/26.23 | |
% 170.47/26.23 | | (19) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.23 | | e1)
% 170.47/26.23 | |
% 170.47/26.23 | | BETA: splitting (19) gives:
% 170.47/26.23 | |
% 170.47/26.23 | | Case 1:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (20) all_58_11 = e1 & op(e1, e0) = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (4), (8), (20) are inconsistent by sub-proof #547.
% 170.47/26.23 | | |
% 170.47/26.23 | | Case 2:
% 170.47/26.23 | | |
% 170.47/26.23 | | | (21) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | ALPHA: (21) implies:
% 170.47/26.23 | | | (22) all_58_15 = e1
% 170.47/26.23 | | |
% 170.47/26.23 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (22)
% 170.47/26.23 | | | are inconsistent by sub-proof #539.
% 170.47/26.23 | | |
% 170.47/26.23 | | End of split
% 170.47/26.23 | |
% 170.47/26.23 | End of split
% 170.47/26.23 |
% 170.47/26.23 End of proof
% 170.47/26.23
% 170.47/26.23 Sub-proof #526 shows that the following formulas are inconsistent:
% 170.47/26.23 ----------------------------------------------------------------
% 170.47/26.23 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.23 (2) op(e2, e0) = e2
% 170.47/26.23 (3) op(e2, e0) = e1
% 170.47/26.23 (4) ~ (e2 = e1)
% 170.47/26.23
% 170.47/26.23 Begin of proof
% 170.47/26.23 |
% 170.47/26.24 | GROUND_INST: instantiating (1) with e2, e1, e0, e2, simplifying with (2), (3)
% 170.47/26.24 | gives:
% 170.47/26.24 | (5) e2 = e1
% 170.47/26.24 |
% 170.47/26.24 | REDUCE: (4), (5) imply:
% 170.47/26.24 | (6) $false
% 170.47/26.24 |
% 170.47/26.24 | CLOSE: (6) is inconsistent.
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #527 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) ~ (e3 = e1)
% 170.47/26.24 (2) ~ (e1 = e0)
% 170.47/26.24 (3) all_58_11 = e2
% 170.47/26.24 (4) ~ (e3 = e0)
% 170.47/26.24 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.24 (6) ~ (e2 = e0)
% 170.47/26.24 (7) all_58_9 = e1
% 170.47/26.24 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.47/26.24 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.47/26.24 (9) op(e2, e0) = e2
% 170.47/26.24 (10) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.24 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.24 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.24 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.24 (11) op(e2, e0) = all_52_13
% 170.47/26.24 (12) ~ (e3 = e2)
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | BETA: splitting (10) gives:
% 170.47/26.24 |
% 170.47/26.24 | Case 1:
% 170.47/26.24 | |
% 170.47/26.24 | | (13) all_58_15 = e0 & op(e0, e0) = e0
% 170.47/26.24 | |
% 170.47/26.24 | | ALPHA: (13) implies:
% 170.47/26.24 | | (14) all_58_15 = e0
% 170.47/26.24 | |
% 170.47/26.24 | | BETA: splitting (8) gives:
% 170.47/26.24 | |
% 170.47/26.24 | | Case 1:
% 170.47/26.24 | | |
% 170.47/26.24 | | | (15) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 170.47/26.24 | | | e3)
% 170.47/26.24 | | |
% 170.47/26.24 | | | REF_CLOSE: (1), (5), (7), (9), (12), (15) are inconsistent by sub-proof
% 170.47/26.24 | | | #528.
% 170.47/26.24 | | |
% 170.47/26.24 | | Case 2:
% 170.47/26.24 | | |
% 170.47/26.24 | | | (16) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0)
% 170.47/26.24 | | | = e3)
% 170.47/26.24 | | |
% 170.47/26.24 | | | BETA: splitting (16) gives:
% 170.47/26.24 | | |
% 170.47/26.24 | | | Case 1:
% 170.47/26.24 | | | |
% 170.47/26.24 | | | | (17) all_58_11 = e3 & op(e1, e0) = e3
% 170.47/26.24 | | | |
% 170.47/26.24 | | | | REF_CLOSE: (3), (12), (17) are inconsistent by sub-proof #730.
% 170.47/26.24 | | | |
% 170.47/26.24 | | | Case 2:
% 170.47/26.24 | | | |
% 170.47/26.24 | | | | (18) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.24 | | | |
% 170.47/26.24 | | | | REF_CLOSE: (4), (14), (18) are inconsistent by sub-proof #812.
% 170.47/26.24 | | | |
% 170.47/26.24 | | | End of split
% 170.47/26.24 | | |
% 170.47/26.24 | | End of split
% 170.47/26.24 | |
% 170.47/26.24 | Case 2:
% 170.47/26.24 | |
% 170.47/26.24 | | (19) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.24 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 170.47/26.24 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 170.47/26.24 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.47/26.24 | |
% 170.47/26.24 | | ALPHA: (19) implies:
% 170.47/26.24 | | (20) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.24 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.47/26.24 | |
% 170.47/26.24 | | BETA: splitting (20) gives:
% 170.47/26.24 | |
% 170.47/26.24 | | Case 1:
% 170.47/26.24 | | |
% 170.47/26.24 | | | (21) all_58_9 = e0 & op(e3, e0) = e0
% 170.47/26.24 | | |
% 170.47/26.24 | | | REF_CLOSE: (2), (7), (21) are inconsistent by sub-proof #897.
% 170.47/26.24 | | |
% 170.47/26.24 | | Case 2:
% 170.47/26.24 | | |
% 170.47/26.24 | | | (22) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.24 | | | = e0)
% 170.47/26.24 | | |
% 170.47/26.24 | | | REF_CLOSE: (3), (5), (6), (9), (11), (22) are inconsistent by sub-proof
% 170.47/26.24 | | | #540.
% 170.47/26.24 | | |
% 170.47/26.24 | | End of split
% 170.47/26.24 | |
% 170.47/26.24 | End of split
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #528 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) ~ (e3 = e1)
% 170.47/26.24 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.24 (3) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.24 (4) all_58_9 = e1
% 170.47/26.24 (5) op(e2, e0) = e2
% 170.47/26.24 (6) ~ (e3 = e2)
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | BETA: splitting (3) gives:
% 170.47/26.24 |
% 170.47/26.24 | Case 1:
% 170.47/26.24 | |
% 170.47/26.24 | | (7) all_58_9 = e3 & op(e3, e0) = e3
% 170.47/26.24 | |
% 170.47/26.24 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #893.
% 170.47/26.24 | |
% 170.47/26.24 | Case 2:
% 170.47/26.24 | |
% 170.47/26.24 | | (8) all_58_10 = e3 & op(e2, e0) = e3
% 170.47/26.24 | |
% 170.47/26.24 | | ALPHA: (8) implies:
% 170.47/26.24 | | (9) op(e2, e0) = e3
% 170.47/26.24 | |
% 170.47/26.24 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #682.
% 170.47/26.24 | |
% 170.47/26.24 | End of split
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #529 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) all_54_7 = all_52_13
% 170.47/26.24 (2) all_54_7 = e0
% 170.47/26.24 (3) ~ (all_52_13 = e0)
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.24 | (4) all_52_13 = e0
% 170.47/26.24 |
% 170.47/26.24 | SIMP: (4) implies:
% 170.47/26.24 | (5) all_52_13 = e0
% 170.47/26.24 |
% 170.47/26.24 | REDUCE: (3), (5) imply:
% 170.47/26.24 | (6) $false
% 170.47/26.24 |
% 170.47/26.24 | CLOSE: (6) is inconsistent.
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #530 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) all_58_12 = e1
% 170.47/26.24 (2) all_58_14 = e2
% 170.47/26.24 (3) ~ (e1 = e0)
% 170.47/26.24 (4) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 170.47/26.24 (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.24 (5) ~ (e2 = e0)
% 170.47/26.24 (6) all_58_13 = e1
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | BETA: splitting (4) gives:
% 170.47/26.24 |
% 170.47/26.24 | Case 1:
% 170.47/26.24 | |
% 170.47/26.24 | | (7) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.24 | |
% 170.47/26.24 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #859.
% 170.47/26.24 | |
% 170.47/26.24 | Case 2:
% 170.47/26.24 | |
% 170.47/26.24 | | (8) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 170.47/26.24 | | e0)
% 170.47/26.24 | |
% 170.47/26.24 | | BETA: splitting (8) gives:
% 170.47/26.24 | |
% 170.47/26.24 | | Case 1:
% 170.47/26.24 | | |
% 170.47/26.24 | | | (9) all_58_13 = e0 & op(e0, e2) = e0
% 170.47/26.24 | | |
% 170.47/26.24 | | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #582.
% 170.47/26.24 | | |
% 170.47/26.24 | | Case 2:
% 170.47/26.24 | | |
% 170.47/26.24 | | | (10) all_58_14 = e0 & op(e0, e1) = e0
% 170.47/26.24 | | |
% 170.47/26.24 | | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #858.
% 170.47/26.24 | | |
% 170.47/26.24 | | End of split
% 170.47/26.24 | |
% 170.47/26.24 | End of split
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #531 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.24 (2) op(e0, e3) = e1
% 170.47/26.24 (3) op(e0, e3) = e0
% 170.47/26.24 (4) ~ (e1 = e0)
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | GROUND_INST: instantiating (1) with e0, e1, e3, e0, simplifying with (2), (3)
% 170.47/26.24 | gives:
% 170.47/26.24 | (5) e1 = e0
% 170.47/26.24 |
% 170.47/26.24 | REDUCE: (4), (5) imply:
% 170.47/26.24 | (6) $false
% 170.47/26.24 |
% 170.47/26.24 | CLOSE: (6) is inconsistent.
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #532 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) all_54_7 = all_52_13
% 170.47/26.24 (2) all_54_7 = e2
% 170.47/26.24 (3) ~ (all_52_13 = e2)
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.24 | (4) all_52_13 = e2
% 170.47/26.24 |
% 170.47/26.24 | SIMP: (4) implies:
% 170.47/26.24 | (5) all_52_13 = e2
% 170.47/26.24 |
% 170.47/26.24 | REDUCE: (3), (5) imply:
% 170.47/26.24 | (6) $false
% 170.47/26.24 |
% 170.47/26.24 | CLOSE: (6) is inconsistent.
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #533 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) all_54_7 = all_52_13
% 170.47/26.24 (2) all_54_7 = e3
% 170.47/26.24 (3) ~ (all_52_13 = e3)
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.24 | (4) all_52_13 = e3
% 170.47/26.24 |
% 170.47/26.24 | SIMP: (4) implies:
% 170.47/26.24 | (5) all_52_13 = e3
% 170.47/26.24 |
% 170.47/26.24 | REDUCE: (3), (5) imply:
% 170.47/26.24 | (6) $false
% 170.47/26.24 |
% 170.47/26.24 | CLOSE: (6) is inconsistent.
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #534 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) ~ (e3 = e1)
% 170.47/26.24 (2) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.24 (3) all_58_15 = e3
% 170.47/26.24 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.24 (5) ~ (e2 = e1)
% 170.47/26.24 (6) op(e0, e1) = e2
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | BETA: splitting (2) gives:
% 170.47/26.24 |
% 170.47/26.24 | Case 1:
% 170.47/26.24 | |
% 170.47/26.24 | | (7) all_58_14 = e1 & op(e0, e1) = e1
% 170.47/26.24 | |
% 170.47/26.24 | | ALPHA: (7) implies:
% 170.47/26.24 | | (8) op(e0, e1) = e1
% 170.47/26.24 | |
% 170.47/26.24 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #967.
% 170.47/26.24 | |
% 170.47/26.24 | Case 2:
% 170.47/26.24 | |
% 170.47/26.24 | | (9) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.24 | |
% 170.47/26.24 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #831.
% 170.47/26.24 | |
% 170.47/26.24 | End of split
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #535 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) ~ (all_52_1 = e3)
% 170.47/26.24 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.24 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.24 (3) ~ (all_8_2 = e3)
% 170.47/26.24 (4) ~ (e3 = e1)
% 170.47/26.24 (5) ~ (e1 = e0)
% 170.47/26.24 (6) all_58_11 = e2
% 170.47/26.24 (7) op(e2, e3) = all_52_1
% 170.47/26.24 (8) all_58_5 = e3
% 170.47/26.24 (9) all_58_11 = e3 & op(e1, e0) = e3
% 170.47/26.24 (10) op(e2, e2) = all_8_2
% 170.47/26.24 (11) ~ (e3 = e0)
% 170.47/26.24 (12) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.24 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.24 (13) all_58_3 = e2
% 170.47/26.24 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.24 (15) ~ (e2 = e0)
% 170.47/26.24 (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.24 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.24 (17) ~ (e2 = e1)
% 170.47/26.24 (18) ~ (e3 = e2)
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | ALPHA: (9) implies:
% 170.47/26.24 | (19) all_58_11 = e3
% 170.47/26.24 |
% 170.47/26.24 | COMBINE_EQS: (6), (19) imply:
% 170.47/26.24 | (20) e3 = e2
% 170.47/26.24 |
% 170.47/26.24 | SIMP: (20) implies:
% 170.47/26.24 | (21) e3 = e2
% 170.47/26.24 |
% 170.47/26.24 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14),
% 170.47/26.24 | (15), (16), (17), (18), (21) are inconsistent by sub-proof #560.
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #536 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.47/26.24 (2) all_58_6 = e3
% 170.47/26.24 (3) ~ (e3 = e0)
% 170.47/26.24 (4) all_58_12 = e3
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | BETA: splitting (1) gives:
% 170.47/26.24 |
% 170.47/26.24 | Case 1:
% 170.47/26.24 | |
% 170.47/26.24 | | (5) all_58_6 = e0 & op(e1, e3) = e0
% 170.47/26.24 | |
% 170.47/26.24 | | ALPHA: (5) implies:
% 170.47/26.24 | | (6) all_58_6 = e0
% 170.47/26.24 | |
% 170.47/26.24 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #537.
% 170.47/26.24 | |
% 170.47/26.24 | Case 2:
% 170.47/26.24 | |
% 170.47/26.24 | | (7) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.24 | |
% 170.47/26.24 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #646.
% 170.47/26.24 | |
% 170.47/26.24 | End of split
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #537 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) all_58_6 = e3
% 170.47/26.24 (2) all_58_6 = e0
% 170.47/26.24 (3) ~ (e3 = e0)
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.24 | (4) e3 = e0
% 170.47/26.24 |
% 170.47/26.24 | SIMP: (4) implies:
% 170.47/26.24 | (5) e3 = e0
% 170.47/26.24 |
% 170.47/26.24 | REDUCE: (3), (5) imply:
% 170.47/26.24 | (6) $false
% 170.47/26.24 |
% 170.47/26.24 | CLOSE: (6) is inconsistent.
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #538 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) all_58_15 = e1
% 170.47/26.24 (2) ~ (e3 = e1)
% 170.47/26.24 (3) all_56_12 = e0
% 170.47/26.24 (4) ~ (e1 = e0)
% 170.47/26.24 (5) ~ (all_56_12 = e0) | (all_56_11 = e2 & op(e2, e0) = e2)
% 170.47/26.24 (6) all_58_11 = e2
% 170.47/26.24 (7) ~ (e3 = e0)
% 170.47/26.24 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.24 (9) ~ (e2 = e0)
% 170.47/26.24 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.47/26.24 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.47/26.24 (11) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.24 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.24 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.24 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.24 (12) op(e2, e0) = all_52_13
% 170.47/26.24 (13) ~ (e3 = e2)
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | BETA: splitting (5) gives:
% 170.47/26.24 |
% 170.47/26.24 | Case 1:
% 170.47/26.24 | |
% 170.47/26.24 | | (14) ~ (all_56_12 = e0)
% 170.47/26.24 | |
% 170.47/26.24 | | REDUCE: (3), (14) imply:
% 170.47/26.24 | | (15) $false
% 170.47/26.24 | |
% 170.47/26.24 | | CLOSE: (15) is inconsistent.
% 170.47/26.24 | |
% 170.47/26.24 | Case 2:
% 170.47/26.24 | |
% 170.47/26.24 | | (16) all_56_11 = e2 & op(e2, e0) = e2
% 170.47/26.24 | |
% 170.47/26.24 | | ALPHA: (16) implies:
% 170.47/26.24 | | (17) op(e2, e0) = e2
% 170.47/26.24 | |
% 170.47/26.24 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (17)
% 170.47/26.24 | | are inconsistent by sub-proof #539.
% 170.47/26.24 | |
% 170.47/26.24 | End of split
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #539 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) all_58_15 = e1
% 170.47/26.24 (2) ~ (e3 = e1)
% 170.47/26.24 (3) ~ (e1 = e0)
% 170.47/26.24 (4) all_58_11 = e2
% 170.47/26.24 (5) ~ (e3 = e0)
% 170.47/26.24 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.24 (7) ~ (e2 = e0)
% 170.47/26.24 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.47/26.24 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.47/26.24 (9) op(e2, e0) = e2
% 170.47/26.24 (10) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.24 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.24 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.24 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.24 (11) op(e2, e0) = all_52_13
% 170.47/26.24 (12) ~ (e3 = e2)
% 170.47/26.24
% 170.47/26.24 Begin of proof
% 170.47/26.24 |
% 170.47/26.24 | BETA: splitting (10) gives:
% 170.47/26.24 |
% 170.47/26.24 | Case 1:
% 170.47/26.24 | |
% 170.47/26.24 | | (13) all_58_15 = e0 & op(e0, e0) = e0
% 170.47/26.24 | |
% 170.47/26.24 | | REF_CLOSE: (1), (3), (13) are inconsistent by sub-proof #541.
% 170.47/26.24 | |
% 170.47/26.24 | Case 2:
% 170.47/26.24 | |
% 170.47/26.24 | | (14) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.24 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 170.47/26.24 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 170.47/26.24 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.47/26.24 | |
% 170.47/26.24 | | ALPHA: (14) implies:
% 170.47/26.24 | | (15) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.24 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.47/26.24 | |
% 170.47/26.24 | | BETA: splitting (15) gives:
% 170.47/26.24 | |
% 170.47/26.24 | | Case 1:
% 170.47/26.24 | | |
% 170.47/26.24 | | | (16) all_58_9 = e0 & op(e3, e0) = e0
% 170.47/26.24 | | |
% 170.47/26.24 | | | ALPHA: (16) implies:
% 170.47/26.24 | | | (17) all_58_9 = e0
% 170.47/26.24 | | |
% 170.47/26.24 | | | BETA: splitting (8) gives:
% 170.47/26.24 | | |
% 170.47/26.24 | | | Case 1:
% 170.47/26.24 | | | |
% 170.47/26.24 | | | | (18) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0)
% 170.47/26.24 | | | | = e3)
% 170.47/26.24 | | | |
% 170.47/26.24 | | | | BETA: splitting (18) gives:
% 170.47/26.24 | | | |
% 170.47/26.24 | | | | Case 1:
% 170.47/26.24 | | | | |
% 170.47/26.24 | | | | | (19) all_58_9 = e3 & op(e3, e0) = e3
% 170.47/26.24 | | | | |
% 170.47/26.24 | | | | | ALPHA: (19) implies:
% 170.47/26.24 | | | | | (20) all_58_9 = e3
% 170.47/26.24 | | | | |
% 170.47/26.24 | | | | | REF_CLOSE: (5), (17), (20) are inconsistent by sub-proof #835.
% 170.47/26.24 | | | | |
% 170.47/26.24 | | | | Case 2:
% 170.47/26.24 | | | | |
% 170.47/26.24 | | | | | (21) all_58_10 = e3 & op(e2, e0) = e3
% 170.47/26.24 | | | | |
% 170.47/26.24 | | | | | ALPHA: (21) implies:
% 170.47/26.24 | | | | | (22) op(e2, e0) = e3
% 170.47/26.24 | | | | |
% 170.47/26.24 | | | | | REF_CLOSE: (6), (9), (12), (22) are inconsistent by sub-proof #682.
% 170.47/26.24 | | | | |
% 170.47/26.24 | | | | End of split
% 170.47/26.24 | | | |
% 170.47/26.24 | | | Case 2:
% 170.47/26.24 | | | |
% 170.47/26.24 | | | | (23) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 170.47/26.24 | | | | e0) = e3)
% 170.47/26.24 | | | |
% 170.47/26.24 | | | | REF_CLOSE: (1), (2), (4), (12), (23) are inconsistent by sub-proof #877.
% 170.47/26.24 | | | |
% 170.47/26.24 | | | End of split
% 170.47/26.24 | | |
% 170.47/26.24 | | Case 2:
% 170.47/26.24 | | |
% 170.47/26.24 | | | (24) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.24 | | | = e0)
% 170.47/26.24 | | |
% 170.47/26.24 | | | REF_CLOSE: (4), (6), (7), (9), (11), (24) are inconsistent by sub-proof
% 170.47/26.24 | | | #540.
% 170.47/26.24 | | |
% 170.47/26.24 | | End of split
% 170.47/26.24 | |
% 170.47/26.24 | End of split
% 170.47/26.24 |
% 170.47/26.24 End of proof
% 170.47/26.24
% 170.47/26.24 Sub-proof #540 shows that the following formulas are inconsistent:
% 170.47/26.24 ----------------------------------------------------------------
% 170.47/26.24 (1) all_58_11 = e2
% 170.47/26.25 (2) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.47/26.25 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.25 (4) ~ (e2 = e0)
% 170.47/26.25 (5) op(e2, e0) = e2
% 170.47/26.25 (6) op(e2, e0) = all_52_13
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | BETA: splitting (2) gives:
% 170.47/26.25 |
% 170.47/26.25 | Case 1:
% 170.47/26.25 | |
% 170.47/26.25 | | (7) all_58_10 = e0 & op(e2, e0) = e0
% 170.47/26.25 | |
% 170.47/26.25 | | ALPHA: (7) implies:
% 170.47/26.25 | | (8) op(e2, e0) = e0
% 170.47/26.25 | |
% 170.47/26.25 | | REF_CLOSE: (3), (4), (5), (6), (8) are inconsistent by sub-proof #684.
% 170.47/26.25 | |
% 170.47/26.25 | Case 2:
% 170.47/26.25 | |
% 170.47/26.25 | | (9) all_58_11 = e0 & op(e1, e0) = e0
% 170.47/26.25 | |
% 170.47/26.25 | | ALPHA: (9) implies:
% 170.47/26.25 | | (10) all_58_11 = e0
% 170.47/26.25 | |
% 170.47/26.25 | | REF_CLOSE: (1), (4), (10) are inconsistent by sub-proof #879.
% 170.47/26.25 | |
% 170.47/26.25 | End of split
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #541 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) all_58_15 = e0 & op(e0, e0) = e0
% 170.47/26.25 (2) all_58_15 = e1
% 170.47/26.25 (3) ~ (e1 = e0)
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | ALPHA: (1) implies:
% 170.47/26.25 | (4) all_58_15 = e0
% 170.47/26.25 |
% 170.47/26.25 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.25 | (5) e1 = e0
% 170.47/26.25 |
% 170.47/26.25 | REDUCE: (3), (5) imply:
% 170.47/26.25 | (6) $false
% 170.47/26.25 |
% 170.47/26.25 | CLOSE: (6) is inconsistent.
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #542 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) all_58_10 = e3 & op(e2, e0) = e3
% 170.47/26.25 (2) all_58_10 = e0
% 170.47/26.25 (3) ~ (e3 = e0)
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | ALPHA: (1) implies:
% 170.47/26.25 | (4) all_58_10 = e3
% 170.47/26.25 |
% 170.47/26.25 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.25 | (5) e3 = e0
% 170.47/26.25 |
% 170.47/26.25 | REDUCE: (3), (5) imply:
% 170.47/26.25 | (6) $false
% 170.47/26.25 |
% 170.47/26.25 | CLOSE: (6) is inconsistent.
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #543 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) all_58_14 = e2
% 170.47/26.25 (2) ~ (e3 = e1)
% 170.47/26.25 (3) op(e1, e3) = all_52_2
% 170.47/26.25 (4) ~ (e1 = e0)
% 170.47/26.25 (5) all_58_11 = e2
% 170.47/26.25 (6) all_58_5 = e3
% 170.47/26.25 (7) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 170.47/26.25 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.25 (8) all_58_7 = e0
% 170.47/26.25 (9) ~ (e3 = e0)
% 170.47/26.25 (10) all_58_1 = e3
% 170.47/26.25 (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.25 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.25 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.25 (13) ~ (e2 = e0)
% 170.47/26.25 (14) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.47/26.25 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.47/26.25 (15) op(e1, e3) = e3
% 170.47/26.25 (16) all_58_9 = e3
% 170.47/26.25 (17) op(e3, e3) = e2
% 170.47/26.25 (18) ~ (e2 = e1)
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | BETA: splitting (14) gives:
% 170.47/26.25 |
% 170.47/26.25 | Case 1:
% 170.47/26.25 | |
% 170.47/26.25 | | (19) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 170.47/26.25 | | e1)
% 170.47/26.25 | |
% 170.47/26.25 | | REF_CLOSE: (2), (3), (4), (8), (12), (15), (19) are inconsistent by
% 170.47/26.25 | | sub-proof #558.
% 170.47/26.25 | |
% 170.47/26.25 | Case 2:
% 170.47/26.25 | |
% 170.47/26.25 | | (20) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 170.47/26.25 | | e1)
% 170.47/26.25 | |
% 170.47/26.25 | | BETA: splitting (20) gives:
% 170.47/26.25 | |
% 170.47/26.25 | | Case 1:
% 170.47/26.25 | | |
% 170.47/26.25 | | | (21) all_58_8 = e1 & op(e1, e1) = e1
% 170.47/26.25 | | |
% 170.47/26.25 | | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (10), (11), (12), (13), (16),
% 170.47/26.25 | | | (17), (18), (21) are inconsistent by sub-proof #564.
% 170.47/26.25 | | |
% 170.47/26.25 | | Case 2:
% 170.47/26.25 | | |
% 170.47/26.25 | | | (22) all_58_11 = e1 & op(e1, e0) = e1
% 170.47/26.25 | | |
% 170.47/26.25 | | | REF_CLOSE: (5), (18), (22) are inconsistent by sub-proof #547.
% 170.47/26.25 | | |
% 170.47/26.25 | | End of split
% 170.47/26.25 | |
% 170.47/26.25 | End of split
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #544 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) all_58_15 = e1
% 170.47/26.25 (2) all_58_14 = e2
% 170.47/26.25 (3) ~ (e1 = e0)
% 170.47/26.25 (4) ~ (e3 = e0)
% 170.47/26.25 (5) ~ (e2 = e0)
% 170.47/26.25 (6) all_58_13 = e1
% 170.47/26.25 (7) all_58_12 = e3
% 170.47/26.25 (8) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.25 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 170.47/26.25 e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.25 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | BETA: splitting (8) gives:
% 170.47/26.25 |
% 170.47/26.25 | Case 1:
% 170.47/26.25 | |
% 170.47/26.25 | | (9) all_58_15 = e0 & op(e0, e0) = e0
% 170.47/26.25 | |
% 170.47/26.25 | | ALPHA: (9) implies:
% 170.47/26.25 | | (10) all_58_15 = e0
% 170.47/26.25 | |
% 170.47/26.25 | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #881.
% 170.47/26.25 | |
% 170.47/26.25 | Case 2:
% 170.47/26.25 | |
% 170.47/26.25 | | (11) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.25 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 170.47/26.25 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 170.47/26.25 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.47/26.25 | |
% 170.47/26.25 | | ALPHA: (11) implies:
% 170.47/26.25 | | (12) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 170.47/26.25 | | e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.25 | |
% 170.47/26.25 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (12) are inconsistent by sub-proof
% 170.47/26.25 | | #545.
% 170.47/26.25 | |
% 170.47/26.25 | End of split
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #545 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) all_58_14 = e2
% 170.47/26.25 (2) ~ (e1 = e0)
% 170.47/26.25 (3) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 170.47/26.25 (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.25 (4) ~ (e3 = e0)
% 170.47/26.25 (5) ~ (e2 = e0)
% 170.47/26.25 (6) all_58_13 = e1
% 170.47/26.25 (7) all_58_12 = e3
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | BETA: splitting (3) gives:
% 170.47/26.25 |
% 170.47/26.25 | Case 1:
% 170.47/26.25 | |
% 170.47/26.25 | | (8) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.25 | |
% 170.47/26.25 | | ALPHA: (8) implies:
% 170.47/26.25 | | (9) all_58_12 = e0
% 170.47/26.25 | |
% 170.47/26.25 | | REF_CLOSE: (4), (7), (9) are inconsistent by sub-proof #608.
% 170.47/26.25 | |
% 170.47/26.25 | Case 2:
% 170.47/26.25 | |
% 170.47/26.25 | | (10) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 170.47/26.25 | | e0)
% 170.47/26.25 | |
% 170.47/26.25 | | BETA: splitting (10) gives:
% 170.47/26.25 | |
% 170.47/26.25 | | Case 1:
% 170.47/26.25 | | |
% 170.47/26.25 | | | (11) all_58_13 = e0 & op(e0, e2) = e0
% 170.47/26.25 | | |
% 170.47/26.25 | | | ALPHA: (11) implies:
% 170.47/26.25 | | | (12) all_58_13 = e0
% 170.47/26.25 | | |
% 170.47/26.25 | | | REF_CLOSE: (2), (6), (12) are inconsistent by sub-proof #546.
% 170.47/26.25 | | |
% 170.47/26.25 | | Case 2:
% 170.47/26.25 | | |
% 170.47/26.25 | | | (13) all_58_14 = e0 & op(e0, e1) = e0
% 170.47/26.25 | | |
% 170.47/26.25 | | | ALPHA: (13) implies:
% 170.47/26.25 | | | (14) all_58_14 = e0
% 170.47/26.25 | | |
% 170.47/26.25 | | | REF_CLOSE: (1), (5), (14) are inconsistent by sub-proof #806.
% 170.47/26.25 | | |
% 170.47/26.25 | | End of split
% 170.47/26.25 | |
% 170.47/26.25 | End of split
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #546 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) all_58_13 = e1
% 170.47/26.25 (2) all_58_13 = e0
% 170.47/26.25 (3) ~ (e1 = e0)
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.25 | (4) e1 = e0
% 170.47/26.25 |
% 170.47/26.25 | SIMP: (4) implies:
% 170.47/26.25 | (5) e1 = e0
% 170.47/26.25 |
% 170.47/26.25 | REDUCE: (3), (5) imply:
% 170.47/26.25 | (6) $false
% 170.47/26.25 |
% 170.47/26.25 | CLOSE: (6) is inconsistent.
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #547 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) all_58_11 = e1 & op(e1, e0) = e1
% 170.47/26.25 (2) all_58_11 = e2
% 170.47/26.25 (3) ~ (e2 = e1)
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | ALPHA: (1) implies:
% 170.47/26.25 | (4) all_58_11 = e1
% 170.47/26.25 |
% 170.47/26.25 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.25 | (5) e2 = e1
% 170.47/26.25 |
% 170.47/26.25 | REDUCE: (3), (5) imply:
% 170.47/26.25 | (6) $false
% 170.47/26.25 |
% 170.47/26.25 | CLOSE: (6) is inconsistent.
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #548 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) ~ (e1 = e0)
% 170.47/26.25 (2) all_58_5 = e3
% 170.47/26.25 (3) ~ (e3 = e0)
% 170.47/26.25 (4) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.25 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.25 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 170.47/26.25 (6) op(e2, e0) = e1
% 170.47/26.25 (7) all_58_3 = e2
% 170.47/26.25 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.25 (9) ~ (e2 = e0)
% 170.47/26.25 (10) op(e3, e3) = e2
% 170.47/26.25 (11) ~ (e2 = e1)
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | BETA: splitting (5) gives:
% 170.47/26.25 |
% 170.47/26.25 | Case 1:
% 170.47/26.25 | |
% 170.47/26.25 | | (12) all_58_0 = e1 & op(e3, e3) = e1
% 170.47/26.25 | |
% 170.47/26.25 | | ALPHA: (12) implies:
% 170.47/26.25 | | (13) op(e3, e3) = e1
% 170.47/26.25 | |
% 170.47/26.25 | | REF_CLOSE: (8), (10), (11), (13) are inconsistent by sub-proof #957.
% 170.47/26.25 | |
% 170.47/26.25 | Case 2:
% 170.47/26.25 | |
% 170.47/26.25 | | (14) all_58_2 = e1 & op(e2, e3) = e1
% 170.47/26.25 | |
% 170.47/26.25 | | ALPHA: (14) implies:
% 170.47/26.25 | | (15) all_58_2 = e1
% 170.47/26.25 | |
% 170.47/26.25 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (15) are inconsistent by
% 170.47/26.25 | | sub-proof #549.
% 170.47/26.25 | |
% 170.47/26.25 | End of split
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #549 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) ~ (e1 = e0)
% 170.47/26.25 (2) all_58_5 = e3
% 170.47/26.25 (3) ~ (e3 = e0)
% 170.47/26.25 (4) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.25 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.25 (5) op(e2, e0) = e1
% 170.47/26.25 (6) all_58_3 = e2
% 170.47/26.25 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.25 (8) ~ (e2 = e0)
% 170.47/26.25 (9) all_58_2 = e1
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | BETA: splitting (4) gives:
% 170.47/26.25 |
% 170.47/26.25 | Case 1:
% 170.47/26.25 | |
% 170.47/26.25 | | (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 170.47/26.25 | | e0)
% 170.47/26.25 | |
% 170.47/26.25 | | REF_CLOSE: (1), (6), (8), (9), (10) are inconsistent by sub-proof #763.
% 170.47/26.25 | |
% 170.47/26.25 | Case 2:
% 170.47/26.25 | |
% 170.47/26.25 | | (11) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.25 | | e0)
% 170.47/26.25 | |
% 170.47/26.25 | | BETA: splitting (11) gives:
% 170.47/26.25 | |
% 170.47/26.25 | | Case 1:
% 170.47/26.25 | | |
% 170.47/26.25 | | | (12) all_58_5 = e0 & op(e2, e1) = e0
% 170.47/26.25 | | |
% 170.47/26.25 | | | ALPHA: (12) implies:
% 170.47/26.25 | | | (13) all_58_5 = e0
% 170.47/26.25 | | |
% 170.47/26.25 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #919.
% 170.47/26.25 | | |
% 170.47/26.25 | | Case 2:
% 170.47/26.25 | | |
% 170.47/26.25 | | | (14) all_58_10 = e0 & op(e2, e0) = e0
% 170.47/26.25 | | |
% 170.47/26.25 | | | ALPHA: (14) implies:
% 170.47/26.25 | | | (15) op(e2, e0) = e0
% 170.47/26.25 | | |
% 170.47/26.25 | | | REF_CLOSE: (1), (5), (7), (15) are inconsistent by sub-proof #849.
% 170.47/26.25 | | |
% 170.47/26.25 | | End of split
% 170.47/26.25 | |
% 170.47/26.25 | End of split
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #550 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) all_54_2 = all_52_8
% 170.47/26.25 (2) all_54_2 = e3
% 170.47/26.25 (3) ~ (all_52_8 = e3)
% 170.47/26.25
% 170.47/26.25 Begin of proof
% 170.47/26.25 |
% 170.47/26.25 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.25 | (4) all_52_8 = e3
% 170.47/26.25 |
% 170.47/26.25 | SIMP: (4) implies:
% 170.47/26.25 | (5) all_52_8 = e3
% 170.47/26.25 |
% 170.47/26.25 | REDUCE: (3), (5) imply:
% 170.47/26.25 | (6) $false
% 170.47/26.25 |
% 170.47/26.25 | CLOSE: (6) is inconsistent.
% 170.47/26.25 |
% 170.47/26.25 End of proof
% 170.47/26.25
% 170.47/26.25 Sub-proof #551 shows that the following formulas are inconsistent:
% 170.47/26.25 ----------------------------------------------------------------
% 170.47/26.25 (1) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 170.47/26.25 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 170.47/26.25 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.25 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.25 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.47/26.25 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.25 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.25 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.25 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.25 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 170.47/26.25 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 170.47/26.25 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.25 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.25 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.25 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.47/26.25 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 170.47/26.25 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.25 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.25 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.25 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 170.47/26.25 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.25 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.25 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.25 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.25 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 170.47/26.25 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 170.47/26.25 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.47/26.25 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.25 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.25 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.47/26.25 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.25 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.25 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.25 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.25 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 170.47/26.25 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 170.47/26.25 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.47/26.25 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.25 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.25 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.47/26.25 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 170.47/26.25 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.25 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.25 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.25 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 170.47/26.25 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.47/26.25 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 170.47/26.25 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 170.47/26.25 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 170.47/26.25 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 170.47/26.25 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.47/26.25 (2) all_54_2 = all_52_8
% 170.47/26.25 (3) ~ (all_52_1 = e3)
% 170.47/26.25 (4) all_58_14 = e2
% 170.47/26.25 (5) all_56_1 = e3
% 170.47/26.25 (6) all_56_10 = e2
% 170.47/26.25 (7) ~ (all_4_2 = e2)
% 170.47/26.25 (8) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 170.47/26.25 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.25 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.25 (10) ~ (all_56_15 = e3) | (all_56_6 = e0 & op(e0, e3) = e0)
% 170.47/26.25 (11) ~ (all_6_2 = e3)
% 170.47/26.25 (12) all_54_10 = all_6_2
% 170.47/26.25 (13) ~ (all_4_2 = e1)
% 170.47/26.25 (14) all_58_8 = e1
% 170.47/26.25 (15) ~ (all_52_6 = all_52_7)
% 170.47/26.25 (16) ~ (e3 = e1)
% 170.47/26.25 (17) all_56_14 = all_6_2
% 170.47/26.25 (18) op(e3, e1) = all_52_8
% 170.47/26.25 (19) ~ (e1 = e0)
% 170.47/26.25 (20) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.25 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.47/26.25 e3)
% 170.47/26.25 (21) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 170.47/26.25 (22) op(e1, e2) = all_52_6
% 170.47/26.25 (23) op(e2, e3) = all_52_1
% 170.47/26.25 (24) all_58_5 = e3
% 170.47/26.25 (25) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 170.47/26.25 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.25 (26) ~ (all_52_7 = all_4_2)
% 170.47/26.25 (27) ~ (all_52_6 = all_6_2)
% 170.47/26.25 (28) all_58_7 = e0
% 170.47/26.25 (29) ~ (all_52_7 = e3)
% 170.47/26.25 (30) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 170.47/26.25 (31) all_54_15 = all_4_2
% 170.47/26.25 (32) ~ (all_6_2 = e2)
% 170.47/26.25 (33) ~ (all_52_6 = e2)
% 170.47/26.25 (34) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 170.47/26.25 (35) all_56_15 = all_4_2
% 170.47/26.26 (36) ~ (e3 = e0)
% 170.47/26.26 (37) ~ (all_52_8 = e2)
% 170.47/26.26 (38) ~ (all_52_8 = e3)
% 170.47/26.26 (39) ~ (all_6_2 = e0)
% 170.47/26.26 (40) all_58_15 = e3
% 170.47/26.26 (41) all_58_1 = e3
% 170.47/26.26 (42) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.26 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.26 (43) all_58_3 = e2
% 170.47/26.26 (44) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.26 (45) ~ (all_52_8 = all_6_2)
% 170.47/26.26 (46) ~ (e2 = e0)
% 170.47/26.26 (47) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 170.47/26.26 (48) ~ (all_52_7 = e2)
% 170.47/26.26 (49) op(e3, e3) = e2
% 170.47/26.26 (50) ~ (e2 = e1)
% 170.47/26.26 (51) ~ (all_52_4 = e2)
% 170.47/26.26 (52) op(e3, e2) = all_52_4
% 170.47/26.26 (53) all_54_9 = all_52_6
% 170.47/26.26 (54) ~ (all_52_6 = e3)
% 170.47/26.26 (55) op(e0, e1) = e2
% 170.47/26.26 (56) op(e0, e2) = all_52_7
% 170.47/26.26 (57) all_54_13 = all_52_7
% 170.47/26.26 (58) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.26 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.26 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.26 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.26 (59) ~ (e3 = e2)
% 170.47/26.26
% 170.47/26.26 Begin of proof
% 170.47/26.26 |
% 170.47/26.26 | BETA: splitting (9) gives:
% 170.47/26.26 |
% 170.47/26.26 | Case 1:
% 170.47/26.26 | |
% 170.47/26.26 | | (60) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 170.47/26.26 | | e1)
% 170.47/26.26 | |
% 170.47/26.26 | | BETA: splitting (60) gives:
% 170.47/26.26 | |
% 170.47/26.26 | | Case 1:
% 170.47/26.26 | | |
% 170.47/26.26 | | | (61) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.26 | | |
% 170.47/26.26 | | | REF_CLOSE: (16), (41), (61) are inconsistent by sub-proof #711.
% 170.47/26.26 | | |
% 170.47/26.26 | | Case 2:
% 170.47/26.26 | | |
% 170.47/26.26 | | | (62) all_58_3 = e1 & op(e2, e2) = e1
% 170.47/26.26 | | |
% 170.47/26.26 | | | ALPHA: (62) implies:
% 170.47/26.26 | | | (63) all_58_3 = e1
% 170.47/26.26 | | |
% 170.47/26.26 | | | REF_CLOSE: (43), (50), (63) are inconsistent by sub-proof #924.
% 170.47/26.26 | | |
% 170.47/26.26 | | End of split
% 170.47/26.26 | |
% 170.47/26.26 | Case 2:
% 170.47/26.26 | |
% 170.47/26.26 | | (64) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 170.47/26.26 | | e1)
% 170.47/26.26 | |
% 170.47/26.26 | | BETA: splitting (64) gives:
% 170.47/26.26 | |
% 170.47/26.26 | | Case 1:
% 170.47/26.26 | | |
% 170.47/26.26 | | | (65) all_58_7 = e1 & op(e1, e2) = e1
% 170.47/26.26 | | |
% 170.47/26.26 | | | REF_CLOSE: (19), (28), (65) are inconsistent by sub-proof #867.
% 170.47/26.26 | | |
% 170.47/26.26 | | Case 2:
% 170.47/26.26 | | |
% 170.47/26.26 | | | (66) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.26 | | |
% 170.47/26.26 | | | ALPHA: (66) implies:
% 170.47/26.26 | | | (67) op(e0, e2) = e1
% 170.47/26.26 | | |
% 170.47/26.26 | | | BETA: splitting (58) gives:
% 170.47/26.26 | | |
% 170.47/26.26 | | | Case 1:
% 170.47/26.26 | | | |
% 170.47/26.26 | | | | (68) all_58_15 = e0 & op(e0, e0) = e0
% 170.47/26.26 | | | |
% 170.47/26.26 | | | | ALPHA: (68) implies:
% 170.47/26.26 | | | | (69) all_58_15 = e0
% 170.47/26.26 | | | |
% 170.47/26.26 | | | | REF_CLOSE: (36), (40), (69) are inconsistent by sub-proof #860.
% 170.47/26.26 | | | |
% 170.47/26.26 | | | Case 2:
% 170.47/26.26 | | | |
% 170.47/26.26 | | | | (70) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 170.47/26.26 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 170.47/26.26 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 170.47/26.26 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.47/26.26 | | | |
% 170.47/26.26 | | | | ALPHA: (70) implies:
% 170.47/26.26 | | | | (71) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 170.47/26.26 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.26 | | | |
% 170.47/26.26 | | | | BETA: splitting (71) gives:
% 170.47/26.26 | | | |
% 170.47/26.26 | | | | Case 1:
% 170.47/26.26 | | | | |
% 170.47/26.26 | | | | | (72) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.26 | | | | |
% 170.47/26.26 | | | | | ALPHA: (72) implies:
% 170.47/26.26 | | | | | (73) all_58_12 = e0
% 170.47/26.26 | | | | |
% 170.47/26.26 | | | | | BETA: splitting (21) gives:
% 170.47/26.26 | | | | |
% 170.47/26.26 | | | | | Case 1:
% 170.47/26.26 | | | | | |
% 170.47/26.26 | | | | | | (74) all_54_10 = e2
% 170.47/26.26 | | | | | |
% 170.47/26.26 | | | | | | REF_CLOSE: (12), (32), (74) are inconsistent by sub-proof #981.
% 170.47/26.26 | | | | | |
% 170.47/26.26 | | | | | Case 2:
% 170.47/26.26 | | | | | |
% 170.47/26.26 | | | | | | (75) ~ (all_54_10 = e2)
% 170.47/26.26 | | | | | | (76) all_54_10 = e1 | all_54_10 = e0
% 170.47/26.26 | | | | | |
% 170.47/26.26 | | | | | | BETA: splitting (76) gives:
% 170.47/26.26 | | | | | |
% 170.47/26.26 | | | | | | Case 1:
% 170.47/26.26 | | | | | | |
% 170.47/26.26 | | | | | | | (77) all_54_10 = e1
% 170.47/26.26 | | | | | | |
% 170.47/26.26 | | | | | | | COMBINE_EQS: (12), (77) imply:
% 170.47/26.26 | | | | | | | (78) all_6_2 = e1
% 170.47/26.26 | | | | | | |
% 170.47/26.26 | | | | | | | SIMP: (78) implies:
% 170.47/26.26 | | | | | | | (79) all_6_2 = e1
% 170.47/26.26 | | | | | | |
% 170.47/26.26 | | | | | | | COMBINE_EQS: (17), (79) imply:
% 170.47/26.26 | | | | | | | (80) all_56_14 = e1
% 170.47/26.26 | | | | | | |
% 170.47/26.26 | | | | | | | REDUCE: (27), (79) imply:
% 170.47/26.26 | | | | | | | (81) ~ (all_52_6 = e1)
% 170.47/26.26 | | | | | | |
% 170.47/26.26 | | | | | | | REDUCE: (45), (79) imply:
% 170.47/26.26 | | | | | | | (82) ~ (all_52_8 = e1)
% 170.47/26.26 | | | | | | |
% 170.47/26.26 | | | | | | | REDUCE: (11), (79) imply:
% 170.47/26.26 | | | | | | | (83) ~ (e3 = e1)
% 170.47/26.26 | | | | | | |
% 170.47/26.26 | | | | | | | REDUCE: (32), (79) imply:
% 170.47/26.26 | | | | | | | (84) ~ (e2 = e1)
% 170.47/26.26 | | | | | | |
% 170.47/26.26 | | | | | | | BETA: splitting (42) gives:
% 170.47/26.26 | | | | | | |
% 170.47/26.26 | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | |
% 170.47/26.26 | | | | | | | | (85) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 &
% 170.47/26.26 | | | | | | | | op(e3, e2) = e1)
% 170.47/26.26 | | | | | | | |
% 170.47/26.26 | | | | | | | | BETA: splitting (85) gives:
% 170.47/26.26 | | | | | | | |
% 170.47/26.26 | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | (86) all_58_0 = e1 & op(e3, e3) = e1
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | ALPHA: (86) implies:
% 170.47/26.26 | | | | | | | | | (87) op(e3, e3) = e1
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | REF_CLOSE: (44), (49), (50), (87) are inconsistent by
% 170.47/26.26 | | | | | | | | | sub-proof #957.
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | (88) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | ALPHA: (88) implies:
% 170.47/26.26 | | | | | | | | | (89) all_58_1 = e1
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | COMBINE_EQS: (41), (89) imply:
% 170.47/26.26 | | | | | | | | | (90) e3 = e1
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | COMBINE_EQS: (40), (90) imply:
% 170.47/26.26 | | | | | | | | | (91) all_58_15 = e1
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | REF_CLOSE: (4), (16), (20), (29), (36), (44), (56), (59),
% 170.47/26.26 | | | | | | | | | (73), (91) are inconsistent by sub-proof #555.
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | End of split
% 170.47/26.26 | | | | | | | |
% 170.47/26.26 | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | |
% 170.47/26.26 | | | | | | | | (92) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 &
% 170.47/26.26 | | | | | | | | op(e3, e0) = e1)
% 170.47/26.26 | | | | | | | |
% 170.47/26.26 | | | | | | | | BETA: splitting (92) gives:
% 170.47/26.26 | | | | | | | |
% 170.47/26.26 | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | (93) all_58_4 = e1 & op(e3, e1) = e1
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | ALPHA: (93) implies:
% 170.47/26.26 | | | | | | | | | (94) all_58_4 = e1
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | REF_CLOSE: (4), (14), (19), (24), (25), (36), (46), (94) are
% 170.47/26.26 | | | | | | | | | inconsistent by sub-proof #717.
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | (95) all_58_9 = e1 & op(e3, e0) = e1
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | ALPHA: (95) implies:
% 170.47/26.26 | | | | | | | | | (96) op(e3, e0) = e1
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | BETA: splitting (34) gives:
% 170.47/26.26 | | | | | | | | |
% 170.47/26.26 | | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | (97) all_54_9 = e3
% 170.47/26.26 | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | REF_CLOSE: (53), (54), (97) are inconsistent by sub-proof
% 170.47/26.26 | | | | | | | | | | #741.
% 170.47/26.26 | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | (98) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 170.47/26.26 | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | BETA: splitting (98) gives:
% 170.47/26.26 | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | (99) all_54_9 = e2
% 170.47/26.26 | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | REF_CLOSE: (33), (53), (99) are inconsistent by sub-proof
% 170.47/26.26 | | | | | | | | | | | #740.
% 170.47/26.26 | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | (100) ~ (all_54_9 = e2)
% 170.47/26.26 | | | | | | | | | | | (101) all_54_9 = e1 | all_54_9 = e0
% 170.47/26.26 | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | BETA: splitting (101) gives:
% 170.47/26.26 | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | (102) all_54_9 = e1
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | REF_CLOSE: (53), (81), (102) are inconsistent by sub-proof
% 170.47/26.26 | | | | | | | | | | | | #739.
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | (103) all_54_9 = e0
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | COMBINE_EQS: (53), (103) imply:
% 170.47/26.26 | | | | | | | | | | | | (104) all_52_6 = e0
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | SIMP: (104) implies:
% 170.47/26.26 | | | | | | | | | | | | (105) all_52_6 = e0
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | REDUCE: (15), (105) imply:
% 170.47/26.26 | | | | | | | | | | | | (106) ~ (all_52_7 = e0)
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | SIMP: (106) implies:
% 170.47/26.26 | | | | | | | | | | | | (107) ~ (all_52_7 = e0)
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | REDUCE: (81), (105) imply:
% 170.47/26.26 | | | | | | | | | | | | (108) ~ (e1 = e0)
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | BETA: splitting (47) gives:
% 170.47/26.26 | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | (109) all_54_2 = e3
% 170.47/26.26 | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | COMBINE_EQS: (2), (109) imply:
% 170.47/26.26 | | | | | | | | | | | | | (110) all_52_8 = e3
% 170.47/26.26 | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | REDUCE: (38), (110) imply:
% 170.47/26.26 | | | | | | | | | | | | | (111) $false
% 170.47/26.26 | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | CLOSE: (111) is inconsistent.
% 170.47/26.26 | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | (112) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 170.47/26.26 | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | BETA: splitting (1) gives:
% 170.47/26.26 | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | (113) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 170.47/26.26 | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.26 | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 170.47/26.26 | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.47/26.26 | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 170.47/26.26 | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 170.47/26.26 | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_6))))
% 170.47/26.26 | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 170.47/26.26 | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | (114) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 170.47/26.26 | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.26 | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.26 | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.26 | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.26 | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.26 | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.26 | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.26 | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.47/26.26 | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | REF_CLOSE: (3), (23), (44), (51), (52), (114) are
% 170.47/26.26 | | | | | | | | | | | | | | | inconsistent by sub-proof #619.
% 170.47/26.26 | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | (115) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 170.47/26.26 | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.47/26.26 | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.47/26.26 | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.26 | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.47/26.26 | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.26 | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.47/26.26 | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.26 | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 170.47/26.26 | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 170.47/26.26 | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 170.47/26.26 | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.26 | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.47/26.26 | | | | | | | | | | | | | | | $i(all_56_6))))
% 170.47/26.26 | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 170.47/26.26 | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | (116) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 170.47/26.26 | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.26 | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.47/26.26 | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.47/26.26 | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 170.47/26.26 | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 170.47/26.26 | | | | | | | | | | | | | | | | (117) ~ (all_56_14 = e1)
% 170.47/26.26 | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | REDUCE: (80), (117) imply:
% 170.47/26.26 | | | | | | | | | | | | | | | | (118) $false
% 170.47/26.26 | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | CLOSE: (118) is inconsistent.
% 170.47/26.26 | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | (119) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 170.47/26.26 | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.47/26.26 | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.47/26.26 | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.26 | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.47/26.26 | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 170.47/26.26 | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.26 | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.26 | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.26 | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.47/26.26 | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 170.47/26.26 | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | | (120) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) =
% 170.47/26.26 | | | | | | | | | | | | | | | | | e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.26 | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.47/26.26 | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.47/26.26 | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 170.47/26.26 | | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 170.47/26.26 | | | | | | | | | | | | | | | | | (121) op(e1, e2) = e2
% 170.47/26.26 | | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (33), (44), (121) are inconsistent by
% 170.47/26.26 | | | | | | | | | | | | | | | | | sub-proof #986.
% 170.47/26.26 | | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | | (122) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) =
% 170.47/26.26 | | | | | | | | | | | | | | | | | e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.26 | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1,
% 170.47/26.26 | | | | | | | | | | | | | | | | | e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) & op(e0,
% 170.47/26.26 | | | | | | | | | | | | | | | | | e3) = all_56_6 & $i(all_56_6)))
% 170.47/26.26 | | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 170.47/26.26 | | | | | | | | | | | | | | | | | (123) op(e3, e1) = e1
% 170.47/26.26 | | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (18), (37), (44), (82), (112), (123) are
% 170.47/26.26 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #568.
% 170.47/26.26 | | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | | End of split
% 170.47/26.26 | | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | | End of split
% 170.47/26.26 | | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | End of split
% 170.47/26.26 | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | Case 2:
% 170.47/26.26 | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | (124) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 170.47/26.26 | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.26 | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 170.47/26.26 | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.26 | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.26 | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 170.47/26.26 | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.47/26.26 | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.47/26.26 | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 170.47/26.26 | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 170.47/26.26 | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.47/26.26 | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 170.47/26.26 | | | | | | | | | | | | | |
% 170.47/26.26 | | | | | | | | | | | | | | Case 1:
% 170.47/26.26 | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | (125) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 170.47/26.27 | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.27 | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.27 | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.27 | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.27 | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.27 | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.27 | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.27 | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.47/26.27 | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (19), (44), (96), (125) are inconsistent
% 170.47/26.27 | | | | | | | | | | | | | | | by sub-proof #552.
% 170.47/26.27 | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | Case 2:
% 170.47/26.27 | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | (126) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 170.47/26.27 | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.27 | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.27 | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.27 | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.27 | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.27 | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.47/26.27 | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.27 | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 170.47/26.27 | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.47/26.27 | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.47/26.27 | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.47/26.27 | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 170.47/26.27 | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 170.47/26.27 | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.47/26.27 | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 170.47/26.27 | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | Case 1:
% 170.47/26.27 | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | (127) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 170.47/26.27 | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 170.47/26.27 | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 170.47/26.27 | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 170.47/26.27 | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 170.47/26.27 | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 170.47/26.27 | | | | | | | | | | | | | | | | (128) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3,
% 170.47/26.27 | | | | | | | | | | | | | | | | e2) = all_56_1 & $i(all_56_1))
% 170.47/26.27 | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (128) are inconsistent by sub-proof
% 170.47/26.27 | | | | | | | | | | | | | | | | #554.
% 170.47/26.27 | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | Case 2:
% 170.47/26.27 | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | (129) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 170.47/26.27 | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.47/26.27 | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.47/26.27 | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.27 | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.47/26.27 | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 170.47/26.27 | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 170.47/26.27 | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 170.47/26.27 | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 170.47/26.27 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 170.47/26.27 | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 170.47/26.27 | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 170.47/26.27 | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 170.47/26.27 | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 170.47/26.27 | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.27 | | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | | (130) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 170.47/26.27 | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 170.47/26.27 | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.47/26.27 | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.47/26.27 | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 170.47/26.27 | | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 170.47/26.27 | | | | | | | | | | | | | | | | | (131) ~ (all_56_14 = e1)
% 170.47/26.27 | | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | | REDUCE: (80), (131) imply:
% 170.47/26.27 | | | | | | | | | | | | | | | | | (132) $false
% 170.47/26.27 | | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | | CLOSE: (132) is inconsistent.
% 170.47/26.27 | | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.27 | | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | | (133) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.47/26.27 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.47/26.27 | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.47/26.27 | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.47/26.27 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 170.47/26.27 | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 170.47/26.27 | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 170.47/26.27 | | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10), (13), (26), (30), (31), (35),
% 170.47/26.27 | | | | | | | | | | | | | | | | | (44), (48), (55), (56), (57), (107), (133) are
% 170.47/26.27 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #696.
% 170.47/26.27 | | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | | End of split
% 170.47/26.27 | | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | | End of split
% 170.47/26.27 | | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | | End of split
% 170.47/26.27 | | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | | End of split
% 170.47/26.27 | | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | | End of split
% 170.47/26.27 | | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | | End of split
% 170.47/26.27 | | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | | End of split
% 170.47/26.27 | | | | | | | | | |
% 170.47/26.27 | | | | | | | | | End of split
% 170.47/26.27 | | | | | | | | |
% 170.47/26.27 | | | | | | | | End of split
% 170.47/26.27 | | | | | | | |
% 170.47/26.27 | | | | | | | End of split
% 170.47/26.27 | | | | | | |
% 170.47/26.27 | | | | | | Case 2:
% 170.47/26.27 | | | | | | |
% 170.47/26.27 | | | | | | | (134) all_54_10 = e0
% 170.47/26.27 | | | | | | |
% 170.47/26.27 | | | | | | | REF_CLOSE: (12), (39), (134) are inconsistent by sub-proof #979.
% 170.47/26.27 | | | | | | |
% 170.47/26.27 | | | | | | End of split
% 170.47/26.27 | | | | | |
% 170.47/26.27 | | | | | End of split
% 170.47/26.27 | | | | |
% 170.47/26.27 | | | | Case 2:
% 170.47/26.27 | | | | |
% 170.47/26.27 | | | | | (135) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 170.47/26.27 | | | | | e1) = e0)
% 170.47/26.27 | | | | |
% 170.47/26.27 | | | | | BETA: splitting (135) gives:
% 170.47/26.27 | | | | |
% 170.47/26.27 | | | | | Case 1:
% 170.47/26.27 | | | | | |
% 170.47/26.27 | | | | | | (136) all_58_13 = e0 & op(e0, e2) = e0
% 170.47/26.27 | | | | | |
% 170.47/26.27 | | | | | | ALPHA: (136) implies:
% 170.47/26.27 | | | | | | (137) op(e0, e2) = e0
% 170.47/26.27 | | | | | |
% 170.47/26.27 | | | | | | REF_CLOSE: (19), (44), (56), (67), (137) are inconsistent by
% 170.47/26.27 | | | | | | sub-proof #889.
% 170.47/26.27 | | | | | |
% 170.47/26.27 | | | | | Case 2:
% 170.47/26.27 | | | | | |
% 170.47/26.27 | | | | | | (138) all_58_14 = e0 & op(e0, e1) = e0
% 170.47/26.27 | | | | | |
% 170.47/26.27 | | | | | | REF_CLOSE: (4), (46), (138) are inconsistent by sub-proof #858.
% 170.47/26.27 | | | | | |
% 170.47/26.27 | | | | | End of split
% 170.47/26.27 | | | | |
% 170.47/26.27 | | | | End of split
% 170.47/26.27 | | | |
% 170.47/26.27 | | | End of split
% 170.47/26.27 | | |
% 170.47/26.27 | | End of split
% 170.47/26.27 | |
% 170.47/26.27 | End of split
% 170.47/26.27 |
% 170.47/26.27 End of proof
% 170.47/26.27
% 170.47/26.27 Sub-proof #552 shows that the following formulas are inconsistent:
% 170.47/26.27 ----------------------------------------------------------------
% 170.47/26.27 (1) all_56_1 = e3
% 170.47/26.27 (2) all_56_10 = e2
% 170.47/26.27 (3) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 =
% 170.47/26.27 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 170.47/26.27 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.27 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.27 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.47/26.27 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.27 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.27 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.27 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.27 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.47/26.27 (4) ~ (e1 = e0)
% 170.47/26.27 (5) op(e3, e0) = e1
% 170.47/26.27 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.27
% 170.47/26.27 Begin of proof
% 170.47/26.27 |
% 170.47/26.27 | BETA: splitting (3) gives:
% 170.47/26.27 |
% 170.47/26.27 | Case 1:
% 170.47/26.27 | |
% 170.47/26.27 | | (7) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~
% 170.47/26.27 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 170.47/26.27 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 170.47/26.27 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 170.47/26.27 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 170.47/26.27 | |
% 170.47/26.27 | | ALPHA: (7) implies:
% 170.47/26.27 | | (8) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 170.47/26.27 | | $i(all_56_1))
% 170.47/26.27 | |
% 170.47/26.27 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #554.
% 170.47/26.27 | |
% 170.47/26.27 | Case 2:
% 170.47/26.27 | |
% 170.47/26.27 | | (9) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 170.47/26.27 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 170.47/26.27 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.27 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 170.47/26.27 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 170.47/26.27 | |
% 170.47/26.27 | | ALPHA: (9) implies:
% 170.47/26.27 | | (10) op(e3, e0) = e0
% 170.47/26.27 | |
% 170.47/26.27 | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #553.
% 170.47/26.27 | |
% 170.47/26.27 | End of split
% 170.47/26.27 |
% 170.47/26.27 End of proof
% 170.47/26.27
% 170.47/26.27 Sub-proof #553 shows that the following formulas are inconsistent:
% 170.47/26.27 ----------------------------------------------------------------
% 170.47/26.27 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.27 (2) op(e3, e0) = e1
% 170.47/26.27 (3) op(e3, e0) = e0
% 170.47/26.27 (4) ~ (e1 = e0)
% 170.47/26.27
% 170.47/26.27 Begin of proof
% 170.47/26.27 |
% 170.47/26.27 | GROUND_INST: instantiating (1) with e0, e1, e0, e3, simplifying with (2), (3)
% 170.47/26.27 | gives:
% 170.47/26.27 | (5) e1 = e0
% 170.47/26.27 |
% 170.47/26.27 | REDUCE: (4), (5) imply:
% 170.47/26.27 | (6) $false
% 170.47/26.27 |
% 170.47/26.27 | CLOSE: (6) is inconsistent.
% 170.47/26.27 |
% 170.47/26.27 End of proof
% 170.47/26.27
% 170.47/26.27 Sub-proof #554 shows that the following formulas are inconsistent:
% 170.47/26.27 ----------------------------------------------------------------
% 170.47/26.27 (1) ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 170.47/26.27 $i(all_56_1))
% 170.47/26.27 (2) all_56_10 = e2
% 170.47/26.27 (3) all_56_1 = e3
% 170.47/26.27
% 170.47/26.27 Begin of proof
% 170.47/26.27 |
% 170.47/26.27 | BETA: splitting (1) gives:
% 170.47/26.27 |
% 170.47/26.27 | Case 1:
% 170.47/26.27 | |
% 170.47/26.27 | | (4) ~ (all_56_10 = e2)
% 170.47/26.27 | |
% 170.47/26.27 | | REDUCE: (2), (4) imply:
% 170.47/26.27 | | (5) $false
% 170.47/26.27 | |
% 170.47/26.27 | | CLOSE: (5) is inconsistent.
% 170.47/26.27 | |
% 170.47/26.27 | Case 2:
% 170.47/26.27 | |
% 170.47/26.27 | | (6) ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)
% 170.47/26.27 | |
% 170.47/26.27 | | ALPHA: (6) implies:
% 170.47/26.27 | | (7) ~ (all_56_1 = e3)
% 170.47/26.27 | |
% 170.47/26.27 | | REDUCE: (3), (7) imply:
% 170.47/26.27 | | (8) $false
% 170.47/26.27 | |
% 170.47/26.27 | | CLOSE: (8) is inconsistent.
% 170.47/26.27 | |
% 170.47/26.27 | End of split
% 170.47/26.27 |
% 170.47/26.27 End of proof
% 170.47/26.27
% 170.47/26.27 Sub-proof #555 shows that the following formulas are inconsistent:
% 170.47/26.27 ----------------------------------------------------------------
% 170.47/26.27 (1) all_58_15 = e1
% 170.47/26.27 (2) all_58_14 = e2
% 170.47/26.27 (3) ~ (e3 = e1)
% 170.47/26.27 (4) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 170.47/26.27 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.47/26.27 (5) ~ (all_52_7 = e3)
% 170.47/26.27 (6) ~ (e3 = e0)
% 170.47/26.27 (7) all_58_12 = e0
% 170.47/26.27 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.27 (9) op(e0, e2) = all_52_7
% 170.47/26.27 (10) ~ (e3 = e2)
% 170.47/26.27
% 170.47/26.27 Begin of proof
% 170.47/26.27 |
% 170.47/26.27 | BETA: splitting (4) gives:
% 170.47/26.27 |
% 170.47/26.27 | Case 1:
% 170.47/26.27 | |
% 170.47/26.27 | | (11) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 170.47/26.27 | | e3)
% 170.47/26.27 | |
% 170.47/26.27 | | REF_CLOSE: (5), (6), (7), (8), (9), (11) are inconsistent by sub-proof #557.
% 170.47/26.27 | |
% 170.47/26.27 | Case 2:
% 170.47/26.27 | |
% 170.47/26.27 | | (12) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.47/26.27 | | e3)
% 170.47/26.27 | |
% 170.47/26.27 | | BETA: splitting (12) gives:
% 170.47/26.27 | |
% 170.47/26.27 | | Case 1:
% 170.47/26.27 | | |
% 170.47/26.27 | | | (13) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.27 | | |
% 170.47/26.27 | | | ALPHA: (13) implies:
% 170.47/26.27 | | | (14) all_58_14 = e3
% 170.47/26.27 | | |
% 170.47/26.27 | | | REF_CLOSE: (2), (10), (14) are inconsistent by sub-proof #855.
% 170.47/26.27 | | |
% 170.47/26.27 | | Case 2:
% 170.47/26.27 | | |
% 170.47/26.27 | | | (15) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.27 | | |
% 170.47/26.27 | | | ALPHA: (15) implies:
% 170.47/26.27 | | | (16) all_58_15 = e3
% 170.47/26.27 | | |
% 170.47/26.27 | | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #556.
% 170.47/26.27 | | |
% 170.47/26.27 | | End of split
% 170.47/26.27 | |
% 170.47/26.27 | End of split
% 170.47/26.27 |
% 170.47/26.27 End of proof
% 170.47/26.27
% 170.47/26.27 Sub-proof #556 shows that the following formulas are inconsistent:
% 170.47/26.27 ----------------------------------------------------------------
% 170.47/26.27 (1) all_58_15 = e3
% 170.47/26.27 (2) all_58_15 = e1
% 170.47/26.27 (3) ~ (e3 = e1)
% 170.47/26.27
% 170.47/26.27 Begin of proof
% 170.47/26.27 |
% 170.47/26.27 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.27 | (4) e3 = e1
% 170.47/26.27 |
% 170.47/26.27 | SIMP: (4) implies:
% 170.47/26.27 | (5) e3 = e1
% 170.47/26.27 |
% 170.47/26.27 | REDUCE: (3), (5) imply:
% 170.47/26.27 | (6) $false
% 170.47/26.27 |
% 170.47/26.27 | CLOSE: (6) is inconsistent.
% 170.47/26.27 |
% 170.47/26.27 End of proof
% 170.47/26.27
% 170.47/26.27 Sub-proof #557 shows that the following formulas are inconsistent:
% 170.47/26.27 ----------------------------------------------------------------
% 170.47/26.27 (1) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.27 (2) ~ (all_52_7 = e3)
% 170.47/26.27 (3) ~ (e3 = e0)
% 170.47/26.27 (4) all_58_12 = e0
% 170.47/26.27 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.27 (6) op(e0, e2) = all_52_7
% 170.47/26.27
% 170.47/26.27 Begin of proof
% 170.47/26.27 |
% 170.47/26.27 | BETA: splitting (1) gives:
% 170.47/26.27 |
% 170.47/26.27 | Case 1:
% 170.47/26.27 | |
% 170.47/26.27 | | (7) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.27 | |
% 170.47/26.27 | | ALPHA: (7) implies:
% 170.47/26.27 | | (8) all_58_12 = e3
% 170.47/26.27 | |
% 170.47/26.27 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #608.
% 170.47/26.27 | |
% 170.47/26.27 | Case 2:
% 170.47/26.27 | |
% 170.47/26.27 | | (9) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.27 | |
% 170.47/26.27 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #962.
% 170.47/26.27 | |
% 170.47/26.27 | End of split
% 170.47/26.27 |
% 170.47/26.27 End of proof
% 170.47/26.27
% 170.47/26.27 Sub-proof #558 shows that the following formulas are inconsistent:
% 170.47/26.27 ----------------------------------------------------------------
% 170.47/26.27 (1) ~ (e3 = e1)
% 170.47/26.27 (2) op(e1, e3) = all_52_2
% 170.47/26.27 (3) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1)
% 170.47/26.27 (4) ~ (e1 = e0)
% 170.47/26.27 (5) all_58_7 = e0
% 170.47/26.27 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.27 (7) op(e1, e3) = e3
% 170.47/26.27
% 170.47/26.27 Begin of proof
% 170.47/26.27 |
% 170.47/26.27 | BETA: splitting (3) gives:
% 170.47/26.27 |
% 170.47/26.27 | Case 1:
% 170.47/26.27 | |
% 170.47/26.27 | | (8) all_58_6 = e1 & op(e1, e3) = e1
% 170.47/26.27 | |
% 170.47/26.27 | | ALPHA: (8) implies:
% 170.47/26.27 | | (9) op(e1, e3) = e1
% 170.47/26.27 | |
% 170.47/26.27 | | REF_CLOSE: (1), (2), (6), (7), (9) are inconsistent by sub-proof #750.
% 170.47/26.27 | |
% 170.47/26.27 | Case 2:
% 170.47/26.27 | |
% 170.47/26.27 | | (10) all_58_7 = e1 & op(e1, e2) = e1
% 170.47/26.27 | |
% 170.47/26.27 | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #867.
% 170.47/26.27 | |
% 170.47/26.27 | End of split
% 170.47/26.27 |
% 170.47/26.27 End of proof
% 170.47/26.27
% 170.47/26.27 Sub-proof #559 shows that the following formulas are inconsistent:
% 170.47/26.27 ----------------------------------------------------------------
% 170.47/26.27 (1) all_58_6 = e0 & op(e1, e3) = e0
% 170.47/26.27 (2) all_58_6 = e3
% 170.47/26.27 (3) ~ (e3 = e0)
% 170.47/26.27
% 170.47/26.27 Begin of proof
% 170.47/26.27 |
% 170.47/26.27 | ALPHA: (1) implies:
% 170.47/26.27 | (4) all_58_6 = e0
% 170.47/26.27 |
% 170.47/26.27 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.27 | (5) e3 = e0
% 170.47/26.27 |
% 170.47/26.27 | REDUCE: (3), (5) imply:
% 170.47/26.27 | (6) $false
% 170.47/26.27 |
% 170.47/26.27 | CLOSE: (6) is inconsistent.
% 170.47/26.27 |
% 170.47/26.27 End of proof
% 170.47/26.27
% 170.47/26.27 Sub-proof #560 shows that the following formulas are inconsistent:
% 170.47/26.27 ----------------------------------------------------------------
% 170.47/26.27 (1) ~ (all_52_1 = e3)
% 170.47/26.27 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.27 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.27 (3) ~ (all_8_2 = e3)
% 170.47/26.27 (4) ~ (e3 = e1)
% 170.47/26.27 (5) ~ (e1 = e0)
% 170.47/26.27 (6) op(e2, e3) = all_52_1
% 170.47/26.27 (7) all_58_5 = e3
% 170.47/26.27 (8) op(e2, e2) = all_8_2
% 170.47/26.27 (9) ~ (e3 = e0)
% 170.47/26.27 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.27 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.27 (11) all_58_3 = e2
% 170.47/26.27 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.27 (13) ~ (e2 = e0)
% 170.47/26.27 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.27 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.27 (15) ~ (e2 = e1)
% 170.47/26.27 (16) ~ (e3 = e2)
% 170.47/26.27 (17) e3 = e2
% 170.47/26.27
% 170.47/26.27 Begin of proof
% 170.47/26.27 |
% 170.47/26.27 | COMBINE_EQS: (7), (17) imply:
% 170.47/26.27 | (18) all_58_5 = e2
% 170.47/26.27 |
% 170.47/26.27 | BETA: splitting (14) gives:
% 170.47/26.27 |
% 170.47/26.27 | Case 1:
% 170.47/26.27 | |
% 170.47/26.27 | | (19) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.47/26.27 | | e3)
% 170.47/26.27 | |
% 170.47/26.27 | | REF_CLOSE: (1), (3), (6), (8), (12), (19) are inconsistent by sub-proof
% 170.47/26.27 | | #692.
% 170.47/26.27 | |
% 170.47/26.27 | Case 2:
% 170.47/26.27 | |
% 170.47/26.27 | | (20) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 170.47/26.27 | | e3)
% 170.47/26.27 | |
% 170.47/26.27 | | BETA: splitting (20) gives:
% 170.47/26.27 | |
% 170.47/26.27 | | Case 1:
% 170.47/26.27 | | |
% 170.47/26.27 | | | (21) all_58_5 = e3 & op(e2, e1) = e3
% 170.47/26.27 | | |
% 170.47/26.27 | | | REF_CLOSE: (16), (18), (21) are inconsistent by sub-proof #561.
% 170.47/26.27 | | |
% 170.47/26.27 | | Case 2:
% 170.47/26.27 | | |
% 170.47/26.27 | | | (22) all_58_10 = e3 & op(e2, e0) = e3
% 170.47/26.27 | | |
% 170.47/26.27 | | | ALPHA: (22) implies:
% 170.47/26.27 | | | (23) all_58_10 = e3
% 170.47/26.27 | | |
% 170.47/26.27 | | | REF_CLOSE: (2), (4), (5), (9), (10), (11), (13), (15), (18), (23) are
% 170.47/26.27 | | | inconsistent by sub-proof #850.
% 170.47/26.27 | | |
% 170.47/26.27 | | End of split
% 170.47/26.27 | |
% 170.47/26.27 | End of split
% 170.47/26.27 |
% 170.47/26.27 End of proof
% 170.47/26.27
% 170.47/26.27 Sub-proof #561 shows that the following formulas are inconsistent:
% 170.47/26.27 ----------------------------------------------------------------
% 170.47/26.27 (1) all_58_5 = e3 & op(e2, e1) = e3
% 170.47/26.27 (2) all_58_5 = e2
% 170.47/26.27 (3) ~ (e3 = e2)
% 170.47/26.27
% 170.47/26.27 Begin of proof
% 170.47/26.27 |
% 170.47/26.27 | ALPHA: (1) implies:
% 170.47/26.27 | (4) all_58_5 = e3
% 170.47/26.27 |
% 170.47/26.27 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.27 | (5) e3 = e2
% 170.47/26.27 |
% 170.47/26.27 | SIMP: (5) implies:
% 170.47/26.28 | (6) e3 = e2
% 170.47/26.28 |
% 170.47/26.28 | REDUCE: (3), (6) imply:
% 170.47/26.28 | (7) $false
% 170.47/26.28 |
% 170.47/26.28 | CLOSE: (7) is inconsistent.
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #562 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (2) op(e2, e0) = all_52_13
% 170.47/26.28 (3) op(e2, e0) = e3
% 170.47/26.28 (4) ~ (all_52_13 = e3)
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | GROUND_INST: instantiating (1) with all_52_13, e3, e0, e2, simplifying with
% 170.47/26.28 | (2), (3) gives:
% 170.47/26.28 | (5) all_52_13 = e3
% 170.47/26.28 |
% 170.47/26.28 | REDUCE: (4), (5) imply:
% 170.47/26.28 | (6) $false
% 170.47/26.28 |
% 170.47/26.28 | CLOSE: (6) is inconsistent.
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #563 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) all_58_14 = e2
% 170.47/26.28 (2) ~ (e3 = e1)
% 170.47/26.28 (3) ~ (e1 = e0)
% 170.47/26.28 (4) all_58_5 = e3
% 170.47/26.28 (5) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 170.47/26.28 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.28 (6) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_14 = e1 & op(e0, e1) = e1)
% 170.47/26.28 (7) ~ (e3 = e0)
% 170.47/26.28 (8) all_58_1 = e3
% 170.47/26.28 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.28 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.28 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (11) ~ (e2 = e0)
% 170.47/26.28 (12) all_58_9 = e3
% 170.47/26.28 (13) op(e3, e3) = e2
% 170.47/26.28 (14) ~ (e2 = e1)
% 170.47/26.28 (15) op(e0, e1) = e2
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | BETA: splitting (6) gives:
% 170.47/26.28 |
% 170.47/26.28 | Case 1:
% 170.47/26.28 | |
% 170.47/26.28 | | (16) all_58_8 = e1 & op(e1, e1) = e1
% 170.47/26.28 | |
% 170.47/26.28 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 170.47/26.28 | | (14), (16) are inconsistent by sub-proof #564.
% 170.47/26.28 | |
% 170.47/26.28 | Case 2:
% 170.47/26.28 | |
% 170.47/26.28 | | (17) all_58_14 = e1 & op(e0, e1) = e1
% 170.47/26.28 | |
% 170.47/26.28 | | ALPHA: (17) implies:
% 170.47/26.28 | | (18) op(e0, e1) = e1
% 170.47/26.28 | |
% 170.47/26.28 | | REF_CLOSE: (10), (14), (15), (18) are inconsistent by sub-proof #967.
% 170.47/26.28 | |
% 170.47/26.28 | End of split
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #564 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) all_58_14 = e2
% 170.47/26.28 (2) ~ (e3 = e1)
% 170.47/26.28 (3) all_58_8 = e1 & op(e1, e1) = e1
% 170.47/26.28 (4) ~ (e1 = e0)
% 170.47/26.28 (5) all_58_5 = e3
% 170.47/26.28 (6) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 170.47/26.28 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.28 (7) ~ (e3 = e0)
% 170.47/26.28 (8) all_58_1 = e3
% 170.47/26.28 (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.28 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.28 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (11) ~ (e2 = e0)
% 170.47/26.28 (12) all_58_9 = e3
% 170.47/26.28 (13) op(e3, e3) = e2
% 170.47/26.28 (14) ~ (e2 = e1)
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | ALPHA: (3) implies:
% 170.47/26.28 | (15) all_58_8 = e1
% 170.47/26.28 |
% 170.47/26.28 | BETA: splitting (9) gives:
% 170.47/26.28 |
% 170.47/26.28 | Case 1:
% 170.47/26.28 | |
% 170.47/26.28 | | (16) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 170.47/26.28 | | e1)
% 170.47/26.28 | |
% 170.47/26.28 | | REF_CLOSE: (2), (8), (10), (13), (14), (16) are inconsistent by sub-proof
% 170.47/26.28 | | #565.
% 170.47/26.28 | |
% 170.47/26.28 | Case 2:
% 170.47/26.28 | |
% 170.47/26.28 | | (17) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 170.47/26.28 | | e1)
% 170.47/26.28 | |
% 170.47/26.28 | | BETA: splitting (17) gives:
% 170.47/26.28 | |
% 170.47/26.28 | | Case 1:
% 170.47/26.28 | | |
% 170.47/26.28 | | | (18) all_58_4 = e1 & op(e3, e1) = e1
% 170.47/26.28 | | |
% 170.47/26.28 | | | ALPHA: (18) implies:
% 170.47/26.28 | | | (19) all_58_4 = e1
% 170.47/26.28 | | |
% 170.47/26.28 | | | REF_CLOSE: (1), (4), (5), (6), (7), (11), (15), (19) are inconsistent by
% 170.47/26.28 | | | sub-proof #717.
% 170.47/26.28 | | |
% 170.47/26.28 | | Case 2:
% 170.47/26.28 | | |
% 170.47/26.28 | | | (20) all_58_9 = e1 & op(e3, e0) = e1
% 170.47/26.28 | | |
% 170.47/26.28 | | | REF_CLOSE: (2), (12), (20) are inconsistent by sub-proof #836.
% 170.47/26.28 | | |
% 170.47/26.28 | | End of split
% 170.47/26.28 | |
% 170.47/26.28 | End of split
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #565 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) ~ (e3 = e1)
% 170.47/26.28 (2) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 170.47/26.28 (3) all_58_1 = e3
% 170.47/26.28 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (5) op(e3, e3) = e2
% 170.47/26.28 (6) ~ (e2 = e1)
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | BETA: splitting (2) gives:
% 170.47/26.28 |
% 170.47/26.28 | Case 1:
% 170.47/26.28 | |
% 170.47/26.28 | | (7) all_58_0 = e1 & op(e3, e3) = e1
% 170.47/26.28 | |
% 170.47/26.28 | | ALPHA: (7) implies:
% 170.47/26.28 | | (8) op(e3, e3) = e1
% 170.47/26.28 | |
% 170.47/26.28 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #957.
% 170.47/26.28 | |
% 170.47/26.28 | Case 2:
% 170.47/26.28 | |
% 170.47/26.28 | | (9) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.28 | |
% 170.47/26.28 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #711.
% 170.47/26.28 | |
% 170.47/26.28 | End of split
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #566 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) all_54_2 = all_52_8
% 170.47/26.28 (2) all_54_10 = all_6_2
% 170.47/26.28 (3) ~ (e3 = e1)
% 170.47/26.28 (4) op(e3, e1) = all_52_8
% 170.47/26.28 (5) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 170.47/26.28 (6) ~ (all_6_2 = e2)
% 170.47/26.28 (7) ~ (all_52_8 = e2)
% 170.47/26.28 (8) ~ (all_52_8 = e3)
% 170.47/26.28 (9) ~ (all_6_2 = e0)
% 170.47/26.28 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (11) ~ (all_52_8 = all_6_2)
% 170.47/26.28 (12) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 170.47/26.28 (13) op(e2, e1) = e3
% 170.47/26.28 (14) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_5 = e1 & op(e2, e1) = e1)
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | BETA: splitting (14) gives:
% 170.47/26.28 |
% 170.47/26.28 | Case 1:
% 170.47/26.28 | |
% 170.47/26.28 | | (15) all_58_4 = e1 & op(e3, e1) = e1
% 170.47/26.28 | |
% 170.47/26.28 | | ALPHA: (15) implies:
% 170.47/26.28 | | (16) op(e3, e1) = e1
% 170.47/26.28 | |
% 170.47/26.28 | | BETA: splitting (5) gives:
% 170.47/26.28 | |
% 170.47/26.28 | | Case 1:
% 170.47/26.28 | | |
% 170.47/26.28 | | | (17) all_54_10 = e2
% 170.47/26.28 | | |
% 170.47/26.28 | | | REF_CLOSE: (2), (6), (17) are inconsistent by sub-proof #981.
% 170.47/26.28 | | |
% 170.47/26.28 | | Case 2:
% 170.47/26.28 | | |
% 170.47/26.28 | | | (18) all_54_10 = e1 | all_54_10 = e0
% 170.47/26.28 | | |
% 170.47/26.28 | | | BETA: splitting (18) gives:
% 170.47/26.28 | | |
% 170.47/26.28 | | | Case 1:
% 170.47/26.28 | | | |
% 170.47/26.28 | | | | (19) all_54_10 = e1
% 170.47/26.28 | | | |
% 170.47/26.28 | | | | COMBINE_EQS: (2), (19) imply:
% 170.47/26.28 | | | | (20) all_6_2 = e1
% 170.47/26.28 | | | |
% 170.47/26.28 | | | | SIMP: (20) implies:
% 170.47/26.28 | | | | (21) all_6_2 = e1
% 170.47/26.28 | | | |
% 170.47/26.28 | | | | REDUCE: (11), (21) imply:
% 170.47/26.28 | | | | (22) ~ (all_52_8 = e1)
% 170.47/26.28 | | | |
% 170.47/26.28 | | | | REF_CLOSE: (1), (4), (7), (8), (10), (12), (16), (22) are inconsistent
% 170.47/26.28 | | | | by sub-proof #567.
% 170.47/26.28 | | | |
% 170.47/26.28 | | | Case 2:
% 170.47/26.28 | | | |
% 170.47/26.28 | | | | (23) all_54_10 = e0
% 170.47/26.28 | | | |
% 170.47/26.28 | | | | REF_CLOSE: (2), (9), (23) are inconsistent by sub-proof #979.
% 170.47/26.28 | | | |
% 170.47/26.28 | | | End of split
% 170.47/26.28 | | |
% 170.47/26.28 | | End of split
% 170.47/26.28 | |
% 170.47/26.28 | Case 2:
% 170.47/26.28 | |
% 170.47/26.28 | | (24) all_58_5 = e1 & op(e2, e1) = e1
% 170.47/26.28 | |
% 170.47/26.28 | | ALPHA: (24) implies:
% 170.47/26.28 | | (25) op(e2, e1) = e1
% 170.47/26.28 | |
% 170.47/26.28 | | REF_CLOSE: (3), (10), (13), (25) are inconsistent by sub-proof #686.
% 170.47/26.28 | |
% 170.47/26.28 | End of split
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #567 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) all_54_2 = all_52_8
% 170.47/26.28 (2) op(e3, e1) = all_52_8
% 170.47/26.28 (3) ~ (all_52_8 = e1)
% 170.47/26.28 (4) op(e3, e1) = e1
% 170.47/26.28 (5) ~ (all_52_8 = e2)
% 170.47/26.28 (6) ~ (all_52_8 = e3)
% 170.47/26.28 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (8) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | BETA: splitting (8) gives:
% 170.47/26.28 |
% 170.47/26.28 | Case 1:
% 170.47/26.28 | |
% 170.47/26.28 | | (9) all_54_2 = e3
% 170.47/26.28 | |
% 170.47/26.28 | | COMBINE_EQS: (1), (9) imply:
% 170.47/26.28 | | (10) all_52_8 = e3
% 170.47/26.28 | |
% 170.47/26.28 | | REDUCE: (6), (10) imply:
% 170.47/26.28 | | (11) $false
% 170.47/26.28 | |
% 170.47/26.28 | | CLOSE: (11) is inconsistent.
% 170.47/26.28 | |
% 170.47/26.28 | Case 2:
% 170.47/26.28 | |
% 170.47/26.28 | | (12) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 170.47/26.28 | |
% 170.47/26.28 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (12) are inconsistent by sub-proof
% 170.47/26.28 | | #568.
% 170.47/26.28 | |
% 170.47/26.28 | End of split
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #568 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 170.47/26.28 (2) all_54_2 = all_52_8
% 170.47/26.28 (3) op(e3, e1) = all_52_8
% 170.47/26.28 (4) ~ (all_52_8 = e1)
% 170.47/26.28 (5) op(e3, e1) = e1
% 170.47/26.28 (6) ~ (all_52_8 = e2)
% 170.47/26.28 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | BETA: splitting (1) gives:
% 170.47/26.28 |
% 170.47/26.28 | Case 1:
% 170.47/26.28 | |
% 170.47/26.28 | | (8) all_54_2 = e2
% 170.47/26.28 | |
% 170.47/26.28 | | COMBINE_EQS: (2), (8) imply:
% 170.47/26.28 | | (9) all_52_8 = e2
% 170.47/26.28 | |
% 170.47/26.28 | | REDUCE: (6), (9) imply:
% 170.47/26.28 | | (10) $false
% 170.47/26.28 | |
% 170.47/26.28 | | CLOSE: (10) is inconsistent.
% 170.47/26.28 | |
% 170.47/26.28 | Case 2:
% 170.47/26.28 | |
% 170.47/26.28 | | (11) all_54_2 = e1 | all_54_2 = e0
% 170.47/26.28 | |
% 170.47/26.28 | | BETA: splitting (11) gives:
% 170.47/26.28 | |
% 170.47/26.28 | | Case 1:
% 170.47/26.28 | | |
% 170.47/26.28 | | | (12) all_54_2 = e1
% 170.47/26.28 | | |
% 170.47/26.28 | | | COMBINE_EQS: (2), (12) imply:
% 170.47/26.28 | | | (13) all_52_8 = e1
% 170.47/26.28 | | |
% 170.47/26.28 | | | REDUCE: (4), (13) imply:
% 170.47/26.28 | | | (14) $false
% 170.47/26.28 | | |
% 170.47/26.28 | | | CLOSE: (14) is inconsistent.
% 170.47/26.28 | | |
% 170.47/26.28 | | Case 2:
% 170.47/26.28 | | |
% 170.47/26.28 | | | (15) all_54_2 = e0
% 170.47/26.28 | | |
% 170.47/26.28 | | | COMBINE_EQS: (2), (15) imply:
% 170.47/26.28 | | | (16) all_52_8 = e0
% 170.47/26.28 | | |
% 170.47/26.28 | | | REDUCE: (4), (16) imply:
% 170.47/26.28 | | | (17) ~ (e1 = e0)
% 170.47/26.28 | | |
% 170.47/26.28 | | | SIMP: (17) implies:
% 170.47/26.28 | | | (18) ~ (e1 = e0)
% 170.47/26.28 | | |
% 170.47/26.28 | | | REDUCE: (3), (16) imply:
% 170.47/26.28 | | | (19) op(e3, e1) = e0
% 170.47/26.28 | | |
% 170.47/26.28 | | | REF_CLOSE: (5), (7), (18), (19) are inconsistent by sub-proof #569.
% 170.47/26.28 | | |
% 170.47/26.28 | | End of split
% 170.47/26.28 | |
% 170.47/26.28 | End of split
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #569 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (2) op(e3, e1) = e1
% 170.47/26.28 (3) op(e3, e1) = e0
% 170.47/26.28 (4) ~ (e1 = e0)
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | GROUND_INST: instantiating (1) with e0, e1, e1, e3, simplifying with (2), (3)
% 170.47/26.28 | gives:
% 170.47/26.28 | (5) e1 = e0
% 170.47/26.28 |
% 170.47/26.28 | REDUCE: (4), (5) imply:
% 170.47/26.28 | (6) $false
% 170.47/26.28 |
% 170.47/26.28 | CLOSE: (6) is inconsistent.
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #570 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) op(e2, e1) = all_52_9
% 170.47/26.28 (2) op(e3, e1) = all_52_8
% 170.47/26.28 (3) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2)
% 170.47/26.28 (4) ~ (all_52_8 = e2)
% 170.47/26.28 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (6) ~ (all_52_9 = e2)
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | BETA: splitting (3) gives:
% 170.47/26.28 |
% 170.47/26.28 | Case 1:
% 170.47/26.28 | |
% 170.47/26.28 | | (7) all_58_4 = e2 & op(e3, e1) = e2
% 170.47/26.28 | |
% 170.47/26.28 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #572.
% 170.47/26.28 | |
% 170.47/26.28 | Case 2:
% 170.47/26.28 | |
% 170.47/26.28 | | (8) all_58_5 = e2 & op(e2, e1) = e2
% 170.47/26.28 | |
% 170.47/26.28 | | ALPHA: (8) implies:
% 170.47/26.28 | | (9) op(e2, e1) = e2
% 170.47/26.28 | |
% 170.47/26.28 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #571.
% 170.47/26.28 | |
% 170.47/26.28 | End of split
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #571 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (2) op(e2, e1) = all_52_9
% 170.47/26.28 (3) op(e2, e1) = e2
% 170.47/26.28 (4) ~ (all_52_9 = e2)
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | GROUND_INST: instantiating (1) with all_52_9, e2, e1, e2, simplifying with
% 170.47/26.28 | (2), (3) gives:
% 170.47/26.28 | (5) all_52_9 = e2
% 170.47/26.28 |
% 170.47/26.28 | REDUCE: (4), (5) imply:
% 170.47/26.28 | (6) $false
% 170.47/26.28 |
% 170.47/26.28 | CLOSE: (6) is inconsistent.
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #572 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) all_58_4 = e2 & op(e3, e1) = e2
% 170.47/26.28 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (3) op(e3, e1) = all_52_8
% 170.47/26.28 (4) ~ (all_52_8 = e2)
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | ALPHA: (1) implies:
% 170.47/26.28 | (5) op(e3, e1) = e2
% 170.47/26.28 |
% 170.47/26.28 | GROUND_INST: instantiating (2) with all_52_8, e2, e1, e3, simplifying with
% 170.47/26.28 | (3), (5) gives:
% 170.47/26.28 | (6) all_52_8 = e2
% 170.47/26.28 |
% 170.47/26.28 | REDUCE: (4), (6) imply:
% 170.47/26.28 | (7) $false
% 170.47/26.28 |
% 170.47/26.28 | CLOSE: (7) is inconsistent.
% 170.47/26.28 |
% 170.47/26.28 End of proof
% 170.47/26.28
% 170.47/26.28 Sub-proof #573 shows that the following formulas are inconsistent:
% 170.47/26.28 ----------------------------------------------------------------
% 170.47/26.28 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.47/26.28 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.47/26.28 (2) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.47/26.28 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.47/26.28 (3) ~ (e3 = e1)
% 170.47/26.28 (4) ~ (e1 = e0)
% 170.47/26.28 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.28 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.28 (6) op(e1, e2) = all_52_6
% 170.47/26.28 (7) ~ (all_6_2 = e2)
% 170.47/26.28 (8) op(e1, e1) = all_6_2
% 170.47/26.28 (9) ~ (all_52_6 = e2)
% 170.47/26.28 (10) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.47/26.28 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.47/26.28 (11) ~ (e3 = e0)
% 170.47/26.28 (12) all_58_12 = e2 & op(e0, e3) = e2
% 170.47/26.28 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.28 (14) ~ (e2 = e0)
% 170.47/26.28 (15) op(e1, e0) = all_52_14
% 170.47/26.28 (16) ~ (all_52_14 = e2)
% 170.47/26.28 (17) ~ (e2 = e1)
% 170.47/26.28 (18) ~ (e3 = e2)
% 170.47/26.28
% 170.47/26.28 Begin of proof
% 170.47/26.28 |
% 170.47/26.28 | ALPHA: (12) implies:
% 170.47/26.28 | (19) all_58_12 = e2
% 170.47/26.28 |
% 170.47/26.28 | BETA: splitting (2) gives:
% 170.47/26.28 |
% 170.47/26.28 | Case 1:
% 170.47/26.28 | |
% 170.47/26.28 | | (20) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 170.47/26.28 | | e2)
% 170.47/26.28 | |
% 170.47/26.28 | | BETA: splitting (20) gives:
% 170.47/26.28 | |
% 170.47/26.28 | | Case 1:
% 170.47/26.28 | | |
% 170.47/26.28 | | | (21) all_58_6 = e2 & op(e1, e3) = e2
% 170.47/26.28 | | |
% 170.47/26.28 | | | ALPHA: (21) implies:
% 170.47/26.28 | | | (22) all_58_6 = e2
% 170.47/26.28 | | |
% 170.47/26.28 | | | REF_CLOSE: (1), (3), (4), (5), (10), (11), (13), (14), (17), (18), (19),
% 170.47/26.28 | | | (22) are inconsistent by sub-proof #574.
% 170.47/26.28 | | |
% 170.47/26.28 | | Case 2:
% 170.47/26.28 | | |
% 170.47/26.28 | | | (23) all_58_7 = e2 & op(e1, e2) = e2
% 170.47/26.28 | | |
% 170.47/26.28 | | | ALPHA: (23) implies:
% 170.47/26.28 | | | (24) op(e1, e2) = e2
% 170.47/26.28 | | |
% 170.47/26.28 | | | REF_CLOSE: (6), (9), (13), (24) are inconsistent by sub-proof #986.
% 170.47/26.28 | | |
% 170.47/26.28 | | End of split
% 170.47/26.28 | |
% 170.47/26.28 | Case 2:
% 170.47/26.28 | |
% 170.47/26.28 | | (25) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 170.47/26.28 | | e2)
% 170.47/26.28 | |
% 170.47/26.28 | | BETA: splitting (25) gives:
% 170.47/26.28 | |
% 170.47/26.28 | | Case 1:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (26) all_58_8 = e2 & op(e1, e1) = e2
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (7), (8), (13), (26) are inconsistent by sub-proof #845.
% 170.47/26.29 | | |
% 170.47/26.29 | | Case 2:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (27) all_58_11 = e2 & op(e1, e0) = e2
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (13), (15), (16), (27) are inconsistent by sub-proof #660.
% 170.47/26.29 | | |
% 170.47/26.29 | | End of split
% 170.47/26.29 | |
% 170.47/26.29 | End of split
% 170.47/26.29 |
% 170.47/26.29 End of proof
% 170.47/26.29
% 170.47/26.29 Sub-proof #574 shows that the following formulas are inconsistent:
% 170.47/26.29 ----------------------------------------------------------------
% 170.47/26.29 (1) all_58_12 = e2
% 170.47/26.29 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.47/26.29 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.47/26.29 (3) ~ (e3 = e1)
% 170.47/26.29 (4) ~ (e1 = e0)
% 170.47/26.29 (5) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.29 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.29 (6) all_58_6 = e2
% 170.47/26.29 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.47/26.29 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.47/26.29 (8) ~ (e3 = e0)
% 170.47/26.29 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.29 (10) ~ (e2 = e0)
% 170.47/26.29 (11) ~ (e2 = e1)
% 170.47/26.29 (12) ~ (e3 = e2)
% 170.47/26.29
% 170.47/26.29 Begin of proof
% 170.47/26.29 |
% 170.47/26.29 | BETA: splitting (2) gives:
% 170.47/26.29 |
% 170.47/26.29 | Case 1:
% 170.47/26.29 | |
% 170.47/26.29 | | (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 170.47/26.29 | | e0)
% 170.47/26.29 | |
% 170.47/26.29 | | BETA: splitting (13) gives:
% 170.47/26.29 | |
% 170.47/26.29 | | Case 1:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (14) all_58_0 = e0 & op(e3, e3) = e0
% 170.47/26.29 | | |
% 170.47/26.29 | | | ALPHA: (14) implies:
% 170.47/26.29 | | | (15) op(e3, e3) = e0
% 170.47/26.29 | | |
% 170.47/26.29 | | | BETA: splitting (5) gives:
% 170.47/26.29 | | |
% 170.47/26.29 | | | Case 1:
% 170.47/26.29 | | | |
% 170.47/26.29 | | | | (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 170.47/26.29 | | | | = e3)
% 170.47/26.29 | | | |
% 170.47/26.29 | | | | BETA: splitting (16) gives:
% 170.47/26.29 | | | |
% 170.47/26.29 | | | | Case 1:
% 170.47/26.29 | | | | |
% 170.47/26.29 | | | | | (17) all_58_0 = e3 & op(e3, e3) = e3
% 170.47/26.29 | | | | |
% 170.47/26.29 | | | | | ALPHA: (17) implies:
% 170.47/26.29 | | | | | (18) all_58_0 = e3
% 170.47/26.29 | | | | |
% 170.47/26.29 | | | | | BETA: splitting (2) gives:
% 170.47/26.29 | | | | |
% 170.47/26.29 | | | | | Case 1:
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | BETA: splitting (13) gives:
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | Case 1:
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | REF_CLOSE: (8), (14), (18) are inconsistent by sub-proof #898.
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | Case 2:
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | (19) all_58_2 = e0 & op(e2, e3) = e0
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | ALPHA: (19) implies:
% 170.47/26.29 | | | | | | | (20) all_58_2 = e0
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (11), (18), (20) are
% 170.47/26.29 | | | | | | | inconsistent by sub-proof #577.
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | End of split
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | Case 2:
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0,
% 170.47/26.29 | | | | | | e3) = e0)
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | BETA: splitting (21) gives:
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | Case 1:
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | (22) all_58_6 = e0 & op(e1, e3) = e0
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | REF_CLOSE: (6), (10), (22) are inconsistent by sub-proof #769.
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | Case 2:
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | (23) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | REF_CLOSE: (1), (10), (23) are inconsistent by sub-proof #886.
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | End of split
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | End of split
% 170.47/26.29 | | | | |
% 170.47/26.29 | | | | Case 2:
% 170.47/26.29 | | | | |
% 170.47/26.29 | | | | | (24) all_58_2 = e3 & op(e2, e3) = e3
% 170.47/26.29 | | | | |
% 170.47/26.29 | | | | | ALPHA: (24) implies:
% 170.47/26.29 | | | | | (25) all_58_2 = e3
% 170.47/26.29 | | | | |
% 170.47/26.29 | | | | | BETA: splitting (7) gives:
% 170.47/26.29 | | | | |
% 170.47/26.29 | | | | | Case 1:
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2,
% 170.47/26.29 | | | | | | e3) = e1)
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | BETA: splitting (26) gives:
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | Case 1:
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | (27) all_58_0 = e1 & op(e3, e3) = e1
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | ALPHA: (27) implies:
% 170.47/26.29 | | | | | | | (28) op(e3, e3) = e1
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | REF_CLOSE: (4), (9), (15), (28) are inconsistent by sub-proof
% 170.47/26.29 | | | | | | | #907.
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | Case 2:
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | (29) all_58_2 = e1 & op(e2, e3) = e1
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | ALPHA: (29) implies:
% 170.47/26.29 | | | | | | | (30) all_58_2 = e1
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | REF_CLOSE: (3), (25), (30) are inconsistent by sub-proof #938.
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | End of split
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | Case 2:
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | (31) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0,
% 170.47/26.29 | | | | | | e3) = e1)
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | BETA: splitting (31) gives:
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | | Case 1:
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | (32) all_58_6 = e1 & op(e1, e3) = e1
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | ALPHA: (32) implies:
% 170.47/26.29 | | | | | | | (33) all_58_6 = e1
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | REF_CLOSE: (6), (11), (33) are inconsistent by sub-proof #823.
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | Case 2:
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | (34) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | | REF_CLOSE: (1), (11), (34) are inconsistent by sub-proof #891.
% 170.47/26.29 | | | | | | |
% 170.47/26.29 | | | | | | End of split
% 170.47/26.29 | | | | | |
% 170.47/26.29 | | | | | End of split
% 170.47/26.29 | | | | |
% 170.47/26.29 | | | | End of split
% 170.47/26.29 | | | |
% 170.47/26.29 | | | Case 2:
% 170.47/26.29 | | | |
% 170.47/26.29 | | | | (35) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 170.47/26.29 | | | | = e3)
% 170.47/26.29 | | | |
% 170.47/26.29 | | | | REF_CLOSE: (1), (6), (12), (35) are inconsistent by sub-proof #576.
% 170.47/26.29 | | | |
% 170.47/26.29 | | | End of split
% 170.47/26.29 | | |
% 170.47/26.29 | | Case 2:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (36) all_58_2 = e0 & op(e2, e3) = e0
% 170.47/26.29 | | |
% 170.47/26.29 | | | ALPHA: (36) implies:
% 170.47/26.29 | | | (37) all_58_2 = e0
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (11), (12), (37) are
% 170.47/26.29 | | | inconsistent by sub-proof #575.
% 170.47/26.29 | | |
% 170.47/26.29 | | End of split
% 170.47/26.29 | |
% 170.47/26.29 | Case 2:
% 170.47/26.29 | |
% 170.47/26.29 | | (38) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 170.47/26.29 | | e0)
% 170.47/26.29 | |
% 170.47/26.29 | | BETA: splitting (38) gives:
% 170.47/26.29 | |
% 170.47/26.29 | | Case 1:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (39) all_58_6 = e0 & op(e1, e3) = e0
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (6), (10), (39) are inconsistent by sub-proof #769.
% 170.47/26.29 | | |
% 170.47/26.29 | | Case 2:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (40) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.29 | | |
% 170.47/26.29 | | | ALPHA: (40) implies:
% 170.47/26.29 | | | (41) all_58_12 = e0
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (1), (10), (41) are inconsistent by sub-proof #729.
% 170.47/26.29 | | |
% 170.47/26.29 | | End of split
% 170.47/26.29 | |
% 170.47/26.29 | End of split
% 170.47/26.29 |
% 170.47/26.29 End of proof
% 170.47/26.29
% 170.47/26.29 Sub-proof #575 shows that the following formulas are inconsistent:
% 170.47/26.29 ----------------------------------------------------------------
% 170.47/26.29 (1) all_58_12 = e2
% 170.47/26.29 (2) ~ (e3 = e1)
% 170.47/26.29 (3) ~ (e1 = e0)
% 170.47/26.29 (4) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.29 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.29 (5) all_58_6 = e2
% 170.47/26.29 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.47/26.29 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.47/26.29 (7) ~ (e3 = e0)
% 170.47/26.29 (8) ~ (e2 = e1)
% 170.47/26.29 (9) all_58_2 = e0
% 170.47/26.29 (10) ~ (e3 = e2)
% 170.47/26.29
% 170.47/26.29 Begin of proof
% 170.47/26.29 |
% 170.47/26.29 | BETA: splitting (4) gives:
% 170.47/26.29 |
% 170.47/26.29 | Case 1:
% 170.47/26.29 | |
% 170.47/26.29 | | (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 170.47/26.29 | | e3)
% 170.47/26.29 | |
% 170.47/26.29 | | BETA: splitting (11) gives:
% 170.47/26.29 | |
% 170.47/26.29 | | Case 1:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (12) all_58_0 = e3 & op(e3, e3) = e3
% 170.47/26.29 | | |
% 170.47/26.29 | | | ALPHA: (12) implies:
% 170.47/26.29 | | | (13) all_58_0 = e3
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (13) are inconsistent by
% 170.47/26.29 | | | sub-proof #577.
% 170.47/26.29 | | |
% 170.47/26.29 | | Case 2:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (14) all_58_2 = e3 & op(e2, e3) = e3
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (7), (9), (14) are inconsistent by sub-proof #744.
% 170.47/26.29 | | |
% 170.47/26.29 | | End of split
% 170.47/26.29 | |
% 170.47/26.29 | Case 2:
% 170.47/26.29 | |
% 170.47/26.29 | | (15) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 170.47/26.29 | | e3)
% 170.47/26.29 | |
% 170.47/26.29 | | REF_CLOSE: (1), (5), (10), (15) are inconsistent by sub-proof #576.
% 170.47/26.29 | |
% 170.47/26.29 | End of split
% 170.47/26.29 |
% 170.47/26.29 End of proof
% 170.47/26.29
% 170.47/26.29 Sub-proof #576 shows that the following formulas are inconsistent:
% 170.47/26.29 ----------------------------------------------------------------
% 170.47/26.29 (1) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.29 (2) all_58_6 = e2
% 170.47/26.29 (3) ~ (e3 = e2)
% 170.47/26.29 (4) all_58_12 = e2
% 170.47/26.29
% 170.47/26.29 Begin of proof
% 170.47/26.29 |
% 170.47/26.29 | BETA: splitting (1) gives:
% 170.47/26.29 |
% 170.47/26.29 | Case 1:
% 170.47/26.29 | |
% 170.47/26.29 | | (5) all_58_6 = e3 & op(e1, e3) = e3
% 170.47/26.29 | |
% 170.47/26.29 | | ALPHA: (5) implies:
% 170.47/26.29 | | (6) all_58_6 = e3
% 170.47/26.29 | |
% 170.47/26.29 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #822.
% 170.47/26.29 | |
% 170.47/26.29 | Case 2:
% 170.47/26.29 | |
% 170.47/26.29 | | (7) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.29 | |
% 170.47/26.29 | | ALPHA: (7) implies:
% 170.47/26.29 | | (8) all_58_12 = e3
% 170.47/26.29 | |
% 170.47/26.29 | | COMBINE_EQS: (4), (8) imply:
% 170.47/26.29 | | (9) e3 = e2
% 170.47/26.29 | |
% 170.47/26.29 | | REDUCE: (3), (9) imply:
% 170.47/26.29 | | (10) $false
% 170.47/26.29 | |
% 170.47/26.29 | | CLOSE: (10) is inconsistent.
% 170.47/26.29 | |
% 170.47/26.29 | End of split
% 170.47/26.29 |
% 170.47/26.29 End of proof
% 170.47/26.29
% 170.47/26.29 Sub-proof #577 shows that the following formulas are inconsistent:
% 170.47/26.29 ----------------------------------------------------------------
% 170.47/26.29 (1) all_58_12 = e2
% 170.47/26.29 (2) ~ (e3 = e1)
% 170.47/26.29 (3) ~ (e1 = e0)
% 170.47/26.29 (4) all_58_6 = e2
% 170.47/26.29 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.47/26.29 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.47/26.29 (6) all_58_0 = e3
% 170.47/26.29 (7) ~ (e2 = e1)
% 170.47/26.29 (8) all_58_2 = e0
% 170.47/26.29
% 170.47/26.29 Begin of proof
% 170.47/26.29 |
% 170.47/26.29 | BETA: splitting (5) gives:
% 170.47/26.29 |
% 170.47/26.29 | Case 1:
% 170.47/26.29 | |
% 170.47/26.29 | | (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 170.47/26.29 | |
% 170.47/26.29 | | REF_CLOSE: (2), (3), (6), (8), (9) are inconsistent by sub-proof #775.
% 170.47/26.29 | |
% 170.47/26.29 | Case 2:
% 170.47/26.29 | |
% 170.47/26.29 | | (10) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 170.47/26.29 | | e1)
% 170.47/26.29 | |
% 170.47/26.29 | | BETA: splitting (10) gives:
% 170.47/26.29 | |
% 170.47/26.29 | | Case 1:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (11) all_58_6 = e1 & op(e1, e3) = e1
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (4), (7), (11) are inconsistent by sub-proof #774.
% 170.47/26.29 | | |
% 170.47/26.29 | | Case 2:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (12) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (1), (7), (12) are inconsistent by sub-proof #891.
% 170.47/26.29 | | |
% 170.47/26.29 | | End of split
% 170.47/26.29 | |
% 170.47/26.29 | End of split
% 170.47/26.29 |
% 170.47/26.29 End of proof
% 170.47/26.29
% 170.47/26.29 Sub-proof #578 shows that the following formulas are inconsistent:
% 170.47/26.29 ----------------------------------------------------------------
% 170.47/26.29 (1) op(e2, e1) = all_52_9
% 170.47/26.29 (2) op(e0, e1) = all_52_11
% 170.47/26.29 (3) ~ (all_52_9 = e3)
% 170.47/26.29 (4) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.29 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.29 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.29 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.29 (6) all_58_0 = e1
% 170.47/26.29 (7) ~ (all_8_2 = e3)
% 170.47/26.29 (8) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.29 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.29 (9) ~ (e3 = e1)
% 170.47/26.29 (10) all_58_13 = e0 & op(e0, e2) = e0
% 170.47/26.29 (11) ~ (e1 = e0)
% 170.47/26.29 (12) all_58_8 = e0
% 170.47/26.29 (13) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.47/26.29 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.47/26.29 (14) op(e2, e2) = all_8_2
% 170.47/26.29 (15) ~ (e3 = e0)
% 170.47/26.29 (16) all_58_1 = e3
% 170.47/26.29 (17) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.29 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.29 (18) all_58_3 = e2
% 170.47/26.29 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.29 (20) ~ (e2 = e0)
% 170.47/26.29 (21) ~ (e2 = e1)
% 170.47/26.29 (22) ~ (all_52_11 = e3)
% 170.47/26.29 (23) op(e0, e2) = all_52_7
% 170.47/26.29 (24) all_58_4 = e2
% 170.47/26.29 (25) ~ (e3 = e2)
% 170.47/26.29
% 170.47/26.29 Begin of proof
% 170.47/26.29 |
% 170.47/26.29 | ALPHA: (10) implies:
% 170.47/26.29 | (26) all_58_13 = e0
% 170.47/26.29 | (27) op(e0, e2) = e0
% 170.47/26.29 |
% 170.47/26.29 | BETA: splitting (13) gives:
% 170.47/26.29 |
% 170.47/26.29 | Case 1:
% 170.47/26.29 | |
% 170.47/26.29 | | (28) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 170.47/26.29 | | e3)
% 170.47/26.29 | |
% 170.47/26.29 | | REF_CLOSE: (1), (3), (6), (8), (9), (11), (15), (16), (17), (19), (20),
% 170.47/26.29 | | (24), (25), (28) are inconsistent by sub-proof #579.
% 170.47/26.29 | |
% 170.47/26.29 | Case 2:
% 170.47/26.29 | |
% 170.47/26.29 | | (29) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 170.47/26.29 | | e3)
% 170.47/26.29 | |
% 170.47/26.29 | | BETA: splitting (29) gives:
% 170.47/26.29 | |
% 170.47/26.29 | | Case 1:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (30) all_58_8 = e3 & op(e1, e1) = e3
% 170.47/26.29 | | |
% 170.47/26.29 | | | ALPHA: (30) implies:
% 170.47/26.29 | | | (31) all_58_8 = e3
% 170.47/26.29 | | |
% 170.47/26.29 | | | COMBINE_EQS: (12), (31) imply:
% 170.47/26.29 | | | (32) e3 = e0
% 170.47/26.29 | | |
% 170.47/26.29 | | | SIMP: (32) implies:
% 170.47/26.29 | | | (33) e3 = e0
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (4), (5), (7), (9), (11), (14), (15), (16), (18), (19), (21),
% 170.47/26.29 | | | (23), (26), (27), (33) are inconsistent by sub-proof #590.
% 170.47/26.29 | | |
% 170.47/26.29 | | Case 2:
% 170.47/26.29 | | |
% 170.47/26.29 | | | (34) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.29 | | |
% 170.47/26.29 | | | REF_CLOSE: (2), (19), (22), (34) are inconsistent by sub-proof #960.
% 170.47/26.29 | | |
% 170.47/26.29 | | End of split
% 170.47/26.29 | |
% 170.47/26.29 | End of split
% 170.47/26.29 |
% 170.47/26.29 End of proof
% 170.47/26.29
% 170.47/26.29 Sub-proof #579 shows that the following formulas are inconsistent:
% 170.47/26.29 ----------------------------------------------------------------
% 170.47/26.29 (1) op(e2, e1) = all_52_9
% 170.47/26.29 (2) ~ (all_52_9 = e3)
% 170.47/26.29 (3) all_58_0 = e1
% 170.47/26.29 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.29 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.29 (5) ~ (e3 = e1)
% 170.47/26.29 (6) ~ (e1 = e0)
% 170.47/26.29 (7) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3)
% 170.47/26.29 (8) ~ (e3 = e0)
% 170.47/26.29 (9) all_58_1 = e3
% 170.47/26.29 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.29 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.29 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.29 (12) ~ (e2 = e0)
% 170.47/26.29 (13) all_58_4 = e2
% 170.47/26.29 (14) ~ (e3 = e2)
% 170.47/26.29
% 170.47/26.29 Begin of proof
% 170.47/26.29 |
% 170.47/26.29 | BETA: splitting (7) gives:
% 170.47/26.29 |
% 170.47/26.29 | Case 1:
% 170.47/26.29 | |
% 170.47/26.29 | | (15) all_58_4 = e3 & op(e3, e1) = e3
% 170.47/26.29 | |
% 170.47/26.29 | | ALPHA: (15) implies:
% 170.47/26.29 | | (16) all_58_4 = e3
% 170.47/26.29 | |
% 170.47/26.29 | | COMBINE_EQS: (13), (16) imply:
% 170.47/26.29 | | (17) e3 = e2
% 170.47/26.29 | |
% 170.47/26.29 | | SIMP: (17) implies:
% 170.47/26.29 | | (18) e3 = e2
% 170.47/26.29 | |
% 170.47/26.29 | | COMBINE_EQS: (9), (18) imply:
% 170.47/26.29 | | (19) all_58_1 = e2
% 170.47/26.29 | |
% 170.47/26.29 | | REF_CLOSE: (3), (4), (5), (6), (8), (10), (12), (13), (14), (19) are
% 170.47/26.29 | | inconsistent by sub-proof #900.
% 170.47/26.29 | |
% 170.47/26.29 | Case 2:
% 170.47/26.29 | |
% 170.47/26.29 | | (20) all_58_5 = e3 & op(e2, e1) = e3
% 170.47/26.29 | |
% 170.47/26.29 | | ALPHA: (20) implies:
% 170.47/26.29 | | (21) op(e2, e1) = e3
% 170.47/26.29 | |
% 170.47/26.29 | | REF_CLOSE: (1), (2), (11), (21) are inconsistent by sub-proof #951.
% 170.47/26.29 | |
% 170.47/26.29 | End of split
% 170.47/26.29 |
% 170.47/26.29 End of proof
% 170.47/26.29
% 170.47/26.29 Sub-proof #580 shows that the following formulas are inconsistent:
% 170.47/26.29 ----------------------------------------------------------------
% 170.47/26.29 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.29 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.29 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.47/26.29 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.29 (3) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.29 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.29 (4) all_54_12 = all_52_3
% 170.47/26.29 (5) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.29 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.29 (6) op(e0, e0) = e2
% 170.47/26.29 (7) all_58_0 = e1
% 170.47/26.29 (8) ~ (all_8_2 = e3)
% 170.47/26.29 (9) ~ (all_52_3 = e2)
% 170.47/26.29 (10) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.29 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.29 (11) ~ (all_52_3 = e1)
% 170.47/26.29 (12) ~ (e3 = e1)
% 170.47/26.29 (13) op(e3, e3) = e1
% 170.47/26.30 (14) ~ (all_52_1 = all_52_3)
% 170.47/26.30 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.30 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.30 e1)
% 170.47/26.30 (16) op(e3, e1) = all_52_8
% 170.47/26.30 (17) ~ (e1 = e0)
% 170.47/26.30 (18) all_58_14 = e1
% 170.47/26.30 (19) all_56_10 = e1
% 170.47/26.30 (20) all_58_10 = e3
% 170.47/26.30 (21) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.30 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.30 (22) op(e1, e2) = all_52_6
% 170.47/26.30 (23) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.47/26.30 | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.30 (24) op(e2, e3) = all_52_1
% 170.47/26.30 (25) op(e3, e1) = e3
% 170.47/26.30 (26) op(e0, e2) = e0
% 170.47/26.30 (27) op(e2, e2) = all_8_2
% 170.47/26.30 (28) all_58_6 = e2
% 170.47/26.30 (29) ~ (e3 = e0)
% 170.47/26.30 (30) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.30 (31) all_58_1 = e3
% 170.47/26.30 (32) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.30 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.30 (33) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.30 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.30 (34) all_58_3 = e2
% 170.47/26.30 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.30 (36) ~ (e2 = e0)
% 170.47/26.30 (37) all_58_12 = e3
% 170.47/26.30 (38) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.47/26.30 (39) ~ (e2 = e1)
% 170.47/26.30 (40) all_58_7 = e0 & op(e1, e2) = e0
% 170.47/26.30 (41) op(e3, e2) = all_52_4
% 170.47/26.30 (42) ~ (all_52_3 = e0)
% 170.47/26.30 (43) ~ (all_52_6 = e3)
% 170.47/26.30 (44) op(e0, e2) = all_52_7
% 170.47/26.30 (45) ~ (all_52_4 = e1)
% 170.47/26.30 (46) all_58_4 = e2
% 170.47/26.30 (47) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.30 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.30 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.30 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.30 (48) op(e3, e1) = e2
% 170.47/26.30 (49) ~ (e3 = e2)
% 170.47/26.30
% 170.47/26.30 Begin of proof
% 170.47/26.30 |
% 170.47/26.30 | ALPHA: (40) implies:
% 170.47/26.30 | (50) all_58_7 = e0
% 170.47/26.30 |
% 170.47/26.30 | BETA: splitting (2) gives:
% 170.47/26.30 |
% 170.47/26.30 | Case 1:
% 170.47/26.30 | |
% 170.47/26.30 | | (51) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 170.47/26.30 | | e1)
% 170.47/26.30 | |
% 170.47/26.30 | | REF_CLOSE: (4), (9), (10), (11), (12), (13), (14), (16), (17), (19), (20),
% 170.47/26.30 | | (21), (24), (28), (29), (30), (31), (32), (33), (35), (36), (37),
% 170.47/26.30 | | (38), (39), (42), (46), (48), (49), (51) are inconsistent by
% 170.47/26.30 | | sub-proof #587.
% 170.47/26.30 | |
% 170.47/26.30 | Case 2:
% 170.47/26.30 | |
% 170.47/26.30 | | (52) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.30 | | e1)
% 170.47/26.30 | |
% 170.47/26.30 | | BETA: splitting (52) gives:
% 170.47/26.30 | |
% 170.47/26.30 | | Case 1:
% 170.47/26.30 | | |
% 170.47/26.30 | | | (53) all_58_11 = e1 & op(e1, e0) = e1
% 170.47/26.30 | | |
% 170.47/26.30 | | | ALPHA: (53) implies:
% 170.47/26.30 | | | (54) all_58_11 = e1
% 170.47/26.30 | | |
% 170.47/26.30 | | | BETA: splitting (5) gives:
% 170.47/26.30 | | |
% 170.47/26.30 | | | Case 1:
% 170.47/26.30 | | | |
% 170.47/26.30 | | | | (55) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 170.47/26.30 | | | | = e1)
% 170.47/26.30 | | | |
% 170.47/26.30 | | | | BETA: splitting (55) gives:
% 170.47/26.30 | | | |
% 170.47/26.30 | | | | Case 1:
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | (56) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | REF_CLOSE: (35), (41), (45), (56) are inconsistent by sub-proof #863.
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | Case 2:
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | (57) all_58_3 = e1 & op(e2, e2) = e1
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | REF_CLOSE: (34), (39), (57) are inconsistent by sub-proof #914.
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | End of split
% 170.47/26.30 | | | |
% 170.47/26.30 | | | Case 2:
% 170.47/26.30 | | | |
% 170.47/26.30 | | | | (58) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 170.47/26.30 | | | | = e1)
% 170.47/26.30 | | | |
% 170.47/26.30 | | | | BETA: splitting (58) gives:
% 170.47/26.30 | | | |
% 170.47/26.30 | | | | Case 1:
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | (59) all_58_7 = e1 & op(e1, e2) = e1
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | ALPHA: (59) implies:
% 170.47/26.30 | | | | | (60) all_58_7 = e1
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | COMBINE_EQS: (50), (60) imply:
% 170.47/26.30 | | | | | (61) e1 = e0
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | SIMP: (61) implies:
% 170.47/26.30 | | | | | (62) e1 = e0
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | COMBINE_EQS: (54), (62) imply:
% 170.47/26.30 | | | | | (63) all_58_11 = e0
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12),
% 170.47/26.30 | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 170.47/26.30 | | | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 170.47/26.30 | | | | | (35), (36), (37), (38), (39), (42), (43), (44), (46), (47),
% 170.47/26.30 | | | | | (48), (49), (63) are inconsistent by sub-proof #583.
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | Case 2:
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | (64) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | ALPHA: (64) implies:
% 170.47/26.30 | | | | | (65) all_58_13 = e1
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | | REF_CLOSE: (17), (18), (23), (29), (37), (65) are inconsistent by
% 170.47/26.30 | | | | | sub-proof #581.
% 170.47/26.30 | | | | |
% 170.47/26.30 | | | | End of split
% 170.47/26.30 | | | |
% 170.47/26.30 | | | End of split
% 170.47/26.30 | | |
% 170.47/26.30 | | Case 2:
% 170.47/26.30 | | |
% 170.47/26.30 | | | (66) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.30 | | |
% 170.47/26.30 | | | ALPHA: (66) implies:
% 170.47/26.30 | | | (67) op(e0, e0) = e1
% 170.47/26.30 | | |
% 170.47/26.30 | | | REF_CLOSE: (6), (35), (39), (67) are inconsistent by sub-proof #640.
% 170.47/26.30 | | |
% 170.47/26.30 | | End of split
% 170.47/26.30 | |
% 170.47/26.30 | End of split
% 170.47/26.30 |
% 170.47/26.30 End of proof
% 170.47/26.30
% 170.47/26.30 Sub-proof #581 shows that the following formulas are inconsistent:
% 170.47/26.30 ----------------------------------------------------------------
% 170.47/26.30 (1) ~ (e1 = e0)
% 170.47/26.30 (2) all_58_14 = e1
% 170.47/26.30 (3) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 170.47/26.30 (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.30 (4) ~ (e3 = e0)
% 170.47/26.30 (5) all_58_13 = e1
% 170.47/26.30 (6) all_58_12 = e3
% 170.47/26.30
% 170.47/26.30 Begin of proof
% 170.47/26.30 |
% 170.47/26.30 | BETA: splitting (3) gives:
% 170.47/26.30 |
% 170.47/26.30 | Case 1:
% 170.47/26.30 | |
% 170.47/26.30 | | (7) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.30 | |
% 170.47/26.30 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #646.
% 170.47/26.30 | |
% 170.47/26.30 | Case 2:
% 170.47/26.30 | |
% 170.47/26.30 | | (8) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 170.47/26.30 | | e0)
% 170.47/26.30 | |
% 170.47/26.30 | | BETA: splitting (8) gives:
% 170.47/26.30 | |
% 170.47/26.30 | | Case 1:
% 170.47/26.30 | | |
% 170.47/26.30 | | | (9) all_58_13 = e0 & op(e0, e2) = e0
% 170.47/26.30 | | |
% 170.47/26.30 | | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #582.
% 170.47/26.30 | | |
% 170.47/26.30 | | Case 2:
% 170.47/26.30 | | |
% 170.47/26.30 | | | (10) all_58_14 = e0 & op(e0, e1) = e0
% 170.47/26.30 | | |
% 170.47/26.30 | | | ALPHA: (10) implies:
% 170.47/26.30 | | | (11) all_58_14 = e0
% 170.47/26.30 | | |
% 170.47/26.30 | | | REF_CLOSE: (1), (2), (11) are inconsistent by sub-proof #586.
% 170.47/26.30 | | |
% 170.47/26.30 | | End of split
% 170.47/26.30 | |
% 170.47/26.30 | End of split
% 170.47/26.30 |
% 170.47/26.30 End of proof
% 170.47/26.30
% 170.47/26.30 Sub-proof #582 shows that the following formulas are inconsistent:
% 170.47/26.30 ----------------------------------------------------------------
% 170.47/26.30 (1) all_58_13 = e0 & op(e0, e2) = e0
% 170.47/26.30 (2) all_58_13 = e1
% 170.47/26.30 (3) ~ (e1 = e0)
% 170.47/26.30
% 170.47/26.30 Begin of proof
% 170.47/26.30 |
% 170.47/26.30 | ALPHA: (1) implies:
% 170.47/26.30 | (4) all_58_13 = e0
% 170.47/26.30 |
% 170.47/26.30 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.30 | (5) e1 = e0
% 170.47/26.30 |
% 170.47/26.30 | REDUCE: (3), (5) imply:
% 170.47/26.30 | (6) $false
% 170.47/26.30 |
% 170.47/26.30 | CLOSE: (6) is inconsistent.
% 170.47/26.30 |
% 170.47/26.30 End of proof
% 170.47/26.30
% 170.47/26.30 Sub-proof #583 shows that the following formulas are inconsistent:
% 170.47/26.30 ----------------------------------------------------------------
% 170.47/26.30 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.30 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.30 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.47/26.30 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.30 (3) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.30 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.30 (4) all_54_12 = all_52_3
% 170.47/26.30 (5) op(e0, e0) = e2
% 170.47/26.30 (6) all_58_0 = e1
% 170.47/26.30 (7) ~ (all_8_2 = e3)
% 170.47/26.30 (8) ~ (all_52_3 = e2)
% 170.47/26.30 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.30 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.30 (10) ~ (all_52_3 = e1)
% 170.47/26.30 (11) ~ (e3 = e1)
% 170.47/26.30 (12) op(e3, e3) = e1
% 170.47/26.30 (13) ~ (all_52_1 = all_52_3)
% 170.47/26.30 (14) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.30 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.30 e1)
% 170.47/26.30 (15) op(e3, e1) = all_52_8
% 170.47/26.30 (16) ~ (e1 = e0)
% 170.47/26.30 (17) all_58_14 = e1
% 170.47/26.30 (18) all_56_10 = e1
% 170.47/26.30 (19) all_58_10 = e3
% 170.47/26.30 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.30 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.30 (21) op(e1, e2) = all_52_6
% 170.47/26.30 (22) op(e2, e3) = all_52_1
% 170.47/26.30 (23) op(e3, e1) = e3
% 170.47/26.30 (24) all_58_11 = e0
% 170.47/26.30 (25) op(e0, e2) = e0
% 170.47/26.30 (26) op(e2, e2) = all_8_2
% 170.47/26.30 (27) all_58_6 = e2
% 170.47/26.30 (28) ~ (e3 = e0)
% 170.47/26.30 (29) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.30 (30) all_58_1 = e3
% 170.47/26.30 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.30 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.30 (32) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.30 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.30 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.30 (34) ~ (e2 = e0)
% 170.47/26.30 (35) all_58_12 = e3
% 170.47/26.30 (36) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.47/26.30 (37) ~ (e2 = e1)
% 170.47/26.30 (38) ~ (all_52_3 = e0)
% 170.47/26.30 (39) ~ (all_52_6 = e3)
% 170.47/26.30 (40) op(e0, e2) = all_52_7
% 170.47/26.30 (41) all_58_4 = e2
% 170.47/26.30 (42) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.30 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.30 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.30 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.30 (43) op(e3, e1) = e2
% 170.47/26.30 (44) ~ (e3 = e2)
% 170.47/26.30
% 170.47/26.30 Begin of proof
% 170.47/26.30 |
% 170.47/26.30 | BETA: splitting (2) gives:
% 170.47/26.30 |
% 170.47/26.30 | Case 1:
% 170.47/26.30 | |
% 170.47/26.30 | | (45) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 170.47/26.30 | | e1)
% 170.47/26.30 | |
% 170.47/26.30 | | REF_CLOSE: (4), (8), (9), (10), (11), (12), (13), (15), (16), (18), (19),
% 170.47/26.30 | | (20), (22), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 170.47/26.30 | | (36), (37), (38), (41), (43), (44), (45) are inconsistent by
% 170.47/26.30 | | sub-proof #587.
% 170.47/26.30 | |
% 170.47/26.30 | Case 2:
% 170.47/26.30 | |
% 170.47/26.30 | | (46) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.30 | | e1)
% 170.47/26.30 | |
% 170.47/26.30 | | BETA: splitting (46) gives:
% 170.47/26.30 | |
% 170.47/26.30 | | Case 1:
% 170.47/26.30 | | |
% 170.47/26.30 | | | (47) all_58_11 = e1 & op(e1, e0) = e1
% 170.47/26.30 | | |
% 170.47/26.30 | | | ALPHA: (47) implies:
% 170.47/26.30 | | | (48) all_58_11 = e1
% 170.47/26.30 | | |
% 170.47/26.30 | | | COMBINE_EQS: (24), (48) imply:
% 170.47/26.30 | | | (49) e1 = e0
% 170.47/26.30 | | |
% 170.47/26.30 | | | SIMP: (49) implies:
% 170.47/26.30 | | | (50) e1 = e0
% 170.47/26.30 | | |
% 170.47/26.30 | | | COMBINE_EQS: (17), (50) imply:
% 170.47/26.30 | | | (51) all_58_14 = e0
% 170.47/26.30 | | |
% 170.47/26.30 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 170.47/26.30 | | | (14), (15), (16), (20), (21), (22), (23), (25), (26), (27),
% 170.47/26.30 | | | (28), (29), (31), (32), (33), (34), (37), (38), (39), (40),
% 170.47/26.30 | | | (41), (42), (43), (44), (51) are inconsistent by sub-proof
% 170.47/26.30 | | | #584.
% 170.47/26.30 | | |
% 170.47/26.30 | | Case 2:
% 170.47/26.30 | | |
% 170.47/26.30 | | | (52) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.30 | | |
% 170.47/26.30 | | | ALPHA: (52) implies:
% 170.47/26.30 | | | (53) op(e0, e0) = e1
% 170.47/26.30 | | |
% 170.47/26.30 | | | REF_CLOSE: (5), (33), (37), (53) are inconsistent by sub-proof #640.
% 170.47/26.30 | | |
% 170.47/26.30 | | End of split
% 170.47/26.30 | |
% 170.47/26.30 | End of split
% 170.47/26.30 |
% 170.47/26.30 End of proof
% 170.47/26.30
% 170.47/26.30 Sub-proof #584 shows that the following formulas are inconsistent:
% 170.47/26.30 ----------------------------------------------------------------
% 170.47/26.30 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.30 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.30 (2) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.30 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.30 (3) all_54_12 = all_52_3
% 170.47/26.30 (4) op(e0, e0) = e2
% 170.47/26.30 (5) all_58_0 = e1
% 170.47/26.30 (6) ~ (all_8_2 = e3)
% 170.47/26.30 (7) ~ (all_52_3 = e2)
% 170.47/26.30 (8) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.30 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.30 (9) ~ (all_52_3 = e1)
% 170.47/26.30 (10) ~ (e3 = e1)
% 170.47/26.30 (11) op(e3, e3) = e1
% 170.47/26.30 (12) ~ (all_52_1 = all_52_3)
% 170.47/26.30 (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.30 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.30 e1)
% 170.47/26.30 (14) op(e3, e1) = all_52_8
% 170.47/26.30 (15) ~ (e1 = e0)
% 170.47/26.30 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.30 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.30 (17) op(e1, e2) = all_52_6
% 170.47/26.30 (18) op(e2, e3) = all_52_1
% 170.47/26.30 (19) op(e3, e1) = e3
% 170.47/26.30 (20) op(e0, e2) = e0
% 170.47/26.30 (21) op(e2, e2) = all_8_2
% 170.47/26.30 (22) all_58_6 = e2
% 170.47/26.30 (23) ~ (e3 = e0)
% 170.47/26.30 (24) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.30 (25) all_58_14 = e0
% 170.47/26.30 (26) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.30 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.30 (27) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.30 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.30 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.30 (29) ~ (e2 = e0)
% 170.47/26.30 (30) ~ (e2 = e1)
% 170.47/26.30 (31) ~ (all_52_3 = e0)
% 170.47/26.30 (32) ~ (all_52_6 = e3)
% 170.47/26.30 (33) op(e0, e2) = all_52_7
% 170.47/26.30 (34) all_58_4 = e2
% 170.47/26.30 (35) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.30 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.30 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.30 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.30 (36) op(e3, e1) = e2
% 170.47/26.30 (37) ~ (e3 = e2)
% 170.47/26.30
% 170.47/26.30 Begin of proof
% 170.47/26.30 |
% 170.47/26.30 | BETA: splitting (13) gives:
% 170.47/26.30 |
% 170.47/26.30 | Case 1:
% 170.47/26.30 | |
% 170.47/26.30 | | (38) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 170.47/26.30 | | e1)
% 170.47/26.30 | |
% 170.47/26.30 | | BETA: splitting (38) gives:
% 170.47/26.30 | |
% 170.47/26.30 | | Case 1:
% 170.47/26.30 | | |
% 170.47/26.30 | | | (39) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.30 | | |
% 170.47/26.30 | | | ALPHA: (39) implies:
% 170.47/26.30 | | | (40) all_58_12 = e1
% 170.47/26.30 | | |
% 170.47/26.31 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 170.47/26.31 | | | (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 170.47/26.31 | | | (26), (27), (28), (29), (30), (31), (32), (34), (35), (36),
% 170.47/26.31 | | | (37), (40) are inconsistent by sub-proof #593.
% 170.47/26.31 | | |
% 170.47/26.31 | | Case 2:
% 170.47/26.31 | | |
% 170.47/26.31 | | | (41) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.31 | | |
% 170.47/26.31 | | | ALPHA: (41) implies:
% 170.47/26.31 | | | (42) op(e0, e2) = e1
% 170.47/26.31 | | |
% 170.47/26.31 | | | REF_CLOSE: (15), (20), (28), (33), (42) are inconsistent by sub-proof
% 170.47/26.31 | | | #889.
% 170.47/26.31 | | |
% 170.47/26.31 | | End of split
% 170.47/26.31 | |
% 170.47/26.31 | Case 2:
% 170.47/26.31 | |
% 170.47/26.31 | | (43) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.31 | | e1)
% 170.47/26.31 | |
% 170.47/26.31 | | REF_CLOSE: (4), (15), (25), (28), (30), (43) are inconsistent by sub-proof
% 170.47/26.31 | | #585.
% 170.47/26.31 | |
% 170.47/26.31 | End of split
% 170.47/26.31 |
% 170.47/26.31 End of proof
% 170.47/26.31
% 170.47/26.31 Sub-proof #585 shows that the following formulas are inconsistent:
% 170.47/26.31 ----------------------------------------------------------------
% 170.47/26.31 (1) op(e0, e0) = e2
% 170.47/26.31 (2) ~ (e1 = e0)
% 170.47/26.31 (3) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.31 (4) all_58_14 = e0
% 170.47/26.31 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.31 (6) ~ (e2 = e1)
% 170.47/26.31
% 170.47/26.31 Begin of proof
% 170.47/26.31 |
% 170.47/26.31 | BETA: splitting (3) gives:
% 170.47/26.31 |
% 170.47/26.31 | Case 1:
% 170.47/26.31 | |
% 170.47/26.31 | | (7) all_58_14 = e1 & op(e0, e1) = e1
% 170.47/26.31 | |
% 170.47/26.31 | | ALPHA: (7) implies:
% 170.47/26.31 | | (8) all_58_14 = e1
% 170.47/26.31 | |
% 170.47/26.31 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #586.
% 170.47/26.31 | |
% 170.47/26.31 | Case 2:
% 170.47/26.31 | |
% 170.47/26.31 | | (9) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.31 | |
% 170.47/26.31 | | ALPHA: (9) implies:
% 170.47/26.31 | | (10) op(e0, e0) = e1
% 170.47/26.31 | |
% 170.47/26.31 | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #640.
% 170.47/26.31 | |
% 170.47/26.31 | End of split
% 170.47/26.31 |
% 170.47/26.31 End of proof
% 170.47/26.31
% 170.47/26.31 Sub-proof #586 shows that the following formulas are inconsistent:
% 170.47/26.31 ----------------------------------------------------------------
% 170.47/26.31 (1) all_58_14 = e1
% 170.47/26.31 (2) all_58_14 = e0
% 170.47/26.31 (3) ~ (e1 = e0)
% 170.47/26.31
% 170.47/26.31 Begin of proof
% 170.47/26.31 |
% 170.47/26.31 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.31 | (4) e1 = e0
% 170.47/26.31 |
% 170.47/26.31 | SIMP: (4) implies:
% 170.47/26.31 | (5) e1 = e0
% 170.47/26.31 |
% 170.47/26.31 | REDUCE: (3), (5) imply:
% 170.47/26.31 | (6) $false
% 170.47/26.31 |
% 170.47/26.31 | CLOSE: (6) is inconsistent.
% 170.47/26.31 |
% 170.47/26.31 End of proof
% 170.47/26.31
% 170.47/26.31 Sub-proof #587 shows that the following formulas are inconsistent:
% 170.47/26.31 ----------------------------------------------------------------
% 170.47/26.31 (1) all_54_12 = all_52_3
% 170.47/26.31 (2) ~ (all_52_3 = e2)
% 170.47/26.31 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.31 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.31 (4) ~ (all_52_3 = e1)
% 170.47/26.31 (5) ~ (e3 = e1)
% 170.47/26.31 (6) op(e3, e3) = e1
% 170.47/26.31 (7) ~ (all_52_1 = all_52_3)
% 170.47/26.31 (8) op(e3, e1) = all_52_8
% 170.47/26.31 (9) ~ (e1 = e0)
% 170.47/26.31 (10) all_56_10 = e1
% 170.47/26.31 (11) all_58_10 = e3
% 170.47/26.31 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.31 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.31 (13) op(e2, e3) = all_52_1
% 170.47/26.31 (14) all_58_6 = e2
% 170.47/26.31 (15) ~ (e3 = e0)
% 170.47/26.31 (16) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.31 (17) all_58_1 = e3
% 170.47/26.31 (18) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.31 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.31 (19) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.31 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.31 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.31 (21) ~ (e2 = e0)
% 170.47/26.31 (22) all_58_12 = e3
% 170.47/26.31 (23) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.47/26.31 (24) ~ (e2 = e1)
% 170.47/26.31 (25) ~ (all_52_3 = e0)
% 170.47/26.31 (26) all_58_4 = e2
% 170.47/26.31 (27) op(e3, e1) = e2
% 170.47/26.31 (28) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.31 (29) ~ (e3 = e2)
% 170.47/26.31
% 170.47/26.31 Begin of proof
% 170.47/26.31 |
% 170.47/26.31 | BETA: splitting (28) gives:
% 170.47/26.31 |
% 170.47/26.31 | Case 1:
% 170.47/26.31 | |
% 170.47/26.31 | | (30) all_58_9 = e1 & op(e3, e0) = e1
% 170.47/26.31 | |
% 170.47/26.31 | | ALPHA: (30) implies:
% 170.47/26.31 | | (31) all_58_9 = e1
% 170.47/26.31 | |
% 170.47/26.31 | | REF_CLOSE: (3), (5), (6), (8), (9), (10), (15), (19), (20), (21), (23),
% 170.47/26.31 | | (24), (26), (27), (29), (31) are inconsistent by sub-proof #801.
% 170.47/26.31 | |
% 170.47/26.31 | Case 2:
% 170.47/26.31 | |
% 170.47/26.31 | | (32) all_58_10 = e1 & op(e2, e0) = e1
% 170.47/26.31 | |
% 170.47/26.31 | | ALPHA: (32) implies:
% 170.47/26.31 | | (33) all_58_10 = e1
% 170.47/26.31 | |
% 170.47/26.31 | | COMBINE_EQS: (11), (33) imply:
% 170.47/26.31 | | (34) e3 = e1
% 170.47/26.31 | |
% 170.47/26.31 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (12), (13), (14), (15), (16),
% 170.47/26.31 | | (17), (18), (19), (20), (21), (22), (24), (25), (26), (29), (34)
% 170.47/26.31 | | are inconsistent by sub-proof #599.
% 170.47/26.31 | |
% 170.47/26.31 | End of split
% 170.47/26.31 |
% 170.47/26.31 End of proof
% 170.47/26.31
% 170.47/26.31 Sub-proof #588 shows that the following formulas are inconsistent:
% 170.47/26.31 ----------------------------------------------------------------
% 170.47/26.31 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.31 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.31 (2) op(e0, e1) = all_52_11
% 170.47/26.31 (3) all_58_15 = e2
% 170.47/26.31 (4) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.31 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.31 (5) all_54_12 = all_52_3
% 170.47/26.31 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.31 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.31 (7) op(e0, e0) = e2
% 170.47/26.31 (8) ~ (all_8_2 = e3)
% 170.47/26.31 (9) all_58_9 = e0
% 170.47/26.31 (10) ~ (all_52_3 = e2)
% 170.47/26.31 (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.31 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.31 (12) ~ (all_52_3 = e1)
% 170.47/26.31 (13) ~ (e3 = e1)
% 170.47/26.31 (14) op(e3, e3) = e1
% 170.47/26.31 (15) ~ (all_52_1 = all_52_3)
% 170.47/26.31 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.31 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.31 e1)
% 170.47/26.31 (17) op(e3, e1) = all_52_8
% 170.47/26.31 (18) ~ (e1 = e0)
% 170.47/26.31 (19) all_56_10 = e1
% 170.47/26.31 (20) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.31 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.47/26.31 e3)
% 170.47/26.31 (21) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.31 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.31 (22) op(e2, e3) = all_52_1
% 170.47/26.31 (23) op(e3, e1) = e3
% 170.47/26.31 (24) op(e0, e2) = e0
% 170.47/26.31 (25) op(e2, e2) = all_8_2
% 170.47/26.31 (26) all_58_6 = e2
% 170.47/26.31 (27) ~ (e3 = e0)
% 170.47/26.31 (28) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.31 (29) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.31 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.47/26.31 (30) ~ (all_52_3 = all_52_11)
% 170.47/26.31 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.31 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.31 (32) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.31 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.31 (33) all_58_3 = e2
% 170.47/26.31 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.31 (35) ~ (e2 = e0)
% 170.47/26.31 (36) all_58_12 = e3
% 170.47/26.31 (37) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.47/26.31 (38) ~ (e2 = e1)
% 170.47/26.31 (39) all_58_9 = e3 & op(e3, e0) = e3
% 170.47/26.31 (40) op(e3, e2) = all_52_4
% 170.47/26.31 (41) ~ (all_52_3 = e0)
% 170.47/26.31 (42) op(e0, e2) = all_52_7
% 170.47/26.31 (43) ~ (all_52_4 = e1)
% 170.47/26.31 (44) all_58_4 = e2
% 170.47/26.31 (45) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.31 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.31 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.31 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.31 (46) op(e3, e1) = e2
% 170.47/26.31 (47) ~ (e3 = e2)
% 170.47/26.31
% 170.47/26.31 Begin of proof
% 170.47/26.31 |
% 170.47/26.31 | ALPHA: (39) implies:
% 170.47/26.31 | (48) all_58_9 = e3
% 170.47/26.31 |
% 170.47/26.31 | COMBINE_EQS: (9), (48) imply:
% 170.47/26.31 | (49) e3 = e0
% 170.47/26.31 |
% 170.47/26.31 | SIMP: (49) implies:
% 170.47/26.31 | (50) e3 = e0
% 170.47/26.31 |
% 170.47/26.31 | COMBINE_EQS: (36), (50) imply:
% 170.47/26.31 | (51) all_58_12 = e0
% 170.47/26.31 |
% 170.47/26.31 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 170.47/26.31 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 170.47/26.31 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 170.47/26.31 | (37), (38), (40), (41), (42), (43), (44), (45), (46), (47), (51)
% 170.47/26.31 | are inconsistent by sub-proof #589.
% 170.47/26.31 |
% 170.47/26.31 End of proof
% 170.47/26.31
% 170.47/26.31 Sub-proof #589 shows that the following formulas are inconsistent:
% 170.47/26.31 ----------------------------------------------------------------
% 170.47/26.31 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.31 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.31 (2) op(e0, e1) = all_52_11
% 170.47/26.31 (3) all_58_15 = e2
% 170.47/26.31 (4) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.31 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.31 (5) all_54_12 = all_52_3
% 170.47/26.31 (6) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.31 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.31 (7) op(e0, e0) = e2
% 170.47/26.31 (8) ~ (all_8_2 = e3)
% 170.47/26.31 (9) ~ (all_52_3 = e2)
% 170.47/26.31 (10) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.31 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.31 (11) ~ (all_52_3 = e1)
% 170.47/26.31 (12) ~ (e3 = e1)
% 170.47/26.31 (13) op(e3, e3) = e1
% 170.47/26.31 (14) ~ (all_52_1 = all_52_3)
% 170.47/26.31 (15) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.31 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.31 e1)
% 170.47/26.31 (16) op(e3, e1) = all_52_8
% 170.47/26.31 (17) ~ (e1 = e0)
% 170.47/26.31 (18) all_56_10 = e1
% 170.47/26.31 (19) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.31 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.47/26.31 e3)
% 170.47/26.31 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.31 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.31 (21) op(e2, e3) = all_52_1
% 170.47/26.31 (22) op(e3, e1) = e3
% 170.47/26.31 (23) op(e0, e2) = e0
% 170.47/26.31 (24) op(e2, e2) = all_8_2
% 170.47/26.31 (25) all_58_6 = e2
% 170.47/26.31 (26) ~ (e3 = e0)
% 170.47/26.31 (27) all_58_12 = e0
% 170.47/26.31 (28) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.31 (29) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.31 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.47/26.31 (30) ~ (all_52_3 = all_52_11)
% 170.47/26.31 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.31 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.31 (32) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.31 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.31 (33) all_58_3 = e2
% 170.47/26.31 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.31 (35) ~ (e2 = e0)
% 170.47/26.31 (36) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.47/26.31 (37) ~ (e2 = e1)
% 170.47/26.31 (38) op(e3, e2) = all_52_4
% 170.47/26.31 (39) ~ (all_52_3 = e0)
% 170.47/26.31 (40) op(e0, e2) = all_52_7
% 170.47/26.31 (41) ~ (all_52_4 = e1)
% 170.47/26.31 (42) all_58_4 = e2
% 170.47/26.31 (43) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.31 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.31 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.31 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.31 (44) op(e3, e1) = e2
% 170.47/26.31 (45) ~ (e3 = e2)
% 170.47/26.31
% 170.47/26.31 Begin of proof
% 170.47/26.31 |
% 170.47/26.31 | BETA: splitting (29) gives:
% 170.47/26.31 |
% 170.47/26.31 | Case 1:
% 170.47/26.31 | |
% 170.47/26.31 | | (46) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 170.47/26.31 | | e0)
% 170.47/26.31 | |
% 170.47/26.31 | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (11), (12), (13), (14), (15), (16),
% 170.47/26.31 | | (17), (20), (21), (22), (23), (24), (25), (26), (28), (33), (34),
% 170.47/26.31 | | (35), (37), (39), (40), (43), (44), (45), (46) are inconsistent
% 170.47/26.31 | | by sub-proof #592.
% 170.47/26.31 | |
% 170.47/26.31 | Case 2:
% 170.47/26.31 | |
% 170.47/26.31 | | (47) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 170.47/26.31 | | e0)
% 170.47/26.31 | |
% 170.47/26.31 | | BETA: splitting (47) gives:
% 170.47/26.31 | |
% 170.47/26.31 | | Case 1:
% 170.47/26.31 | | |
% 170.47/26.31 | | | (48) all_58_7 = e0 & op(e1, e2) = e0
% 170.47/26.31 | | |
% 170.47/26.31 | | | ALPHA: (48) implies:
% 170.47/26.31 | | | (49) all_58_7 = e0
% 170.47/26.31 | | |
% 170.47/26.31 | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 170.47/26.31 | | | (15), (16), (17), (20), (21), (22), (23), (24), (25), (26),
% 170.47/26.31 | | | (27), (28), (31), (32), (33), (34), (35), (37), (39), (40),
% 170.47/26.31 | | | (42), (43), (44), (45), (49) are inconsistent by sub-proof
% 170.47/26.31 | | | #591.
% 170.47/26.31 | | |
% 170.47/26.31 | | Case 2:
% 170.47/26.31 | | |
% 170.47/26.31 | | | (50) all_58_13 = e0 & op(e0, e2) = e0
% 170.47/26.31 | | |
% 170.47/26.31 | | | ALPHA: (50) implies:
% 170.47/26.31 | | | (51) all_58_13 = e0
% 170.47/26.31 | | |
% 170.47/26.31 | | | BETA: splitting (31) gives:
% 170.47/26.31 | | |
% 170.47/26.31 | | | Case 1:
% 170.47/26.31 | | | |
% 170.47/26.31 | | | | (52) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 170.47/26.31 | | | | = e1)
% 170.47/26.31 | | | |
% 170.47/26.31 | | | | BETA: splitting (52) gives:
% 170.47/26.31 | | | |
% 170.47/26.31 | | | | Case 1:
% 170.47/26.31 | | | | |
% 170.47/26.31 | | | | | (53) all_58_0 = e1 & op(e3, e3) = e1
% 170.47/26.31 | | | | |
% 170.47/26.31 | | | | | ALPHA: (53) implies:
% 170.47/26.31 | | | | | (54) all_58_0 = e1
% 170.47/26.31 | | | | |
% 170.47/26.31 | | | | | BETA: splitting (4) gives:
% 170.47/26.31 | | | | |
% 170.47/26.31 | | | | | Case 1:
% 170.47/26.31 | | | | | |
% 170.47/26.31 | | | | | | (55) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2,
% 170.47/26.31 | | | | | | e2) = e3)
% 170.47/26.31 | | | | | |
% 170.47/26.31 | | | | | | BETA: splitting (55) gives:
% 170.47/26.31 | | | | | |
% 170.47/26.31 | | | | | | Case 1:
% 170.47/26.31 | | | | | | |
% 170.47/26.31 | | | | | | | (56) all_58_1 = e3 & op(e3, e2) = e3
% 170.47/26.31 | | | | | | |
% 170.47/26.31 | | | | | | | ALPHA: (56) implies:
% 170.47/26.31 | | | | | | | (57) all_58_1 = e3
% 170.47/26.31 | | | | | | |
% 170.47/26.31 | | | | | | | BETA: splitting (28) gives:
% 170.47/26.31 | | | | | | |
% 170.47/26.31 | | | | | | | Case 1:
% 170.47/26.31 | | | | | | | |
% 170.47/26.31 | | | | | | | | (58) all_54_12 = e3
% 170.47/26.31 | | | | | | | |
% 170.47/26.31 | | | | | | | | COMBINE_EQS: (5), (58) imply:
% 170.47/26.31 | | | | | | | | (59) all_52_3 = e3
% 170.47/26.31 | | | | | | | |
% 170.47/26.31 | | | | | | | | SIMP: (59) implies:
% 170.47/26.32 | | | | | | | | (60) all_52_3 = e3
% 170.47/26.32 | | | | | | | |
% 170.47/26.32 | | | | | | | | REDUCE: (30), (60) imply:
% 170.47/26.32 | | | | | | | | (61) ~ (all_52_11 = e3)
% 170.47/26.32 | | | | | | | |
% 170.47/26.32 | | | | | | | | SIMP: (61) implies:
% 170.47/26.32 | | | | | | | | (62) ~ (all_52_11 = e3)
% 170.47/26.32 | | | | | | | |
% 170.47/26.32 | | | | | | | | BETA: splitting (19) gives:
% 170.47/26.32 | | | | | | | |
% 170.47/26.32 | | | | | | | | Case 1:
% 170.47/26.32 | | | | | | | | |
% 170.47/26.32 | | | | | | | | | (63) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 170.47/26.32 | | | | | | | | | op(e0, e2) = e3)
% 170.47/26.32 | | | | | | | | |
% 170.47/26.32 | | | | | | | | | BETA: splitting (63) gives:
% 170.47/26.32 | | | | | | | | |
% 170.47/26.32 | | | | | | | | | Case 1:
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | (64) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | ALPHA: (64) implies:
% 170.47/26.32 | | | | | | | | | | (65) all_58_12 = e3
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | COMBINE_EQS: (27), (65) imply:
% 170.47/26.32 | | | | | | | | | | (66) e3 = e0
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | SIMP: (66) implies:
% 170.47/26.32 | | | | | | | | | | (67) e3 = e0
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | REF_CLOSE: (4), (6), (8), (12), (17), (23), (24), (26), (33),
% 170.47/26.32 | | | | | | | | | | (34), (37), (40), (51), (57), (67) are
% 170.47/26.32 | | | | | | | | | | inconsistent by sub-proof #590.
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | Case 2:
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | (68) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | ALPHA: (68) implies:
% 170.47/26.32 | | | | | | | | | | (69) all_58_13 = e3
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | REF_CLOSE: (6), (12), (17), (26), (29), (33), (35), (37),
% 170.47/26.32 | | | | | | | | | | (57), (69) are inconsistent by sub-proof #707.
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | End of split
% 170.47/26.32 | | | | | | | | |
% 170.47/26.32 | | | | | | | | Case 2:
% 170.47/26.32 | | | | | | | | |
% 170.47/26.32 | | | | | | | | | (70) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 170.47/26.32 | | | | | | | | | op(e0, e0) = e3)
% 170.47/26.32 | | | | | | | | |
% 170.47/26.32 | | | | | | | | | BETA: splitting (70) gives:
% 170.47/26.32 | | | | | | | | |
% 170.47/26.32 | | | | | | | | | Case 1:
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | (71) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | REF_CLOSE: (2), (34), (62), (71) are inconsistent by
% 170.47/26.32 | | | | | | | | | | sub-proof #960.
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | Case 2:
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | (72) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | ALPHA: (72) implies:
% 170.47/26.32 | | | | | | | | | | (73) all_58_15 = e3
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | COMBINE_EQS: (3), (73) imply:
% 170.47/26.32 | | | | | | | | | | (74) e3 = e2
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | SIMP: (74) implies:
% 170.47/26.32 | | | | | | | | | | (75) e3 = e2
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | COMBINE_EQS: (57), (75) imply:
% 170.47/26.32 | | | | | | | | | | (76) all_58_1 = e2
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | | REF_CLOSE: (10), (12), (17), (26), (32), (35), (42), (45),
% 170.47/26.32 | | | | | | | | | | (54), (76) are inconsistent by sub-proof #900.
% 170.47/26.32 | | | | | | | | | |
% 170.47/26.32 | | | | | | | | | End of split
% 170.47/26.32 | | | | | | | | |
% 170.47/26.32 | | | | | | | | End of split
% 170.47/26.32 | | | | | | | |
% 170.47/26.32 | | | | | | | Case 2:
% 170.47/26.32 | | | | | | | |
% 170.47/26.32 | | | | | | | | (77) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.32 | | | | | | | |
% 170.47/26.32 | | | | | | | | REF_CLOSE: (5), (9), (11), (39), (77) are inconsistent by
% 170.47/26.32 | | | | | | | | sub-proof #675.
% 170.47/26.32 | | | | | | | |
% 170.47/26.32 | | | | | | | End of split
% 170.47/26.32 | | | | | | |
% 170.47/26.32 | | | | | | Case 2:
% 170.47/26.32 | | | | | | |
% 170.47/26.32 | | | | | | | (78) all_58_3 = e3 & op(e2, e2) = e3
% 170.47/26.32 | | | | | | |
% 170.47/26.32 | | | | | | | REF_CLOSE: (8), (24), (34), (78) are inconsistent by sub-proof
% 170.47/26.32 | | | | | | | #973.
% 170.47/26.32 | | | | | | |
% 170.47/26.32 | | | | | | End of split
% 170.47/26.32 | | | | | |
% 170.47/26.32 | | | | | Case 2:
% 170.47/26.32 | | | | | |
% 170.47/26.32 | | | | | | (79) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0,
% 170.47/26.32 | | | | | | e2) = e3)
% 170.47/26.32 | | | | | |
% 170.47/26.32 | | | | | | BETA: splitting (79) gives:
% 170.47/26.32 | | | | | |
% 170.47/26.32 | | | | | | Case 1:
% 170.47/26.32 | | | | | | |
% 170.47/26.32 | | | | | | | (80) all_58_7 = e3 & op(e1, e2) = e3
% 170.47/26.32 | | | | | | |
% 170.47/26.32 | | | | | | | REF_CLOSE: (3), (6), (7), (12), (15), (17), (19), (23), (26),
% 170.47/26.32 | | | | | | | (27), (33), (34), (37), (40), (45), (51), (80) are
% 170.47/26.32 | | | | | | | inconsistent by sub-proof #607.
% 170.47/26.32 | | | | | | |
% 170.47/26.32 | | | | | | Case 2:
% 170.47/26.32 | | | | | | |
% 170.47/26.32 | | | | | | | (81) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.32 | | | | | | |
% 170.47/26.32 | | | | | | | REF_CLOSE: (26), (51), (81) are inconsistent by sub-proof #634.
% 170.47/26.32 | | | | | | |
% 170.47/26.32 | | | | | | End of split
% 170.47/26.32 | | | | | |
% 170.47/26.32 | | | | | End of split
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | Case 2:
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | (82) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | REF_CLOSE: (34), (38), (41), (82) are inconsistent by sub-proof #863.
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | End of split
% 170.47/26.32 | | | |
% 170.47/26.32 | | | Case 2:
% 170.47/26.32 | | | |
% 170.47/26.32 | | | | (83) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 170.47/26.32 | | | | = e1)
% 170.47/26.32 | | | |
% 170.47/26.32 | | | | BETA: splitting (83) gives:
% 170.47/26.32 | | | |
% 170.47/26.32 | | | | Case 1:
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | (84) all_58_4 = e1 & op(e3, e1) = e1
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | REF_CLOSE: (37), (42), (84) are inconsistent by sub-proof #943.
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | Case 2:
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | (85) all_58_9 = e1 & op(e3, e0) = e1
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | ALPHA: (85) implies:
% 170.47/26.32 | | | | | (86) all_58_9 = e1
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | REF_CLOSE: (10), (12), (13), (16), (17), (18), (26), (32), (34), (35),
% 170.47/26.32 | | | | | (36), (37), (42), (44), (45), (86) are inconsistent by
% 170.47/26.32 | | | | | sub-proof #801.
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | End of split
% 170.47/26.32 | | | |
% 170.47/26.32 | | | End of split
% 170.47/26.32 | | |
% 170.47/26.32 | | End of split
% 170.47/26.32 | |
% 170.47/26.32 | End of split
% 170.47/26.32 |
% 170.47/26.32 End of proof
% 170.47/26.32
% 170.47/26.32 Sub-proof #590 shows that the following formulas are inconsistent:
% 170.47/26.32 ----------------------------------------------------------------
% 170.47/26.32 (1) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.32 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.32 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.32 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.32 (3) ~ (all_8_2 = e3)
% 170.47/26.32 (4) ~ (e3 = e1)
% 170.47/26.32 (5) all_58_13 = e0
% 170.47/26.32 (6) ~ (e1 = e0)
% 170.47/26.32 (7) op(e0, e2) = e0
% 170.47/26.32 (8) op(e2, e2) = all_8_2
% 170.47/26.32 (9) ~ (e3 = e0)
% 170.47/26.32 (10) e3 = e0
% 170.47/26.32 (11) all_58_1 = e3
% 170.47/26.32 (12) all_58_3 = e2
% 170.47/26.32 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.32 (14) ~ (e2 = e1)
% 170.47/26.32 (15) op(e0, e2) = all_52_7
% 170.47/26.32
% 170.47/26.32 Begin of proof
% 170.47/26.32 |
% 170.47/26.32 | COMBINE_EQS: (10), (11) imply:
% 170.47/26.32 | (16) all_58_1 = e0
% 170.47/26.32 |
% 170.47/26.32 | BETA: splitting (1) gives:
% 170.47/26.32 |
% 170.47/26.32 | Case 1:
% 170.47/26.32 | |
% 170.47/26.32 | | (17) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.47/26.32 | | e3)
% 170.47/26.32 | |
% 170.47/26.32 | | BETA: splitting (17) gives:
% 170.47/26.32 | |
% 170.47/26.32 | | Case 1:
% 170.47/26.32 | | |
% 170.47/26.32 | | | (18) all_58_1 = e3 & op(e3, e2) = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | REF_CLOSE: (9), (16), (18) are inconsistent by sub-proof #803.
% 170.47/26.32 | | |
% 170.47/26.32 | | Case 2:
% 170.47/26.32 | | |
% 170.47/26.32 | | | (19) all_58_3 = e3 & op(e2, e2) = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | REF_CLOSE: (3), (8), (13), (19) are inconsistent by sub-proof #973.
% 170.47/26.32 | | |
% 170.47/26.32 | | End of split
% 170.47/26.32 | |
% 170.47/26.32 | Case 2:
% 170.47/26.32 | |
% 170.47/26.32 | | (20) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 170.47/26.32 | | e3)
% 170.47/26.32 | |
% 170.47/26.32 | | BETA: splitting (20) gives:
% 170.47/26.32 | |
% 170.47/26.32 | | Case 1:
% 170.47/26.32 | | |
% 170.47/26.32 | | | (21) all_58_7 = e3 & op(e1, e2) = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | ALPHA: (21) implies:
% 170.47/26.32 | | | (22) all_58_7 = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | REF_CLOSE: (2), (4), (6), (7), (12), (13), (14), (15), (16), (22) are
% 170.47/26.32 | | | inconsistent by sub-proof #656.
% 170.47/26.32 | | |
% 170.47/26.32 | | Case 2:
% 170.47/26.32 | | |
% 170.47/26.32 | | | (23) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | ALPHA: (23) implies:
% 170.47/26.32 | | | (24) all_58_13 = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | REF_CLOSE: (5), (9), (24) are inconsistent by sub-proof #708.
% 170.47/26.32 | | |
% 170.47/26.32 | | End of split
% 170.47/26.32 | |
% 170.47/26.32 | End of split
% 170.47/26.32 |
% 170.47/26.32 End of proof
% 170.47/26.32
% 170.47/26.32 Sub-proof #591 shows that the following formulas are inconsistent:
% 170.47/26.32 ----------------------------------------------------------------
% 170.47/26.32 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.32 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.32 (2) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.32 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.32 (3) all_54_12 = all_52_3
% 170.47/26.32 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.32 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.32 (5) ~ (all_8_2 = e3)
% 170.47/26.32 (6) ~ (all_52_3 = e2)
% 170.47/26.32 (7) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.32 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.32 (8) ~ (all_52_3 = e1)
% 170.47/26.32 (9) ~ (e3 = e1)
% 170.47/26.32 (10) op(e3, e3) = e1
% 170.47/26.32 (11) ~ (all_52_1 = all_52_3)
% 170.47/26.32 (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.32 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.32 e1)
% 170.47/26.32 (13) op(e3, e1) = all_52_8
% 170.47/26.32 (14) ~ (e1 = e0)
% 170.47/26.32 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.32 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.32 (16) op(e2, e3) = all_52_1
% 170.47/26.32 (17) op(e3, e1) = e3
% 170.47/26.32 (18) all_58_7 = e0
% 170.47/26.32 (19) op(e0, e2) = e0
% 170.47/26.32 (20) op(e2, e2) = all_8_2
% 170.47/26.32 (21) all_58_6 = e2
% 170.47/26.32 (22) ~ (e3 = e0)
% 170.47/26.32 (23) all_58_12 = e0
% 170.47/26.32 (24) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.32 (25) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.32 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.32 (26) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.32 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.32 (27) all_58_3 = e2
% 170.47/26.32 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.32 (29) ~ (e2 = e0)
% 170.47/26.32 (30) ~ (e2 = e1)
% 170.47/26.32 (31) ~ (all_52_3 = e0)
% 170.47/26.32 (32) op(e0, e2) = all_52_7
% 170.47/26.32 (33) all_58_4 = e2
% 170.47/26.32 (34) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.32 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.32 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.32 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.32 (35) op(e3, e1) = e2
% 170.47/26.32 (36) ~ (e3 = e2)
% 170.47/26.32
% 170.47/26.32 Begin of proof
% 170.47/26.32 |
% 170.47/26.32 | BETA: splitting (2) gives:
% 170.47/26.32 |
% 170.47/26.32 | Case 1:
% 170.47/26.32 | |
% 170.47/26.32 | | (37) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.47/26.32 | | e3)
% 170.47/26.32 | |
% 170.47/26.32 | | BETA: splitting (37) gives:
% 170.47/26.32 | |
% 170.47/26.32 | | Case 1:
% 170.47/26.32 | | |
% 170.47/26.32 | | | (38) all_58_1 = e3 & op(e3, e2) = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | ALPHA: (38) implies:
% 170.47/26.32 | | | (39) all_58_1 = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | BETA: splitting (15) gives:
% 170.47/26.32 | | |
% 170.47/26.32 | | | Case 1:
% 170.47/26.32 | | | |
% 170.47/26.32 | | | | (40) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 170.47/26.32 | | | | = e3)
% 170.47/26.32 | | | |
% 170.47/26.32 | | | | REF_CLOSE: (3), (6), (7), (8), (9), (11), (14), (16), (22), (24), (25),
% 170.47/26.32 | | | | (28), (29), (30), (31), (33), (39), (40) are inconsistent by
% 170.47/26.32 | | | | sub-proof #604.
% 170.47/26.32 | | | |
% 170.47/26.32 | | | Case 2:
% 170.47/26.32 | | | |
% 170.47/26.32 | | | | (41) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 170.47/26.32 | | | | = e3)
% 170.47/26.32 | | | |
% 170.47/26.32 | | | | BETA: splitting (41) gives:
% 170.47/26.32 | | | |
% 170.47/26.32 | | | | Case 1:
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | (42) all_58_6 = e3 & op(e1, e3) = e3
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | REF_CLOSE: (7), (9), (14), (21), (22), (25), (26), (29), (30), (33),
% 170.47/26.32 | | | | | (36), (39), (42) are inconsistent by sub-proof #606.
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | Case 2:
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | (43) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | ALPHA: (43) implies:
% 170.47/26.32 | | | | | (44) all_58_12 = e3
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | COMBINE_EQS: (23), (44) imply:
% 170.47/26.32 | | | | | (45) e3 = e0
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | COMBINE_EQS: (39), (45) imply:
% 170.47/26.32 | | | | | (46) all_58_1 = e0
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 170.47/26.32 | | | | | (13), (14), (15), (16), (17), (19), (20), (21), (22), (24),
% 170.47/26.32 | | | | | (27), (28), (29), (30), (31), (32), (34), (35), (36), (46)
% 170.47/26.32 | | | | | are inconsistent by sub-proof #594.
% 170.47/26.32 | | | | |
% 170.47/26.32 | | | | End of split
% 170.47/26.32 | | | |
% 170.47/26.32 | | | End of split
% 170.47/26.32 | | |
% 170.47/26.32 | | Case 2:
% 170.47/26.32 | | |
% 170.47/26.32 | | | (47) all_58_3 = e3 & op(e2, e2) = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | REF_CLOSE: (5), (20), (28), (47) are inconsistent by sub-proof #973.
% 170.47/26.32 | | |
% 170.47/26.32 | | End of split
% 170.47/26.32 | |
% 170.47/26.32 | Case 2:
% 170.47/26.32 | |
% 170.47/26.32 | | (48) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 170.47/26.32 | | e3)
% 170.47/26.32 | |
% 170.47/26.32 | | BETA: splitting (48) gives:
% 170.47/26.32 | |
% 170.47/26.32 | | Case 1:
% 170.47/26.32 | | |
% 170.47/26.32 | | | (49) all_58_7 = e3 & op(e1, e2) = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | ALPHA: (49) implies:
% 170.47/26.32 | | | (50) all_58_7 = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | REF_CLOSE: (18), (22), (50) are inconsistent by sub-proof #748.
% 170.47/26.32 | | |
% 170.47/26.32 | | Case 2:
% 170.47/26.32 | | |
% 170.47/26.32 | | | (51) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.32 | | |
% 170.47/26.32 | | | REF_CLOSE: (1), (3), (6), (8), (9), (10), (11), (12), (13), (14), (15),
% 170.47/26.32 | | | (16), (17), (21), (22), (24), (28), (29), (30), (31), (34),
% 170.47/26.32 | | | (35), (36), (51) are inconsistent by sub-proof #598.
% 170.47/26.32 | | |
% 170.47/26.32 | | End of split
% 170.47/26.32 | |
% 170.47/26.32 | End of split
% 170.47/26.32 |
% 170.47/26.32 End of proof
% 170.47/26.32
% 170.47/26.32 Sub-proof #592 shows that the following formulas are inconsistent:
% 170.47/26.32 ----------------------------------------------------------------
% 170.47/26.32 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.32 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.32 (2) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.32 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.32 (3) all_54_12 = all_52_3
% 170.47/26.32 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.32 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.32 (5) ~ (all_8_2 = e3)
% 170.47/26.32 (6) ~ (all_52_3 = e2)
% 170.47/26.32 (7) ~ (all_52_3 = e1)
% 170.47/26.32 (8) ~ (e3 = e1)
% 170.47/26.32 (9) op(e3, e3) = e1
% 170.47/26.32 (10) ~ (all_52_1 = all_52_3)
% 170.47/26.32 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.32 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.32 e1)
% 170.47/26.32 (12) op(e3, e1) = all_52_8
% 170.47/26.32 (13) ~ (e1 = e0)
% 170.47/26.32 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.32 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.32 (15) op(e2, e3) = all_52_1
% 170.47/26.32 (16) op(e3, e1) = e3
% 170.47/26.32 (17) op(e0, e2) = e0
% 170.47/26.32 (18) op(e2, e2) = all_8_2
% 170.47/26.32 (19) all_58_6 = e2
% 170.47/26.32 (20) ~ (e3 = e0)
% 170.47/26.32 (21) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.32 (22) all_58_3 = e2
% 170.47/26.32 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.32 (24) ~ (e2 = e0)
% 170.47/26.32 (25) ~ (e2 = e1)
% 170.47/26.32 (26) ~ (all_52_3 = e0)
% 170.47/26.32 (27) op(e0, e2) = all_52_7
% 170.47/26.32 (28) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 170.47/26.32 (29) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.32 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.32 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.32 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.32 (30) op(e3, e1) = e2
% 170.47/26.32 (31) ~ (e3 = e2)
% 170.47/26.32
% 170.47/26.32 Begin of proof
% 170.47/26.32 |
% 170.47/26.32 | BETA: splitting (28) gives:
% 170.47/26.32 |
% 170.47/26.32 | Case 1:
% 170.47/26.32 | |
% 170.47/26.32 | | (32) all_58_1 = e0 & op(e3, e2) = e0
% 170.47/26.32 | |
% 170.47/26.32 | | ALPHA: (32) implies:
% 170.47/26.32 | | (33) all_58_1 = e0
% 170.47/26.32 | |
% 170.47/26.32 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 170.47/26.32 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 170.47/26.32 | | (24), (25), (26), (27), (29), (30), (31), (33) are inconsistent
% 170.47/26.32 | | by sub-proof #594.
% 170.47/26.32 | |
% 170.47/26.32 | Case 2:
% 170.47/26.32 | |
% 170.47/26.32 | | (34) all_58_3 = e0 & op(e2, e2) = e0
% 170.47/26.32 | |
% 170.47/26.32 | | REF_CLOSE: (22), (24), (34) are inconsistent by sub-proof #934.
% 170.47/26.32 | |
% 170.47/26.32 | End of split
% 170.47/26.32 |
% 170.47/26.32 End of proof
% 170.47/26.32
% 170.47/26.32 Sub-proof #593 shows that the following formulas are inconsistent:
% 170.47/26.32 ----------------------------------------------------------------
% 170.47/26.32 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.32 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.32 (2) all_58_12 = e1
% 170.47/26.32 (3) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.32 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.32 (4) all_54_12 = all_52_3
% 170.47/26.32 (5) all_58_0 = e1
% 170.47/26.32 (6) ~ (all_8_2 = e3)
% 170.47/26.32 (7) ~ (all_52_3 = e2)
% 170.47/26.32 (8) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.32 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.32 (9) ~ (all_52_3 = e1)
% 170.47/26.32 (10) ~ (e3 = e1)
% 170.47/26.32 (11) op(e3, e3) = e1
% 170.47/26.32 (12) ~ (all_52_1 = all_52_3)
% 170.47/26.33 (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.33 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.33 e1)
% 170.47/26.33 (14) op(e3, e1) = all_52_8
% 170.47/26.33 (15) ~ (e1 = e0)
% 170.47/26.33 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.33 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.33 (17) op(e1, e2) = all_52_6
% 170.47/26.33 (18) op(e2, e3) = all_52_1
% 170.47/26.33 (19) op(e3, e1) = e3
% 170.47/26.33 (20) op(e2, e2) = all_8_2
% 170.47/26.33 (21) all_58_6 = e2
% 170.47/26.33 (22) ~ (e3 = e0)
% 170.47/26.33 (23) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.33 (24) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.33 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.33 (25) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.33 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.33 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.33 (27) ~ (e2 = e0)
% 170.47/26.33 (28) ~ (e2 = e1)
% 170.47/26.33 (29) ~ (all_52_3 = e0)
% 170.47/26.33 (30) ~ (all_52_6 = e3)
% 170.47/26.33 (31) all_58_4 = e2
% 170.47/26.33 (32) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.33 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.33 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.33 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.33 (33) op(e3, e1) = e2
% 170.47/26.33 (34) ~ (e3 = e2)
% 170.47/26.33
% 170.47/26.33 Begin of proof
% 170.47/26.33 |
% 170.47/26.33 | BETA: splitting (3) gives:
% 170.47/26.33 |
% 170.47/26.33 | Case 1:
% 170.47/26.33 | |
% 170.47/26.33 | | (35) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.47/26.33 | | e3)
% 170.47/26.33 | |
% 170.47/26.33 | | BETA: splitting (35) gives:
% 170.47/26.33 | |
% 170.47/26.33 | | Case 1:
% 170.47/26.33 | | |
% 170.47/26.33 | | | (36) all_58_1 = e3 & op(e3, e2) = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | ALPHA: (36) implies:
% 170.47/26.33 | | | (37) all_58_1 = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | BETA: splitting (16) gives:
% 170.47/26.33 | | |
% 170.47/26.33 | | | Case 1:
% 170.47/26.33 | | | |
% 170.47/26.33 | | | | (38) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3)
% 170.47/26.33 | | | | = e3)
% 170.47/26.33 | | | |
% 170.47/26.33 | | | | REF_CLOSE: (4), (7), (8), (9), (10), (12), (15), (18), (22), (23), (24),
% 170.47/26.33 | | | | (26), (27), (28), (29), (31), (37), (38) are inconsistent by
% 170.47/26.33 | | | | sub-proof #604.
% 170.47/26.33 | | | |
% 170.47/26.33 | | | Case 2:
% 170.47/26.33 | | | |
% 170.47/26.33 | | | | (39) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3)
% 170.47/26.33 | | | | = e3)
% 170.47/26.33 | | | |
% 170.47/26.33 | | | | BETA: splitting (39) gives:
% 170.47/26.33 | | | |
% 170.47/26.33 | | | | Case 1:
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | | (40) all_58_6 = e3 & op(e1, e3) = e3
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | | ALPHA: (40) implies:
% 170.47/26.33 | | | | | (41) all_58_6 = e3
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | | COMBINE_EQS: (21), (41) imply:
% 170.47/26.33 | | | | | (42) e3 = e2
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | | SIMP: (42) implies:
% 170.47/26.33 | | | | | (43) e3 = e2
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | | COMBINE_EQS: (37), (43) imply:
% 170.47/26.33 | | | | | (44) all_58_1 = e2
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | | REF_CLOSE: (5), (8), (10), (15), (22), (25), (27), (31), (34), (44)
% 170.47/26.33 | | | | | are inconsistent by sub-proof #900.
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | Case 2:
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | | (45) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | | ALPHA: (45) implies:
% 170.47/26.33 | | | | | (46) all_58_12 = e3
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | | REF_CLOSE: (2), (10), (46) are inconsistent by sub-proof #600.
% 170.47/26.33 | | | | |
% 170.47/26.33 | | | | End of split
% 170.47/26.33 | | | |
% 170.47/26.33 | | | End of split
% 170.47/26.33 | | |
% 170.47/26.33 | | Case 2:
% 170.47/26.33 | | |
% 170.47/26.33 | | | (47) all_58_3 = e3 & op(e2, e2) = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | REF_CLOSE: (6), (20), (26), (47) are inconsistent by sub-proof #973.
% 170.47/26.33 | | |
% 170.47/26.33 | | End of split
% 170.47/26.33 | |
% 170.47/26.33 | Case 2:
% 170.47/26.33 | |
% 170.47/26.33 | | (48) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 170.47/26.33 | | e3)
% 170.47/26.33 | |
% 170.47/26.33 | | REF_CLOSE: (1), (4), (7), (9), (10), (11), (12), (13), (14), (15), (16),
% 170.47/26.33 | | (17), (18), (19), (21), (22), (23), (26), (27), (28), (29), (30),
% 170.47/26.33 | | (32), (33), (34), (48) are inconsistent by sub-proof #597.
% 170.47/26.33 | |
% 170.47/26.33 | End of split
% 170.47/26.33 |
% 170.47/26.33 End of proof
% 170.47/26.33
% 170.47/26.33 Sub-proof #594 shows that the following formulas are inconsistent:
% 170.47/26.33 ----------------------------------------------------------------
% 170.47/26.33 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.33 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.33 (2) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.33 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.33 (3) all_54_12 = all_52_3
% 170.47/26.33 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.33 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.33 (5) ~ (all_8_2 = e3)
% 170.47/26.33 (6) ~ (all_52_3 = e2)
% 170.47/26.33 (7) ~ (all_52_3 = e1)
% 170.47/26.33 (8) ~ (e3 = e1)
% 170.47/26.33 (9) op(e3, e3) = e1
% 170.47/26.33 (10) ~ (all_52_1 = all_52_3)
% 170.47/26.33 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.33 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.33 e1)
% 170.47/26.33 (12) op(e3, e1) = all_52_8
% 170.47/26.33 (13) ~ (e1 = e0)
% 170.47/26.33 (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.33 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.33 (15) op(e2, e3) = all_52_1
% 170.47/26.33 (16) op(e3, e1) = e3
% 170.47/26.33 (17) op(e0, e2) = e0
% 170.47/26.33 (18) op(e2, e2) = all_8_2
% 170.47/26.33 (19) all_58_6 = e2
% 170.47/26.33 (20) ~ (e3 = e0)
% 170.47/26.33 (21) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.33 (22) all_58_3 = e2
% 170.47/26.33 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.33 (24) ~ (e2 = e0)
% 170.47/26.33 (25) ~ (e2 = e1)
% 170.47/26.33 (26) ~ (all_52_3 = e0)
% 170.47/26.33 (27) op(e0, e2) = all_52_7
% 170.47/26.33 (28) all_58_1 = e0
% 170.47/26.33 (29) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.33 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.33 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.33 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.33 (30) op(e3, e1) = e2
% 170.47/26.33 (31) ~ (e3 = e2)
% 170.47/26.33
% 170.47/26.33 Begin of proof
% 170.47/26.33 |
% 170.47/26.33 | BETA: splitting (2) gives:
% 170.47/26.33 |
% 170.47/26.33 | Case 1:
% 170.47/26.33 | |
% 170.47/26.33 | | (32) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.47/26.33 | | e3)
% 170.47/26.33 | |
% 170.47/26.33 | | BETA: splitting (32) gives:
% 170.47/26.33 | |
% 170.47/26.33 | | Case 1:
% 170.47/26.33 | | |
% 170.47/26.33 | | | (33) all_58_1 = e3 & op(e3, e2) = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | REF_CLOSE: (20), (28), (33) are inconsistent by sub-proof #803.
% 170.47/26.33 | | |
% 170.47/26.33 | | Case 2:
% 170.47/26.33 | | |
% 170.47/26.33 | | | (34) all_58_3 = e3 & op(e2, e2) = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | REF_CLOSE: (5), (18), (23), (34) are inconsistent by sub-proof #973.
% 170.47/26.33 | | |
% 170.47/26.33 | | End of split
% 170.47/26.33 | |
% 170.47/26.33 | Case 2:
% 170.47/26.33 | |
% 170.47/26.33 | | (35) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 170.47/26.33 | | e3)
% 170.47/26.33 | |
% 170.47/26.33 | | BETA: splitting (35) gives:
% 170.47/26.33 | |
% 170.47/26.33 | | Case 1:
% 170.47/26.33 | | |
% 170.47/26.33 | | | (36) all_58_7 = e3 & op(e1, e2) = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | ALPHA: (36) implies:
% 170.47/26.33 | | | (37) all_58_7 = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | REF_CLOSE: (4), (8), (13), (17), (22), (23), (25), (27), (28), (37) are
% 170.47/26.33 | | | inconsistent by sub-proof #656.
% 170.47/26.33 | | |
% 170.47/26.33 | | Case 2:
% 170.47/26.33 | | |
% 170.47/26.33 | | | (38) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 170.47/26.33 | | | (15), (16), (19), (20), (21), (23), (24), (25), (26), (29),
% 170.47/26.33 | | | (30), (31), (38) are inconsistent by sub-proof #598.
% 170.47/26.33 | | |
% 170.47/26.33 | | End of split
% 170.47/26.33 | |
% 170.47/26.33 | End of split
% 170.47/26.33 |
% 170.47/26.33 End of proof
% 170.47/26.33
% 170.47/26.33 Sub-proof #595 shows that the following formulas are inconsistent:
% 170.47/26.33 ----------------------------------------------------------------
% 170.47/26.33 (1) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 170.47/26.33 (2) all_54_1 = all_52_4
% 170.47/26.33 (3) ~ (all_52_4 = e0)
% 170.47/26.33 (4) ~ (all_52_4 = e2)
% 170.47/26.33 (5) ~ (all_52_4 = e1)
% 170.47/26.33
% 170.47/26.33 Begin of proof
% 170.47/26.33 |
% 170.47/26.33 | BETA: splitting (1) gives:
% 170.47/26.33 |
% 170.47/26.33 | Case 1:
% 170.47/26.33 | |
% 170.47/26.33 | | (6) all_54_1 = e2
% 170.47/26.33 | |
% 170.47/26.33 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #955.
% 170.47/26.33 | |
% 170.47/26.33 | Case 2:
% 170.47/26.33 | |
% 170.47/26.33 | | (7) all_54_1 = e1 | all_54_1 = e0
% 170.47/26.33 | |
% 170.47/26.33 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #596.
% 170.47/26.33 | |
% 170.47/26.33 | End of split
% 170.47/26.33 |
% 170.47/26.33 End of proof
% 170.47/26.33
% 170.47/26.33 Sub-proof #596 shows that the following formulas are inconsistent:
% 170.47/26.33 ----------------------------------------------------------------
% 170.47/26.33 (1) all_54_1 = e1 | all_54_1 = e0
% 170.47/26.33 (2) all_54_1 = all_52_4
% 170.47/26.33 (3) ~ (all_52_4 = e1)
% 170.47/26.33 (4) ~ (all_52_4 = e0)
% 170.47/26.33
% 170.47/26.33 Begin of proof
% 170.47/26.33 |
% 170.47/26.33 | BETA: splitting (1) gives:
% 170.47/26.33 |
% 170.47/26.33 | Case 1:
% 170.47/26.33 | |
% 170.47/26.33 | | (5) all_54_1 = e1
% 170.47/26.33 | |
% 170.47/26.33 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #954.
% 170.47/26.33 | |
% 170.47/26.33 | Case 2:
% 170.47/26.33 | |
% 170.47/26.33 | | (6) all_54_1 = e0
% 170.47/26.33 | |
% 170.47/26.33 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #614.
% 170.47/26.33 | |
% 170.47/26.33 | End of split
% 170.47/26.33 |
% 170.47/26.33 End of proof
% 170.47/26.33
% 170.47/26.33 Sub-proof #597 shows that the following formulas are inconsistent:
% 170.47/26.33 ----------------------------------------------------------------
% 170.47/26.33 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.33 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.33 (2) all_54_12 = all_52_3
% 170.47/26.33 (3) ~ (all_52_3 = e2)
% 170.47/26.33 (4) ~ (all_52_3 = e1)
% 170.47/26.33 (5) ~ (e3 = e1)
% 170.47/26.33 (6) op(e3, e3) = e1
% 170.47/26.33 (7) ~ (all_52_1 = all_52_3)
% 170.47/26.33 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.47/26.33 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.33 (9) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.33 (10) op(e3, e1) = all_52_8
% 170.47/26.33 (11) ~ (e1 = e0)
% 170.47/26.33 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.33 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.33 (13) op(e1, e2) = all_52_6
% 170.47/26.33 (14) op(e2, e3) = all_52_1
% 170.47/26.33 (15) op(e3, e1) = e3
% 170.47/26.33 (16) all_58_6 = e2
% 170.47/26.33 (17) ~ (e3 = e0)
% 170.47/26.33 (18) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.33 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.33 (20) ~ (e2 = e0)
% 170.47/26.33 (21) ~ (e2 = e1)
% 170.47/26.33 (22) ~ (all_52_3 = e0)
% 170.47/26.33 (23) ~ (all_52_6 = e3)
% 170.47/26.33 (24) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.33 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.33 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.33 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.33 (25) op(e3, e1) = e2
% 170.47/26.33 (26) ~ (e3 = e2)
% 170.47/26.33
% 170.47/26.33 Begin of proof
% 170.47/26.33 |
% 170.47/26.33 | BETA: splitting (9) gives:
% 170.47/26.33 |
% 170.47/26.33 | Case 1:
% 170.47/26.33 | |
% 170.47/26.33 | | (27) all_58_7 = e3 & op(e1, e2) = e3
% 170.47/26.33 | |
% 170.47/26.33 | | ALPHA: (27) implies:
% 170.47/26.33 | | (28) op(e1, e2) = e3
% 170.47/26.33 | |
% 170.47/26.33 | | REF_CLOSE: (13), (19), (23), (28) are inconsistent by sub-proof #668.
% 170.47/26.33 | |
% 170.47/26.33 | Case 2:
% 170.47/26.33 | |
% 170.47/26.33 | | (29) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.33 | |
% 170.47/26.33 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14),
% 170.47/26.33 | | (15), (16), (17), (18), (19), (20), (21), (22), (24), (25), (26),
% 170.47/26.33 | | (29) are inconsistent by sub-proof #598.
% 170.47/26.33 | |
% 170.47/26.33 | End of split
% 170.47/26.33 |
% 170.47/26.33 End of proof
% 170.47/26.33
% 170.47/26.33 Sub-proof #598 shows that the following formulas are inconsistent:
% 170.47/26.33 ----------------------------------------------------------------
% 170.47/26.33 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.33 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.33 (2) all_54_12 = all_52_3
% 170.47/26.33 (3) ~ (all_52_3 = e2)
% 170.47/26.33 (4) ~ (all_52_3 = e1)
% 170.47/26.33 (5) ~ (e3 = e1)
% 170.47/26.33 (6) op(e3, e3) = e1
% 170.47/26.33 (7) ~ (all_52_1 = all_52_3)
% 170.47/26.33 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.47/26.33 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.33 (9) op(e3, e1) = all_52_8
% 170.47/26.33 (10) ~ (e1 = e0)
% 170.47/26.33 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.33 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.33 (12) op(e2, e3) = all_52_1
% 170.47/26.33 (13) op(e3, e1) = e3
% 170.47/26.33 (14) all_58_6 = e2
% 170.47/26.33 (15) ~ (e3 = e0)
% 170.47/26.33 (16) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.33 (17) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.33 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.33 (19) ~ (e2 = e0)
% 170.47/26.33 (20) ~ (e2 = e1)
% 170.47/26.33 (21) ~ (all_52_3 = e0)
% 170.47/26.33 (22) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.33 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.33 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.33 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.33 (23) op(e3, e1) = e2
% 170.47/26.33 (24) ~ (e3 = e2)
% 170.47/26.33
% 170.47/26.33 Begin of proof
% 170.47/26.33 |
% 170.47/26.33 | ALPHA: (17) implies:
% 170.47/26.33 | (25) all_58_13 = e3
% 170.47/26.33 |
% 170.47/26.33 | BETA: splitting (11) gives:
% 170.47/26.33 |
% 170.47/26.33 | Case 1:
% 170.47/26.33 | |
% 170.47/26.33 | | (26) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 170.47/26.33 | | e3)
% 170.47/26.33 | |
% 170.47/26.33 | | BETA: splitting (26) gives:
% 170.47/26.33 | |
% 170.47/26.33 | | Case 1:
% 170.47/26.33 | | |
% 170.47/26.33 | | | (27) all_58_0 = e3 & op(e3, e3) = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | ALPHA: (27) implies:
% 170.47/26.33 | | | (28) op(e3, e3) = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | REF_CLOSE: (6), (9), (13), (18), (20), (23), (28) are inconsistent by
% 170.47/26.33 | | | sub-proof #804.
% 170.47/26.33 | | |
% 170.47/26.33 | | Case 2:
% 170.47/26.33 | | |
% 170.47/26.33 | | | (29) all_58_2 = e3 & op(e2, e3) = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | ALPHA: (29) implies:
% 170.47/26.33 | | | (30) op(e2, e3) = e3
% 170.47/26.33 | | |
% 170.47/26.33 | | | REF_CLOSE: (2), (3), (4), (7), (12), (16), (18), (21), (30) are
% 170.47/26.33 | | | inconsistent by sub-proof #605.
% 170.47/26.33 | | |
% 170.47/26.33 | | End of split
% 170.47/26.33 | |
% 170.47/26.33 | Case 2:
% 170.47/26.33 | |
% 170.47/26.33 | | (31) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 170.47/26.33 | | e3)
% 170.47/26.33 | |
% 170.47/26.33 | | REF_CLOSE: (1), (5), (8), (10), (14), (15), (19), (20), (22), (24), (25),
% 170.47/26.33 | | (31) are inconsistent by sub-proof #611.
% 170.47/26.33 | |
% 170.47/26.33 | End of split
% 170.47/26.33 |
% 170.47/26.33 End of proof
% 170.47/26.33
% 170.47/26.33 Sub-proof #599 shows that the following formulas are inconsistent:
% 170.47/26.33 ----------------------------------------------------------------
% 170.47/26.33 (1) all_54_12 = all_52_3
% 170.47/26.33 (2) ~ (all_52_3 = e2)
% 170.47/26.33 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.33 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.33 (4) ~ (all_52_3 = e1)
% 170.47/26.33 (5) ~ (e3 = e1)
% 170.47/26.33 (6) e3 = e1
% 170.47/26.33 (7) ~ (all_52_1 = all_52_3)
% 170.47/26.33 (8) ~ (e1 = e0)
% 170.47/26.33 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.33 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.33 (10) op(e2, e3) = all_52_1
% 170.47/26.33 (11) all_58_6 = e2
% 170.47/26.33 (12) ~ (e3 = e0)
% 170.47/26.33 (13) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.34 (14) all_58_1 = e3
% 170.47/26.34 (15) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.34 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.34 (16) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.34 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.34 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.34 (18) ~ (e2 = e0)
% 170.47/26.34 (19) all_58_12 = e3
% 170.47/26.34 (20) ~ (e2 = e1)
% 170.47/26.34 (21) ~ (all_52_3 = e0)
% 170.47/26.34 (22) all_58_4 = e2
% 170.47/26.34 (23) ~ (e3 = e2)
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | COMBINE_EQS: (6), (19) imply:
% 170.47/26.34 | (24) all_58_12 = e1
% 170.47/26.34 |
% 170.47/26.34 | BETA: splitting (9) gives:
% 170.47/26.34 |
% 170.47/26.34 | Case 1:
% 170.47/26.34 | |
% 170.47/26.34 | | (25) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) =
% 170.47/26.34 | | e3)
% 170.47/26.34 | |
% 170.47/26.34 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (12), (13), (14), (15),
% 170.47/26.34 | | (17), (18), (20), (21), (22), (25) are inconsistent by sub-proof
% 170.47/26.34 | | #604.
% 170.47/26.34 | |
% 170.47/26.34 | Case 2:
% 170.47/26.34 | |
% 170.47/26.34 | | (26) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) =
% 170.47/26.34 | | e3)
% 170.47/26.34 | |
% 170.47/26.34 | | BETA: splitting (26) gives:
% 170.47/26.34 | |
% 170.47/26.34 | | Case 1:
% 170.47/26.34 | | |
% 170.47/26.34 | | | (27) all_58_6 = e3 & op(e1, e3) = e3
% 170.47/26.34 | | |
% 170.47/26.34 | | | REF_CLOSE: (3), (5), (8), (11), (12), (14), (15), (16), (18), (20), (22),
% 170.47/26.34 | | | (23), (27) are inconsistent by sub-proof #606.
% 170.47/26.34 | | |
% 170.47/26.34 | | Case 2:
% 170.47/26.34 | | |
% 170.47/26.34 | | | (28) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.34 | | |
% 170.47/26.34 | | | REF_CLOSE: (5), (19), (24) are inconsistent by sub-proof #600.
% 170.47/26.34 | | |
% 170.47/26.34 | | End of split
% 170.47/26.34 | |
% 170.47/26.34 | End of split
% 170.47/26.34 |
% 170.47/26.34 End of proof
% 170.47/26.34
% 170.47/26.34 Sub-proof #600 shows that the following formulas are inconsistent:
% 170.47/26.34 ----------------------------------------------------------------
% 170.47/26.34 (1) all_58_12 = e3
% 170.47/26.34 (2) all_58_12 = e1
% 170.47/26.34 (3) ~ (e3 = e1)
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.34 | (4) e3 = e1
% 170.47/26.34 |
% 170.47/26.34 | SIMP: (4) implies:
% 170.47/26.34 | (5) e3 = e1
% 170.47/26.34 |
% 170.47/26.34 | REDUCE: (3), (5) imply:
% 170.47/26.34 | (6) $false
% 170.47/26.34 |
% 170.47/26.34 | CLOSE: (6) is inconsistent.
% 170.47/26.34 |
% 170.47/26.34 End of proof
% 170.47/26.34
% 170.47/26.34 Sub-proof #601 shows that the following formulas are inconsistent:
% 170.47/26.34 ----------------------------------------------------------------
% 170.47/26.34 (1) all_54_9 = all_52_6
% 170.47/26.34 (2) all_54_9 = e0
% 170.47/26.34 (3) ~ (all_52_6 = e0)
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.34 | (4) all_52_6 = e0
% 170.47/26.34 |
% 170.47/26.34 | SIMP: (4) implies:
% 170.47/26.34 | (5) all_52_6 = e0
% 170.47/26.34 |
% 170.47/26.34 | REDUCE: (3), (5) imply:
% 170.47/26.34 | (6) $false
% 170.47/26.34 |
% 170.47/26.34 | CLOSE: (6) is inconsistent.
% 170.47/26.34 |
% 170.47/26.34 End of proof
% 170.47/26.34
% 170.47/26.34 Sub-proof #602 shows that the following formulas are inconsistent:
% 170.47/26.34 ----------------------------------------------------------------
% 170.47/26.34 (1) ~ (all_52_14 = e1)
% 170.47/26.34 (2) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 170.47/26.34 (3) ~ (all_52_14 = e0)
% 170.47/26.34 (4) all_54_11 = all_52_14
% 170.47/26.34 (5) ~ (all_52_14 = e2)
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | BETA: splitting (2) gives:
% 170.47/26.34 |
% 170.47/26.34 | Case 1:
% 170.47/26.34 | |
% 170.47/26.34 | | (6) all_54_11 = e2
% 170.47/26.34 | |
% 170.47/26.34 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #622.
% 170.47/26.34 | |
% 170.47/26.34 | Case 2:
% 170.47/26.34 | |
% 170.47/26.34 | | (7) all_54_11 = e1 | all_54_11 = e0
% 170.47/26.34 | |
% 170.47/26.34 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #732.
% 170.47/26.34 | |
% 170.47/26.34 | End of split
% 170.47/26.34 |
% 170.47/26.34 End of proof
% 170.47/26.34
% 170.47/26.34 Sub-proof #603 shows that the following formulas are inconsistent:
% 170.47/26.34 ----------------------------------------------------------------
% 170.47/26.34 (1) all_54_12 = all_52_3
% 170.47/26.34 (2) ~ (all_8_2 = e3)
% 170.47/26.34 (3) ~ (all_52_3 = e2)
% 170.47/26.34 (4) ~ (all_52_3 = e1)
% 170.47/26.34 (5) ~ (all_52_1 = all_52_3)
% 170.47/26.34 (6) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 170.47/26.34 (7) op(e2, e3) = all_52_1
% 170.47/26.34 (8) op(e2, e2) = all_8_2
% 170.47/26.34 (9) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.34 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.34 (11) ~ (all_52_3 = e0)
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | BETA: splitting (6) gives:
% 170.47/26.34 |
% 170.47/26.34 | Case 1:
% 170.47/26.34 | |
% 170.47/26.34 | | (12) all_58_2 = e3 & op(e2, e3) = e3
% 170.47/26.34 | |
% 170.47/26.34 | | ALPHA: (12) implies:
% 170.47/26.34 | | (13) op(e2, e3) = e3
% 170.47/26.34 | |
% 170.47/26.34 | | REF_CLOSE: (1), (3), (4), (5), (7), (9), (10), (11), (13) are inconsistent
% 170.47/26.34 | | by sub-proof #605.
% 170.47/26.34 | |
% 170.47/26.34 | Case 2:
% 170.47/26.34 | |
% 170.47/26.34 | | (14) all_58_3 = e3 & op(e2, e2) = e3
% 170.47/26.34 | |
% 170.47/26.34 | | REF_CLOSE: (2), (8), (10), (14) are inconsistent by sub-proof #973.
% 170.47/26.34 | |
% 170.47/26.34 | End of split
% 170.47/26.34 |
% 170.47/26.34 End of proof
% 170.47/26.34
% 170.47/26.34 Sub-proof #604 shows that the following formulas are inconsistent:
% 170.47/26.34 ----------------------------------------------------------------
% 170.47/26.34 (1) all_54_12 = all_52_3
% 170.47/26.34 (2) ~ (all_52_3 = e2)
% 170.47/26.34 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.34 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.34 (4) ~ (all_52_3 = e1)
% 170.47/26.34 (5) ~ (e3 = e1)
% 170.47/26.34 (6) ~ (all_52_1 = all_52_3)
% 170.47/26.34 (7) ~ (e1 = e0)
% 170.47/26.34 (8) op(e2, e3) = all_52_1
% 170.47/26.34 (9) ~ (e3 = e0)
% 170.47/26.34 (10) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.34 (11) all_58_1 = e3
% 170.47/26.34 (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.34 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.34 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.34 (14) ~ (e2 = e0)
% 170.47/26.34 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3)
% 170.47/26.34 (16) ~ (e2 = e1)
% 170.47/26.34 (17) ~ (all_52_3 = e0)
% 170.47/26.34 (18) all_58_4 = e2
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | BETA: splitting (15) gives:
% 170.47/26.34 |
% 170.47/26.34 | Case 1:
% 170.47/26.34 | |
% 170.47/26.34 | | (19) all_58_0 = e3 & op(e3, e3) = e3
% 170.47/26.34 | |
% 170.47/26.34 | | ALPHA: (19) implies:
% 170.47/26.34 | | (20) all_58_0 = e3
% 170.47/26.34 | |
% 170.47/26.34 | | REF_CLOSE: (3), (5), (7), (9), (11), (12), (14), (16), (18), (20) are
% 170.47/26.34 | | inconsistent by sub-proof #641.
% 170.47/26.34 | |
% 170.47/26.34 | Case 2:
% 170.47/26.34 | |
% 170.47/26.34 | | (21) all_58_2 = e3 & op(e2, e3) = e3
% 170.47/26.34 | |
% 170.47/26.34 | | ALPHA: (21) implies:
% 170.47/26.34 | | (22) op(e2, e3) = e3
% 170.47/26.34 | |
% 170.47/26.34 | | REF_CLOSE: (1), (2), (4), (6), (8), (10), (13), (17), (22) are inconsistent
% 170.47/26.34 | | by sub-proof #605.
% 170.47/26.34 | |
% 170.47/26.34 | End of split
% 170.47/26.34 |
% 170.47/26.34 End of proof
% 170.47/26.34
% 170.47/26.34 Sub-proof #605 shows that the following formulas are inconsistent:
% 170.47/26.34 ----------------------------------------------------------------
% 170.47/26.34 (1) all_54_12 = all_52_3
% 170.47/26.34 (2) ~ (all_52_3 = e2)
% 170.47/26.34 (3) ~ (all_52_3 = e1)
% 170.47/26.34 (4) ~ (all_52_1 = all_52_3)
% 170.47/26.34 (5) op(e2, e3) = e3
% 170.47/26.34 (6) op(e2, e3) = all_52_1
% 170.47/26.34 (7) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.34 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.34 (9) ~ (all_52_3 = e0)
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | BETA: splitting (7) gives:
% 170.47/26.34 |
% 170.47/26.34 | Case 1:
% 170.47/26.34 | |
% 170.47/26.34 | | (10) all_54_12 = e3
% 170.47/26.34 | |
% 170.47/26.34 | | COMBINE_EQS: (1), (10) imply:
% 170.47/26.34 | | (11) all_52_3 = e3
% 170.47/26.34 | |
% 170.47/26.34 | | SIMP: (11) implies:
% 170.47/26.34 | | (12) all_52_3 = e3
% 170.47/26.34 | |
% 170.47/26.34 | | REDUCE: (4), (12) imply:
% 170.47/26.34 | | (13) ~ (all_52_1 = e3)
% 170.47/26.34 | |
% 170.47/26.34 | | REF_CLOSE: (5), (6), (8), (13) are inconsistent by sub-proof #989.
% 170.47/26.34 | |
% 170.47/26.34 | Case 2:
% 170.47/26.34 | |
% 170.47/26.34 | | (14) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.34 | |
% 170.47/26.34 | | REF_CLOSE: (1), (2), (3), (9), (14) are inconsistent by sub-proof #675.
% 170.47/26.34 | |
% 170.47/26.34 | End of split
% 170.47/26.34 |
% 170.47/26.34 End of proof
% 170.47/26.34
% 170.47/26.34 Sub-proof #606 shows that the following formulas are inconsistent:
% 170.47/26.34 ----------------------------------------------------------------
% 170.47/26.34 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.34 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.34 (2) ~ (e3 = e1)
% 170.47/26.34 (3) ~ (e1 = e0)
% 170.47/26.34 (4) all_58_6 = e3 & op(e1, e3) = e3
% 170.47/26.34 (5) all_58_6 = e2
% 170.47/26.34 (6) ~ (e3 = e0)
% 170.47/26.34 (7) all_58_1 = e3
% 170.47/26.34 (8) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.34 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.34 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.34 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.34 (10) ~ (e2 = e0)
% 170.47/26.34 (11) ~ (e2 = e1)
% 170.47/26.34 (12) all_58_4 = e2
% 170.47/26.34 (13) ~ (e3 = e2)
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | ALPHA: (4) implies:
% 170.47/26.34 | (14) all_58_6 = e3
% 170.47/26.34 |
% 170.47/26.34 | COMBINE_EQS: (5), (14) imply:
% 170.47/26.34 | (15) e3 = e2
% 170.47/26.34 |
% 170.47/26.34 | SIMP: (15) implies:
% 170.47/26.34 | (16) e3 = e2
% 170.47/26.34 |
% 170.47/26.34 | COMBINE_EQS: (7), (16) imply:
% 170.47/26.34 | (17) all_58_1 = e2
% 170.47/26.34 |
% 170.47/26.34 | REF_CLOSE: (1), (2), (3), (6), (8), (9), (10), (11), (12), (13), (17) are
% 170.47/26.34 | inconsistent by sub-proof #895.
% 170.47/26.34 |
% 170.47/26.34 End of proof
% 170.47/26.34
% 170.47/26.34 Sub-proof #607 shows that the following formulas are inconsistent:
% 170.47/26.34 ----------------------------------------------------------------
% 170.47/26.34 (1) all_58_15 = e2
% 170.47/26.34 (2) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.34 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.34 (3) op(e0, e0) = e2
% 170.47/26.34 (4) ~ (e3 = e1)
% 170.47/26.34 (5) all_58_13 = e0
% 170.47/26.34 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.47/26.34 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.34 (7) ~ (e1 = e0)
% 170.47/26.34 (8) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 170.47/26.34 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.47/26.34 (9) op(e0, e2) = e0
% 170.47/26.34 (10) ~ (e3 = e0)
% 170.47/26.34 (11) all_58_12 = e0
% 170.47/26.34 (12) all_58_3 = e2
% 170.47/26.34 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.34 (14) ~ (e2 = e1)
% 170.47/26.34 (15) all_58_7 = e3 & op(e1, e2) = e3
% 170.47/26.34 (16) op(e0, e2) = all_52_7
% 170.47/26.34 (17) ~ (e3 = e2)
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | ALPHA: (15) implies:
% 170.47/26.34 | (18) all_58_7 = e3
% 170.47/26.34 |
% 170.47/26.34 | BETA: splitting (8) gives:
% 170.47/26.34 |
% 170.47/26.34 | Case 1:
% 170.47/26.34 | |
% 170.47/26.34 | | (19) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 170.47/26.34 | | e3)
% 170.47/26.34 | |
% 170.47/26.34 | | BETA: splitting (19) gives:
% 170.47/26.34 | |
% 170.47/26.34 | | Case 1:
% 170.47/26.34 | | |
% 170.47/26.34 | | | (20) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.34 | | |
% 170.47/26.34 | | | ALPHA: (20) implies:
% 170.47/26.34 | | | (21) all_58_12 = e3
% 170.47/26.34 | | |
% 170.47/26.34 | | | REF_CLOSE: (10), (11), (21) are inconsistent by sub-proof #608.
% 170.47/26.34 | | |
% 170.47/26.34 | | Case 2:
% 170.47/26.34 | | |
% 170.47/26.34 | | | (22) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.34 | | |
% 170.47/26.34 | | | REF_CLOSE: (5), (10), (22) are inconsistent by sub-proof #634.
% 170.47/26.34 | | |
% 170.47/26.34 | | End of split
% 170.47/26.34 | |
% 170.47/26.34 | Case 2:
% 170.47/26.34 | |
% 170.47/26.34 | | (23) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.47/26.34 | | e3)
% 170.47/26.34 | |
% 170.47/26.34 | | BETA: splitting (23) gives:
% 170.47/26.34 | |
% 170.47/26.34 | | Case 1:
% 170.47/26.34 | | |
% 170.47/26.34 | | | (24) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.34 | | |
% 170.47/26.34 | | | ALPHA: (24) implies:
% 170.47/26.34 | | | (25) all_58_14 = e3
% 170.47/26.34 | | |
% 170.47/26.34 | | | BETA: splitting (2) gives:
% 170.47/26.34 | | |
% 170.47/26.34 | | | Case 1:
% 170.47/26.34 | | | |
% 170.47/26.34 | | | | (26) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 170.47/26.34 | | | | = e1)
% 170.47/26.34 | | | |
% 170.47/26.34 | | | | BETA: splitting (26) gives:
% 170.47/26.34 | | | |
% 170.47/26.34 | | | | Case 1:
% 170.47/26.34 | | | | |
% 170.47/26.34 | | | | | (27) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.34 | | | | |
% 170.47/26.34 | | | | | ALPHA: (27) implies:
% 170.47/26.34 | | | | | (28) all_58_1 = e1
% 170.47/26.34 | | | | |
% 170.47/26.34 | | | | | BETA: splitting (6) gives:
% 170.47/26.34 | | | | |
% 170.47/26.34 | | | | | Case 1:
% 170.47/26.34 | | | | | |
% 170.47/26.34 | | | | | | (29) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 170.47/26.34 | | | | | | op(e0, e2) = e1)
% 170.47/26.34 | | | | | |
% 170.47/26.34 | | | | | | BETA: splitting (29) gives:
% 170.47/26.34 | | | | | |
% 170.47/26.34 | | | | | | Case 1:
% 170.47/26.34 | | | | | | |
% 170.47/26.34 | | | | | | | (30) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.34 | | | | | | |
% 170.47/26.34 | | | | | | | ALPHA: (30) implies:
% 170.47/26.34 | | | | | | | (31) all_58_12 = e1
% 170.47/26.34 | | | | | | |
% 170.47/26.34 | | | | | | | COMBINE_EQS: (11), (31) imply:
% 170.47/26.34 | | | | | | | (32) e1 = e0
% 170.47/26.34 | | | | | | |
% 170.47/26.34 | | | | | | | COMBINE_EQS: (28), (32) imply:
% 170.47/26.34 | | | | | | | (33) all_58_1 = e0
% 170.47/26.34 | | | | | | |
% 170.47/26.34 | | | | | | | REF_CLOSE: (2), (4), (7), (9), (12), (13), (14), (16), (18), (33)
% 170.47/26.34 | | | | | | | are inconsistent by sub-proof #656.
% 170.47/26.34 | | | | | | |
% 170.47/26.34 | | | | | | Case 2:
% 170.47/26.34 | | | | | | |
% 170.47/26.34 | | | | | | | (34) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.34 | | | | | | |
% 170.47/26.34 | | | | | | | ALPHA: (34) implies:
% 170.47/26.34 | | | | | | | (35) op(e0, e2) = e1
% 170.47/26.34 | | | | | | |
% 170.47/26.34 | | | | | | | REF_CLOSE: (7), (9), (13), (16), (35) are inconsistent by
% 170.47/26.34 | | | | | | | sub-proof #889.
% 170.47/26.34 | | | | | | |
% 170.47/26.34 | | | | | | End of split
% 170.47/26.34 | | | | | |
% 170.47/26.34 | | | | | Case 2:
% 170.47/26.34 | | | | | |
% 170.47/26.34 | | | | | | (36) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 170.47/26.34 | | | | | | op(e0, e0) = e1)
% 170.47/26.34 | | | | | |
% 170.47/26.34 | | | | | | REF_CLOSE: (3), (4), (13), (14), (25), (36) are inconsistent by
% 170.47/26.34 | | | | | | sub-proof #632.
% 170.47/26.34 | | | | | |
% 170.47/26.34 | | | | | End of split
% 170.47/26.34 | | | | |
% 170.47/26.34 | | | | Case 2:
% 170.47/26.34 | | | | |
% 170.47/26.34 | | | | | (37) all_58_3 = e1 & op(e2, e2) = e1
% 170.47/26.34 | | | | |
% 170.47/26.34 | | | | | REF_CLOSE: (12), (14), (37) are inconsistent by sub-proof #914.
% 170.47/26.34 | | | | |
% 170.47/26.34 | | | | End of split
% 170.47/26.34 | | | |
% 170.47/26.34 | | | Case 2:
% 170.47/26.34 | | | |
% 170.47/26.34 | | | | (38) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 170.47/26.34 | | | | = e1)
% 170.47/26.34 | | | |
% 170.47/26.34 | | | | REF_CLOSE: (4), (7), (9), (13), (16), (18), (38) are inconsistent by
% 170.47/26.34 | | | | sub-proof #657.
% 170.47/26.34 | | | |
% 170.47/26.34 | | | End of split
% 170.47/26.34 | | |
% 170.47/26.34 | | Case 2:
% 170.47/26.34 | | |
% 170.47/26.34 | | | (39) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.34 | | |
% 170.47/26.34 | | | ALPHA: (39) implies:
% 170.47/26.34 | | | (40) all_58_15 = e3
% 170.47/26.34 | | |
% 170.47/26.34 | | | REF_CLOSE: (1), (17), (40) are inconsistent by sub-proof #856.
% 170.47/26.34 | | |
% 170.47/26.34 | | End of split
% 170.47/26.34 | |
% 170.47/26.34 | End of split
% 170.47/26.34 |
% 170.47/26.34 End of proof
% 170.47/26.34
% 170.47/26.34 Sub-proof #608 shows that the following formulas are inconsistent:
% 170.47/26.34 ----------------------------------------------------------------
% 170.47/26.34 (1) all_58_12 = e3
% 170.47/26.34 (2) all_58_12 = e0
% 170.47/26.34 (3) ~ (e3 = e0)
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.34 | (4) e3 = e0
% 170.47/26.34 |
% 170.47/26.34 | SIMP: (4) implies:
% 170.47/26.34 | (5) e3 = e0
% 170.47/26.34 |
% 170.47/26.34 | REDUCE: (3), (5) imply:
% 170.47/26.34 | (6) $false
% 170.47/26.34 |
% 170.47/26.34 | CLOSE: (6) is inconsistent.
% 170.47/26.34 |
% 170.47/26.34 End of proof
% 170.47/26.34
% 170.47/26.34 Sub-proof #609 shows that the following formulas are inconsistent:
% 170.47/26.34 ----------------------------------------------------------------
% 170.47/26.34 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.34 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.34 (2) all_58_15 = e2
% 170.47/26.34 (3) op(e0, e0) = e2
% 170.47/26.34 (4) ~ (e3 = e1)
% 170.47/26.34 (5) all_58_13 = e0
% 170.47/26.34 (6) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.47/26.34 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.34 (7) ~ (e1 = e0)
% 170.47/26.34 (8) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 170.47/26.34 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.47/26.34 (9) op(e0, e2) = e0
% 170.47/26.34 (10) all_58_6 = e2
% 170.47/26.34 (11) ~ (e3 = e0)
% 170.47/26.34 (12) all_58_6 = e0 & op(e1, e3) = e0
% 170.47/26.34 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.34 (14) ~ (e2 = e0)
% 170.47/26.34 (15) ~ (e2 = e1)
% 170.47/26.34 (16) op(e0, e2) = all_52_7
% 170.47/26.34 (17) ~ (e3 = e2)
% 170.47/26.34
% 170.47/26.34 Begin of proof
% 170.47/26.34 |
% 170.47/26.34 | ALPHA: (12) implies:
% 170.47/26.34 | (18) all_58_6 = e0
% 170.47/26.34 |
% 170.47/26.34 | COMBINE_EQS: (10), (18) imply:
% 170.47/26.34 | (19) e2 = e0
% 170.47/26.34 |
% 170.47/26.34 | SIMP: (19) implies:
% 170.47/26.34 | (20) e2 = e0
% 170.47/26.34 |
% 170.47/26.34 | COMBINE_EQS: (2), (20) imply:
% 170.47/26.35 | (21) all_58_15 = e0
% 170.47/26.35 |
% 170.47/26.35 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (13), (14), (15),
% 170.47/26.35 | (16), (17), (21) are inconsistent by sub-proof #628.
% 170.47/26.35 |
% 170.47/26.35 End of proof
% 170.47/26.35
% 170.47/26.35 Sub-proof #610 shows that the following formulas are inconsistent:
% 170.47/26.35 ----------------------------------------------------------------
% 170.47/26.35 (1) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.35 (2) ~ (e1 = e0)
% 170.47/26.35 (3) all_58_7 = e0
% 170.47/26.35 (4) op(e0, e2) = e0
% 170.47/26.35 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.35 (6) op(e0, e2) = all_52_7
% 170.47/26.35
% 170.47/26.35 Begin of proof
% 170.47/26.35 |
% 170.47/26.35 | BETA: splitting (1) gives:
% 170.47/26.35 |
% 170.47/26.35 | Case 1:
% 170.47/26.35 | |
% 170.47/26.35 | | (7) all_58_7 = e1 & op(e1, e2) = e1
% 170.47/26.35 | |
% 170.47/26.35 | | ALPHA: (7) implies:
% 170.47/26.35 | | (8) all_58_7 = e1
% 170.47/26.35 | |
% 170.47/26.35 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #710.
% 170.47/26.35 | |
% 170.47/26.35 | Case 2:
% 170.47/26.35 | |
% 170.47/26.35 | | (9) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.35 | |
% 170.47/26.35 | | ALPHA: (9) implies:
% 170.47/26.35 | | (10) op(e0, e2) = e1
% 170.47/26.35 | |
% 170.47/26.35 | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #889.
% 170.47/26.35 | |
% 170.47/26.35 | End of split
% 170.47/26.35 |
% 170.47/26.35 End of proof
% 170.47/26.35
% 170.47/26.35 Sub-proof #611 shows that the following formulas are inconsistent:
% 170.47/26.35 ----------------------------------------------------------------
% 170.47/26.35 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.35 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.35 (2) ~ (e3 = e1)
% 170.47/26.35 (3) all_58_13 = e3
% 170.47/26.35 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.47/26.35 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.35 (5) ~ (e1 = e0)
% 170.47/26.35 (6) all_58_6 = e2
% 170.47/26.35 (7) ~ (e3 = e0)
% 170.47/26.35 (8) ~ (e2 = e0)
% 170.47/26.35 (9) ~ (e2 = e1)
% 170.47/26.35 (10) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.35 (11) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.35 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.35 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.35 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.35 (12) ~ (e3 = e2)
% 170.47/26.35
% 170.47/26.35 Begin of proof
% 170.47/26.35 |
% 170.47/26.35 | BETA: splitting (10) gives:
% 170.47/26.35 |
% 170.47/26.35 | Case 1:
% 170.47/26.35 | |
% 170.47/26.35 | | (13) all_58_6 = e3 & op(e1, e3) = e3
% 170.47/26.35 | |
% 170.47/26.35 | | ALPHA: (13) implies:
% 170.47/26.35 | | (14) all_58_6 = e3
% 170.47/26.35 | |
% 170.47/26.35 | | REF_CLOSE: (6), (12), (14) are inconsistent by sub-proof #822.
% 170.47/26.35 | |
% 170.47/26.35 | Case 2:
% 170.47/26.35 | |
% 170.47/26.35 | | (15) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.35 | |
% 170.47/26.35 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (15) are
% 170.47/26.35 | | inconsistent by sub-proof #643.
% 170.47/26.35 | |
% 170.47/26.35 | End of split
% 170.47/26.35 |
% 170.47/26.35 End of proof
% 170.47/26.35
% 170.47/26.35 Sub-proof #612 shows that the following formulas are inconsistent:
% 170.47/26.35 ----------------------------------------------------------------
% 170.47/26.35 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.35 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.35 (2) op(e2, e1) = all_52_9
% 170.47/26.35 (3) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 170.47/26.35 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 170.47/26.35 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.35 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.35 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.47/26.35 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.35 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.35 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.35 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.35 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 170.47/26.35 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 170.47/26.35 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.35 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.35 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.35 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.47/26.35 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 170.47/26.35 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.35 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.35 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.35 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 170.47/26.35 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.35 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.35 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.35 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.35 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 170.47/26.35 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 170.47/26.35 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.47/26.35 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.35 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.35 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.47/26.35 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.35 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.35 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.35 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.35 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 170.47/26.35 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 170.47/26.35 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.47/26.35 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.35 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.35 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.47/26.35 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 170.47/26.35 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.35 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.35 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.35 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 170.47/26.35 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.47/26.35 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 170.47/26.35 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 170.47/26.35 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 170.47/26.35 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 170.47/26.35 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.47/26.35 (4) ~ (all_52_6 = all_52_14)
% 170.47/26.35 (5) ~ (all_52_1 = e3)
% 170.47/26.35 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.35 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.35 (7) all_54_14 = all_52_11
% 170.47/26.35 (8) all_58_15 = e2
% 170.47/26.35 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.47/26.35 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.47/26.35 (10) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.35 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.35 (11) all_54_12 = all_52_3
% 170.47/26.35 (12) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.35 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.35 (13) op(e0, e0) = e2
% 170.47/26.35 (14) ~ (all_8_2 = e3)
% 170.47/26.35 (15) ~ (all_56_14 = e0) | (all_56_13 = e1 & op(e1, e0) = e1)
% 170.47/26.35 (16) ~ (all_52_3 = e3)
% 170.47/26.35 (17) all_54_10 = all_6_2
% 170.47/26.35 (18) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 170.47/26.35 (19) ~ (all_52_1 = all_52_13)
% 170.47/26.35 (20) ~ (all_52_3 = e2)
% 170.47/26.35 (21) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.35 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.35 (22) all_56_14 = all_6_2
% 170.47/26.35 (23) ~ (all_52_1 = all_52_3)
% 170.47/26.35 (24) all_58_13 = e0
% 170.47/26.35 (25) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.35 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.35 e1)
% 170.47/26.35 (26) ~ (all_52_12 = e3)
% 170.47/26.35 (27) ~ (all_52_9 = all_52_11)
% 170.47/26.35 (28) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.35 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.47/26.35 e3)
% 170.47/26.35 (29) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.35 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.35 (30) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 170.47/26.35 (31) ~ (all_52_1 = e2)
% 170.47/26.35 (32) op(e1, e2) = all_52_6
% 170.47/26.35 (33) ~ (all_52_12 = e2)
% 170.47/26.35 (34) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.47/26.35 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.47/26.35 (35) op(e2, e3) = all_52_1
% 170.47/26.35 (36) ~ (all_52_6 = all_6_2)
% 170.47/26.35 (37) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 170.47/26.35 (38) all_54_1 = all_52_4
% 170.47/26.35 (39) ~ (all_52_14 = all_6_2)
% 170.47/26.35 (40) op(e0, e2) = e0
% 170.47/26.35 (41) op(e2, e2) = all_8_2
% 170.47/26.35 (42) all_56_12 = e2
% 170.47/26.35 (43) ~ (all_6_2 = e2)
% 170.47/26.35 (44) all_58_6 = e2
% 170.47/26.35 (45) op(e1, e1) = all_6_2
% 170.47/26.35 (46) ~ (all_52_6 = e2)
% 170.47/26.35 (47) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 170.47/26.35 (48) ~ (all_52_12 = all_52_14)
% 170.47/26.35 (49) all_54_4 = all_52_1
% 170.47/26.35 (50) ~ (all_52_11 = e2)
% 170.47/26.35 (51) ~ (e3 = e0)
% 170.47/26.35 (52) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 170.47/26.35 (53) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 170.47/26.35 (54) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.35 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.35 (55) ~ (all_52_13 = all_52_14)
% 170.47/26.35 (56) ~ (all_52_4 = e0)
% 170.47/26.35 (57) ~ (all_52_13 = e2)
% 170.47/26.35 (58) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.35 (59) ~ (all_52_4 = e3)
% 170.47/26.35 (60) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 170.47/26.35 (61) all_54_11 = all_52_14
% 170.47/26.35 (62) ~ (all_52_3 = all_52_11)
% 170.47/26.35 (63) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.47/26.35 (64) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.35 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.35 (65) ~ (all_52_11 = all_6_2)
% 170.47/26.35 (66) all_58_3 = e2
% 170.47/26.35 (67) ~ (all_52_4 = all_52_12)
% 170.47/26.35 (68) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.35 (69) ~ (e2 = e0)
% 170.47/26.35 (70) op(e1, e3) = e2
% 170.47/26.35 (71) ~ (all_52_12 = all_52_13)
% 170.47/26.35 (72) ~ (all_52_14 = e2)
% 170.47/26.35 (73) op(e3, e3) = e3
% 170.47/26.35 (74) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.35 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.35 (75) all_54_3 = all_52_12
% 170.47/26.35 (76) ~ (all_52_4 = e2)
% 170.47/26.35 (77) op(e3, e2) = all_52_4
% 170.47/26.35 (78) ~ (all_52_3 = e0)
% 170.47/26.35 (79) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.47/26.35 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.47/26.35 (80) all_54_9 = all_52_6
% 170.47/26.35 (81) op(e0, e2) = all_52_7
% 170.47/26.35 (82) all_54_7 = all_52_13
% 170.47/26.35 (83) ~ (all_52_11 = e0)
% 170.47/26.35 (84) all_58_4 = e2
% 170.47/26.35 (85) all_58_2 = e0
% 170.47/26.35 (86) ~ (all_52_9 = all_52_13)
% 170.47/26.35 (87) all_56_10 = e3
% 170.47/26.35 (88) ~ (e3 = e2)
% 170.47/26.35
% 170.47/26.35 Begin of proof
% 170.47/26.35 |
% 170.47/26.35 | BETA: splitting (10) gives:
% 170.47/26.35 |
% 170.47/26.35 | Case 1:
% 170.47/26.35 | |
% 170.47/26.35 | | (89) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.47/26.35 | | e3)
% 170.47/26.35 | |
% 170.47/26.35 | | REF_CLOSE: (14), (41), (59), (68), (77), (89) are inconsistent by sub-proof
% 170.47/26.35 | | #972.
% 170.47/26.35 | |
% 170.47/26.35 | Case 2:
% 170.47/26.35 | |
% 170.47/26.35 | | (90) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 170.47/26.35 | | e3)
% 170.47/26.35 | |
% 170.47/26.35 | | BETA: splitting (90) gives:
% 170.47/26.35 | |
% 170.47/26.35 | | Case 1:
% 170.47/26.35 | | |
% 170.47/26.35 | | | (91) all_58_7 = e3 & op(e1, e2) = e3
% 170.47/26.35 | | |
% 170.47/26.35 | | | ALPHA: (91) implies:
% 170.47/26.35 | | | (92) all_58_7 = e3
% 170.47/26.35 | | | (93) op(e1, e2) = e3
% 170.47/26.35 | | |
% 170.47/26.35 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13),
% 170.47/26.35 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 170.47/26.35 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 170.47/26.35 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 170.47/26.35 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 170.47/26.35 | | | (54), (55), (56), (57), (58), (59), (60), (61), (62), (63),
% 170.47/26.35 | | | (64), (65), (66), (67), (68), (69), (70), (71), (72), (73),
% 170.47/26.35 | | | (74), (75), (76), (77), (78), (79), (80), (81), (82), (83),
% 170.47/26.35 | | | (84), (85), (86), (87), (88), (92), (93) are inconsistent by
% 170.47/26.35 | | | sub-proof #613.
% 170.47/26.35 | | |
% 170.47/26.35 | | Case 2:
% 170.47/26.35 | | |
% 170.47/26.35 | | | (94) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.35 | | |
% 170.47/26.35 | | | ALPHA: (94) implies:
% 170.47/26.35 | | | (95) all_58_13 = e3
% 170.47/26.35 | | |
% 170.47/26.35 | | | REF_CLOSE: (24), (51), (95) are inconsistent by sub-proof #708.
% 170.47/26.35 | | |
% 170.47/26.35 | | End of split
% 170.47/26.35 | |
% 170.47/26.35 | End of split
% 170.47/26.35 |
% 170.47/26.35 End of proof
% 170.47/26.35
% 170.47/26.35 Sub-proof #613 shows that the following formulas are inconsistent:
% 170.47/26.35 ----------------------------------------------------------------
% 170.47/26.35 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.35 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.35 (2) op(e2, e1) = all_52_9
% 170.47/26.35 (3) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 170.47/26.35 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 170.47/26.35 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.35 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.35 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.47/26.35 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.35 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.35 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.35 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.35 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 170.47/26.35 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 170.47/26.35 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.35 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.35 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.35 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.47/26.35 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 170.47/26.36 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.36 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.36 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.36 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 170.47/26.36 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.36 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.36 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.36 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.36 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_5 = e1 & ~
% 170.47/26.36 (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 = e2) | ( ~
% 170.47/26.36 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.47/26.36 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.36 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.36 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.47/26.36 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.36 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.36 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.36 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.36 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_11 = e0 & ~
% 170.47/26.36 (all_56_12 = e2) & op(e2, e0) = e0 & ( ~ (all_56_10 = e2) | ( ~
% 170.47/26.36 (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.47/26.36 (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.36 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.36 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.47/26.36 (all_56_14 = e1) & op(e1, e0) = e0 & ( ~ (all_56_10 = e1) | ( ~
% 170.47/26.36 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.36 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.36 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.36 op(e0, e1) = all_56_8 & $i(all_56_8)))) | ( ~ (all_56_15 = e0) & (
% 170.47/26.36 ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.47/26.36 $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 170.47/26.36 op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~ (all_56_14 = e0) | (
% 170.47/26.36 ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 170.47/26.36 ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 170.47/26.36 | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.47/26.36 (4) ~ (all_52_6 = all_52_14)
% 170.47/26.36 (5) ~ (all_52_1 = e3)
% 170.47/26.36 (6) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.36 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.36 (7) all_54_14 = all_52_11
% 170.47/26.36 (8) all_58_15 = e2
% 170.47/26.36 (9) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.47/26.36 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.47/26.36 (10) all_54_12 = all_52_3
% 170.47/26.36 (11) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.36 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.36 (12) op(e0, e0) = e2
% 170.47/26.36 (13) ~ (all_8_2 = e3)
% 170.47/26.36 (14) ~ (all_56_14 = e0) | (all_56_13 = e1 & op(e1, e0) = e1)
% 170.47/26.36 (15) ~ (all_52_3 = e3)
% 170.47/26.36 (16) all_54_10 = all_6_2
% 170.47/26.36 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 170.47/26.36 (18) ~ (all_52_1 = all_52_13)
% 170.47/26.36 (19) ~ (all_52_3 = e2)
% 170.47/26.36 (20) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.36 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.36 (21) all_56_14 = all_6_2
% 170.47/26.36 (22) ~ (all_52_1 = all_52_3)
% 170.47/26.36 (23) all_58_13 = e0
% 170.47/26.36 (24) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.36 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.36 e1)
% 170.47/26.36 (25) ~ (all_52_12 = e3)
% 170.47/26.36 (26) ~ (all_52_9 = all_52_11)
% 170.47/26.36 (27) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.36 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.47/26.36 e3)
% 170.47/26.36 (28) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.36 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.36 (29) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 170.47/26.36 (30) ~ (all_52_1 = e2)
% 170.47/26.36 (31) op(e1, e2) = all_52_6
% 170.47/26.36 (32) ~ (all_52_12 = e2)
% 170.47/26.36 (33) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.47/26.36 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.47/26.36 (34) op(e2, e3) = all_52_1
% 170.47/26.36 (35) ~ (all_52_6 = all_6_2)
% 170.47/26.36 (36) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 170.47/26.36 (37) all_54_1 = all_52_4
% 170.47/26.36 (38) ~ (all_52_14 = all_6_2)
% 170.47/26.36 (39) op(e0, e2) = e0
% 170.47/26.36 (40) op(e2, e2) = all_8_2
% 170.47/26.36 (41) all_56_12 = e2
% 170.47/26.36 (42) ~ (all_6_2 = e2)
% 170.47/26.36 (43) all_58_6 = e2
% 170.47/26.36 (44) op(e1, e1) = all_6_2
% 170.47/26.36 (45) ~ (all_52_6 = e2)
% 170.47/26.36 (46) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 170.47/26.36 (47) ~ (all_52_12 = all_52_14)
% 170.47/26.36 (48) all_54_4 = all_52_1
% 170.47/26.36 (49) ~ (all_52_11 = e2)
% 170.47/26.36 (50) ~ (e3 = e0)
% 170.47/26.36 (51) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 170.47/26.36 (52) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 170.47/26.36 (53) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.36 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.36 (54) ~ (all_52_13 = all_52_14)
% 170.47/26.36 (55) ~ (all_52_4 = e0)
% 170.47/26.36 (56) ~ (all_52_13 = e2)
% 170.47/26.36 (57) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.36 (58) ~ (all_52_4 = e3)
% 170.47/26.36 (59) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 170.47/26.36 (60) all_54_11 = all_52_14
% 170.47/26.36 (61) ~ (all_52_3 = all_52_11)
% 170.47/26.36 (62) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.47/26.36 (63) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.36 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.36 (64) ~ (all_52_11 = all_6_2)
% 170.47/26.36 (65) all_58_3 = e2
% 170.47/26.36 (66) ~ (all_52_4 = all_52_12)
% 170.47/26.36 (67) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.36 (68) ~ (e2 = e0)
% 170.47/26.36 (69) op(e1, e3) = e2
% 170.47/26.36 (70) ~ (all_52_12 = all_52_13)
% 170.47/26.36 (71) ~ (all_52_14 = e2)
% 170.47/26.36 (72) op(e3, e3) = e3
% 170.47/26.36 (73) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.36 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.36 (74) all_54_3 = all_52_12
% 170.47/26.36 (75) op(e1, e2) = e3
% 170.47/26.36 (76) ~ (all_52_4 = e2)
% 170.47/26.36 (77) op(e3, e2) = all_52_4
% 170.47/26.36 (78) ~ (all_52_3 = e0)
% 170.47/26.36 (79) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.47/26.36 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.47/26.36 (80) all_54_9 = all_52_6
% 170.47/26.36 (81) op(e0, e2) = all_52_7
% 170.47/26.36 (82) all_54_7 = all_52_13
% 170.47/26.36 (83) ~ (all_52_11 = e0)
% 170.47/26.36 (84) all_58_4 = e2
% 170.47/26.36 (85) all_58_2 = e0
% 170.47/26.36 (86) ~ (all_52_9 = all_52_13)
% 170.47/26.36 (87) all_58_7 = e3
% 170.47/26.36 (88) all_56_10 = e3
% 170.47/26.36 (89) ~ (e3 = e2)
% 170.47/26.36
% 170.47/26.36 Begin of proof
% 170.47/26.36 |
% 170.47/26.36 | BETA: splitting (51) gives:
% 170.47/26.36 |
% 170.47/26.36 | Case 1:
% 170.47/26.36 | |
% 170.47/26.36 | | (90) all_54_1 = e3
% 170.47/26.36 | |
% 170.47/26.36 | | REF_CLOSE: (37), (58), (90) are inconsistent by sub-proof #956.
% 170.47/26.36 | |
% 170.47/26.36 | Case 2:
% 170.47/26.36 | |
% 170.47/26.36 | | (91) ~ (all_54_1 = e3)
% 170.47/26.36 | | (92) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 170.47/26.36 | |
% 170.47/26.36 | | BETA: splitting (92) gives:
% 170.47/26.36 | |
% 170.47/26.36 | | Case 1:
% 170.47/26.36 | | |
% 170.47/26.36 | | | (93) all_54_1 = e2
% 170.47/26.36 | | |
% 170.47/26.36 | | | REF_CLOSE: (37), (76), (93) are inconsistent by sub-proof #955.
% 170.47/26.36 | | |
% 170.47/26.36 | | Case 2:
% 170.47/26.36 | | |
% 170.47/26.36 | | | (94) ~ (all_54_1 = e2)
% 170.47/26.36 | | | (95) all_54_1 = e1 | all_54_1 = e0
% 170.47/26.36 | | |
% 170.47/26.36 | | | BETA: splitting (95) gives:
% 170.47/26.36 | | |
% 170.47/26.36 | | | Case 1:
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | (96) all_54_1 = e1
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | COMBINE_EQS: (37), (96) imply:
% 170.47/26.36 | | | | (97) all_52_4 = e1
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | SIMP: (97) implies:
% 170.47/26.36 | | | | (98) all_52_4 = e1
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | REDUCE: (66), (98) imply:
% 170.47/26.36 | | | | (99) ~ (all_52_12 = e1)
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | SIMP: (99) implies:
% 170.47/26.36 | | | | (100) ~ (all_52_12 = e1)
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | REDUCE: (58), (98) imply:
% 170.47/26.36 | | | | (101) ~ (e3 = e1)
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | SIMP: (101) implies:
% 170.47/26.36 | | | | (102) ~ (e3 = e1)
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | REDUCE: (76), (98) imply:
% 170.47/26.36 | | | | (103) ~ (e2 = e1)
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | SIMP: (103) implies:
% 170.47/26.36 | | | | (104) ~ (e2 = e1)
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | REDUCE: (55), (98) imply:
% 170.47/26.36 | | | | (105) ~ (e1 = e0)
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | BETA: splitting (20) gives:
% 170.47/26.36 | | | |
% 170.47/26.36 | | | | Case 1:
% 170.47/26.36 | | | | |
% 170.47/26.36 | | | | | (106) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 170.47/26.36 | | | | | e2) = e0)
% 170.47/26.36 | | | | |
% 170.47/26.36 | | | | | BETA: splitting (106) gives:
% 170.47/26.36 | | | | |
% 170.47/26.36 | | | | | Case 1:
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | (107) all_58_0 = e0 & op(e3, e3) = e0
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | ALPHA: (107) implies:
% 170.47/26.36 | | | | | | (108) op(e3, e3) = e0
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | REF_CLOSE: (50), (67), (72), (108) are inconsistent by sub-proof
% 170.47/26.36 | | | | | | #949.
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | Case 2:
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | (109) all_58_1 = e0 & op(e3, e2) = e0
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | ALPHA: (109) implies:
% 170.47/26.36 | | | | | | (110) all_58_1 = e0
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | REF_CLOSE: (11), (39), (65), (67), (81), (87), (102), (104), (105),
% 170.47/26.36 | | | | | | (110) are inconsistent by sub-proof #656.
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | End of split
% 170.47/26.36 | | | | |
% 170.47/26.36 | | | | Case 2:
% 170.47/26.36 | | | | |
% 170.47/26.36 | | | | | (111) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 170.47/26.36 | | | | | e0) = e0)
% 170.47/26.36 | | | | |
% 170.47/26.36 | | | | | BETA: splitting (111) gives:
% 170.47/26.36 | | | | |
% 170.47/26.36 | | | | | Case 1:
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | (112) all_58_4 = e0 & op(e3, e1) = e0
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | ALPHA: (112) implies:
% 170.47/26.36 | | | | | | (113) all_58_4 = e0
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | COMBINE_EQS: (84), (113) imply:
% 170.47/26.36 | | | | | | (114) e2 = e0
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | COMBINE_EQS: (8), (114) imply:
% 170.47/26.36 | | | | | | (115) all_58_15 = e0
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | REF_CLOSE: (1), (12), (23), (24), (27), (39), (50), (67), (68),
% 170.47/26.36 | | | | | | (81), (89), (102), (104), (105), (115) are inconsistent
% 170.47/26.36 | | | | | | by sub-proof #628.
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | Case 2:
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | (116) all_58_9 = e0 & op(e3, e0) = e0
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | ALPHA: (116) implies:
% 170.47/26.36 | | | | | | (117) all_58_9 = e0
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | BETA: splitting (27) gives:
% 170.47/26.36 | | | | | |
% 170.47/26.36 | | | | | | Case 1:
% 170.47/26.36 | | | | | | |
% 170.47/26.36 | | | | | | | (118) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 &
% 170.47/26.36 | | | | | | | op(e0, e2) = e3)
% 170.47/26.36 | | | | | | |
% 170.47/26.36 | | | | | | | BETA: splitting (118) gives:
% 170.47/26.36 | | | | | | |
% 170.47/26.36 | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | | (119) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | | ALPHA: (119) implies:
% 170.47/26.36 | | | | | | | | (120) all_58_12 = e3
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | | BETA: splitting (57) gives:
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | |
% 170.47/26.36 | | | | | | | | | (121) all_54_12 = e3
% 170.47/26.36 | | | | | | | | |
% 170.47/26.36 | | | | | | | | | REF_CLOSE: (10), (15), (121) are inconsistent by sub-proof
% 170.47/26.36 | | | | | | | | | #738.
% 170.47/26.36 | | | | | | | | |
% 170.47/26.36 | | | | | | | | Case 2:
% 170.47/26.36 | | | | | | | | |
% 170.47/26.36 | | | | | | | | | (122) ~ (all_54_12 = e3)
% 170.47/26.36 | | | | | | | | | (123) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.36 | | | | | | | | |
% 170.47/26.36 | | | | | | | | | BETA: splitting (123) gives:
% 170.47/26.36 | | | | | | | | |
% 170.47/26.36 | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | (124) all_54_12 = e2
% 170.47/26.36 | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | REF_CLOSE: (10), (19), (124) are inconsistent by sub-proof
% 170.47/26.36 | | | | | | | | | | #676.
% 170.47/26.36 | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | Case 2:
% 170.47/26.36 | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | (125) ~ (all_54_12 = e2)
% 170.47/26.36 | | | | | | | | | | (126) all_54_12 = e1 | all_54_12 = e0
% 170.47/26.36 | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | REF_CLOSE: (2), (5), (6), (7), (10), (12), (13), (15), (19),
% 170.47/26.36 | | | | | | | | | | (24), (26), (33), (34), (39), (40), (44), (49),
% 170.47/26.36 | | | | | | | | | | (53), (61), (62), (64), (65), (67), (68), (73),
% 170.47/26.36 | | | | | | | | | | (78), (79), (81), (83), (84), (120), (126) are
% 170.47/26.36 | | | | | | | | | | inconsistent by sub-proof #623.
% 170.47/26.36 | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | End of split
% 170.47/26.36 | | | | | | | | |
% 170.47/26.36 | | | | | | | | End of split
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | Case 2:
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | | (127) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | | REF_CLOSE: (23), (50), (127) are inconsistent by sub-proof #634.
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | End of split
% 170.47/26.36 | | | | | | |
% 170.47/26.36 | | | | | | Case 2:
% 170.47/26.36 | | | | | | |
% 170.47/26.36 | | | | | | | (128) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 &
% 170.47/26.36 | | | | | | | op(e0, e0) = e3)
% 170.47/26.36 | | | | | | |
% 170.47/26.36 | | | | | | | BETA: splitting (128) gives:
% 170.47/26.36 | | | | | | |
% 170.47/26.36 | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | | (129) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | | ALPHA: (129) implies:
% 170.47/26.36 | | | | | | | | (130) all_58_14 = e3
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | | BETA: splitting (11) gives:
% 170.47/26.36 | | | | | | | |
% 170.47/26.36 | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | |
% 170.47/26.36 | | | | | | | | | (131) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 &
% 170.47/26.36 | | | | | | | | | op(e2, e2) = e1)
% 170.47/26.36 | | | | | | | | |
% 170.47/26.36 | | | | | | | | | BETA: splitting (131) gives:
% 170.47/26.36 | | | | | | | | |
% 170.47/26.36 | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | (132) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.36 | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | ALPHA: (132) implies:
% 170.47/26.36 | | | | | | | | | | (133) all_58_1 = e1
% 170.47/26.36 | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | BETA: splitting (57) gives:
% 170.47/26.36 | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | (134) all_54_12 = e3
% 170.47/26.36 | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | REF_CLOSE: (10), (15), (134) are inconsistent by sub-proof
% 170.47/26.36 | | | | | | | | | | | #738.
% 170.47/26.36 | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | Case 2:
% 170.47/26.36 | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | (135) ~ (all_54_12 = e3)
% 170.47/26.36 | | | | | | | | | | | (136) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.36 | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | BETA: splitting (136) gives:
% 170.47/26.36 | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | (137) all_54_12 = e2
% 170.47/26.36 | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | REF_CLOSE: (10), (19), (137) are inconsistent by sub-proof
% 170.47/26.36 | | | | | | | | | | | | #676.
% 170.47/26.36 | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | Case 2:
% 170.47/26.36 | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | (138) ~ (all_54_12 = e2)
% 170.47/26.36 | | | | | | | | | | | | (139) all_54_12 = e1 | all_54_12 = e0
% 170.47/26.36 | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | BETA: splitting (24) gives:
% 170.47/26.36 | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | (140) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 170.47/26.36 | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 170.47/26.36 | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | BETA: splitting (140) gives:
% 170.47/26.36 | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | (141) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.36 | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | ALPHA: (141) implies:
% 170.47/26.36 | | | | | | | | | | | | | | (142) all_58_12 = e1
% 170.47/26.36 | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | BETA: splitting (46) gives:
% 170.47/26.36 | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | (143) all_54_9 = e3
% 170.47/26.36 | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | COMBINE_EQS: (80), (143) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | (144) all_52_6 = e3
% 170.47/26.36 | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | SIMP: (144) implies:
% 170.47/26.36 | | | | | | | | | | | | | | | (145) all_52_6 = e3
% 170.47/26.36 | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | REDUCE: (4), (145) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | (146) ~ (all_52_14 = e3)
% 170.47/26.36 | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | SIMP: (146) implies:
% 170.47/26.36 | | | | | | | | | | | | | | | (147) ~ (all_52_14 = e3)
% 170.47/26.36 | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | REDUCE: (35), (145) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | (148) ~ (all_6_2 = e3)
% 170.47/26.36 | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | SIMP: (148) implies:
% 170.47/26.36 | | | | | | | | | | | | | | | (149) ~ (all_6_2 = e3)
% 170.47/26.36 | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 170.47/26.36 | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | (150) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3
% 170.47/26.36 | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 170.47/26.36 | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 170.47/26.36 | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | (151) all_58_0 = e3 & op(e3, e3) = e3
% 170.47/26.36 | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 170.47/26.36 | | | | | | | | | | | | | | | | | (152) all_58_0 = e3
% 170.47/26.36 | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 170.47/26.36 | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | (153) all_54_3 = e3
% 170.47/26.36 | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (153) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | (154) all_52_12 = e3
% 170.47/26.36 | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | REDUCE: (25), (154) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | (155) $false
% 170.47/26.36 | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 170.47/26.36 | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.36 | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | (156) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 170.47/26.36 | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 170.47/26.36 | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | (157) all_54_3 = e2
% 170.47/26.36 | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (157) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | (158) all_52_12 = e2
% 170.47/26.36 | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | REDUCE: (32), (158) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | (159) $false
% 170.47/26.36 | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | CLOSE: (159) is inconsistent.
% 170.47/26.36 | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | (160) ~ (all_54_3 = e2)
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | (161) all_54_3 = e1 | all_54_3 = e0
% 170.47/26.36 | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | (162) all_54_3 = e1
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (162) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | (163) all_52_12 = e1
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | REDUCE: (100), (163) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | (164) $false
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | (165) all_54_3 = e0
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (74), (165) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | (166) all_52_12 = e0
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | REDUCE: (70), (166) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | (167) ~ (all_52_13 = e0)
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | SIMP: (167) implies:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | (168) ~ (all_52_13 = e0)
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | REDUCE: (47), (166) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | (169) ~ (all_52_14 = e0)
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | SIMP: (169) implies:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | (170) ~ (all_52_14 = e0)
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | REDUCE: (32), (166) imply:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | (171) ~ (e2 = e0)
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | (172) all_54_11 = e3
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (147), (172) are inconsistent by sub-proof
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | #742.
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | (173) ~ (all_54_11 = e3)
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | (174) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | | (175) all_54_11 = e2
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (71), (175) are inconsistent by sub-proof
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | | #622.
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.36 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | (176) ~ (all_54_11 = e2)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | (177) all_54_11 = e1 | all_54_11 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | (178) all_54_11 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (60), (178) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | (179) all_52_14 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (179) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | (180) all_52_14 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (54), (180) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | (181) ~ (all_52_13 = e1)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (38), (180) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | (182) ~ (all_6_2 = e1)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (182) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | (183) ~ (all_6_2 = e1)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (184) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (185) all_58_2 = e1 & op(e2, e3) = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (186) all_58_2 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (85), (186) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (187) e1 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (187) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (188) e1 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (188) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (189) all_58_1 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (63), (84), (102), (104), (105), (117), (152),
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (189) are inconsistent by sub-proof #639.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (190) all_58_3 = e1 & op(e2, e2) = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (65), (104), (190) are inconsistent by sub-proof
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | #914.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | (191) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (192) all_58_5 = e1 & op(e2, e1) = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (193) all_58_5 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | (194) op(e2, e1) = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (195) all_54_7 = e3
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (195) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (196) all_52_13 = e3
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (196) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (197) ~ (all_52_9 = e3)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (198) all_54_10 = e3
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (149), (198) are inconsistent by sub-proof
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | #982.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (199) ~ (all_54_10 = e3)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (200) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (13), (40), (43), (50), (67), (68), (105),
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (142), (152), (201) are inconsistent by sub-proof
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #620.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (202) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203) all_58_5 = e3 & op(e2, e1) = e3
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (204) op(e2, e1) = e3
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (67), (197), (204) are inconsistent by
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #951.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (205) all_58_10 = e3 & op(e2, e0) = e3
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206) all_58_10 = e3
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207) all_54_10 = e2
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (42), (207) are inconsistent by sub-proof
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #981.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (208) ~ (all_54_10 = e2)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209) all_54_10 = e1 | all_54_10 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210) all_54_10 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (183), (210) are inconsistent by sub-proof
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #980.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211) all_54_10 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (211) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212) all_6_2 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (212) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213) all_6_2 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (21), (213) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214) all_56_14 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (183), (213) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215) ~ (e1 = e0)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216) ~ (all_56_14 = e0)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (214), (216) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217) $false
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (217) is inconsistent.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218) all_56_13 = e1 & op(e1, e0) = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219) all_56_13 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (221) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (34), (67), (76), (77), (221) are
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #619.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_3 = e2 & ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e3) = all_56_0 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e0) & op(e0, e3) = all_56_6 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))))
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (224) op(e1, e3) = e3
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225) all_54_12 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (225) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (226) all_52_3 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (226) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227) all_52_3 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (22), (227) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228) ~ (all_52_1 = e1)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (59) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229) all_54_4 = e3
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (48), (229) are inconsistent by sub-proof
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #618.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230) ~ (all_54_4 = e3)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232) all_54_4 = e2
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (30), (48), (232) are inconsistent by sub-proof
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #691.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (233) ~ (all_54_4 = e2)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234) all_54_4 = e1 | all_54_4 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (235) all_54_4 = e1
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (228), (235) are inconsistent by sub-proof
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #617.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236) all_54_4 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (48), (236) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237) all_52_1 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (237) implies:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238) all_52_1 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (238) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239) ~ (e3 = e0)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (67) with e2, e3, e3, e1,
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (69), (224) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (240) e3 = e2
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (206), (240) imply:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (241) all_58_10 = e2
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (40), (50), (53), (65), (67), (68), (73),
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (89), (102), (105), (193), (194), (241) are
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #909.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (242) all_54_12 = e0
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (78), (242) are inconsistent by sub-proof
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #653.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (243) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | (all_56_4 = e1 & ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (45), (67), (88), (243) are inconsistent by
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #985.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (244) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6)))) |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (244) gives:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (245) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (88), (245) are inconsistent by sub-proof
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #983.
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (246) (all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 170.47/26.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 =
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e2) = all_56_1 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e0) & op(e0, e2) = all_56_7 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)))) | (all_56_13 = e0 & ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e1) & op(e1, e0) = e0 & ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_8 & $i(all_56_8)))) | (
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0,
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e3) | (all_56_7 = e2 & op(e0, e2) =
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) | (all_56_8 = e1 & op(e0, e1) = e1)))
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247) all_56_11 = e0 & ~ (all_56_12 = e2) & op(e2, e0)
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e2) | ( ~ (all_56_1 = e3)
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = all_56_1 & $i(all_56_1))) & ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1,
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_3 & $i(all_56_3))) & ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) | ( ~ (all_56_7 = e0) & op(e0,
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_7 & $i(all_56_7)))
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248) ~ (all_56_12 = e2)
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (248) imply:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (249) $false
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (249) is inconsistent.
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (250) (all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 =
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e1) = all_56_4 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e0) & op(e0, e1) = all_56_8 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)))) | ( ~ (all_56_15 = e0) & ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) | ( ~ (all_56_9 = e3) &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_56_9 & $i(all_56_9))) & ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) | ( ~ (all_56_11 = e2) &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_56_11 & $i(all_56_11))) & (
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))) &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 =
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2) | (all_56_8 = e1 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = e1)))
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (250) gives:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (251) all_56_13 = e0 & ~ (all_56_14 = e1) & op(e1, e0)
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0 & ( ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3)
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2,
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_5 & $i(all_56_5))) & ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0,
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_8 & $i(all_56_8)))
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (251) implies:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) all_56_13 = e0
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (17), (21), (42), (105), (149), (183),
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (252) are inconsistent by sub-proof #976.
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (253) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e3) & op(e3, e0) = all_56_9 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ( ~ (all_56_14 = e0) | ( ~
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3)
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1 & op(e0, e1) = e1))
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (253) implies:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (254) ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) &
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_13 & $i(all_56_13))
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (214), (219), (254) are inconsistent by sub-proof
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #616.
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (255) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (82), (168), (181), (255) are inconsistent
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #615.
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | (256) all_58_10 = e1 & op(e2, e0) = e1
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | (257) all_58_10 = e1
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (258) all_54_7 = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (258) imply:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (259) all_52_13 = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (86), (259) imply:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (260) ~ (all_52_9 = e3)
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (261) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (13), (40), (43), (50), (67), (68), (105),
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (142), (152), (261) are inconsistent by sub-proof
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | #620.
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (262) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (262) gives:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (263) all_58_5 = e3 & op(e2, e1) = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (264) op(e2, e1) = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (67), (260), (264) are inconsistent by
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #951.
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (265) all_58_10 = e3 & op(e2, e0) = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (266) all_58_10 = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (266) imply:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (267) e3 = e1
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (267) implies:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (268) e3 = e1
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (268) imply:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_58_14 = e1
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (13), (33), (40), (44), (50), (53),
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (65), (67), (68), (73), (79), (84), (89), (102),
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (104), (105), (149), (260), (266), (269) are
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #625.
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (82), (168), (181), (270) are inconsistent
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #615.
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | (271) all_54_11 = e0
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (60), (170), (271) are inconsistent by sub-proof
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | | #733.
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | (272) all_58_2 = e3 & op(e2, e3) = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 170.47/26.38 | | | | | | | | | | | | | | | | | (273) op(e2, e3) = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (34), (67), (273) are inconsistent by
% 170.47/26.38 | | | | | | | | | | | | | | | | | sub-proof #989.
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | (274) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 =
% 170.47/26.38 | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 170.47/26.38 | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 170.47/26.38 | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | (275) all_58_6 = e3 & op(e1, e3) = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 170.47/26.38 | | | | | | | | | | | | | | | | | (276) all_58_6 = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (89), (276) are inconsistent by sub-proof
% 170.47/26.38 | | | | | | | | | | | | | | | | | #822.
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | (277) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | ALPHA: (277) implies:
% 170.47/26.38 | | | | | | | | | | | | | | | | | (278) all_58_12 = e3
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (6), (7), (10), (12), (13), (15), (19),
% 170.47/26.38 | | | | | | | | | | | | | | | | | (24), (26), (33), (34), (39), (40), (44), (49),
% 170.47/26.38 | | | | | | | | | | | | | | | | | (53), (61), (62), (64), (65), (67), (68), (73),
% 170.47/26.38 | | | | | | | | | | | | | | | | | (78), (79), (81), (83), (84), (139), (278) are
% 170.47/26.38 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 170.47/26.38 | | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | (279) ~ (all_54_9 = e3)
% 170.47/26.38 | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | REDUCE: (80), (279) imply:
% 170.47/26.38 | | | | | | | | | | | | | | | (280) ~ (all_52_6 = e3)
% 170.47/26.38 | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | | REF_CLOSE: (31), (67), (75), (280) are inconsistent by
% 170.47/26.38 | | | | | | | | | | | | | | | sub-proof #668.
% 170.47/26.38 | | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | (281) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.38 | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | ALPHA: (281) implies:
% 170.47/26.38 | | | | | | | | | | | | | | (282) op(e0, e2) = e1
% 170.47/26.38 | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | | REF_CLOSE: (39), (67), (81), (105), (282) are inconsistent by
% 170.47/26.38 | | | | | | | | | | | | | | sub-proof #889.
% 170.47/26.38 | | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | (283) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 170.47/26.38 | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 170.47/26.38 | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | | REF_CLOSE: (12), (67), (102), (104), (130), (283) are
% 170.47/26.38 | | | | | | | | | | | | | inconsistent by sub-proof #632.
% 170.47/26.38 | | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | (284) all_58_3 = e1 & op(e2, e2) = e1
% 170.47/26.38 | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | | REF_CLOSE: (65), (104), (284) are inconsistent by sub-proof
% 170.47/26.38 | | | | | | | | | | #914.
% 170.47/26.38 | | | | | | | | | |
% 170.47/26.38 | | | | | | | | | End of split
% 170.47/26.38 | | | | | | | | |
% 170.47/26.38 | | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | | |
% 170.47/26.38 | | | | | | | | | (285) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 &
% 170.47/26.38 | | | | | | | | | op(e0, e2) = e1)
% 170.47/26.38 | | | | | | | | |
% 170.47/26.38 | | | | | | | | | REF_CLOSE: (39), (67), (81), (87), (102), (105), (285) are
% 170.47/26.38 | | | | | | | | | inconsistent by sub-proof #657.
% 170.47/26.38 | | | | | | | | |
% 170.47/26.38 | | | | | | | | End of split
% 170.47/26.38 | | | | | | | |
% 170.47/26.38 | | | | | | | Case 2:
% 170.47/26.38 | | | | | | | |
% 170.47/26.38 | | | | | | | | (286) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.38 | | | | | | | |
% 170.47/26.38 | | | | | | | | ALPHA: (286) implies:
% 170.47/26.38 | | | | | | | | (287) all_58_15 = e3
% 170.47/26.38 | | | | | | | |
% 170.47/26.38 | | | | | | | | REF_CLOSE: (8), (89), (287) are inconsistent by sub-proof #856.
% 170.47/26.38 | | | | | | | |
% 170.47/26.38 | | | | | | | End of split
% 170.47/26.38 | | | | | | |
% 170.47/26.38 | | | | | | End of split
% 170.47/26.38 | | | | | |
% 170.47/26.38 | | | | | End of split
% 170.47/26.38 | | | | |
% 170.47/26.38 | | | | End of split
% 170.47/26.38 | | | |
% 170.47/26.38 | | | Case 2:
% 170.47/26.38 | | | |
% 170.47/26.38 | | | | (288) all_54_1 = e0
% 170.47/26.38 | | | |
% 170.47/26.38 | | | | REF_CLOSE: (37), (55), (288) are inconsistent by sub-proof #614.
% 170.47/26.38 | | | |
% 170.47/26.38 | | | End of split
% 170.47/26.38 | | |
% 170.47/26.38 | | End of split
% 170.47/26.38 | |
% 170.47/26.38 | End of split
% 170.47/26.38 |
% 170.47/26.38 End of proof
% 170.47/26.38
% 170.47/26.38 Sub-proof #614 shows that the following formulas are inconsistent:
% 170.47/26.38 ----------------------------------------------------------------
% 170.47/26.38 (1) all_54_1 = all_52_4
% 170.47/26.38 (2) all_54_1 = e0
% 170.47/26.38 (3) ~ (all_52_4 = e0)
% 170.47/26.38
% 170.47/26.38 Begin of proof
% 170.47/26.38 |
% 170.47/26.38 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.38 | (4) all_52_4 = e0
% 170.47/26.38 |
% 170.47/26.38 | SIMP: (4) implies:
% 170.47/26.38 | (5) all_52_4 = e0
% 170.47/26.38 |
% 170.47/26.38 | REDUCE: (3), (5) imply:
% 170.47/26.38 | (6) $false
% 170.47/26.38 |
% 170.47/26.38 | CLOSE: (6) is inconsistent.
% 170.47/26.38 |
% 170.47/26.38 End of proof
% 170.47/26.38
% 170.47/26.38 Sub-proof #615 shows that the following formulas are inconsistent:
% 170.47/26.38 ----------------------------------------------------------------
% 170.47/26.38 (1) ~ (all_52_13 = e0)
% 170.47/26.38 (2) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 170.47/26.38 (3) ~ (all_52_13 = e1)
% 170.47/26.38 (4) ~ (all_52_13 = e2)
% 170.47/26.38 (5) all_54_7 = all_52_13
% 170.47/26.38
% 170.47/26.38 Begin of proof
% 170.47/26.38 |
% 170.47/26.38 | BETA: splitting (2) gives:
% 170.47/26.38 |
% 170.47/26.38 | Case 1:
% 170.47/26.38 | |
% 170.47/26.38 | | (6) all_54_7 = e2
% 170.47/26.38 | |
% 170.47/26.38 | | COMBINE_EQS: (5), (6) imply:
% 170.47/26.38 | | (7) all_52_13 = e2
% 170.47/26.38 | |
% 170.47/26.38 | | REDUCE: (4), (7) imply:
% 170.47/26.38 | | (8) $false
% 170.47/26.38 | |
% 170.47/26.38 | | CLOSE: (8) is inconsistent.
% 170.47/26.38 | |
% 170.47/26.38 | Case 2:
% 170.47/26.38 | |
% 170.47/26.38 | | (9) all_54_7 = e1 | all_54_7 = e0
% 170.47/26.38 | |
% 170.47/26.38 | | BETA: splitting (9) gives:
% 170.47/26.38 | |
% 170.47/26.38 | | Case 1:
% 170.47/26.38 | | |
% 170.47/26.38 | | | (10) all_54_7 = e1
% 170.47/26.38 | | |
% 170.47/26.38 | | | COMBINE_EQS: (5), (10) imply:
% 170.47/26.38 | | | (11) all_52_13 = e1
% 170.47/26.38 | | |
% 170.47/26.38 | | | REDUCE: (3), (11) imply:
% 170.47/26.38 | | | (12) $false
% 170.47/26.38 | | |
% 170.47/26.38 | | | CLOSE: (12) is inconsistent.
% 170.47/26.38 | | |
% 170.47/26.38 | | Case 2:
% 170.47/26.38 | | |
% 170.47/26.38 | | | (13) all_54_7 = e0
% 170.47/26.38 | | |
% 170.47/26.38 | | | COMBINE_EQS: (5), (13) imply:
% 170.47/26.38 | | | (14) all_52_13 = e0
% 170.47/26.38 | | |
% 170.47/26.38 | | | REDUCE: (1), (14) imply:
% 170.47/26.38 | | | (15) $false
% 170.47/26.38 | | |
% 170.47/26.38 | | | CLOSE: (15) is inconsistent.
% 170.47/26.38 | | |
% 170.47/26.38 | | End of split
% 170.47/26.38 | |
% 170.47/26.38 | End of split
% 170.47/26.38 |
% 170.47/26.38 End of proof
% 170.47/26.38
% 170.47/26.38 Sub-proof #616 shows that the following formulas are inconsistent:
% 170.47/26.38 ----------------------------------------------------------------
% 170.47/26.38 (1) ~ (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.47/26.38 $i(all_56_13))
% 170.47/26.38 (2) all_56_14 = e0
% 170.47/26.38 (3) all_56_13 = e1
% 170.47/26.38
% 170.47/26.38 Begin of proof
% 170.47/26.38 |
% 170.47/26.38 | BETA: splitting (1) gives:
% 170.47/26.38 |
% 170.47/26.38 | Case 1:
% 170.47/26.38 | |
% 170.47/26.38 | | (4) ~ (all_56_14 = e0)
% 170.47/26.38 | |
% 170.47/26.38 | | REDUCE: (2), (4) imply:
% 170.47/26.38 | | (5) $false
% 170.47/26.38 | |
% 170.47/26.38 | | CLOSE: (5) is inconsistent.
% 170.47/26.38 | |
% 170.47/26.38 | Case 2:
% 170.47/26.38 | |
% 170.47/26.38 | | (6) ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 & $i(all_56_13)
% 170.47/26.38 | |
% 170.47/26.38 | | ALPHA: (6) implies:
% 170.47/26.38 | | (7) ~ (all_56_13 = e1)
% 170.47/26.38 | |
% 170.47/26.38 | | REDUCE: (3), (7) imply:
% 170.47/26.38 | | (8) $false
% 170.47/26.38 | |
% 170.47/26.38 | | CLOSE: (8) is inconsistent.
% 170.47/26.38 | |
% 170.47/26.38 | End of split
% 170.47/26.38 |
% 170.47/26.38 End of proof
% 170.47/26.38
% 170.47/26.38 Sub-proof #617 shows that the following formulas are inconsistent:
% 170.47/26.38 ----------------------------------------------------------------
% 170.47/26.38 (1) all_54_4 = all_52_1
% 170.47/26.38 (2) all_54_4 = e1
% 170.47/26.38 (3) ~ (all_52_1 = e1)
% 170.47/26.38
% 170.47/26.38 Begin of proof
% 170.47/26.38 |
% 170.47/26.38 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.38 | (4) all_52_1 = e1
% 170.47/26.38 |
% 170.47/26.38 | SIMP: (4) implies:
% 170.47/26.38 | (5) all_52_1 = e1
% 170.47/26.38 |
% 170.47/26.38 | REDUCE: (3), (5) imply:
% 170.47/26.38 | (6) $false
% 170.47/26.38 |
% 170.47/26.38 | CLOSE: (6) is inconsistent.
% 170.47/26.38 |
% 170.47/26.38 End of proof
% 170.47/26.38
% 170.47/26.38 Sub-proof #618 shows that the following formulas are inconsistent:
% 170.47/26.38 ----------------------------------------------------------------
% 170.47/26.38 (1) all_54_4 = all_52_1
% 170.47/26.38 (2) all_54_4 = e3
% 170.47/26.38 (3) ~ (all_52_1 = e3)
% 170.47/26.38
% 170.47/26.38 Begin of proof
% 170.47/26.38 |
% 170.47/26.38 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.38 | (4) all_52_1 = e3
% 170.47/26.38 |
% 170.47/26.38 | SIMP: (4) implies:
% 170.47/26.38 | (5) all_52_1 = e3
% 170.47/26.38 |
% 170.47/26.38 | REDUCE: (3), (5) imply:
% 170.47/26.38 | (6) $false
% 170.47/26.38 |
% 170.47/26.38 | CLOSE: (6) is inconsistent.
% 170.47/26.38 |
% 170.47/26.38 End of proof
% 170.47/26.38
% 170.47/26.38 Sub-proof #619 shows that the following formulas are inconsistent:
% 170.47/26.38 ----------------------------------------------------------------
% 170.47/26.38 (1) ~ (all_52_1 = e3)
% 170.47/26.38 (2) op(e2, e3) = all_52_1
% 170.47/26.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.38 (4) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 170.47/26.38 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 170.47/26.38 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.47/26.38 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.47/26.38 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.47/26.38 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 170.47/26.38 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.47/26.38 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.47/26.38 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.47/26.38 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.47/26.38 (5) ~ (all_52_4 = e2)
% 170.47/26.38 (6) op(e3, e2) = all_52_4
% 170.47/26.38
% 170.47/26.38 Begin of proof
% 170.47/26.38 |
% 170.47/26.38 | BETA: splitting (4) gives:
% 170.47/26.38 |
% 170.47/26.38 | Case 1:
% 170.47/26.38 | |
% 170.47/26.38 | | (7) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 170.47/26.38 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 170.47/26.38 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 170.47/26.38 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 170.47/26.38 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 170.47/26.38 | |
% 170.47/26.38 | | ALPHA: (7) implies:
% 170.47/26.38 | | (8) op(e2, e3) = e3
% 170.47/26.38 | |
% 170.47/26.38 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #989.
% 170.47/26.38 | |
% 170.47/26.38 | Case 2:
% 170.47/26.38 | |
% 170.47/26.38 | | (9) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 170.47/26.38 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 170.47/26.38 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.47/26.38 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 170.47/26.38 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 170.47/26.38 | |
% 170.47/26.38 | | ALPHA: (9) implies:
% 170.47/26.38 | | (10) op(e3, e2) = e2
% 170.47/26.38 | |
% 170.47/26.38 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #993.
% 170.47/26.38 | |
% 170.47/26.38 | End of split
% 170.47/26.38 |
% 170.47/26.38 End of proof
% 170.47/26.38
% 170.47/26.38 Sub-proof #620 shows that the following formulas are inconsistent:
% 170.47/26.38 ----------------------------------------------------------------
% 170.47/26.38 (1) all_58_12 = e1
% 170.47/26.38 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.47/26.38 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.47/26.38 (3) ~ (all_8_2 = e3)
% 170.47/26.38 (4) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 170.47/26.38 (5) ~ (e1 = e0)
% 170.47/26.38 (6) op(e2, e2) = all_8_2
% 170.47/26.38 (7) all_58_6 = e2
% 170.47/26.38 (8) ~ (e3 = e0)
% 170.47/26.38 (9) all_58_0 = e3
% 170.47/26.38 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.38 (11) ~ (e2 = e0)
% 170.47/26.38
% 170.47/26.38 Begin of proof
% 170.47/26.38 |
% 170.47/26.38 | BETA: splitting (4) gives:
% 170.47/26.38 |
% 170.47/26.38 | Case 1:
% 170.47/26.38 | |
% 170.47/26.39 | | (12) all_58_2 = e3 & op(e2, e3) = e3
% 170.47/26.39 | |
% 170.47/26.39 | | ALPHA: (12) implies:
% 170.47/26.39 | | (13) all_58_2 = e3
% 170.47/26.39 | |
% 170.47/26.39 | | BETA: splitting (2) gives:
% 170.47/26.39 | |
% 170.47/26.39 | | Case 1:
% 170.47/26.39 | | |
% 170.47/26.39 | | | (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) =
% 170.47/26.39 | | | e0)
% 170.47/26.39 | | |
% 170.47/26.39 | | | BETA: splitting (14) gives:
% 170.47/26.39 | | |
% 170.47/26.39 | | | Case 1:
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | (15) all_58_0 = e0 & op(e3, e3) = e0
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | REF_CLOSE: (8), (9), (15) are inconsistent by sub-proof #898.
% 170.47/26.39 | | | |
% 170.47/26.39 | | | Case 2:
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | (16) all_58_2 = e0 & op(e2, e3) = e0
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | REF_CLOSE: (8), (13), (16) are inconsistent by sub-proof #621.
% 170.47/26.39 | | | |
% 170.47/26.39 | | | End of split
% 170.47/26.39 | | |
% 170.47/26.39 | | Case 2:
% 170.47/26.39 | | |
% 170.47/26.39 | | | (17) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) =
% 170.47/26.39 | | | e0)
% 170.47/26.39 | | |
% 170.47/26.39 | | | BETA: splitting (17) gives:
% 170.47/26.39 | | |
% 170.47/26.39 | | | Case 1:
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | (18) all_58_6 = e0 & op(e1, e3) = e0
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | REF_CLOSE: (7), (11), (18) are inconsistent by sub-proof #769.
% 170.47/26.39 | | | |
% 170.47/26.39 | | | Case 2:
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | (19) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | REF_CLOSE: (1), (5), (19) are inconsistent by sub-proof #859.
% 170.47/26.39 | | | |
% 170.47/26.39 | | | End of split
% 170.47/26.39 | | |
% 170.47/26.39 | | End of split
% 170.47/26.39 | |
% 170.47/26.39 | Case 2:
% 170.47/26.39 | |
% 170.47/26.39 | | (20) all_58_3 = e3 & op(e2, e2) = e3
% 170.47/26.39 | |
% 170.47/26.39 | | REF_CLOSE: (3), (6), (10), (20) are inconsistent by sub-proof #973.
% 170.47/26.39 | |
% 170.47/26.39 | End of split
% 170.47/26.39 |
% 170.47/26.39 End of proof
% 170.47/26.39
% 170.47/26.39 Sub-proof #621 shows that the following formulas are inconsistent:
% 170.47/26.39 ----------------------------------------------------------------
% 170.47/26.39 (1) all_58_2 = e0 & op(e2, e3) = e0
% 170.47/26.39 (2) all_58_2 = e3
% 170.47/26.39 (3) ~ (e3 = e0)
% 170.47/26.39
% 170.47/26.39 Begin of proof
% 170.47/26.39 |
% 170.47/26.39 | ALPHA: (1) implies:
% 170.47/26.39 | (4) all_58_2 = e0
% 170.47/26.39 |
% 170.47/26.39 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.39 | (5) e3 = e0
% 170.47/26.39 |
% 170.47/26.39 | REDUCE: (3), (5) imply:
% 170.47/26.39 | (6) $false
% 170.47/26.39 |
% 170.47/26.39 | CLOSE: (6) is inconsistent.
% 170.47/26.39 |
% 170.47/26.39 End of proof
% 170.47/26.39
% 170.47/26.39 Sub-proof #622 shows that the following formulas are inconsistent:
% 170.47/26.39 ----------------------------------------------------------------
% 170.47/26.39 (1) all_54_11 = all_52_14
% 170.47/26.39 (2) all_54_11 = e2
% 170.47/26.39 (3) ~ (all_52_14 = e2)
% 170.47/26.39
% 170.47/26.39 Begin of proof
% 170.47/26.39 |
% 170.47/26.39 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.39 | (4) all_52_14 = e2
% 170.47/26.39 |
% 170.47/26.39 | SIMP: (4) implies:
% 170.47/26.39 | (5) all_52_14 = e2
% 170.47/26.39 |
% 170.47/26.39 | REDUCE: (3), (5) imply:
% 170.47/26.39 | (6) $false
% 170.47/26.39 |
% 170.47/26.39 | CLOSE: (6) is inconsistent.
% 170.47/26.39 |
% 170.47/26.39 End of proof
% 170.47/26.39
% 170.47/26.39 Sub-proof #623 shows that the following formulas are inconsistent:
% 170.47/26.39 ----------------------------------------------------------------
% 170.47/26.39 (1) op(e2, e1) = all_52_9
% 170.47/26.39 (2) ~ (all_52_1 = e3)
% 170.47/26.39 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.39 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.39 (4) all_54_14 = all_52_11
% 170.47/26.39 (5) all_54_12 = all_52_3
% 170.47/26.39 (6) all_54_12 = e1 | all_54_12 = e0
% 170.47/26.39 (7) op(e0, e0) = e2
% 170.47/26.39 (8) ~ (all_8_2 = e3)
% 170.47/26.39 (9) ~ (all_52_3 = e3)
% 170.47/26.39 (10) ~ (all_52_3 = e2)
% 170.47/26.39 (11) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.39 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.39 e1)
% 170.47/26.39 (12) ~ (all_52_9 = all_52_11)
% 170.47/26.39 (13) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.47/26.39 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.47/26.39 (14) op(e2, e3) = all_52_1
% 170.47/26.39 (15) op(e0, e2) = e0
% 170.47/26.39 (16) op(e2, e2) = all_8_2
% 170.47/26.39 (17) op(e1, e1) = all_6_2
% 170.47/26.39 (18) ~ (all_52_11 = e2)
% 170.47/26.39 (19) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.39 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.39 (20) ~ (all_52_3 = all_52_11)
% 170.47/26.39 (21) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.47/26.39 (22) ~ (all_52_11 = all_6_2)
% 170.47/26.39 (23) all_58_3 = e2
% 170.47/26.39 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.39 (25) ~ (e2 = e0)
% 170.47/26.39 (26) all_58_12 = e3
% 170.47/26.39 (27) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.39 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.39 (28) ~ (all_52_3 = e0)
% 170.47/26.39 (29) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.47/26.39 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.47/26.39 (30) op(e0, e2) = all_52_7
% 170.47/26.39 (31) ~ (all_52_11 = e0)
% 170.47/26.39 (32) all_58_4 = e2
% 170.47/26.39
% 170.47/26.39 Begin of proof
% 170.47/26.39 |
% 170.47/26.39 | BETA: splitting (6) gives:
% 170.47/26.39 |
% 170.47/26.39 | Case 1:
% 170.47/26.39 | |
% 170.47/26.39 | | (33) all_54_12 = e1
% 170.47/26.39 | |
% 170.47/26.39 | | COMBINE_EQS: (5), (33) imply:
% 170.47/26.39 | | (34) all_52_3 = e1
% 170.47/26.39 | |
% 170.47/26.39 | | SIMP: (34) implies:
% 170.47/26.39 | | (35) all_52_3 = e1
% 170.47/26.39 | |
% 170.47/26.39 | | REDUCE: (20), (35) imply:
% 170.47/26.39 | | (36) ~ (all_52_11 = e1)
% 170.47/26.39 | |
% 170.47/26.39 | | SIMP: (36) implies:
% 170.47/26.39 | | (37) ~ (all_52_11 = e1)
% 170.47/26.39 | |
% 170.47/26.39 | | REDUCE: (9), (35) imply:
% 170.47/26.39 | | (38) ~ (e3 = e1)
% 170.47/26.39 | |
% 170.47/26.39 | | SIMP: (38) implies:
% 170.47/26.39 | | (39) ~ (e3 = e1)
% 170.47/26.39 | |
% 170.47/26.39 | | REDUCE: (10), (35) imply:
% 170.47/26.39 | | (40) ~ (e2 = e1)
% 170.47/26.39 | |
% 170.47/26.39 | | SIMP: (40) implies:
% 170.47/26.39 | | (41) ~ (e2 = e1)
% 170.47/26.39 | |
% 170.47/26.39 | | REDUCE: (28), (35) imply:
% 170.47/26.39 | | (42) ~ (e1 = e0)
% 170.47/26.39 | |
% 170.47/26.39 | | BETA: splitting (11) gives:
% 170.47/26.39 | |
% 170.47/26.39 | | Case 1:
% 170.47/26.39 | | |
% 170.47/26.39 | | | (43) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2)
% 170.47/26.39 | | | = e1)
% 170.47/26.39 | | |
% 170.47/26.39 | | | REF_CLOSE: (15), (24), (26), (30), (39), (42), (43) are inconsistent by
% 170.47/26.39 | | | sub-proof #630.
% 170.47/26.39 | | |
% 170.47/26.39 | | Case 2:
% 170.47/26.39 | | |
% 170.47/26.39 | | | (44) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0)
% 170.47/26.39 | | | = e1)
% 170.47/26.39 | | |
% 170.47/26.39 | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (12), (13), (14), (16), (17),
% 170.47/26.39 | | | (18), (19), (21), (22), (23), (24), (25), (27), (29), (31),
% 170.47/26.39 | | | (32), (37), (41), (42), (44) are inconsistent by sub-proof
% 170.47/26.39 | | | #624.
% 170.47/26.39 | | |
% 170.47/26.39 | | End of split
% 170.47/26.39 | |
% 170.47/26.39 | Case 2:
% 170.47/26.39 | |
% 170.47/26.39 | | (45) all_54_12 = e0
% 170.47/26.39 | |
% 170.47/26.39 | | REF_CLOSE: (5), (28), (45) are inconsistent by sub-proof #653.
% 170.47/26.39 | |
% 170.47/26.39 | End of split
% 170.47/26.39 |
% 170.47/26.39 End of proof
% 170.47/26.39
% 170.47/26.39 Sub-proof #624 shows that the following formulas are inconsistent:
% 170.47/26.39 ----------------------------------------------------------------
% 170.47/26.39 (1) op(e2, e1) = all_52_9
% 170.47/26.39 (2) ~ (all_52_1 = e3)
% 170.47/26.39 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.39 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.39 (4) all_54_14 = all_52_11
% 170.47/26.39 (5) op(e0, e0) = e2
% 170.47/26.39 (6) ~ (all_8_2 = e3)
% 170.47/26.39 (7) ~ (all_52_9 = all_52_11)
% 170.47/26.39 (8) ~ (e1 = e0)
% 170.47/26.39 (9) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.39 (10) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.47/26.39 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.47/26.39 (11) op(e2, e3) = all_52_1
% 170.47/26.39 (12) op(e2, e2) = all_8_2
% 170.47/26.39 (13) op(e1, e1) = all_6_2
% 170.47/26.39 (14) ~ (all_52_11 = e2)
% 170.47/26.39 (15) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.39 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.39 (16) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.47/26.39 (17) ~ (all_52_11 = all_6_2)
% 170.47/26.39 (18) all_58_3 = e2
% 170.47/26.39 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.39 (20) ~ (e2 = e0)
% 170.47/26.39 (21) ~ (all_52_11 = e1)
% 170.47/26.39 (22) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.39 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.39 (23) ~ (e2 = e1)
% 170.47/26.39 (24) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.47/26.39 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.47/26.39 (25) ~ (all_52_11 = e0)
% 170.47/26.39 (26) all_58_4 = e2
% 170.47/26.39
% 170.47/26.39 Begin of proof
% 170.47/26.39 |
% 170.47/26.39 | BETA: splitting (9) gives:
% 170.47/26.39 |
% 170.47/26.39 | Case 1:
% 170.47/26.39 | |
% 170.47/26.39 | | (27) all_58_14 = e1 & op(e0, e1) = e1
% 170.47/26.39 | |
% 170.47/26.39 | | ALPHA: (27) implies:
% 170.47/26.39 | | (28) all_58_14 = e1
% 170.47/26.39 | |
% 170.47/26.39 | | BETA: splitting (16) gives:
% 170.47/26.39 | |
% 170.47/26.39 | | Case 1:
% 170.47/26.39 | | |
% 170.47/26.39 | | | (29) all_54_14 = e3
% 170.47/26.39 | | |
% 170.47/26.39 | | | COMBINE_EQS: (4), (29) imply:
% 170.47/26.39 | | | (30) all_52_11 = e3
% 170.47/26.39 | | |
% 170.47/26.39 | | | SIMP: (30) implies:
% 170.47/26.39 | | | (31) all_52_11 = e3
% 170.47/26.39 | | |
% 170.47/26.39 | | | REDUCE: (7), (31) imply:
% 170.47/26.39 | | | (32) ~ (all_52_9 = e3)
% 170.47/26.39 | | |
% 170.47/26.39 | | | REDUCE: (17), (31) imply:
% 170.47/26.39 | | | (33) ~ (all_6_2 = e3)
% 170.47/26.39 | | |
% 170.47/26.39 | | | SIMP: (33) implies:
% 170.47/26.39 | | | (34) ~ (all_6_2 = e3)
% 170.47/26.39 | | |
% 170.47/26.39 | | | REDUCE: (14), (31) imply:
% 170.47/26.39 | | | (35) ~ (e3 = e2)
% 170.47/26.39 | | |
% 170.47/26.39 | | | REDUCE: (21), (31) imply:
% 170.47/26.39 | | | (36) ~ (e3 = e1)
% 170.47/26.39 | | |
% 170.47/26.39 | | | REDUCE: (25), (31) imply:
% 170.47/26.39 | | | (37) ~ (e3 = e0)
% 170.47/26.39 | | |
% 170.47/26.39 | | | BETA: splitting (22) gives:
% 170.47/26.39 | | |
% 170.47/26.39 | | | Case 1:
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | (38) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2)
% 170.47/26.39 | | | | = e3)
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | REF_CLOSE: (2), (6), (11), (12), (19), (38) are inconsistent by
% 170.47/26.39 | | | | sub-proof #692.
% 170.47/26.39 | | | |
% 170.47/26.39 | | | Case 2:
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | (39) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0)
% 170.47/26.39 | | | | = e3)
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | BETA: splitting (39) gives:
% 170.47/26.39 | | | |
% 170.47/26.39 | | | | Case 1:
% 170.47/26.39 | | | | |
% 170.47/26.39 | | | | | (40) all_58_5 = e3 & op(e2, e1) = e3
% 170.47/26.39 | | | | |
% 170.47/26.39 | | | | | ALPHA: (40) implies:
% 170.47/26.39 | | | | | (41) op(e2, e1) = e3
% 170.47/26.39 | | | | |
% 170.47/26.39 | | | | | REF_CLOSE: (1), (19), (32), (41) are inconsistent by sub-proof #951.
% 170.47/26.39 | | | | |
% 170.47/26.39 | | | | Case 2:
% 170.47/26.39 | | | | |
% 170.47/26.39 | | | | | (42) all_58_10 = e3 & op(e2, e0) = e3
% 170.47/26.39 | | | | |
% 170.47/26.39 | | | | | ALPHA: (42) implies:
% 170.47/26.39 | | | | | (43) all_58_10 = e3
% 170.47/26.39 | | | | |
% 170.47/26.39 | | | | | REF_CLOSE: (1), (3), (6), (8), (10), (12), (13), (15), (18), (19),
% 170.47/26.39 | | | | | (20), (22), (23), (24), (26), (28), (32), (34), (35), (36),
% 170.47/26.39 | | | | | (37), (43) are inconsistent by sub-proof #625.
% 170.47/26.39 | | | | |
% 170.47/26.39 | | | | End of split
% 170.47/26.39 | | | |
% 170.47/26.39 | | | End of split
% 170.47/26.39 | | |
% 170.47/26.39 | | Case 2:
% 170.47/26.39 | | |
% 170.47/26.39 | | | (44) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.47/26.39 | | |
% 170.47/26.39 | | | REF_CLOSE: (4), (14), (21), (25), (44) are inconsistent by sub-proof #655.
% 170.47/26.39 | | |
% 170.47/26.39 | | End of split
% 170.47/26.39 | |
% 170.47/26.39 | Case 2:
% 170.47/26.39 | |
% 170.47/26.39 | | (45) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.39 | |
% 170.47/26.39 | | ALPHA: (45) implies:
% 170.47/26.39 | | (46) op(e0, e0) = e1
% 170.47/26.39 | |
% 170.47/26.39 | | REF_CLOSE: (5), (19), (23), (46) are inconsistent by sub-proof #640.
% 170.47/26.39 | |
% 170.47/26.39 | End of split
% 170.47/26.39 |
% 170.47/26.39 End of proof
% 170.47/26.39
% 170.47/26.39 Sub-proof #625 shows that the following formulas are inconsistent:
% 170.47/26.39 ----------------------------------------------------------------
% 170.47/26.39 (1) op(e2, e1) = all_52_9
% 170.47/26.39 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.39 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.39 (3) ~ (all_52_9 = e3)
% 170.47/26.39 (4) ~ (all_8_2 = e3)
% 170.47/26.39 (5) ~ (all_6_2 = e3)
% 170.47/26.39 (6) ~ (e3 = e1)
% 170.47/26.39 (7) ~ (e1 = e0)
% 170.47/26.39 (8) all_58_14 = e1
% 170.47/26.39 (9) all_58_10 = e3
% 170.47/26.39 (10) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.47/26.39 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.47/26.39 (11) op(e2, e2) = all_8_2
% 170.47/26.39 (12) op(e1, e1) = all_6_2
% 170.47/26.39 (13) ~ (e3 = e0)
% 170.47/26.39 (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.39 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.39 (15) all_58_3 = e2
% 170.47/26.39 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.39 (17) ~ (e2 = e0)
% 170.47/26.39 (18) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.39 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.39 (19) ~ (e2 = e1)
% 170.47/26.39 (20) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.47/26.39 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.47/26.39 (21) all_58_4 = e2
% 170.47/26.39 (22) ~ (e3 = e2)
% 170.47/26.39
% 170.47/26.39 Begin of proof
% 170.47/26.39 |
% 170.47/26.39 | BETA: splitting (10) gives:
% 170.47/26.39 |
% 170.47/26.39 | Case 1:
% 170.47/26.39 | |
% 170.47/26.39 | | (23) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 170.47/26.39 | | e3)
% 170.47/26.39 | |
% 170.47/26.39 | | BETA: splitting (23) gives:
% 170.47/26.39 | |
% 170.47/26.39 | | Case 1:
% 170.47/26.39 | | |
% 170.47/26.39 | | | (24) all_58_4 = e3 & op(e3, e1) = e3
% 170.47/26.39 | | |
% 170.47/26.39 | | | REF_CLOSE: (2), (4), (6), (7), (9), (11), (13), (14), (15), (16), (17),
% 170.47/26.39 | | | (18), (19), (20), (21), (22), (24) are inconsistent by
% 170.47/26.39 | | | sub-proof #627.
% 170.47/26.39 | | |
% 170.47/26.39 | | Case 2:
% 170.47/26.39 | | |
% 170.47/26.39 | | | (25) all_58_5 = e3 & op(e2, e1) = e3
% 170.47/26.39 | | |
% 170.47/26.39 | | | ALPHA: (25) implies:
% 170.47/26.39 | | | (26) op(e2, e1) = e3
% 170.47/26.39 | | |
% 170.47/26.39 | | | REF_CLOSE: (1), (3), (16), (26) are inconsistent by sub-proof #951.
% 170.47/26.39 | | |
% 170.47/26.39 | | End of split
% 170.47/26.39 | |
% 170.47/26.39 | Case 2:
% 170.47/26.39 | |
% 170.47/26.39 | | (27) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 170.47/26.39 | | e3)
% 170.47/26.39 | |
% 170.47/26.39 | | BETA: splitting (27) gives:
% 170.47/26.39 | |
% 170.47/26.39 | | Case 1:
% 170.47/26.39 | | |
% 170.47/26.39 | | | (28) all_58_8 = e3 & op(e1, e1) = e3
% 170.47/26.39 | | |
% 170.47/26.39 | | | REF_CLOSE: (5), (12), (16), (28) are inconsistent by sub-proof #961.
% 170.47/26.39 | | |
% 170.47/26.39 | | Case 2:
% 170.47/26.39 | | |
% 170.47/26.39 | | | (29) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.39 | | |
% 170.47/26.39 | | | ALPHA: (29) implies:
% 170.47/26.39 | | | (30) all_58_14 = e3
% 170.47/26.39 | | |
% 170.47/26.39 | | | REF_CLOSE: (6), (8), (30) are inconsistent by sub-proof #626.
% 170.47/26.39 | | |
% 170.47/26.39 | | End of split
% 170.47/26.39 | |
% 170.47/26.39 | End of split
% 170.47/26.39 |
% 170.47/26.39 End of proof
% 170.47/26.39
% 170.47/26.39 Sub-proof #626 shows that the following formulas are inconsistent:
% 170.47/26.39 ----------------------------------------------------------------
% 170.47/26.39 (1) all_58_14 = e3
% 170.47/26.39 (2) all_58_14 = e1
% 170.47/26.39 (3) ~ (e3 = e1)
% 170.47/26.39
% 170.47/26.39 Begin of proof
% 170.47/26.39 |
% 170.47/26.39 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.39 | (4) e3 = e1
% 170.47/26.39 |
% 170.47/26.39 | SIMP: (4) implies:
% 170.47/26.39 | (5) e3 = e1
% 170.47/26.39 |
% 170.47/26.39 | REDUCE: (3), (5) imply:
% 170.47/26.39 | (6) $false
% 170.47/26.39 |
% 170.47/26.39 | CLOSE: (6) is inconsistent.
% 170.47/26.39 |
% 170.47/26.39 End of proof
% 170.47/26.39
% 170.47/26.39 Sub-proof #627 shows that the following formulas are inconsistent:
% 170.47/26.39 ----------------------------------------------------------------
% 170.47/26.39 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.39 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.47/26.39 (2) ~ (all_8_2 = e3)
% 170.47/26.39 (3) all_58_4 = e3 & op(e3, e1) = e3
% 170.47/26.39 (4) ~ (e3 = e1)
% 170.47/26.39 (5) ~ (e1 = e0)
% 170.47/26.39 (6) all_58_10 = e3
% 170.47/26.39 (7) op(e2, e2) = all_8_2
% 170.47/26.39 (8) ~ (e3 = e0)
% 170.47/26.39 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.47/26.39 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.47/26.39 (10) all_58_3 = e2
% 170.47/26.39 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.39 (12) ~ (e2 = e0)
% 170.47/26.39 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.39 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.47/26.39 (14) ~ (e2 = e1)
% 170.47/26.39 (15) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.47/26.39 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.47/26.39 (16) all_58_4 = e2
% 170.47/26.39 (17) ~ (e3 = e2)
% 170.47/26.39
% 170.47/26.39 Begin of proof
% 170.47/26.39 |
% 170.47/26.39 | ALPHA: (3) implies:
% 170.47/26.39 | (18) all_58_4 = e3
% 170.47/26.39 |
% 170.47/26.39 | COMBINE_EQS: (16), (18) imply:
% 170.47/26.39 | (19) e3 = e2
% 170.47/26.39 |
% 170.47/26.39 | SIMP: (19) implies:
% 170.47/26.39 | (20) e3 = e2
% 170.47/26.39 |
% 170.47/26.39 | COMBINE_EQS: (6), (20) imply:
% 170.47/26.39 | (21) all_58_10 = e2
% 170.47/26.39 |
% 170.47/26.39 | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 170.47/26.39 | (15), (17), (21) are inconsistent by sub-proof #908.
% 170.47/26.39 |
% 170.47/26.39 End of proof
% 170.47/26.39
% 170.47/26.39 Sub-proof #628 shows that the following formulas are inconsistent:
% 170.47/26.39 ----------------------------------------------------------------
% 170.47/26.40 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.40 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.40 (2) op(e0, e0) = e2
% 170.47/26.40 (3) ~ (e3 = e1)
% 170.47/26.40 (4) all_58_13 = e0
% 170.47/26.40 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.47/26.40 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.40 (6) ~ (e1 = e0)
% 170.47/26.40 (7) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3) |
% 170.47/26.40 (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.47/26.40 (8) op(e0, e2) = e0
% 170.47/26.40 (9) ~ (e3 = e0)
% 170.47/26.40 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.40 (11) ~ (e2 = e0)
% 170.47/26.40 (12) ~ (e2 = e1)
% 170.47/26.40 (13) all_58_15 = e0
% 170.47/26.40 (14) op(e0, e2) = all_52_7
% 170.47/26.40 (15) ~ (e3 = e2)
% 170.47/26.40
% 170.47/26.40 Begin of proof
% 170.47/26.40 |
% 170.47/26.40 | BETA: splitting (1) gives:
% 170.47/26.40 |
% 170.47/26.40 | Case 1:
% 170.47/26.40 | |
% 170.47/26.40 | | (16) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 170.47/26.40 | | e2)
% 170.47/26.40 | |
% 170.47/26.40 | | BETA: splitting (16) gives:
% 170.47/26.40 | |
% 170.47/26.40 | | Case 1:
% 170.47/26.40 | | |
% 170.47/26.40 | | | (17) all_58_12 = e2 & op(e0, e3) = e2
% 170.47/26.40 | | |
% 170.47/26.40 | | | ALPHA: (17) implies:
% 170.47/26.40 | | | (18) all_58_12 = e2
% 170.47/26.40 | | |
% 170.47/26.40 | | | BETA: splitting (7) gives:
% 170.47/26.40 | | |
% 170.47/26.40 | | | Case 1:
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | (19) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 170.47/26.40 | | | | e2) = e3)
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | BETA: splitting (19) gives:
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | Case 1:
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | (20) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | ALPHA: (20) implies:
% 170.47/26.40 | | | | | (21) all_58_12 = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | REF_CLOSE: (15), (18), (21) are inconsistent by sub-proof #635.
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | Case 2:
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | (22) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | REF_CLOSE: (4), (9), (22) are inconsistent by sub-proof #634.
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | End of split
% 170.47/26.40 | | | |
% 170.47/26.40 | | | Case 2:
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | (23) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 170.47/26.40 | | | | e0) = e3)
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | BETA: splitting (23) gives:
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | Case 1:
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | (24) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | ALPHA: (24) implies:
% 170.47/26.40 | | | | | (25) all_58_14 = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | BETA: splitting (5) gives:
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | Case 1:
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | | (26) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 170.47/26.40 | | | | | | op(e0, e2) = e1)
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | | REF_CLOSE: (6), (8), (10), (12), (14), (18), (26) are inconsistent
% 170.47/26.40 | | | | | | by sub-proof #633.
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | Case 2:
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | | (27) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 170.47/26.40 | | | | | | op(e0, e0) = e1)
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | | REF_CLOSE: (2), (3), (10), (12), (25), (27) are inconsistent by
% 170.47/26.40 | | | | | | sub-proof #632.
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | End of split
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | Case 2:
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | (28) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | ALPHA: (28) implies:
% 170.47/26.40 | | | | | (29) all_58_15 = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | REF_CLOSE: (9), (13), (29) are inconsistent by sub-proof #860.
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | End of split
% 170.47/26.40 | | | |
% 170.47/26.40 | | | End of split
% 170.47/26.40 | | |
% 170.47/26.40 | | Case 2:
% 170.47/26.40 | | |
% 170.47/26.40 | | | (30) all_58_13 = e2 & op(e0, e2) = e2
% 170.47/26.40 | | |
% 170.47/26.40 | | | ALPHA: (30) implies:
% 170.47/26.40 | | | (31) op(e0, e2) = e2
% 170.47/26.40 | | |
% 170.47/26.40 | | | REF_CLOSE: (8), (10), (11), (14), (31) are inconsistent by sub-proof #631.
% 170.47/26.40 | | |
% 170.47/26.40 | | End of split
% 170.47/26.40 | |
% 170.47/26.40 | Case 2:
% 170.47/26.40 | |
% 170.47/26.40 | | (32) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) =
% 170.47/26.40 | | e2)
% 170.47/26.40 | |
% 170.47/26.40 | | BETA: splitting (32) gives:
% 170.47/26.40 | |
% 170.47/26.40 | | Case 1:
% 170.47/26.40 | | |
% 170.47/26.40 | | | (33) all_58_14 = e2 & op(e0, e1) = e2
% 170.47/26.40 | | |
% 170.47/26.40 | | | ALPHA: (33) implies:
% 170.47/26.40 | | | (34) all_58_14 = e2
% 170.47/26.40 | | | (35) op(e0, e1) = e2
% 170.47/26.40 | | |
% 170.47/26.40 | | | BETA: splitting (7) gives:
% 170.47/26.40 | | |
% 170.47/26.40 | | | Case 1:
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | (36) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0,
% 170.47/26.40 | | | | e2) = e3)
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | BETA: splitting (36) gives:
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | Case 1:
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | (37) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | ALPHA: (37) implies:
% 170.47/26.40 | | | | | (38) all_58_12 = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | BETA: splitting (5) gives:
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | Case 1:
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | | (39) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 170.47/26.40 | | | | | | op(e0, e2) = e1)
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | | REF_CLOSE: (3), (6), (8), (10), (14), (38), (39) are inconsistent by
% 170.47/26.40 | | | | | | sub-proof #630.
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | Case 2:
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | | (40) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 170.47/26.40 | | | | | | op(e0, e0) = e1)
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | | REF_CLOSE: (2), (10), (12), (35), (40) are inconsistent by sub-proof
% 170.47/26.40 | | | | | | #629.
% 170.47/26.40 | | | | | |
% 170.47/26.40 | | | | | End of split
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | Case 2:
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | (41) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | ALPHA: (41) implies:
% 170.47/26.40 | | | | | (42) all_58_13 = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | REF_CLOSE: (4), (9), (42) are inconsistent by sub-proof #708.
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | End of split
% 170.47/26.40 | | | |
% 170.47/26.40 | | | Case 2:
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | (43) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0,
% 170.47/26.40 | | | | e0) = e3)
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | BETA: splitting (43) gives:
% 170.47/26.40 | | | |
% 170.47/26.40 | | | | Case 1:
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | (44) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | REF_CLOSE: (15), (34), (44) are inconsistent by sub-proof #809.
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | Case 2:
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | (45) all_58_15 = e3 & op(e0, e0) = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | ALPHA: (45) implies:
% 170.47/26.40 | | | | | (46) all_58_15 = e3
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | | REF_CLOSE: (9), (13), (46) are inconsistent by sub-proof #860.
% 170.47/26.40 | | | | |
% 170.47/26.40 | | | | End of split
% 170.47/26.40 | | | |
% 170.47/26.40 | | | End of split
% 170.47/26.40 | | |
% 170.47/26.40 | | Case 2:
% 170.47/26.40 | | |
% 170.47/26.40 | | | (47) all_58_15 = e2 & op(e0, e0) = e2
% 170.47/26.40 | | |
% 170.47/26.40 | | | REF_CLOSE: (11), (13), (47) are inconsistent by sub-proof #648.
% 170.47/26.40 | | |
% 170.47/26.40 | | End of split
% 170.47/26.40 | |
% 170.47/26.40 | End of split
% 170.47/26.40 |
% 170.47/26.40 End of proof
% 170.47/26.40
% 170.47/26.40 Sub-proof #629 shows that the following formulas are inconsistent:
% 170.47/26.40 ----------------------------------------------------------------
% 170.47/26.40 (1) op(e0, e0) = e2
% 170.47/26.40 (2) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.40 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.40 (4) ~ (e2 = e1)
% 170.47/26.40 (5) op(e0, e1) = e2
% 170.47/26.40
% 170.47/26.40 Begin of proof
% 170.47/26.40 |
% 170.47/26.40 | BETA: splitting (2) gives:
% 170.47/26.40 |
% 170.47/26.40 | Case 1:
% 170.47/26.40 | |
% 170.47/26.40 | | (6) all_58_14 = e1 & op(e0, e1) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | ALPHA: (6) implies:
% 170.47/26.40 | | (7) op(e0, e1) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #967.
% 170.47/26.40 | |
% 170.47/26.40 | Case 2:
% 170.47/26.40 | |
% 170.47/26.40 | | (8) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | ALPHA: (8) implies:
% 170.47/26.40 | | (9) op(e0, e0) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #640.
% 170.47/26.40 | |
% 170.47/26.40 | End of split
% 170.47/26.40 |
% 170.47/26.40 End of proof
% 170.47/26.40
% 170.47/26.40 Sub-proof #630 shows that the following formulas are inconsistent:
% 170.47/26.40 ----------------------------------------------------------------
% 170.47/26.40 (1) ~ (e3 = e1)
% 170.47/26.40 (2) ~ (e1 = e0)
% 170.47/26.40 (3) op(e0, e2) = e0
% 170.47/26.40 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.40 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.40 (6) all_58_12 = e3
% 170.47/26.40 (7) op(e0, e2) = all_52_7
% 170.47/26.40
% 170.47/26.40 Begin of proof
% 170.47/26.40 |
% 170.47/26.40 | BETA: splitting (4) gives:
% 170.47/26.40 |
% 170.47/26.40 | Case 1:
% 170.47/26.40 | |
% 170.47/26.40 | | (8) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #651.
% 170.47/26.40 | |
% 170.47/26.40 | Case 2:
% 170.47/26.40 | |
% 170.47/26.40 | | (9) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | ALPHA: (9) implies:
% 170.47/26.40 | | (10) op(e0, e2) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | REF_CLOSE: (2), (3), (5), (7), (10) are inconsistent by sub-proof #889.
% 170.47/26.40 | |
% 170.47/26.40 | End of split
% 170.47/26.40 |
% 170.47/26.40 End of proof
% 170.47/26.40
% 170.47/26.40 Sub-proof #631 shows that the following formulas are inconsistent:
% 170.47/26.40 ----------------------------------------------------------------
% 170.47/26.40 (1) op(e0, e2) = e2
% 170.47/26.40 (2) op(e0, e2) = e0
% 170.47/26.40 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.40 (4) ~ (e2 = e0)
% 170.47/26.40 (5) op(e0, e2) = all_52_7
% 170.47/26.40
% 170.47/26.40 Begin of proof
% 170.47/26.40 |
% 170.47/26.40 | GROUND_INST: instantiating (3) with all_52_7, e0, e2, e0, simplifying with
% 170.47/26.40 | (2), (5) gives:
% 170.47/26.40 | (6) all_52_7 = e0
% 170.47/26.40 |
% 170.47/26.40 | GROUND_INST: instantiating (3) with all_52_7, e2, e2, e0, simplifying with
% 170.47/26.40 | (1), (5) gives:
% 170.47/26.40 | (7) all_52_7 = e2
% 170.47/26.40 |
% 170.47/26.40 | COMBINE_EQS: (6), (7) imply:
% 170.47/26.40 | (8) e2 = e0
% 170.47/26.40 |
% 170.47/26.40 | REDUCE: (4), (8) imply:
% 170.47/26.40 | (9) $false
% 170.47/26.40 |
% 170.47/26.40 | CLOSE: (9) is inconsistent.
% 170.47/26.40 |
% 170.47/26.40 End of proof
% 170.47/26.40
% 170.47/26.40 Sub-proof #632 shows that the following formulas are inconsistent:
% 170.47/26.40 ----------------------------------------------------------------
% 170.47/26.40 (1) op(e0, e0) = e2
% 170.47/26.40 (2) ~ (e3 = e1)
% 170.47/26.40 (3) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.40 (4) all_58_14 = e3
% 170.47/26.40 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.40 (6) ~ (e2 = e1)
% 170.47/26.40
% 170.47/26.40 Begin of proof
% 170.47/26.40 |
% 170.47/26.40 | BETA: splitting (3) gives:
% 170.47/26.40 |
% 170.47/26.40 | Case 1:
% 170.47/26.40 | |
% 170.47/26.40 | | (7) all_58_14 = e1 & op(e0, e1) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | ALPHA: (7) implies:
% 170.47/26.40 | | (8) all_58_14 = e1
% 170.47/26.40 | |
% 170.47/26.40 | | COMBINE_EQS: (4), (8) imply:
% 170.47/26.40 | | (9) e3 = e1
% 170.47/26.40 | |
% 170.47/26.40 | | REDUCE: (2), (9) imply:
% 170.47/26.40 | | (10) $false
% 170.47/26.40 | |
% 170.47/26.40 | | CLOSE: (10) is inconsistent.
% 170.47/26.40 | |
% 170.47/26.40 | Case 2:
% 170.47/26.40 | |
% 170.47/26.40 | | (11) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | ALPHA: (11) implies:
% 170.47/26.40 | | (12) op(e0, e0) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | REF_CLOSE: (1), (5), (6), (12) are inconsistent by sub-proof #640.
% 170.47/26.40 | |
% 170.47/26.40 | End of split
% 170.47/26.40 |
% 170.47/26.40 End of proof
% 170.47/26.40
% 170.47/26.40 Sub-proof #633 shows that the following formulas are inconsistent:
% 170.47/26.40 ----------------------------------------------------------------
% 170.47/26.40 (1) all_58_12 = e2
% 170.47/26.40 (2) ~ (e1 = e0)
% 170.47/26.40 (3) op(e0, e2) = e0
% 170.47/26.40 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.40 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.40 (6) ~ (e2 = e1)
% 170.47/26.40 (7) op(e0, e2) = all_52_7
% 170.47/26.40
% 170.47/26.40 Begin of proof
% 170.47/26.40 |
% 170.47/26.40 | BETA: splitting (4) gives:
% 170.47/26.40 |
% 170.47/26.40 | Case 1:
% 170.47/26.40 | |
% 170.47/26.40 | | (8) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #891.
% 170.47/26.40 | |
% 170.47/26.40 | Case 2:
% 170.47/26.40 | |
% 170.47/26.40 | | (9) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | ALPHA: (9) implies:
% 170.47/26.40 | | (10) op(e0, e2) = e1
% 170.47/26.40 | |
% 170.47/26.40 | | REF_CLOSE: (2), (3), (5), (7), (10) are inconsistent by sub-proof #889.
% 170.47/26.40 | |
% 170.47/26.40 | End of split
% 170.47/26.40 |
% 170.47/26.40 End of proof
% 170.47/26.40
% 170.47/26.40 Sub-proof #634 shows that the following formulas are inconsistent:
% 170.47/26.40 ----------------------------------------------------------------
% 170.47/26.40 (1) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.40 (2) all_58_13 = e0
% 170.47/26.40 (3) ~ (e3 = e0)
% 170.47/26.40
% 170.47/26.40 Begin of proof
% 170.47/26.40 |
% 170.47/26.40 | ALPHA: (1) implies:
% 170.47/26.40 | (4) all_58_13 = e3
% 170.47/26.40 |
% 170.47/26.40 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.40 | (5) e3 = e0
% 170.47/26.40 |
% 170.47/26.40 | REDUCE: (3), (5) imply:
% 170.47/26.40 | (6) $false
% 170.47/26.40 |
% 170.47/26.40 | CLOSE: (6) is inconsistent.
% 170.47/26.40 |
% 170.47/26.40 End of proof
% 170.47/26.40
% 170.47/26.40 Sub-proof #635 shows that the following formulas are inconsistent:
% 170.47/26.40 ----------------------------------------------------------------
% 170.47/26.40 (1) all_58_12 = e3
% 170.47/26.40 (2) all_58_12 = e2
% 170.47/26.40 (3) ~ (e3 = e2)
% 170.47/26.40
% 170.47/26.40 Begin of proof
% 170.47/26.40 |
% 170.47/26.40 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.40 | (4) e3 = e2
% 170.47/26.40 |
% 170.47/26.40 | SIMP: (4) implies:
% 170.47/26.40 | (5) e3 = e2
% 170.47/26.40 |
% 170.47/26.40 | REDUCE: (3), (5) imply:
% 170.47/26.40 | (6) $false
% 170.47/26.40 |
% 170.47/26.40 | CLOSE: (6) is inconsistent.
% 170.47/26.40 |
% 170.47/26.40 End of proof
% 170.47/26.40
% 170.47/26.40 Sub-proof #636 shows that the following formulas are inconsistent:
% 170.47/26.40 ----------------------------------------------------------------
% 170.47/26.40 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.40 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.40 (2) op(e2, e1) = all_52_9
% 170.47/26.40 (3) ~ (all_52_1 = e3)
% 170.47/26.40 (4) all_54_14 = all_52_11
% 170.47/26.40 (5) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.40 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.40 (6) all_54_12 = all_52_3
% 170.47/26.40 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.40 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.40 (8) op(e0, e0) = e2
% 170.47/26.40 (9) ~ (all_8_2 = e3)
% 170.47/26.40 (10) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.47/26.40 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.47/26.40 (11) ~ (all_6_2 = e3)
% 170.47/26.40 (12) ~ (all_52_3 = e3)
% 170.47/26.40 (13) ~ (all_52_3 = e2)
% 170.47/26.40 (14) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.40 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.40 (15) ~ (e3 = e1)
% 170.47/26.40 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.40 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.40 e1)
% 170.47/26.40 (17) op(e3, e1) = all_52_8
% 170.47/26.40 (18) ~ (all_52_9 = all_52_11)
% 170.47/26.40 (19) ~ (e1 = e0)
% 170.47/26.40 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.40 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.40 (21) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.47/26.40 | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.40 (22) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.47/26.40 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.47/26.40 (23) op(e2, e3) = all_52_1
% 170.47/26.40 (24) op(e0, e2) = e0
% 170.47/26.40 (25) op(e2, e2) = all_8_2
% 170.47/26.40 (26) ~ (all_6_2 = e2)
% 170.47/26.40 (27) all_58_6 = e2
% 170.47/26.40 (28) op(e1, e1) = all_6_2
% 170.47/26.40 (29) ~ (all_52_11 = e2)
% 170.47/26.40 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.47/26.40 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.47/26.40 (31) ~ (e3 = e0)
% 170.47/26.40 (32) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.47/26.40 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.47/26.40 (33) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.40 (34) ~ (all_52_4 = e3)
% 170.47/26.40 (35) ~ (all_52_3 = all_52_11)
% 170.47/26.40 (36) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.47/26.40 (37) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.40 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.40 (38) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.40 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.40 (39) all_58_3 = e2
% 170.47/26.40 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.40 (41) ~ (e2 = e0)
% 170.47/26.40 (42) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.47/26.40 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.47/26.40 (43) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.47/26.40 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.47/26.40 (44) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.47/26.40 (45) ~ (e2 = e1)
% 170.47/26.40 (46) op(e3, e2) = all_52_4
% 170.47/26.40 (47) ~ (all_52_3 = e0)
% 170.47/26.40 (48) op(e0, e2) = all_52_7
% 170.47/26.40 (49) ~ (all_52_11 = e0)
% 170.47/26.40 (50) all_58_4 = e2
% 170.47/26.40 (51) all_58_1 = e0
% 170.47/26.40 (52) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.40 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.41 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.41 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.41 (53) op(e3, e1) = e2
% 170.47/26.41 (54) all_56_10 = e3
% 170.47/26.41 (55) ~ (e3 = e2)
% 170.47/26.41
% 170.47/26.41 Begin of proof
% 170.47/26.41 |
% 170.47/26.41 | BETA: splitting (5) gives:
% 170.47/26.41 |
% 170.47/26.41 | Case 1:
% 170.47/26.41 | |
% 170.47/26.41 | | (56) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.47/26.41 | | e3)
% 170.47/26.41 | |
% 170.47/26.41 | | REF_CLOSE: (9), (25), (34), (40), (46), (56) are inconsistent by sub-proof
% 170.47/26.41 | | #972.
% 170.47/26.41 | |
% 170.47/26.41 | Case 2:
% 170.47/26.41 | |
% 170.47/26.41 | | (57) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) =
% 170.47/26.41 | | e3)
% 170.47/26.41 | |
% 170.47/26.41 | | BETA: splitting (57) gives:
% 170.47/26.41 | |
% 170.47/26.41 | | Case 1:
% 170.47/26.41 | | |
% 170.47/26.41 | | | (58) all_58_7 = e3 & op(e1, e2) = e3
% 170.47/26.41 | | |
% 170.47/26.41 | | | ALPHA: (58) implies:
% 170.47/26.41 | | | (59) all_58_7 = e3
% 170.47/26.41 | | |
% 170.47/26.41 | | | REF_CLOSE: (7), (15), (19), (24), (39), (40), (45), (48), (51), (59) are
% 170.47/26.41 | | | inconsistent by sub-proof #656.
% 170.47/26.41 | | |
% 170.47/26.41 | | Case 2:
% 170.47/26.41 | | |
% 170.47/26.41 | | | (60) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.41 | | |
% 170.47/26.41 | | | ALPHA: (60) implies:
% 170.47/26.41 | | | (61) all_58_13 = e3
% 170.47/26.41 | | |
% 170.47/26.41 | | | BETA: splitting (33) gives:
% 170.47/26.41 | | |
% 170.47/26.41 | | | Case 1:
% 170.47/26.41 | | | |
% 170.47/26.41 | | | | (62) all_54_12 = e3
% 170.47/26.41 | | | |
% 170.47/26.41 | | | | REF_CLOSE: (6), (12), (62) are inconsistent by sub-proof #738.
% 170.47/26.41 | | | |
% 170.47/26.41 | | | Case 2:
% 170.47/26.41 | | | |
% 170.47/26.41 | | | | (63) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.47/26.41 | | | |
% 170.47/26.41 | | | | BETA: splitting (63) gives:
% 170.47/26.41 | | | |
% 170.47/26.41 | | | | Case 1:
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | | (64) all_54_12 = e2
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | | REF_CLOSE: (6), (13), (64) are inconsistent by sub-proof #676.
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | Case 2:
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | | (65) all_54_12 = e1 | all_54_12 = e0
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | | BETA: splitting (22) gives:
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | | Case 1:
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | (66) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2,
% 170.47/26.41 | | | | | | e1) = e3)
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | BETA: splitting (66) gives:
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | Case 1:
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | (67) all_58_4 = e3 & op(e3, e1) = e3
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | REF_CLOSE: (50), (55), (67) are inconsistent by sub-proof #952.
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | Case 2:
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | (68) all_58_5 = e3 & op(e2, e1) = e3
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | REF_CLOSE: (2), (4), (6), (18), (29), (35), (36), (40), (47),
% 170.47/26.41 | | | | | | | (49), (65), (68) are inconsistent by sub-proof #652.
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | End of split
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | Case 2:
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | (69) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0,
% 170.47/26.41 | | | | | | e1) = e3)
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | BETA: splitting (69) gives:
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | Case 1:
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | (70) all_58_8 = e3 & op(e1, e1) = e3
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | REF_CLOSE: (11), (28), (40), (70) are inconsistent by sub-proof
% 170.47/26.41 | | | | | | | #961.
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | Case 2:
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | (71) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | ALPHA: (71) implies:
% 170.47/26.41 | | | | | | | (72) all_58_14 = e3
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 170.47/26.41 | | | | | | | (11), (14), (15), (16), (17), (18), (19), (20), (21),
% 170.47/26.41 | | | | | | | (22), (23), (24), (25), (26), (27), (28), (29), (30),
% 170.47/26.41 | | | | | | | (31), (32), (35), (36), (37), (38), (39), (40), (41),
% 170.47/26.41 | | | | | | | (42), (43), (44), (45), (47), (48), (49), (50), (51),
% 170.47/26.41 | | | | | | | (52), (53), (54), (55), (61), (65), (72) are
% 170.47/26.41 | | | | | | | inconsistent by sub-proof #637.
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | End of split
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | End of split
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | End of split
% 170.47/26.41 | | | |
% 170.47/26.41 | | | End of split
% 170.47/26.41 | | |
% 170.47/26.41 | | End of split
% 170.47/26.41 | |
% 170.47/26.41 | End of split
% 170.47/26.41 |
% 170.47/26.41 End of proof
% 170.47/26.41
% 170.47/26.41 Sub-proof #637 shows that the following formulas are inconsistent:
% 170.47/26.41 ----------------------------------------------------------------
% 170.47/26.41 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.41 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.41 (2) op(e2, e1) = all_52_9
% 170.47/26.41 (3) ~ (all_52_1 = e3)
% 170.47/26.41 (4) all_54_14 = all_52_11
% 170.47/26.41 (5) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.41 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.41 (6) all_54_12 = all_52_3
% 170.47/26.41 (7) all_54_12 = e1 | all_54_12 = e0
% 170.47/26.41 (8) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.41 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.41 (9) op(e0, e0) = e2
% 170.47/26.41 (10) ~ (all_8_2 = e3)
% 170.47/26.41 (11) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.47/26.41 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.47/26.41 (12) ~ (all_6_2 = e3)
% 170.47/26.41 (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.41 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.41 (14) ~ (e3 = e1)
% 170.47/26.41 (15) all_58_13 = e3
% 170.47/26.41 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.41 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.41 e1)
% 170.47/26.41 (17) op(e3, e1) = all_52_8
% 170.47/26.41 (18) ~ (all_52_9 = all_52_11)
% 170.47/26.41 (19) ~ (e1 = e0)
% 170.47/26.41 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.41 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.41 (21) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.47/26.41 | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.41 (22) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.47/26.41 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.47/26.41 (23) op(e2, e3) = all_52_1
% 170.47/26.41 (24) op(e0, e2) = e0
% 170.47/26.41 (25) op(e2, e2) = all_8_2
% 170.47/26.41 (26) ~ (all_6_2 = e2)
% 170.47/26.41 (27) all_58_6 = e2
% 170.47/26.41 (28) op(e1, e1) = all_6_2
% 170.47/26.41 (29) ~ (all_52_11 = e2)
% 170.47/26.41 (30) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.47/26.41 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.47/26.41 (31) ~ (e3 = e0)
% 170.47/26.41 (32) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.47/26.41 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.47/26.41 (33) all_58_14 = e3
% 170.47/26.41 (34) ~ (all_52_3 = all_52_11)
% 170.47/26.41 (35) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.47/26.41 (36) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.41 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.41 (37) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.41 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.41 (38) all_58_3 = e2
% 170.47/26.41 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.41 (40) ~ (e2 = e0)
% 170.47/26.41 (41) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.47/26.41 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.47/26.41 (42) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.47/26.41 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.47/26.41 (43) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.47/26.41 (44) ~ (e2 = e1)
% 170.47/26.41 (45) ~ (all_52_3 = e0)
% 170.47/26.41 (46) op(e0, e2) = all_52_7
% 170.47/26.41 (47) ~ (all_52_11 = e0)
% 170.47/26.41 (48) all_58_4 = e2
% 170.47/26.41 (49) all_58_1 = e0
% 170.47/26.41 (50) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.41 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.41 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.41 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.41 (51) op(e3, e1) = e2
% 170.47/26.41 (52) all_56_10 = e3
% 170.47/26.41 (53) ~ (e3 = e2)
% 170.47/26.41
% 170.47/26.41 Begin of proof
% 170.47/26.41 |
% 170.47/26.41 | BETA: splitting (21) gives:
% 170.47/26.41 |
% 170.47/26.41 | Case 1:
% 170.47/26.41 | |
% 170.47/26.41 | | (54) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.41 | |
% 170.47/26.41 | | ALPHA: (54) implies:
% 170.47/26.41 | | (55) all_58_12 = e0
% 170.47/26.41 | |
% 170.47/26.41 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 170.47/26.41 | | (13), (14), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 170.47/26.41 | | (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), (36),
% 170.47/26.41 | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 170.47/26.41 | | (48), (49), (50), (51), (52), (53), (55) are inconsistent by
% 170.47/26.41 | | sub-proof #638.
% 170.47/26.41 | |
% 170.47/26.41 | Case 2:
% 170.47/26.41 | |
% 170.47/26.41 | | (56) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 170.47/26.41 | | e0)
% 170.47/26.41 | |
% 170.47/26.41 | | BETA: splitting (56) gives:
% 170.47/26.41 | |
% 170.47/26.41 | | Case 1:
% 170.47/26.41 | | |
% 170.47/26.41 | | | (57) all_58_13 = e0 & op(e0, e2) = e0
% 170.47/26.41 | | |
% 170.47/26.41 | | | ALPHA: (57) implies:
% 170.47/26.41 | | | (58) all_58_13 = e0
% 170.47/26.41 | | |
% 170.47/26.41 | | | REF_CLOSE: (15), (31), (58) are inconsistent by sub-proof #708.
% 170.47/26.41 | | |
% 170.47/26.41 | | Case 2:
% 170.47/26.41 | | |
% 170.47/26.41 | | | (59) all_58_14 = e0 & op(e0, e1) = e0
% 170.47/26.41 | | |
% 170.47/26.41 | | | REF_CLOSE: (31), (33), (59) are inconsistent by sub-proof #871.
% 170.47/26.41 | | |
% 170.47/26.41 | | End of split
% 170.47/26.41 | |
% 170.47/26.41 | End of split
% 170.47/26.41 |
% 170.47/26.41 End of proof
% 170.47/26.41
% 170.47/26.41 Sub-proof #638 shows that the following formulas are inconsistent:
% 170.47/26.41 ----------------------------------------------------------------
% 170.47/26.41 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.41 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.41 (2) op(e2, e1) = all_52_9
% 170.47/26.41 (3) ~ (all_52_1 = e3)
% 170.47/26.41 (4) all_54_14 = all_52_11
% 170.47/26.41 (5) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.47/26.41 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.47/26.41 (6) all_54_12 = all_52_3
% 170.47/26.41 (7) all_54_12 = e1 | all_54_12 = e0
% 170.47/26.41 (8) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.47/26.41 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.41 (9) op(e0, e0) = e2
% 170.47/26.41 (10) ~ (all_8_2 = e3)
% 170.47/26.41 (11) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.47/26.41 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.47/26.41 (12) ~ (all_6_2 = e3)
% 170.47/26.41 (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.41 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.41 (14) ~ (e3 = e1)
% 170.47/26.41 (15) all_58_13 = e3
% 170.47/26.41 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.47/26.41 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.41 e1)
% 170.47/26.41 (17) op(e3, e1) = all_52_8
% 170.47/26.41 (18) ~ (all_52_9 = all_52_11)
% 170.47/26.41 (19) ~ (e1 = e0)
% 170.47/26.41 (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 & op(e2, e3) = e3) |
% 170.47/26.41 (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.41 (21) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.47/26.41 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.47/26.41 (22) op(e2, e3) = all_52_1
% 170.47/26.41 (23) op(e0, e2) = e0
% 170.47/26.41 (24) op(e2, e2) = all_8_2
% 170.47/26.41 (25) ~ (all_6_2 = e2)
% 170.47/26.41 (26) all_58_6 = e2
% 170.47/26.41 (27) op(e1, e1) = all_6_2
% 170.47/26.41 (28) ~ (all_52_11 = e2)
% 170.47/26.41 (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.47/26.41 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.47/26.41 (30) ~ (e3 = e0)
% 170.47/26.41 (31) all_58_12 = e0
% 170.47/26.41 (32) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.47/26.41 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.47/26.41 (33) ~ (all_52_3 = all_52_11)
% 170.47/26.41 (34) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.47/26.41 (35) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.41 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.41 (36) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.47/26.41 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.47/26.41 (37) all_58_3 = e2
% 170.47/26.41 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.41 (39) ~ (e2 = e0)
% 170.47/26.41 (40) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.47/26.41 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.47/26.41 (41) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.47/26.41 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.47/26.41 (42) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.47/26.41 (43) ~ (e2 = e1)
% 170.47/26.41 (44) ~ (all_52_3 = e0)
% 170.47/26.41 (45) op(e0, e2) = all_52_7
% 170.47/26.41 (46) ~ (all_52_11 = e0)
% 170.47/26.41 (47) all_58_4 = e2
% 170.47/26.41 (48) all_58_1 = e0
% 170.47/26.41 (49) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.41 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.41 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.41 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.41 (50) op(e3, e1) = e2
% 170.47/26.41 (51) all_56_10 = e3
% 170.47/26.41 (52) ~ (e3 = e2)
% 170.47/26.41
% 170.47/26.41 Begin of proof
% 170.47/26.41 |
% 170.47/26.41 | BETA: splitting (8) gives:
% 170.47/26.41 |
% 170.47/26.41 | Case 1:
% 170.47/26.41 | |
% 170.47/26.41 | | (53) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 170.47/26.41 | | e1)
% 170.47/26.41 | |
% 170.47/26.41 | | BETA: splitting (53) gives:
% 170.47/26.41 | |
% 170.47/26.41 | | Case 1:
% 170.47/26.41 | | |
% 170.47/26.41 | | | (54) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.41 | | |
% 170.47/26.41 | | | REF_CLOSE: (19), (48), (54) are inconsistent by sub-proof #658.
% 170.47/26.41 | | |
% 170.47/26.41 | | Case 2:
% 170.47/26.41 | | |
% 170.47/26.41 | | | (55) all_58_3 = e1 & op(e2, e2) = e1
% 170.47/26.41 | | |
% 170.47/26.41 | | | REF_CLOSE: (37), (43), (55) are inconsistent by sub-proof #914.
% 170.47/26.41 | | |
% 170.47/26.41 | | End of split
% 170.47/26.41 | |
% 170.47/26.41 | Case 2:
% 170.47/26.41 | |
% 170.47/26.41 | | (56) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 170.47/26.41 | | e1)
% 170.47/26.41 | |
% 170.47/26.41 | | BETA: splitting (56) gives:
% 170.47/26.41 | |
% 170.47/26.41 | | Case 1:
% 170.47/26.41 | | |
% 170.47/26.41 | | | (57) all_58_7 = e1 & op(e1, e2) = e1
% 170.47/26.41 | | |
% 170.47/26.41 | | | ALPHA: (57) implies:
% 170.47/26.41 | | | (58) all_58_7 = e1
% 170.47/26.41 | | |
% 170.47/26.41 | | | BETA: splitting (35) gives:
% 170.47/26.41 | | |
% 170.47/26.41 | | | Case 1:
% 170.47/26.41 | | | |
% 170.47/26.41 | | | | (59) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2)
% 170.47/26.41 | | | | = e1)
% 170.47/26.41 | | | |
% 170.47/26.41 | | | | BETA: splitting (59) gives:
% 170.47/26.41 | | | |
% 170.47/26.41 | | | | Case 1:
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | | (60) all_58_0 = e1 & op(e3, e3) = e1
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | | ALPHA: (60) implies:
% 170.47/26.41 | | | | | (61) all_58_0 = e1
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | | BETA: splitting (41) gives:
% 170.47/26.41 | | | | |
% 170.47/26.41 | | | | | Case 1:
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | (62) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 170.47/26.41 | | | | | | e2) = e3)
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | REF_CLOSE: (14), (26), (52), (58), (62) are inconsistent by
% 170.47/26.41 | | | | | | sub-proof #820.
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | Case 2:
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | (63) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 170.47/26.41 | | | | | | e0) = e3)
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | BETA: splitting (63) gives:
% 170.47/26.41 | | | | | |
% 170.47/26.41 | | | | | | Case 1:
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | (64) all_58_8 = e3 & op(e1, e1) = e3
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | REF_CLOSE: (12), (27), (38), (64) are inconsistent by sub-proof
% 170.47/26.41 | | | | | | | #961.
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | Case 2:
% 170.47/26.41 | | | | | | |
% 170.47/26.41 | | | | | | | (65) all_58_11 = e3 & op(e1, e0) = e3
% 170.47/26.41 | | | | | | |
% 170.47/26.42 | | | | | | | ALPHA: (65) implies:
% 170.47/26.42 | | | | | | | (66) all_58_11 = e3
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | | BETA: splitting (20) gives:
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | | (67) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 170.47/26.42 | | | | | | | | op(e2, e3) = e3)
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | | BETA: splitting (67) gives:
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | (68) all_58_0 = e3 & op(e3, e3) = e3
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | REF_CLOSE: (14), (61), (68) are inconsistent by sub-proof
% 170.47/26.42 | | | | | | | | | #905.
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | (69) all_58_2 = e3 & op(e2, e3) = e3
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | ALPHA: (69) implies:
% 170.47/26.42 | | | | | | | | | (70) op(e2, e3) = e3
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | REF_CLOSE: (3), (22), (38), (70) are inconsistent by sub-proof
% 170.47/26.42 | | | | | | | | | #989.
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | End of split
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | | (71) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 170.47/26.42 | | | | | | | | op(e0, e3) = e3)
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | | REF_CLOSE: (1), (14), (15), (16), (19), (26), (30), (32), (39),
% 170.47/26.42 | | | | | | | | (41), (43), (49), (52), (58), (66), (71) are
% 170.47/26.42 | | | | | | | | inconsistent by sub-proof #642.
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | End of split
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | End of split
% 170.47/26.42 | | | | | |
% 170.47/26.42 | | | | | End of split
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | Case 2:
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | (72) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | REF_CLOSE: (19), (48), (72) are inconsistent by sub-proof #658.
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | End of split
% 170.47/26.42 | | | |
% 170.47/26.42 | | | Case 2:
% 170.47/26.42 | | | |
% 170.47/26.42 | | | | (73) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0)
% 170.47/26.42 | | | | = e1)
% 170.47/26.42 | | | |
% 170.47/26.42 | | | | BETA: splitting (73) gives:
% 170.47/26.42 | | | |
% 170.47/26.42 | | | | Case 1:
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | (74) all_58_4 = e1 & op(e3, e1) = e1
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | REF_CLOSE: (43), (47), (74) are inconsistent by sub-proof #943.
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | Case 2:
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | (75) all_58_9 = e1 & op(e3, e0) = e1
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | ALPHA: (75) implies:
% 170.47/26.42 | | | | | (76) all_58_9 = e1
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | BETA: splitting (41) gives:
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | Case 1:
% 170.47/26.42 | | | | | |
% 170.47/26.42 | | | | | | (77) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1,
% 170.47/26.42 | | | | | | e2) = e3)
% 170.47/26.42 | | | | | |
% 170.47/26.42 | | | | | | REF_CLOSE: (14), (26), (52), (58), (77) are inconsistent by
% 170.47/26.42 | | | | | | sub-proof #820.
% 170.47/26.42 | | | | | |
% 170.47/26.42 | | | | | Case 2:
% 170.47/26.42 | | | | | |
% 170.47/26.42 | | | | | | (78) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1,
% 170.47/26.42 | | | | | | e0) = e3)
% 170.47/26.42 | | | | | |
% 170.47/26.42 | | | | | | BETA: splitting (78) gives:
% 170.47/26.42 | | | | | |
% 170.47/26.42 | | | | | | Case 1:
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | | (79) all_58_8 = e3 & op(e1, e1) = e3
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | | REF_CLOSE: (12), (27), (38), (79) are inconsistent by sub-proof
% 170.47/26.42 | | | | | | | #961.
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | Case 2:
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | | (80) all_58_11 = e3 & op(e1, e0) = e3
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | | ALPHA: (80) implies:
% 170.47/26.42 | | | | | | | (81) all_58_11 = e3
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | | BETA: splitting (20) gives:
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | | (82) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_2 = e3 &
% 170.47/26.42 | | | | | | | | op(e2, e3) = e3)
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | | BETA: splitting (82) gives:
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | (83) all_58_0 = e3 & op(e3, e3) = e3
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | ALPHA: (83) implies:
% 170.47/26.42 | | | | | | | | | (84) all_58_0 = e3
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | BETA: splitting (29) gives:
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | (85) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 &
% 170.47/26.42 | | | | | | | | | | op(e2, e3) = e1)
% 170.47/26.42 | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | BETA: splitting (85) gives:
% 170.47/26.42 | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | (86) all_58_0 = e1 & op(e3, e3) = e1
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | ALPHA: (86) implies:
% 170.47/26.42 | | | | | | | | | | | (87) all_58_0 = e1
% 170.47/26.42 | | | | | | | | | | | (88) op(e3, e3) = e1
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | COMBINE_EQS: (84), (87) imply:
% 170.47/26.42 | | | | | | | | | | | (89) e3 = e1
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | COMBINE_EQS: (51), (89) imply:
% 170.47/26.42 | | | | | | | | | | | (90) all_56_10 = e1
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | REF_CLOSE: (13), (14), (17), (19), (30), (36), (38), (39),
% 170.47/26.42 | | | | | | | | | | | (42), (43), (47), (50), (52), (76), (88), (90) are
% 170.47/26.42 | | | | | | | | | | | inconsistent by sub-proof #801.
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | (91) all_58_2 = e1 & op(e2, e3) = e1
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | ALPHA: (91) implies:
% 170.47/26.42 | | | | | | | | | | | (92) all_58_2 = e1
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | BETA: splitting (16) gives:
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | (93) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 =
% 170.47/26.42 | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 170.47/26.42 | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | BETA: splitting (93) gives:
% 170.47/26.42 | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | (94) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | ALPHA: (94) implies:
% 170.47/26.42 | | | | | | | | | | | | | (95) all_58_12 = e1
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | COMBINE_EQS: (31), (95) imply:
% 170.47/26.42 | | | | | | | | | | | | | (96) e1 = e0
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | SIMP: (96) implies:
% 170.47/26.42 | | | | | | | | | | | | | (97) e1 = e0
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | COMBINE_EQS: (92), (97) imply:
% 170.47/26.42 | | | | | | | | | | | | | (98) all_58_2 = e0
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | REF_CLOSE: (14), (19), (26), (29), (31), (43), (84), (98) are
% 170.47/26.42 | | | | | | | | | | | | | inconsistent by sub-proof #772.
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | (99) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | ALPHA: (99) implies:
% 170.47/26.42 | | | | | | | | | | | | | (100) op(e0, e2) = e1
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | REF_CLOSE: (19), (23), (38), (45), (100) are inconsistent by
% 170.47/26.42 | | | | | | | | | | | | | sub-proof #889.
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | (101) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 170.47/26.42 | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 170.47/26.42 | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | BETA: splitting (101) gives:
% 170.47/26.42 | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | (102) all_58_14 = e1 & op(e0, e1) = e1
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | ALPHA: (102) implies:
% 170.47/26.42 | | | | | | | | | | | | | (103) all_58_14 = e1
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | BETA: splitting (32) gives:
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | (104) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 170.47/26.42 | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 170.47/26.42 | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 170.47/26.42 | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | (105) all_58_6 = e0 & op(e1, e3) = e0
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | REF_CLOSE: (26), (39), (105) are inconsistent by sub-proof
% 170.47/26.42 | | | | | | | | | | | | | | | #769.
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | (106) all_58_7 = e0 & op(e1, e2) = e0
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 170.47/26.42 | | | | | | | | | | | | | | | (107) all_58_7 = e0
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | COMBINE_EQS: (58), (107) imply:
% 170.47/26.42 | | | | | | | | | | | | | | | (108) e1 = e0
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | SIMP: (108) implies:
% 170.47/26.42 | | | | | | | | | | | | | | | (109) e1 = e0
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | COMBINE_EQS: (92), (109) imply:
% 170.47/26.42 | | | | | | | | | | | | | | | (110) all_58_2 = e0
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | REF_CLOSE: (14), (19), (26), (29), (31), (43), (84), (110)
% 170.47/26.42 | | | | | | | | | | | | | | | are inconsistent by sub-proof #772.
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | (111) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 170.47/26.42 | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 170.47/26.42 | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 170.47/26.42 | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | (112) all_58_8 = e0 & op(e1, e1) = e0
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 170.47/26.42 | | | | | | | | | | | | | | | (113) all_58_8 = e0
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | (114) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 170.47/26.42 | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 170.47/26.42 | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | (115) all_58_4 = e3 & op(e3, e1) = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 170.47/26.42 | | | | | | | | | | | | | | | | | (116) all_58_4 = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (47), (116) imply:
% 170.47/26.42 | | | | | | | | | | | | | | | | | (117) e3 = e2
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | SIMP: (117) implies:
% 170.47/26.42 | | | | | | | | | | | | | | | | | (118) e3 = e2
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (118) imply:
% 170.47/26.42 | | | | | | | | | | | | | | | | | (119) all_58_11 = e2
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (26), (30), (41), (52), (58), (113), (119)
% 170.47/26.42 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #819.
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | (120) all_58_5 = e3 & op(e2, e1) = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (7), (18), (28), (33), (34), (38),
% 170.47/26.42 | | | | | | | | | | | | | | | | | (44), (46), (120) are inconsistent by sub-proof
% 170.47/26.42 | | | | | | | | | | | | | | | | | #652.
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | (121) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 170.47/26.42 | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 170.47/26.42 | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | BETA: splitting (121) gives:
% 170.47/26.42 | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | (122) all_58_8 = e3 & op(e1, e1) = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (38), (122) are inconsistent by
% 170.47/26.42 | | | | | | | | | | | | | | | | | sub-proof #961.
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | (123) all_58_14 = e3 & op(e0, e1) = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 170.47/26.42 | | | | | | | | | | | | | | | | | (124) all_58_14 = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (103), (124) imply:
% 170.47/26.42 | | | | | | | | | | | | | | | | | (125) e3 = e1
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | SIMP: (125) implies:
% 170.47/26.42 | | | | | | | | | | | | | | | | | (126) e3 = e1
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | COMBINE_EQS: (15), (126) imply:
% 170.47/26.42 | | | | | | | | | | | | | | | | | (127) all_58_13 = e1
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | BETA: splitting (5) gives:
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | (128) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 170.47/26.42 | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 170.47/26.42 | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | (129) all_58_1 = e3 & op(e3, e2) = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | (130) all_58_1 = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (19), (30), (35), (39), (43), (47),
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | (84), (130) are inconsistent by sub-proof #641.
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | (131) all_58_3 = e3 & op(e2, e2) = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (24), (38), (131) are inconsistent by
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | sub-proof #973.
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | (132) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 =
% 170.47/26.42 | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 170.47/26.42 | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 170.47/26.42 | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | (133) all_58_7 = e3 & op(e1, e2) = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | (134) all_58_7 = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (14), (19), (25), (27), (38), (40), (43),
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | (52), (81), (113), (134) are inconsistent by
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | sub-proof #753.
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | (135) all_58_13 = e3 & op(e0, e2) = e3
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | REDUCE: (14), (126) imply:
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | (136) $false
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | | CLOSE: (136) is inconsistent.
% 170.47/26.42 | | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | (137) all_58_11 = e0 & op(e1, e0) = e0
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | | REF_CLOSE: (30), (81), (137) are inconsistent by sub-proof
% 170.47/26.42 | | | | | | | | | | | | | | | #724.
% 170.47/26.42 | | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | (138) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | ALPHA: (138) implies:
% 170.47/26.42 | | | | | | | | | | | | | (139) op(e0, e0) = e1
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | | REF_CLOSE: (9), (38), (43), (139) are inconsistent by
% 170.47/26.42 | | | | | | | | | | | | | sub-proof #640.
% 170.47/26.42 | | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | (140) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1
% 170.47/26.42 | | | | | | | | | | & op(e0, e3) = e1)
% 170.47/26.42 | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | BETA: splitting (140) gives:
% 170.47/26.42 | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | Case 1:
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | (141) all_58_6 = e1 & op(e1, e3) = e1
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | REF_CLOSE: (26), (43), (141) are inconsistent by sub-proof
% 170.47/26.42 | | | | | | | | | | | #774.
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | (142) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | ALPHA: (142) implies:
% 170.47/26.42 | | | | | | | | | | | (143) all_58_12 = e1
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | COMBINE_EQS: (31), (143) imply:
% 170.47/26.42 | | | | | | | | | | | (144) e1 = e0
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | SIMP: (144) implies:
% 170.47/26.42 | | | | | | | | | | | (145) e1 = e0
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | COMBINE_EQS: (76), (145) imply:
% 170.47/26.42 | | | | | | | | | | | (146) all_58_9 = e0
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | | REF_CLOSE: (14), (19), (35), (43), (47), (48), (84), (146)
% 170.47/26.42 | | | | | | | | | | | are inconsistent by sub-proof #639.
% 170.47/26.42 | | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | | |
% 170.47/26.42 | | | | | | | | | End of split
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | (147) all_58_2 = e3 & op(e2, e3) = e3
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | ALPHA: (147) implies:
% 170.47/26.42 | | | | | | | | | (148) op(e2, e3) = e3
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | | REF_CLOSE: (3), (22), (38), (148) are inconsistent by
% 170.47/26.42 | | | | | | | | | sub-proof #989.
% 170.47/26.42 | | | | | | | | |
% 170.47/26.42 | | | | | | | | End of split
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | Case 2:
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | | (149) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 &
% 170.47/26.42 | | | | | | | | op(e0, e3) = e3)
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | | REF_CLOSE: (1), (14), (15), (16), (19), (26), (30), (32), (39),
% 170.47/26.42 | | | | | | | | (41), (43), (49), (52), (58), (81), (149) are
% 170.47/26.42 | | | | | | | | inconsistent by sub-proof #642.
% 170.47/26.42 | | | | | | | |
% 170.47/26.42 | | | | | | | End of split
% 170.47/26.42 | | | | | | |
% 170.47/26.42 | | | | | | End of split
% 170.47/26.42 | | | | | |
% 170.47/26.42 | | | | | End of split
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | End of split
% 170.47/26.42 | | | |
% 170.47/26.42 | | | End of split
% 170.47/26.42 | | |
% 170.47/26.42 | | Case 2:
% 170.47/26.42 | | |
% 170.47/26.42 | | | (150) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | ALPHA: (150) implies:
% 170.47/26.42 | | | (151) op(e0, e2) = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | REF_CLOSE: (19), (23), (38), (45), (151) are inconsistent by sub-proof
% 170.47/26.42 | | | #889.
% 170.47/26.42 | | |
% 170.47/26.42 | | End of split
% 170.47/26.42 | |
% 170.47/26.42 | End of split
% 170.47/26.42 |
% 170.47/26.42 End of proof
% 170.47/26.42
% 170.47/26.42 Sub-proof #639 shows that the following formulas are inconsistent:
% 170.47/26.42 ----------------------------------------------------------------
% 170.47/26.42 (1) all_58_9 = e0
% 170.47/26.42 (2) ~ (e3 = e1)
% 170.47/26.42 (3) ~ (e1 = e0)
% 170.47/26.42 (4) all_58_0 = e3
% 170.47/26.42 (5) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.42 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.42 (6) ~ (e2 = e1)
% 170.47/26.42 (7) all_58_4 = e2
% 170.47/26.42 (8) all_58_1 = e0
% 170.47/26.42
% 170.47/26.42 Begin of proof
% 170.47/26.42 |
% 170.47/26.42 | BETA: splitting (5) gives:
% 170.47/26.42 |
% 170.47/26.42 | Case 1:
% 170.47/26.42 | |
% 170.47/26.42 | | (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1)
% 170.47/26.42 | |
% 170.47/26.42 | | BETA: splitting (9) gives:
% 170.47/26.42 | |
% 170.47/26.42 | | Case 1:
% 170.47/26.42 | | |
% 170.47/26.42 | | | (10) all_58_0 = e1 & op(e3, e3) = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #950.
% 170.47/26.42 | | |
% 170.47/26.42 | | Case 2:
% 170.47/26.42 | | |
% 170.47/26.42 | | | (11) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | REF_CLOSE: (3), (8), (11) are inconsistent by sub-proof #658.
% 170.47/26.42 | | |
% 170.47/26.42 | | End of split
% 170.47/26.42 | |
% 170.47/26.42 | Case 2:
% 170.47/26.42 | |
% 170.47/26.42 | | (12) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 170.47/26.42 | | e1)
% 170.47/26.42 | |
% 170.47/26.42 | | BETA: splitting (12) gives:
% 170.47/26.42 | |
% 170.47/26.42 | | Case 1:
% 170.47/26.42 | | |
% 170.47/26.42 | | | (13) all_58_4 = e1 & op(e3, e1) = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #943.
% 170.47/26.42 | | |
% 170.47/26.42 | | Case 2:
% 170.47/26.42 | | |
% 170.47/26.42 | | | (14) all_58_9 = e1 & op(e3, e0) = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | ALPHA: (14) implies:
% 170.47/26.42 | | | (15) all_58_9 = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | COMBINE_EQS: (1), (15) imply:
% 170.47/26.42 | | | (16) e1 = e0
% 170.47/26.42 | | |
% 170.47/26.42 | | | REDUCE: (3), (16) imply:
% 170.47/26.42 | | | (17) $false
% 170.47/26.42 | | |
% 170.47/26.42 | | | CLOSE: (17) is inconsistent.
% 170.47/26.42 | | |
% 170.47/26.42 | | End of split
% 170.47/26.42 | |
% 170.47/26.42 | End of split
% 170.47/26.42 |
% 170.47/26.42 End of proof
% 170.47/26.42
% 170.47/26.42 Sub-proof #640 shows that the following formulas are inconsistent:
% 170.47/26.42 ----------------------------------------------------------------
% 170.47/26.42 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.47/26.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.47/26.42 (2) op(e0, e0) = e2
% 170.47/26.42 (3) op(e0, e0) = e1
% 170.47/26.42 (4) ~ (e2 = e1)
% 170.47/26.42
% 170.47/26.42 Begin of proof
% 170.47/26.42 |
% 170.47/26.42 | GROUND_INST: instantiating (1) with e1, e2, e0, e0, simplifying with (2), (3)
% 170.47/26.42 | gives:
% 170.47/26.42 | (5) e2 = e1
% 170.47/26.42 |
% 170.47/26.42 | REDUCE: (4), (5) imply:
% 170.47/26.42 | (6) $false
% 170.47/26.42 |
% 170.47/26.42 | CLOSE: (6) is inconsistent.
% 170.47/26.42 |
% 170.47/26.42 End of proof
% 170.47/26.42
% 170.47/26.42 Sub-proof #641 shows that the following formulas are inconsistent:
% 170.47/26.42 ----------------------------------------------------------------
% 170.47/26.42 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.47/26.42 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.42 (2) ~ (e3 = e1)
% 170.47/26.42 (3) ~ (e1 = e0)
% 170.47/26.42 (4) ~ (e3 = e0)
% 170.47/26.42 (5) all_58_1 = e3
% 170.47/26.42 (6) all_58_0 = e3
% 170.47/26.42 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.47/26.42 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.47/26.42 (8) ~ (e2 = e0)
% 170.47/26.42 (9) ~ (e2 = e1)
% 170.47/26.42 (10) all_58_4 = e2
% 170.47/26.42
% 170.47/26.42 Begin of proof
% 170.47/26.42 |
% 170.47/26.42 | BETA: splitting (7) gives:
% 170.47/26.42 |
% 170.47/26.42 | Case 1:
% 170.47/26.42 | |
% 170.47/26.42 | | (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 170.47/26.42 | | e1)
% 170.47/26.42 | |
% 170.47/26.42 | | BETA: splitting (11) gives:
% 170.47/26.42 | |
% 170.47/26.42 | | Case 1:
% 170.47/26.42 | | |
% 170.47/26.42 | | | (12) all_58_0 = e1 & op(e3, e3) = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | REF_CLOSE: (2), (6), (12) are inconsistent by sub-proof #950.
% 170.47/26.42 | | |
% 170.47/26.42 | | Case 2:
% 170.47/26.42 | | |
% 170.47/26.42 | | | (13) all_58_1 = e1 & op(e3, e2) = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #711.
% 170.47/26.42 | | |
% 170.47/26.42 | | End of split
% 170.47/26.42 | |
% 170.47/26.42 | Case 2:
% 170.47/26.42 | |
% 170.47/26.42 | | (14) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 170.47/26.42 | | e1)
% 170.47/26.42 | |
% 170.47/26.42 | | BETA: splitting (14) gives:
% 170.47/26.42 | |
% 170.47/26.42 | | Case 1:
% 170.47/26.42 | | |
% 170.47/26.42 | | | (15) all_58_4 = e1 & op(e3, e1) = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | REF_CLOSE: (9), (10), (15) are inconsistent by sub-proof #943.
% 170.47/26.42 | | |
% 170.47/26.42 | | Case 2:
% 170.47/26.42 | | |
% 170.47/26.42 | | | (16) all_58_9 = e1 & op(e3, e0) = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | ALPHA: (16) implies:
% 170.47/26.42 | | | (17) all_58_9 = e1
% 170.47/26.42 | | |
% 170.47/26.42 | | | BETA: splitting (1) gives:
% 170.47/26.42 | | |
% 170.47/26.42 | | | Case 1:
% 170.47/26.42 | | | |
% 170.47/26.42 | | | | (18) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 170.47/26.42 | | | | = e0)
% 170.47/26.42 | | | |
% 170.47/26.42 | | | | BETA: splitting (18) gives:
% 170.47/26.42 | | | |
% 170.47/26.42 | | | | Case 1:
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | (19) all_58_0 = e0 & op(e3, e3) = e0
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | REF_CLOSE: (4), (6), (19) are inconsistent by sub-proof #898.
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | Case 2:
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | (20) all_58_1 = e0 & op(e3, e2) = e0
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | REF_CLOSE: (4), (5), (20) are inconsistent by sub-proof #794.
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | End of split
% 170.47/26.42 | | | |
% 170.47/26.42 | | | Case 2:
% 170.47/26.42 | | | |
% 170.47/26.42 | | | | (21) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 170.47/26.42 | | | | = e0)
% 170.47/26.42 | | | |
% 170.47/26.42 | | | | BETA: splitting (21) gives:
% 170.47/26.42 | | | |
% 170.47/26.42 | | | | Case 1:
% 170.47/26.42 | | | | |
% 170.47/26.42 | | | | | (22) all_58_4 = e0 & op(e3, e1) = e0
% 170.47/26.42 | | | | |
% 170.47/26.43 | | | | | REF_CLOSE: (8), (10), (22) are inconsistent by sub-proof #902.
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | Case 2:
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | (23) all_58_9 = e0 & op(e3, e0) = e0
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | REF_CLOSE: (3), (17), (23) are inconsistent by sub-proof #880.
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | End of split
% 170.47/26.43 | | | |
% 170.47/26.43 | | | End of split
% 170.47/26.43 | | |
% 170.47/26.43 | | End of split
% 170.47/26.43 | |
% 170.47/26.43 | End of split
% 170.47/26.43 |
% 170.47/26.43 End of proof
% 170.47/26.43
% 170.47/26.43 Sub-proof #642 shows that the following formulas are inconsistent:
% 170.47/26.43 ----------------------------------------------------------------
% 170.47/26.43 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.43 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.43 (2) all_58_7 = e1
% 170.47/26.43 (3) ~ (e3 = e1)
% 170.47/26.43 (4) all_58_13 = e3
% 170.47/26.43 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.47/26.43 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.43 (6) ~ (e1 = e0)
% 170.47/26.43 (7) all_58_6 = e2
% 170.47/26.43 (8) ~ (e3 = e0)
% 170.47/26.43 (9) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.47/26.43 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.47/26.43 (10) all_58_11 = e3
% 170.47/26.43 (11) ~ (e2 = e0)
% 170.47/26.43 (12) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.47/26.43 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.47/26.43 (13) ~ (e2 = e1)
% 170.47/26.43 (14) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_12 = e3 & op(e0, e3) = e3)
% 170.47/26.43 (15) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.43 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.43 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.43 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.43 (16) ~ (e3 = e2)
% 170.47/26.43
% 170.47/26.43 Begin of proof
% 170.47/26.43 |
% 170.47/26.43 | BETA: splitting (14) gives:
% 170.47/26.43 |
% 170.47/26.43 | Case 1:
% 170.47/26.43 | |
% 170.47/26.43 | | (17) all_58_6 = e3 & op(e1, e3) = e3
% 170.47/26.43 | |
% 170.47/26.43 | | ALPHA: (17) implies:
% 170.47/26.43 | | (18) all_58_6 = e3
% 170.47/26.43 | |
% 170.47/26.43 | | COMBINE_EQS: (7), (18) imply:
% 170.47/26.43 | | (19) e3 = e2
% 170.47/26.43 | |
% 170.47/26.43 | | SIMP: (19) implies:
% 170.47/26.43 | | (20) e3 = e2
% 170.47/26.43 | |
% 170.47/26.43 | | COMBINE_EQS: (10), (20) imply:
% 170.47/26.43 | | (21) all_58_11 = e2
% 170.47/26.43 | |
% 170.47/26.43 | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (11), (12), (16), (21) are
% 170.47/26.43 | | inconsistent by sub-proof #726.
% 170.47/26.43 | |
% 170.47/26.43 | Case 2:
% 170.47/26.43 | |
% 170.47/26.43 | | (22) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.43 | |
% 170.47/26.43 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (11), (13), (15), (16), (22) are
% 170.47/26.43 | | inconsistent by sub-proof #643.
% 170.47/26.43 | |
% 170.47/26.43 | End of split
% 170.47/26.43 |
% 170.47/26.43 End of proof
% 170.47/26.43
% 170.47/26.43 Sub-proof #643 shows that the following formulas are inconsistent:
% 170.47/26.43 ----------------------------------------------------------------
% 170.47/26.43 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.43 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.43 (2) ~ (e3 = e1)
% 170.47/26.43 (3) all_58_13 = e3
% 170.47/26.43 (4) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.47/26.43 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.43 (5) ~ (e1 = e0)
% 170.47/26.43 (6) ~ (e3 = e0)
% 170.47/26.43 (7) ~ (e2 = e0)
% 170.47/26.43 (8) all_58_12 = e3 & op(e0, e3) = e3
% 170.47/26.43 (9) ~ (e2 = e1)
% 170.47/26.43 (10) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.43 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.43 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.43 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.43 (11) ~ (e3 = e2)
% 170.47/26.43
% 170.47/26.43 Begin of proof
% 170.47/26.43 |
% 170.47/26.43 | ALPHA: (8) implies:
% 170.47/26.43 | (12) all_58_12 = e3
% 170.47/26.43 |
% 170.47/26.43 | BETA: splitting (4) gives:
% 170.47/26.43 |
% 170.47/26.43 | Case 1:
% 170.47/26.43 | |
% 170.47/26.43 | | (13) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 170.47/26.43 | | e1)
% 170.47/26.43 | |
% 170.47/26.43 | | BETA: splitting (13) gives:
% 170.47/26.43 | |
% 170.47/26.43 | | Case 1:
% 170.47/26.43 | | |
% 170.47/26.43 | | | (14) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | REF_CLOSE: (2), (12), (14) are inconsistent by sub-proof #651.
% 170.47/26.43 | | |
% 170.47/26.43 | | Case 2:
% 170.47/26.43 | | |
% 170.47/26.43 | | | (15) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | REF_CLOSE: (2), (3), (15) are inconsistent by sub-proof #709.
% 170.47/26.43 | | |
% 170.47/26.43 | | End of split
% 170.47/26.43 | |
% 170.47/26.43 | Case 2:
% 170.47/26.43 | |
% 170.47/26.43 | | (16) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.43 | | e1)
% 170.47/26.43 | |
% 170.47/26.43 | | BETA: splitting (16) gives:
% 170.47/26.43 | |
% 170.47/26.43 | | Case 1:
% 170.47/26.43 | | |
% 170.47/26.43 | | | (17) all_58_14 = e1 & op(e0, e1) = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | ALPHA: (17) implies:
% 170.47/26.43 | | | (18) all_58_14 = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | BETA: splitting (10) gives:
% 170.47/26.43 | | |
% 170.47/26.43 | | | Case 1:
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | (19) all_58_15 = e0 & op(e0, e0) = e0
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (11), (12), (19) are
% 170.47/26.43 | | | | inconsistent by sub-proof #647.
% 170.47/26.43 | | | |
% 170.47/26.43 | | | Case 2:
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | (20) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 170.47/26.43 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 170.47/26.43 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 170.47/26.43 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | ALPHA: (20) implies:
% 170.47/26.43 | | | | (21) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 170.47/26.43 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | BETA: splitting (21) gives:
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | Case 1:
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | (22) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | REF_CLOSE: (6), (12), (22) are inconsistent by sub-proof #646.
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | Case 2:
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | (23) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 170.47/26.43 | | | | | e1) = e0)
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | BETA: splitting (23) gives:
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | Case 1:
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | | (24) all_58_13 = e0 & op(e0, e2) = e0
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | | REF_CLOSE: (3), (6), (24) are inconsistent by sub-proof #885.
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | Case 2:
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | | (25) all_58_14 = e0 & op(e0, e1) = e0
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | | REF_CLOSE: (5), (18), (25) are inconsistent by sub-proof #884.
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | End of split
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | End of split
% 170.47/26.43 | | | |
% 170.47/26.43 | | | End of split
% 170.47/26.43 | | |
% 170.47/26.43 | | Case 2:
% 170.47/26.43 | | |
% 170.47/26.43 | | | (26) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | ALPHA: (26) implies:
% 170.47/26.43 | | | (27) all_58_15 = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (27)
% 170.47/26.43 | | | are inconsistent by sub-proof #644.
% 170.47/26.43 | | |
% 170.47/26.43 | | End of split
% 170.47/26.43 | |
% 170.47/26.43 | End of split
% 170.47/26.43 |
% 170.47/26.43 End of proof
% 170.47/26.43
% 170.47/26.43 Sub-proof #644 shows that the following formulas are inconsistent:
% 170.47/26.43 ----------------------------------------------------------------
% 170.47/26.43 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.43 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.43 (2) all_58_15 = e1
% 170.47/26.43 (3) ~ (e3 = e1)
% 170.47/26.43 (4) all_58_13 = e3
% 170.47/26.43 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.47/26.43 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.43 (6) ~ (e1 = e0)
% 170.47/26.43 (7) ~ (e3 = e0)
% 170.47/26.43 (8) ~ (e2 = e0)
% 170.47/26.43 (9) all_58_12 = e3
% 170.47/26.43 (10) ~ (e2 = e1)
% 170.47/26.43 (11) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.47/26.43 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.47/26.43 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.47/26.43 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.47/26.43 (12) ~ (e3 = e2)
% 170.47/26.43
% 170.47/26.43 Begin of proof
% 170.47/26.43 |
% 170.47/26.43 | BETA: splitting (11) gives:
% 170.47/26.43 |
% 170.47/26.43 | Case 1:
% 170.47/26.43 | |
% 170.47/26.43 | | (13) all_58_15 = e0 & op(e0, e0) = e0
% 170.47/26.43 | |
% 170.47/26.43 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (12), (13) are
% 170.47/26.43 | | inconsistent by sub-proof #647.
% 170.47/26.43 | |
% 170.47/26.43 | Case 2:
% 170.47/26.43 | |
% 170.47/26.43 | | (14) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.47/26.43 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 170.47/26.43 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 170.47/26.43 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.47/26.43 | |
% 170.47/26.43 | | ALPHA: (14) implies:
% 170.47/26.43 | | (15) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 170.47/26.43 | | e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.47/26.43 | |
% 170.47/26.43 | | BETA: splitting (1) gives:
% 170.47/26.43 | |
% 170.47/26.43 | | Case 1:
% 170.47/26.43 | | |
% 170.47/26.43 | | | (16) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2)
% 170.47/26.43 | | | = e2)
% 170.47/26.43 | | |
% 170.47/26.43 | | | REF_CLOSE: (4), (9), (12), (16) are inconsistent by sub-proof #650.
% 170.47/26.43 | | |
% 170.47/26.43 | | Case 2:
% 170.47/26.43 | | |
% 170.47/26.43 | | | (17) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0)
% 170.47/26.43 | | | = e2)
% 170.47/26.43 | | |
% 170.47/26.43 | | | BETA: splitting (17) gives:
% 170.47/26.43 | | |
% 170.47/26.43 | | | Case 1:
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | (18) all_58_14 = e2 & op(e0, e1) = e2
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | ALPHA: (18) implies:
% 170.47/26.43 | | | | (19) all_58_14 = e2
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | BETA: splitting (15) gives:
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | Case 1:
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | (20) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | REF_CLOSE: (7), (9), (20) are inconsistent by sub-proof #646.
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | Case 2:
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | (21) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 170.47/26.43 | | | | | e1) = e0)
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | BETA: splitting (21) gives:
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | Case 1:
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | | (22) all_58_13 = e0 & op(e0, e2) = e0
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | | REF_CLOSE: (4), (7), (22) are inconsistent by sub-proof #885.
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | Case 2:
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | | (23) all_58_14 = e0 & op(e0, e1) = e0
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | | REF_CLOSE: (8), (19), (23) are inconsistent by sub-proof #858.
% 170.47/26.43 | | | | | |
% 170.47/26.43 | | | | | End of split
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | End of split
% 170.47/26.43 | | | |
% 170.47/26.43 | | | Case 2:
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | (24) all_58_15 = e2 & op(e0, e0) = e2
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | ALPHA: (24) implies:
% 170.47/26.43 | | | | (25) all_58_15 = e2
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | REF_CLOSE: (2), (10), (25) are inconsistent by sub-proof #645.
% 170.47/26.43 | | | |
% 170.47/26.43 | | | End of split
% 170.47/26.43 | | |
% 170.47/26.43 | | End of split
% 170.47/26.43 | |
% 170.47/26.43 | End of split
% 170.47/26.43 |
% 170.47/26.43 End of proof
% 170.47/26.43
% 170.47/26.43 Sub-proof #645 shows that the following formulas are inconsistent:
% 170.47/26.43 ----------------------------------------------------------------
% 170.47/26.43 (1) all_58_15 = e2
% 170.47/26.43 (2) all_58_15 = e1
% 170.47/26.43 (3) ~ (e2 = e1)
% 170.47/26.43
% 170.47/26.43 Begin of proof
% 170.47/26.43 |
% 170.47/26.43 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.43 | (4) e2 = e1
% 170.47/26.43 |
% 170.47/26.43 | SIMP: (4) implies:
% 170.47/26.43 | (5) e2 = e1
% 170.47/26.43 |
% 170.47/26.43 | REDUCE: (3), (5) imply:
% 170.47/26.43 | (6) $false
% 170.47/26.43 |
% 170.47/26.43 | CLOSE: (6) is inconsistent.
% 170.47/26.43 |
% 170.47/26.43 End of proof
% 170.47/26.43
% 170.47/26.43 Sub-proof #646 shows that the following formulas are inconsistent:
% 170.47/26.43 ----------------------------------------------------------------
% 170.47/26.43 (1) all_58_12 = e0 & op(e0, e3) = e0
% 170.47/26.43 (2) all_58_12 = e3
% 170.47/26.43 (3) ~ (e3 = e0)
% 170.47/26.43
% 170.47/26.43 Begin of proof
% 170.47/26.43 |
% 170.47/26.43 | ALPHA: (1) implies:
% 170.47/26.43 | (4) all_58_12 = e0
% 170.47/26.43 |
% 170.47/26.43 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.43 | (5) e3 = e0
% 170.47/26.43 |
% 170.47/26.43 | REDUCE: (3), (5) imply:
% 170.47/26.43 | (6) $false
% 170.47/26.43 |
% 170.47/26.43 | CLOSE: (6) is inconsistent.
% 170.47/26.43 |
% 170.47/26.43 End of proof
% 170.47/26.43
% 170.47/26.43 Sub-proof #647 shows that the following formulas are inconsistent:
% 170.47/26.43 ----------------------------------------------------------------
% 170.47/26.43 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.47/26.43 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.47/26.43 (2) all_58_15 = e0 & op(e0, e0) = e0
% 170.47/26.43 (3) ~ (e3 = e1)
% 170.47/26.43 (4) all_58_13 = e3
% 170.47/26.43 (5) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 170.47/26.43 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.47/26.43 (6) ~ (e1 = e0)
% 170.47/26.43 (7) ~ (e2 = e0)
% 170.47/26.43 (8) all_58_12 = e3
% 170.47/26.43 (9) ~ (e2 = e1)
% 170.47/26.43 (10) ~ (e3 = e2)
% 170.47/26.43
% 170.47/26.43 Begin of proof
% 170.47/26.43 |
% 170.47/26.43 | ALPHA: (2) implies:
% 170.47/26.43 | (11) all_58_15 = e0
% 170.47/26.43 |
% 170.47/26.43 | BETA: splitting (5) gives:
% 170.47/26.43 |
% 170.47/26.43 | Case 1:
% 170.47/26.43 | |
% 170.47/26.43 | | (12) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 170.47/26.43 | | e1)
% 170.47/26.43 | |
% 170.47/26.43 | | BETA: splitting (12) gives:
% 170.47/26.43 | |
% 170.47/26.43 | | Case 1:
% 170.47/26.43 | | |
% 170.47/26.43 | | | (13) all_58_12 = e1 & op(e0, e3) = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #651.
% 170.47/26.43 | | |
% 170.47/26.43 | | Case 2:
% 170.47/26.43 | | |
% 170.47/26.43 | | | (14) all_58_13 = e1 & op(e0, e2) = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | REF_CLOSE: (3), (4), (14) are inconsistent by sub-proof #709.
% 170.47/26.43 | | |
% 170.47/26.43 | | End of split
% 170.47/26.43 | |
% 170.47/26.43 | Case 2:
% 170.47/26.43 | |
% 170.47/26.43 | | (15) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.47/26.43 | | e1)
% 170.47/26.43 | |
% 170.47/26.43 | | BETA: splitting (15) gives:
% 170.47/26.43 | |
% 170.47/26.43 | | Case 1:
% 170.47/26.43 | | |
% 170.47/26.43 | | | (16) all_58_14 = e1 & op(e0, e1) = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | ALPHA: (16) implies:
% 170.47/26.43 | | | (17) all_58_14 = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | BETA: splitting (1) gives:
% 170.47/26.43 | | |
% 170.47/26.43 | | | Case 1:
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | (18) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0,
% 170.47/26.43 | | | | e2) = e2)
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | REF_CLOSE: (4), (8), (10), (18) are inconsistent by sub-proof #650.
% 170.47/26.43 | | | |
% 170.47/26.43 | | | Case 2:
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | (19) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0,
% 170.47/26.43 | | | | e0) = e2)
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | BETA: splitting (19) gives:
% 170.47/26.43 | | | |
% 170.47/26.43 | | | | Case 1:
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | (20) all_58_14 = e2 & op(e0, e1) = e2
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | ALPHA: (20) implies:
% 170.47/26.43 | | | | | (21) all_58_14 = e2
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | REF_CLOSE: (9), (17), (21) are inconsistent by sub-proof #649.
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | Case 2:
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | (22) all_58_15 = e2 & op(e0, e0) = e2
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | | REF_CLOSE: (7), (11), (22) are inconsistent by sub-proof #648.
% 170.47/26.43 | | | | |
% 170.47/26.43 | | | | End of split
% 170.47/26.43 | | | |
% 170.47/26.43 | | | End of split
% 170.47/26.43 | | |
% 170.47/26.43 | | Case 2:
% 170.47/26.43 | | |
% 170.47/26.43 | | | (23) all_58_15 = e1 & op(e0, e0) = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | ALPHA: (23) implies:
% 170.47/26.43 | | | (24) all_58_15 = e1
% 170.47/26.43 | | |
% 170.47/26.43 | | | COMBINE_EQS: (11), (24) imply:
% 170.47/26.43 | | | (25) e1 = e0
% 170.47/26.43 | | |
% 170.47/26.43 | | | REDUCE: (6), (25) imply:
% 170.47/26.43 | | | (26) $false
% 170.47/26.43 | | |
% 170.47/26.43 | | | CLOSE: (26) is inconsistent.
% 170.47/26.43 | | |
% 170.47/26.43 | | End of split
% 170.47/26.43 | |
% 170.47/26.43 | End of split
% 170.47/26.43 |
% 170.47/26.43 End of proof
% 170.47/26.43
% 170.47/26.43 Sub-proof #648 shows that the following formulas are inconsistent:
% 170.47/26.43 ----------------------------------------------------------------
% 170.47/26.43 (1) all_58_15 = e2 & op(e0, e0) = e2
% 170.47/26.43 (2) all_58_15 = e0
% 170.47/26.43 (3) ~ (e2 = e0)
% 170.47/26.43
% 170.47/26.43 Begin of proof
% 170.47/26.43 |
% 170.47/26.43 | ALPHA: (1) implies:
% 170.47/26.43 | (4) all_58_15 = e2
% 170.47/26.43 |
% 170.47/26.43 | COMBINE_EQS: (2), (4) imply:
% 170.47/26.43 | (5) e2 = e0
% 170.47/26.43 |
% 170.47/26.43 | REDUCE: (3), (5) imply:
% 170.47/26.43 | (6) $false
% 170.47/26.43 |
% 170.47/26.43 | CLOSE: (6) is inconsistent.
% 170.47/26.43 |
% 170.47/26.43 End of proof
% 170.47/26.43
% 170.47/26.43 Sub-proof #649 shows that the following formulas are inconsistent:
% 170.47/26.43 ----------------------------------------------------------------
% 170.47/26.43 (1) all_58_14 = e2
% 170.47/26.43 (2) all_58_14 = e1
% 170.47/26.43 (3) ~ (e2 = e1)
% 170.47/26.43
% 170.47/26.43 Begin of proof
% 170.47/26.43 |
% 170.47/26.43 | COMBINE_EQS: (1), (2) imply:
% 170.47/26.43 | (4) e2 = e1
% 170.47/26.43 |
% 170.47/26.43 | SIMP: (4) implies:
% 170.47/26.43 | (5) e2 = e1
% 170.47/26.43 |
% 170.47/26.43 | REDUCE: (3), (5) imply:
% 170.47/26.43 | (6) $false
% 170.47/26.43 |
% 170.47/26.43 | CLOSE: (6) is inconsistent.
% 170.47/26.43 |
% 170.47/26.43 End of proof
% 170.47/26.43
% 170.47/26.43 Sub-proof #650 shows that the following formulas are inconsistent:
% 170.47/26.43 ----------------------------------------------------------------
% 170.47/26.43 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 170.79/26.43 (2) all_58_12 = e3
% 170.79/26.43 (3) ~ (e3 = e2)
% 170.79/26.43 (4) all_58_13 = e3
% 170.79/26.43
% 170.79/26.43 Begin of proof
% 170.79/26.43 |
% 170.79/26.43 | BETA: splitting (1) gives:
% 170.79/26.43 |
% 170.79/26.43 | Case 1:
% 170.79/26.43 | |
% 170.79/26.43 | | (5) all_58_12 = e2 & op(e0, e3) = e2
% 170.79/26.43 | |
% 170.79/26.43 | | ALPHA: (5) implies:
% 170.79/26.43 | | (6) all_58_12 = e2
% 170.79/26.43 | |
% 170.79/26.43 | | COMBINE_EQS: (2), (6) imply:
% 170.79/26.43 | | (7) e3 = e2
% 170.79/26.43 | |
% 170.79/26.43 | | REDUCE: (3), (7) imply:
% 170.79/26.43 | | (8) $false
% 170.79/26.43 | |
% 170.79/26.43 | | CLOSE: (8) is inconsistent.
% 170.79/26.43 | |
% 170.79/26.43 | Case 2:
% 170.79/26.43 | |
% 170.79/26.43 | | (9) all_58_13 = e2 & op(e0, e2) = e2
% 170.79/26.43 | |
% 170.79/26.43 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #861.
% 170.79/26.43 | |
% 170.79/26.43 | End of split
% 170.79/26.43 |
% 170.79/26.43 End of proof
% 170.79/26.43
% 170.79/26.43 Sub-proof #651 shows that the following formulas are inconsistent:
% 170.79/26.43 ----------------------------------------------------------------
% 170.79/26.43 (1) all_58_12 = e1 & op(e0, e3) = e1
% 170.79/26.43 (2) all_58_12 = e3
% 170.79/26.43 (3) ~ (e3 = e1)
% 170.79/26.43
% 170.79/26.43 Begin of proof
% 170.79/26.43 |
% 170.79/26.43 | ALPHA: (1) implies:
% 170.79/26.43 | (4) all_58_12 = e1
% 170.79/26.43 |
% 170.79/26.43 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.43 | (5) e3 = e1
% 170.79/26.43 |
% 170.79/26.43 | REDUCE: (3), (5) imply:
% 170.79/26.43 | (6) $false
% 170.79/26.43 |
% 170.79/26.43 | CLOSE: (6) is inconsistent.
% 170.79/26.43 |
% 170.79/26.43 End of proof
% 170.79/26.43
% 170.79/26.43 Sub-proof #652 shows that the following formulas are inconsistent:
% 170.79/26.43 ----------------------------------------------------------------
% 170.79/26.43 (1) op(e2, e1) = all_52_9
% 170.79/26.43 (2) all_54_14 = all_52_11
% 170.79/26.43 (3) all_54_12 = all_52_3
% 170.79/26.43 (4) all_54_12 = e1 | all_54_12 = e0
% 170.79/26.43 (5) ~ (all_52_9 = all_52_11)
% 170.79/26.43 (6) ~ (all_52_11 = e2)
% 170.79/26.43 (7) ~ (all_52_3 = all_52_11)
% 170.79/26.43 (8) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.79/26.43 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.43 (10) ~ (all_52_3 = e0)
% 170.79/26.43 (11) all_58_5 = e3 & op(e2, e1) = e3
% 170.79/26.43 (12) ~ (all_52_11 = e0)
% 170.79/26.43
% 170.79/26.43 Begin of proof
% 170.79/26.43 |
% 170.79/26.43 | ALPHA: (11) implies:
% 170.79/26.43 | (13) op(e2, e1) = e3
% 170.79/26.43 |
% 170.79/26.43 | BETA: splitting (4) gives:
% 170.79/26.43 |
% 170.79/26.43 | Case 1:
% 170.79/26.43 | |
% 170.79/26.43 | | (14) all_54_12 = e1
% 170.79/26.43 | |
% 170.79/26.43 | | COMBINE_EQS: (3), (14) imply:
% 170.79/26.43 | | (15) all_52_3 = e1
% 170.79/26.43 | |
% 170.79/26.43 | | SIMP: (15) implies:
% 170.79/26.43 | | (16) all_52_3 = e1
% 170.79/26.43 | |
% 170.79/26.43 | | REDUCE: (7), (16) imply:
% 170.79/26.43 | | (17) ~ (all_52_11 = e1)
% 170.79/26.43 | |
% 170.79/26.43 | | SIMP: (17) implies:
% 170.79/26.43 | | (18) ~ (all_52_11 = e1)
% 170.79/26.43 | |
% 170.79/26.44 | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (12), (13), (18) are inconsistent
% 170.79/26.44 | | by sub-proof #654.
% 170.79/26.44 | |
% 170.79/26.44 | Case 2:
% 170.79/26.44 | |
% 170.79/26.44 | | (19) all_54_12 = e0
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (3), (10), (19) are inconsistent by sub-proof #653.
% 170.79/26.44 | |
% 170.79/26.44 | End of split
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #653 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) all_54_12 = all_52_3
% 170.79/26.44 (2) all_54_12 = e0
% 170.79/26.44 (3) ~ (all_52_3 = e0)
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.44 | (4) all_52_3 = e0
% 170.79/26.44 |
% 170.79/26.44 | SIMP: (4) implies:
% 170.79/26.44 | (5) all_52_3 = e0
% 170.79/26.44 |
% 170.79/26.44 | REDUCE: (3), (5) imply:
% 170.79/26.44 | (6) $false
% 170.79/26.44 |
% 170.79/26.44 | CLOSE: (6) is inconsistent.
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #654 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) op(e2, e1) = all_52_9
% 170.79/26.44 (2) all_54_14 = all_52_11
% 170.79/26.44 (3) ~ (all_52_9 = all_52_11)
% 170.79/26.44 (4) ~ (all_52_11 = e2)
% 170.79/26.44 (5) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.79/26.44 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.44 (7) ~ (all_52_11 = e1)
% 170.79/26.44 (8) op(e2, e1) = e3
% 170.79/26.44 (9) ~ (all_52_11 = e0)
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | BETA: splitting (5) gives:
% 170.79/26.44 |
% 170.79/26.44 | Case 1:
% 170.79/26.44 | |
% 170.79/26.44 | | (10) all_54_14 = e3
% 170.79/26.44 | |
% 170.79/26.44 | | COMBINE_EQS: (2), (10) imply:
% 170.79/26.44 | | (11) all_52_11 = e3
% 170.79/26.44 | |
% 170.79/26.44 | | SIMP: (11) implies:
% 170.79/26.44 | | (12) all_52_11 = e3
% 170.79/26.44 | |
% 170.79/26.44 | | REDUCE: (3), (12) imply:
% 170.79/26.44 | | (13) ~ (all_52_9 = e3)
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (1), (6), (8), (13) are inconsistent by sub-proof #951.
% 170.79/26.44 | |
% 170.79/26.44 | Case 2:
% 170.79/26.44 | |
% 170.79/26.44 | | (14) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (2), (4), (7), (9), (14) are inconsistent by sub-proof #655.
% 170.79/26.44 | |
% 170.79/26.44 | End of split
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #655 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) all_54_14 = all_52_11
% 170.79/26.44 (2) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.79/26.44 (3) ~ (all_52_11 = e2)
% 170.79/26.44 (4) ~ (all_52_11 = e1)
% 170.79/26.44 (5) ~ (all_52_11 = e0)
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | BETA: splitting (2) gives:
% 170.79/26.44 |
% 170.79/26.44 | Case 1:
% 170.79/26.44 | |
% 170.79/26.44 | | (6) all_54_14 = e2
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #737.
% 170.79/26.44 | |
% 170.79/26.44 | Case 2:
% 170.79/26.44 | |
% 170.79/26.44 | | (7) all_54_14 = e1 | all_54_14 = e0
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #964.
% 170.79/26.44 | |
% 170.79/26.44 | End of split
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #656 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.44 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.44 (2) ~ (e3 = e1)
% 170.79/26.44 (3) ~ (e1 = e0)
% 170.79/26.44 (4) op(e0, e2) = e0
% 170.79/26.44 (5) all_58_3 = e2
% 170.79/26.44 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.44 (7) ~ (e2 = e1)
% 170.79/26.44 (8) op(e0, e2) = all_52_7
% 170.79/26.44 (9) all_58_1 = e0
% 170.79/26.44 (10) all_58_7 = e3
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | BETA: splitting (1) gives:
% 170.79/26.44 |
% 170.79/26.44 | Case 1:
% 170.79/26.44 | |
% 170.79/26.44 | | (11) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 170.79/26.44 | | e1)
% 170.79/26.44 | |
% 170.79/26.44 | | BETA: splitting (11) gives:
% 170.79/26.44 | |
% 170.79/26.44 | | Case 1:
% 170.79/26.44 | | |
% 170.79/26.44 | | | (12) all_58_1 = e1 & op(e3, e2) = e1
% 170.79/26.44 | | |
% 170.79/26.44 | | | REF_CLOSE: (3), (9), (12) are inconsistent by sub-proof #658.
% 170.79/26.44 | | |
% 170.79/26.44 | | Case 2:
% 170.79/26.44 | | |
% 170.79/26.44 | | | (13) all_58_3 = e1 & op(e2, e2) = e1
% 170.79/26.44 | | |
% 170.79/26.44 | | | REF_CLOSE: (5), (7), (13) are inconsistent by sub-proof #914.
% 170.79/26.44 | | |
% 170.79/26.44 | | End of split
% 170.79/26.44 | |
% 170.79/26.44 | Case 2:
% 170.79/26.44 | |
% 170.79/26.44 | | (14) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) =
% 170.79/26.44 | | e1)
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (2), (3), (4), (6), (8), (10), (14) are inconsistent by sub-proof
% 170.79/26.44 | | #657.
% 170.79/26.44 | |
% 170.79/26.44 | End of split
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #657 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) ~ (e3 = e1)
% 170.79/26.44 (2) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.44 (3) ~ (e1 = e0)
% 170.79/26.44 (4) op(e0, e2) = e0
% 170.79/26.44 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.44 (6) op(e0, e2) = all_52_7
% 170.79/26.44 (7) all_58_7 = e3
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | BETA: splitting (2) gives:
% 170.79/26.44 |
% 170.79/26.44 | Case 1:
% 170.79/26.44 | |
% 170.79/26.44 | | (8) all_58_7 = e1 & op(e1, e2) = e1
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (1), (7), (8) are inconsistent by sub-proof #757.
% 170.79/26.44 | |
% 170.79/26.44 | Case 2:
% 170.79/26.44 | |
% 170.79/26.44 | | (9) all_58_13 = e1 & op(e0, e2) = e1
% 170.79/26.44 | |
% 170.79/26.44 | | ALPHA: (9) implies:
% 170.79/26.44 | | (10) op(e0, e2) = e1
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #889.
% 170.79/26.44 | |
% 170.79/26.44 | End of split
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #658 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) all_58_1 = e1 & op(e3, e2) = e1
% 170.79/26.44 (2) all_58_1 = e0
% 170.79/26.44 (3) ~ (e1 = e0)
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | ALPHA: (1) implies:
% 170.79/26.44 | (4) all_58_1 = e1
% 170.79/26.44 |
% 170.79/26.44 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.44 | (5) e1 = e0
% 170.79/26.44 |
% 170.79/26.44 | SIMP: (5) implies:
% 170.79/26.44 | (6) e1 = e0
% 170.79/26.44 |
% 170.79/26.44 | REDUCE: (3), (6) imply:
% 170.79/26.44 | (7) $false
% 170.79/26.44 |
% 170.79/26.44 | CLOSE: (7) is inconsistent.
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #659 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) op(e3, e3) = all_10_2
% 170.79/26.44 (2) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2)
% 170.79/26.44 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.44 (4) ~ (all_10_2 = e2)
% 170.79/26.44 (5) ~ (all_52_4 = e2)
% 170.79/26.44 (6) op(e3, e2) = all_52_4
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | BETA: splitting (2) gives:
% 170.79/26.44 |
% 170.79/26.44 | Case 1:
% 170.79/26.44 | |
% 170.79/26.44 | | (7) all_58_0 = e2 & op(e3, e3) = e2
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #666.
% 170.79/26.44 | |
% 170.79/26.44 | Case 2:
% 170.79/26.44 | |
% 170.79/26.44 | | (8) all_58_1 = e2 & op(e3, e2) = e2
% 170.79/26.44 | |
% 170.79/26.44 | | ALPHA: (8) implies:
% 170.79/26.44 | | (9) op(e3, e2) = e2
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #993.
% 170.79/26.44 | |
% 170.79/26.44 | End of split
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #660 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) all_58_11 = e2 & op(e1, e0) = e2
% 170.79/26.44 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.44 (3) op(e1, e0) = all_52_14
% 170.79/26.44 (4) ~ (all_52_14 = e2)
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | ALPHA: (1) implies:
% 170.79/26.44 | (5) op(e1, e0) = e2
% 170.79/26.44 |
% 170.79/26.44 | GROUND_INST: instantiating (2) with all_52_14, e2, e0, e1, simplifying with
% 170.79/26.44 | (3), (5) gives:
% 170.79/26.44 | (6) all_52_14 = e2
% 170.79/26.44 |
% 170.79/26.44 | REDUCE: (4), (6) imply:
% 170.79/26.44 | (7) $false
% 170.79/26.44 |
% 170.79/26.44 | CLOSE: (7) is inconsistent.
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #661 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) op(e3, e0) = all_52_12
% 170.79/26.44 (2) ~ (all_52_12 = e2)
% 170.79/26.44 (3) ~ (all_52_13 = e2)
% 170.79/26.44 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.44 (5) op(e2, e0) = all_52_13
% 170.79/26.44 (6) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | BETA: splitting (6) gives:
% 170.79/26.44 |
% 170.79/26.44 | Case 1:
% 170.79/26.44 | |
% 170.79/26.44 | | (7) all_58_9 = e2 & op(e3, e0) = e2
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #663.
% 170.79/26.44 | |
% 170.79/26.44 | Case 2:
% 170.79/26.44 | |
% 170.79/26.44 | | (8) all_58_10 = e2 & op(e2, e0) = e2
% 170.79/26.44 | |
% 170.79/26.44 | | ALPHA: (8) implies:
% 170.79/26.44 | | (9) op(e2, e0) = e2
% 170.79/26.44 | |
% 170.79/26.44 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #662.
% 170.79/26.44 | |
% 170.79/26.44 | End of split
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #662 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.44 (2) op(e2, e0) = all_52_13
% 170.79/26.44 (3) op(e2, e0) = e2
% 170.79/26.44 (4) ~ (all_52_13 = e2)
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | GROUND_INST: instantiating (1) with all_52_13, e2, e0, e2, simplifying with
% 170.79/26.44 | (2), (3) gives:
% 170.79/26.44 | (5) all_52_13 = e2
% 170.79/26.44 |
% 170.79/26.44 | REDUCE: (4), (5) imply:
% 170.79/26.44 | (6) $false
% 170.79/26.44 |
% 170.79/26.44 | CLOSE: (6) is inconsistent.
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #663 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) all_58_9 = e2 & op(e3, e0) = e2
% 170.79/26.44 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.44 (3) op(e3, e0) = all_52_12
% 170.79/26.44 (4) ~ (all_52_12 = e2)
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | ALPHA: (1) implies:
% 170.79/26.44 | (5) op(e3, e0) = e2
% 170.79/26.44 |
% 170.79/26.44 | GROUND_INST: instantiating (2) with all_52_12, e2, e0, e3, simplifying with
% 170.79/26.44 | (3), (5) gives:
% 170.79/26.44 | (6) all_52_12 = e2
% 170.79/26.44 |
% 170.79/26.44 | REDUCE: (4), (6) imply:
% 170.79/26.44 | (7) $false
% 170.79/26.44 |
% 170.79/26.44 | CLOSE: (7) is inconsistent.
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #664 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.44 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.44 (2) ~ (e3 = e1)
% 170.79/26.44 (3) all_58_2 = e2 & op(e2, e3) = e2
% 170.79/26.44 (4) ~ (e1 = e0)
% 170.79/26.44 (5) op(e1, e2) = all_52_6
% 170.79/26.44 (6) op(e2, e3) = all_52_1
% 170.79/26.44 (7) ~ (all_52_6 = e2)
% 170.79/26.44 (8) ~ (e3 = e0)
% 170.79/26.44 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.44 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.44 (10) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.79/26.44 (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 170.79/26.44 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.44 (12) ~ (e2 = e0)
% 170.79/26.44 (13) ~ (all_52_7 = e2)
% 170.79/26.44 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.44 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.44 (15) ~ (e2 = e1)
% 170.79/26.44 (16) ~ (all_52_4 = e2)
% 170.79/26.44 (17) op(e3, e2) = all_52_4
% 170.79/26.44 (18) op(e0, e2) = all_52_7
% 170.79/26.44 (19) ~ (e3 = e2)
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | ALPHA: (3) implies:
% 170.79/26.44 | (20) op(e2, e3) = e2
% 170.79/26.44 |
% 170.79/26.44 | BETA: splitting (10) gives:
% 170.79/26.44 |
% 170.79/26.44 | Case 1:
% 170.79/26.44 | |
% 170.79/26.44 | | (21) (all_58_1 = e2 & op(e3, e2) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 170.79/26.44 | | e2)
% 170.79/26.44 | |
% 170.79/26.44 | | BETA: splitting (21) gives:
% 170.79/26.44 | |
% 170.79/26.44 | | Case 1:
% 170.79/26.44 | | |
% 170.79/26.44 | | | (22) all_58_1 = e2 & op(e3, e2) = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | ALPHA: (22) implies:
% 170.79/26.44 | | | (23) op(e3, e2) = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | GROUND_INST: instantiating (11) with all_52_4, e2, e2, e3, simplifying
% 170.79/26.44 | | | with (17), (23) gives:
% 170.79/26.44 | | | (24) all_52_4 = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | REDUCE: (16), (24) imply:
% 170.79/26.44 | | | (25) $false
% 170.79/26.44 | | |
% 170.79/26.44 | | | CLOSE: (25) is inconsistent.
% 170.79/26.44 | | |
% 170.79/26.44 | | Case 2:
% 170.79/26.44 | | |
% 170.79/26.44 | | | (26) all_58_3 = e2 & op(e2, e2) = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | ALPHA: (26) implies:
% 170.79/26.44 | | | (27) all_58_3 = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (11), (12), (14), (15), (19),
% 170.79/26.44 | | | (20), (27) are inconsistent by sub-proof #665.
% 170.79/26.44 | | |
% 170.79/26.44 | | End of split
% 170.79/26.44 | |
% 170.79/26.44 | Case 2:
% 170.79/26.44 | |
% 170.79/26.44 | | (28) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) =
% 170.79/26.44 | | e2)
% 170.79/26.44 | |
% 170.79/26.44 | | BETA: splitting (28) gives:
% 170.79/26.44 | |
% 170.79/26.44 | | Case 1:
% 170.79/26.44 | | |
% 170.79/26.44 | | | (29) all_58_7 = e2 & op(e1, e2) = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | ALPHA: (29) implies:
% 170.79/26.44 | | | (30) op(e1, e2) = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | REF_CLOSE: (5), (7), (11), (30) are inconsistent by sub-proof #986.
% 170.79/26.44 | | |
% 170.79/26.44 | | Case 2:
% 170.79/26.44 | | |
% 170.79/26.44 | | | (31) all_58_13 = e2 & op(e0, e2) = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | ALPHA: (31) implies:
% 170.79/26.44 | | | (32) op(e0, e2) = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | GROUND_INST: instantiating (11) with all_52_7, e2, e2, e0, simplifying
% 170.79/26.44 | | | with (18), (32) gives:
% 170.79/26.44 | | | (33) all_52_7 = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | REDUCE: (13), (33) imply:
% 170.79/26.44 | | | (34) $false
% 170.79/26.44 | | |
% 170.79/26.44 | | | CLOSE: (34) is inconsistent.
% 170.79/26.44 | | |
% 170.79/26.44 | | End of split
% 170.79/26.44 | |
% 170.79/26.44 | End of split
% 170.79/26.44 |
% 170.79/26.44 End of proof
% 170.79/26.44
% 170.79/26.44 Sub-proof #665 shows that the following formulas are inconsistent:
% 170.79/26.44 ----------------------------------------------------------------
% 170.79/26.44 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.44 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.44 (2) ~ (e3 = e1)
% 170.79/26.44 (3) ~ (e1 = e0)
% 170.79/26.44 (4) op(e2, e3) = all_52_1
% 170.79/26.44 (5) op(e2, e3) = e2
% 170.79/26.44 (6) ~ (e3 = e0)
% 170.79/26.44 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.44 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.44 (8) all_58_3 = e2
% 170.79/26.44 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.44 (10) ~ (e2 = e0)
% 170.79/26.44 (11) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.44 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.44 (12) ~ (e2 = e1)
% 170.79/26.44 (13) ~ (e3 = e2)
% 170.79/26.44
% 170.79/26.44 Begin of proof
% 170.79/26.44 |
% 170.79/26.44 | BETA: splitting (11) gives:
% 170.79/26.44 |
% 170.79/26.44 | Case 1:
% 170.79/26.44 | |
% 170.79/26.44 | | (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.79/26.44 | | e3)
% 170.79/26.44 | |
% 170.79/26.44 | | BETA: splitting (14) gives:
% 170.79/26.44 | |
% 170.79/26.44 | | Case 1:
% 170.79/26.44 | | |
% 170.79/26.44 | | | (15) all_58_2 = e3 & op(e2, e3) = e3
% 170.79/26.44 | | |
% 170.79/26.44 | | | ALPHA: (15) implies:
% 170.79/26.44 | | | (16) all_58_2 = e3
% 170.79/26.44 | | | (17) op(e2, e3) = e3
% 170.79/26.44 | | |
% 170.79/26.44 | | | GROUND_INST: instantiating (9) with all_52_1, e2, e3, e2, simplifying with
% 170.79/26.44 | | | (4), (5) gives:
% 170.79/26.44 | | | (18) all_52_1 = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | GROUND_INST: instantiating (9) with all_52_1, e3, e3, e2, simplifying with
% 170.79/26.44 | | | (4), (17) gives:
% 170.79/26.44 | | | (19) all_52_1 = e3
% 170.79/26.44 | | |
% 170.79/26.44 | | | COMBINE_EQS: (18), (19) imply:
% 170.79/26.44 | | | (20) e3 = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | COMBINE_EQS: (16), (20) imply:
% 170.79/26.44 | | | (21) all_58_2 = e2
% 170.79/26.44 | | |
% 170.79/26.44 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 170.79/26.44 | | | (13), (21) are inconsistent by sub-proof #779.
% 170.79/26.44 | | |
% 170.79/26.44 | | Case 2:
% 170.79/26.44 | | |
% 170.79/26.44 | | | (22) all_58_3 = e3 & op(e2, e2) = e3
% 170.79/26.44 | | |
% 170.79/26.44 | | | REF_CLOSE: (8), (13), (22) are inconsistent by sub-proof #785.
% 170.79/26.44 | | |
% 170.79/26.44 | | End of split
% 170.79/26.44 | |
% 170.79/26.44 | Case 2:
% 170.79/26.44 | |
% 170.79/26.44 | | (23) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 170.79/26.44 | | e3)
% 170.79/26.44 | |
% 170.79/26.44 | | BETA: splitting (23) gives:
% 170.79/26.44 | |
% 170.79/26.44 | | Case 1:
% 170.79/26.44 | | |
% 170.79/26.44 | | | (24) all_58_5 = e3 & op(e2, e1) = e3
% 170.79/26.44 | | |
% 170.79/26.44 | | | ALPHA: (24) implies:
% 170.79/26.44 | | | (25) all_58_5 = e3
% 170.79/26.44 | | |
% 170.79/26.44 | | | BETA: splitting (1) gives:
% 170.79/26.44 | | |
% 170.79/26.44 | | | Case 1:
% 170.79/26.44 | | | |
% 170.79/26.44 | | | | (26) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 170.79/26.44 | | | | = e1)
% 170.79/26.44 | | | |
% 170.79/26.44 | | | | REF_CLOSE: (4), (5), (8), (9), (12), (26) are inconsistent by sub-proof
% 170.79/26.44 | | | | #783.
% 170.79/26.44 | | | |
% 170.79/26.44 | | | Case 2:
% 170.79/26.44 | | | |
% 170.79/26.44 | | | | (27) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 170.79/26.44 | | | | = e1)
% 170.79/26.44 | | | |
% 170.79/26.44 | | | | BETA: splitting (27) gives:
% 170.79/26.44 | | | |
% 170.79/26.44 | | | | Case 1:
% 170.79/26.44 | | | | |
% 170.79/26.44 | | | | | (28) all_58_5 = e1 & op(e2, e1) = e1
% 170.79/26.44 | | | | |
% 170.79/26.44 | | | | | REF_CLOSE: (2), (25), (28) are inconsistent by sub-proof #828.
% 170.79/26.44 | | | | |
% 170.79/26.44 | | | | Case 2:
% 170.79/26.44 | | | | |
% 170.79/26.44 | | | | | (29) all_58_10 = e1 & op(e2, e0) = e1
% 170.79/26.44 | | | | |
% 170.79/26.44 | | | | | ALPHA: (29) implies:
% 170.79/26.44 | | | | | (30) all_58_10 = e1
% 170.79/26.44 | | | | |
% 170.79/26.44 | | | | | BETA: splitting (7) gives:
% 170.79/26.44 | | | | |
% 170.79/26.44 | | | | | Case 1:
% 170.79/26.44 | | | | | |
% 170.79/26.44 | | | | | | (31) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2,
% 170.79/26.44 | | | | | | e2) = e0)
% 170.79/26.44 | | | | | |
% 170.79/26.44 | | | | | | BETA: splitting (31) gives:
% 170.79/26.44 | | | | | |
% 170.79/26.44 | | | | | | Case 1:
% 170.79/26.44 | | | | | | |
% 170.79/26.44 | | | | | | | (32) all_58_2 = e0 & op(e2, e3) = e0
% 170.79/26.44 | | | | | | |
% 170.79/26.44 | | | | | | | REF_CLOSE: (4), (5), (9), (10), (32) are inconsistent by sub-proof
% 170.79/26.44 | | | | | | | #782.
% 170.79/26.44 | | | | | | |
% 170.79/26.44 | | | | | | Case 2:
% 170.79/26.44 | | | | | | |
% 170.79/26.44 | | | | | | | (33) all_58_3 = e0 & op(e2, e2) = e0
% 170.79/26.44 | | | | | | |
% 170.79/26.44 | | | | | | | REF_CLOSE: (8), (10), (33) are inconsistent by sub-proof #934.
% 170.79/26.44 | | | | | | |
% 170.79/26.44 | | | | | | End of split
% 170.79/26.44 | | | | | |
% 170.79/26.44 | | | | | Case 2:
% 170.79/26.44 | | | | | |
% 170.79/26.45 | | | | | | (34) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2,
% 170.79/26.45 | | | | | | e0) = e0)
% 170.79/26.45 | | | | | |
% 170.79/26.45 | | | | | | BETA: splitting (34) gives:
% 170.79/26.45 | | | | | |
% 170.79/26.45 | | | | | | Case 1:
% 170.79/26.45 | | | | | | |
% 170.79/26.45 | | | | | | | (35) all_58_5 = e0 & op(e2, e1) = e0
% 170.79/26.45 | | | | | | |
% 170.79/26.45 | | | | | | | REF_CLOSE: (6), (25), (35) are inconsistent by sub-proof #926.
% 170.79/26.45 | | | | | | |
% 170.79/26.45 | | | | | | Case 2:
% 170.79/26.45 | | | | | | |
% 170.79/26.45 | | | | | | | (36) all_58_10 = e0 & op(e2, e0) = e0
% 170.79/26.45 | | | | | | |
% 170.79/26.45 | | | | | | | REF_CLOSE: (3), (30), (36) are inconsistent by sub-proof #925.
% 170.79/26.45 | | | | | | |
% 170.79/26.45 | | | | | | End of split
% 170.79/26.45 | | | | | |
% 170.79/26.45 | | | | | End of split
% 170.79/26.45 | | | | |
% 170.79/26.45 | | | | End of split
% 170.79/26.45 | | | |
% 170.79/26.45 | | | End of split
% 170.79/26.45 | | |
% 170.79/26.45 | | Case 2:
% 170.79/26.45 | | |
% 170.79/26.45 | | | (37) all_58_10 = e3 & op(e2, e0) = e3
% 170.79/26.45 | | |
% 170.79/26.45 | | | ALPHA: (37) implies:
% 170.79/26.45 | | | (38) all_58_10 = e3
% 170.79/26.45 | | |
% 170.79/26.45 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (38)
% 170.79/26.45 | | | are inconsistent by sub-proof #780.
% 170.79/26.45 | | |
% 170.79/26.45 | | End of split
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #666 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_58_0 = e2 & op(e3, e3) = e2
% 170.79/26.45 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (3) op(e3, e3) = all_10_2
% 170.79/26.45 (4) ~ (all_10_2 = e2)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | ALPHA: (1) implies:
% 170.79/26.45 | (5) op(e3, e3) = e2
% 170.79/26.45 |
% 170.79/26.45 | GROUND_INST: instantiating (2) with all_10_2, e2, e3, e3, simplifying with
% 170.79/26.45 | (3), (5) gives:
% 170.79/26.45 | (6) all_10_2 = e2
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (4), (6) imply:
% 170.79/26.45 | (7) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (7) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #667 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_5 = all_8_2
% 170.79/26.45 (2) all_54_5 = e3
% 170.79/26.45 (3) ~ (all_8_2 = e3)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.45 | (4) all_8_2 = e3
% 170.79/26.45 |
% 170.79/26.45 | SIMP: (4) implies:
% 170.79/26.45 | (5) all_8_2 = e3
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (3), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #668 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (2) op(e1, e2) = all_52_6
% 170.79/26.45 (3) op(e1, e2) = e3
% 170.79/26.45 (4) ~ (all_52_6 = e3)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | GROUND_INST: instantiating (1) with all_52_6, e3, e2, e1, simplifying with
% 170.79/26.45 | (2), (3) gives:
% 170.79/26.45 | (5) all_52_6 = e3
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (4), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #669 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) op(e2, e1) = all_52_9
% 170.79/26.45 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (3) ~ (e2 = e0)
% 170.79/26.45 (4) ~ (all_52_9 = e0)
% 170.79/26.45 (5) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.45 (6) op(e2, e0) = e2
% 170.79/26.45 (7) op(e2, e0) = all_52_13
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (5) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (8) all_58_5 = e0 & op(e2, e1) = e0
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #670.
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (9) all_58_10 = e0 & op(e2, e0) = e0
% 170.79/26.45 | |
% 170.79/26.45 | | ALPHA: (9) implies:
% 170.79/26.45 | | (10) op(e2, e0) = e0
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (2), (3), (6), (7), (10) are inconsistent by sub-proof #684.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #670 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_58_5 = e0 & op(e2, e1) = e0
% 170.79/26.45 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (3) op(e2, e1) = all_52_9
% 170.79/26.45 (4) ~ (all_52_9 = e0)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | ALPHA: (1) implies:
% 170.79/26.45 | (5) op(e2, e1) = e0
% 170.79/26.45 |
% 170.79/26.45 | GROUND_INST: instantiating (2) with all_52_9, e0, e1, e2, simplifying with
% 170.79/26.45 | (3), (5) gives:
% 170.79/26.45 | (6) all_52_9 = e0
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (4), (6) imply:
% 170.79/26.45 | (7) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (7) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #671 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) ~ (all_52_1 = e0)
% 170.79/26.45 (2) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 170.79/26.45 (3) ~ (all_52_1 = e2)
% 170.79/26.45 (4) all_54_4 = all_52_1
% 170.79/26.45 (5) ~ (all_52_1 = e1)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (2) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (6) all_54_4 = e2
% 170.79/26.45 | |
% 170.79/26.45 | | COMBINE_EQS: (4), (6) imply:
% 170.79/26.45 | | (7) all_52_1 = e2
% 170.79/26.45 | |
% 170.79/26.45 | | REDUCE: (3), (7) imply:
% 170.79/26.45 | | (8) $false
% 170.79/26.45 | |
% 170.79/26.45 | | CLOSE: (8) is inconsistent.
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (9) all_54_4 = e1 | all_54_4 = e0
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #672.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #672 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_4 = e1 | all_54_4 = e0
% 170.79/26.45 (2) all_54_4 = all_52_1
% 170.79/26.45 (3) ~ (all_52_1 = e1)
% 170.79/26.45 (4) ~ (all_52_1 = e0)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (1) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (5) all_54_4 = e1
% 170.79/26.45 | |
% 170.79/26.45 | | COMBINE_EQS: (2), (5) imply:
% 170.79/26.45 | | (6) all_52_1 = e1
% 170.79/26.45 | |
% 170.79/26.45 | | REDUCE: (3), (6) imply:
% 170.79/26.45 | | (7) $false
% 170.79/26.45 | |
% 170.79/26.45 | | CLOSE: (7) is inconsistent.
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (8) all_54_4 = e0
% 170.79/26.45 | |
% 170.79/26.45 | | COMBINE_EQS: (2), (8) imply:
% 170.79/26.45 | | (9) all_52_1 = e0
% 170.79/26.45 | |
% 170.79/26.45 | | REDUCE: (4), (9) imply:
% 170.79/26.45 | | (10) $false
% 170.79/26.45 | |
% 170.79/26.45 | | CLOSE: (10) is inconsistent.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #673 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_6 = all_52_9
% 170.79/26.45 (2) all_54_6 = e0
% 170.79/26.45 (3) ~ (all_52_9 = e0)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.45 | (4) all_52_9 = e0
% 170.79/26.45 |
% 170.79/26.45 | SIMP: (4) implies:
% 170.79/26.45 | (5) all_52_9 = e0
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (3), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #674 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_12 = all_52_3
% 170.79/26.45 (2) ~ (all_52_3 = e3)
% 170.79/26.45 (3) ~ (all_52_3 = e2)
% 170.79/26.45 (4) ~ (all_52_3 = e1)
% 170.79/26.45 (5) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.79/26.45 (6) ~ (all_52_3 = e0)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (5) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (7) all_54_12 = e3
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #738.
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (8) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (1), (3), (4), (6), (8) are inconsistent by sub-proof #675.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #675 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_12 = all_52_3
% 170.79/26.45 (2) ~ (all_52_3 = e2)
% 170.79/26.45 (3) ~ (all_52_3 = e1)
% 170.79/26.45 (4) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.79/26.45 (5) ~ (all_52_3 = e0)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (4) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (6) all_54_12 = e2
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #676.
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (7) all_54_12 = e1 | all_54_12 = e0
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #736.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #676 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_12 = all_52_3
% 170.79/26.45 (2) all_54_12 = e2
% 170.79/26.45 (3) ~ (all_52_3 = e2)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.45 | (4) all_52_3 = e2
% 170.79/26.45 |
% 170.79/26.45 | SIMP: (4) implies:
% 170.79/26.45 | (5) all_52_3 = e2
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (3), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #677 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) op(e2, e1) = all_52_9
% 170.79/26.45 (2) ~ (all_52_9 = e3)
% 170.79/26.45 (3) ~ (all_8_2 = e3)
% 170.79/26.45 (4) ~ (e3 = e1)
% 170.79/26.45 (5) op(e2, e2) = all_8_2
% 170.79/26.45 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (7) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.45 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.45 (8) all_58_2 = e1
% 170.79/26.45 (9) op(e2, e0) = e2
% 170.79/26.45 (10) ~ (e3 = e2)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (7) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (11) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.79/26.45 | | e3)
% 170.79/26.45 | |
% 170.79/26.45 | | BETA: splitting (11) gives:
% 170.79/26.45 | |
% 170.79/26.45 | | Case 1:
% 170.79/26.45 | | |
% 170.79/26.45 | | | (12) all_58_2 = e3 & op(e2, e3) = e3
% 170.79/26.45 | | |
% 170.79/26.45 | | | REF_CLOSE: (4), (8), (12) are inconsistent by sub-proof #679.
% 170.79/26.45 | | |
% 170.79/26.45 | | Case 2:
% 170.79/26.45 | | |
% 170.79/26.45 | | | (13) all_58_3 = e3 & op(e2, e2) = e3
% 170.79/26.45 | | |
% 170.79/26.45 | | | REF_CLOSE: (3), (5), (6), (13) are inconsistent by sub-proof #973.
% 170.79/26.45 | | |
% 170.79/26.45 | | End of split
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (14) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 170.79/26.45 | | e3)
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (1), (2), (6), (9), (10), (14) are inconsistent by sub-proof
% 170.79/26.45 | | #678.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #678 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) op(e2, e1) = all_52_9
% 170.79/26.45 (2) ~ (all_52_9 = e3)
% 170.79/26.45 (3) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.45 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (5) op(e2, e0) = e2
% 170.79/26.45 (6) ~ (e3 = e2)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (3) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (7) all_58_5 = e3 & op(e2, e1) = e3
% 170.79/26.45 | |
% 170.79/26.45 | | ALPHA: (7) implies:
% 170.79/26.45 | | (8) op(e2, e1) = e3
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #951.
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (9) all_58_10 = e3 & op(e2, e0) = e3
% 170.79/26.45 | |
% 170.79/26.45 | | ALPHA: (9) implies:
% 170.79/26.45 | | (10) op(e2, e0) = e3
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #682.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #679 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_58_2 = e3 & op(e2, e3) = e3
% 170.79/26.45 (2) all_58_2 = e1
% 170.79/26.45 (3) ~ (e3 = e1)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | ALPHA: (1) implies:
% 170.79/26.45 | (4) all_58_2 = e3
% 170.79/26.45 |
% 170.79/26.45 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.45 | (5) e3 = e1
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (3), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #680 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_6 = all_52_9
% 170.79/26.45 (2) all_54_6 = e2
% 170.79/26.45 (3) ~ (all_52_9 = e2)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.45 | (4) all_52_9 = e2
% 170.79/26.45 |
% 170.79/26.45 | SIMP: (4) implies:
% 170.79/26.45 | (5) all_52_9 = e2
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (3), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #681 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_6 = all_52_9
% 170.79/26.45 (2) all_54_6 = e3
% 170.79/26.45 (3) ~ (all_52_9 = e3)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.45 | (4) all_52_9 = e3
% 170.79/26.45 |
% 170.79/26.45 | SIMP: (4) implies:
% 170.79/26.45 | (5) all_52_9 = e3
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (3), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #682 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (2) op(e2, e0) = e3
% 170.79/26.45 (3) op(e2, e0) = e2
% 170.79/26.45 (4) ~ (e3 = e2)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | GROUND_INST: instantiating (1) with e2, e3, e0, e2, simplifying with (2), (3)
% 170.79/26.45 | gives:
% 170.79/26.45 | (5) e3 = e2
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (4), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #683 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3,
% 170.79/26.45 e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.79/26.45 (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~
% 170.79/26.45 (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.79/26.45 $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 170.79/26.45 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) = e1))
% 170.79/26.45 (2) all_56_12 = e0
% 170.79/26.45 (3) all_56_11 = e2
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | ALPHA: (1) implies:
% 170.79/26.45 | (4) ~ (all_56_12 = e0) | ( ~ (all_56_11 = e2) & op(e2, e0) = all_56_11 &
% 170.79/26.45 | $i(all_56_11))
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (4) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (5) ~ (all_56_12 = e0)
% 170.79/26.45 | |
% 170.79/26.45 | | REDUCE: (2), (5) imply:
% 170.79/26.45 | | (6) $false
% 170.79/26.45 | |
% 170.79/26.45 | | CLOSE: (6) is inconsistent.
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (7) ~ (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11)
% 170.79/26.45 | |
% 170.79/26.45 | | ALPHA: (7) implies:
% 170.79/26.45 | | (8) ~ (all_56_11 = e2)
% 170.79/26.45 | |
% 170.79/26.45 | | REDUCE: (3), (8) imply:
% 170.79/26.45 | | (9) $false
% 170.79/26.45 | |
% 170.79/26.45 | | CLOSE: (9) is inconsistent.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #684 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) op(e2, e0) = e0
% 170.79/26.45 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (3) ~ (e2 = e0)
% 170.79/26.45 (4) op(e2, e0) = e2
% 170.79/26.45 (5) op(e2, e0) = all_52_13
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | GROUND_INST: instantiating (2) with all_52_13, e0, e0, e2, simplifying with
% 170.79/26.45 | (1), (5) gives:
% 170.79/26.45 | (6) all_52_13 = e0
% 170.79/26.45 |
% 170.79/26.45 | GROUND_INST: instantiating (2) with all_52_13, e2, e0, e2, simplifying with
% 170.79/26.45 | (4), (5) gives:
% 170.79/26.45 | (7) all_52_13 = e2
% 170.79/26.45 |
% 170.79/26.45 | COMBINE_EQS: (6), (7) imply:
% 170.79/26.45 | (8) e2 = e0
% 170.79/26.45 |
% 170.79/26.45 | SIMP: (8) implies:
% 170.79/26.45 | (9) e2 = e0
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (3), (9) imply:
% 170.79/26.45 | (10) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (10) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #685 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 =
% 170.79/26.45 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 170.79/26.45 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.79/26.45 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.79/26.45 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 170.79/26.45 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 170.79/26.45 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.79/26.45 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.79/26.45 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.79/26.45 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.79/26.45 (2) ~ (e3 = e1)
% 170.79/26.45 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (4) op(e2, e1) = e3
% 170.79/26.45 (5) all_56_10 = e3
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (1) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (6) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~
% 170.79/26.45 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 170.79/26.45 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 170.79/26.45 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 170.79/26.45 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 170.79/26.45 | |
% 170.79/26.45 | | ALPHA: (6) implies:
% 170.79/26.45 | | (7) op(e2, e1) = e1
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #686.
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (8) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 170.79/26.45 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 170.79/26.45 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.79/26.45 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 170.79/26.45 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 170.79/26.45 | |
% 170.79/26.45 | | ALPHA: (8) implies:
% 170.79/26.45 | | (9) ~ (all_56_10 = e3)
% 170.79/26.45 | |
% 170.79/26.45 | | REDUCE: (5), (9) imply:
% 170.79/26.45 | | (10) $false
% 170.79/26.45 | |
% 170.79/26.45 | | CLOSE: (10) is inconsistent.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #686 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (2) op(e2, e1) = e3
% 170.79/26.45 (3) op(e2, e1) = e1
% 170.79/26.45 (4) ~ (e3 = e1)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | GROUND_INST: instantiating (1) with e3, e1, e1, e2, simplifying with (2), (3)
% 170.79/26.45 | gives:
% 170.79/26.45 | (5) e3 = e1
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (4), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #687 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_8 = all_52_2
% 170.79/26.45 (2) ~ (all_52_2 = all_52_6)
% 170.79/26.45 (3) op(e1, e2) = all_52_6
% 170.79/26.45 (4) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 170.79/26.45 (5) ~ (all_52_2 = e1)
% 170.79/26.45 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.45 (7) op(e1, e2) = e2
% 170.79/26.45 (8) ~ (all_52_2 = e0)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (4) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (9) all_54_8 = e2
% 170.79/26.45 | |
% 170.79/26.45 | | COMBINE_EQS: (1), (9) imply:
% 170.79/26.45 | | (10) all_52_2 = e2
% 170.79/26.45 | |
% 170.79/26.45 | | SIMP: (10) implies:
% 170.79/26.45 | | (11) all_52_2 = e2
% 170.79/26.45 | |
% 170.79/26.45 | | REDUCE: (2), (11) imply:
% 170.79/26.45 | | (12) ~ (all_52_6 = e2)
% 170.79/26.45 | |
% 170.79/26.45 | | SIMP: (12) implies:
% 170.79/26.45 | | (13) ~ (all_52_6 = e2)
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (3), (6), (7), (13) are inconsistent by sub-proof #986.
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (14) all_54_8 = e1 | all_54_8 = e0
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (1), (5), (8), (14) are inconsistent by sub-proof #688.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #688 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_8 = e1 | all_54_8 = e0
% 170.79/26.45 (2) all_54_8 = all_52_2
% 170.79/26.45 (3) ~ (all_52_2 = e1)
% 170.79/26.45 (4) ~ (all_52_2 = e0)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | BETA: splitting (1) gives:
% 170.79/26.45 |
% 170.79/26.45 | Case 1:
% 170.79/26.45 | |
% 170.79/26.45 | | (5) all_54_8 = e1
% 170.79/26.45 | |
% 170.79/26.45 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #689.
% 170.79/26.45 | |
% 170.79/26.45 | Case 2:
% 170.79/26.45 | |
% 170.79/26.45 | | (6) all_54_8 = e0
% 170.79/26.45 | |
% 170.79/26.45 | | COMBINE_EQS: (2), (6) imply:
% 170.79/26.45 | | (7) all_52_2 = e0
% 170.79/26.45 | |
% 170.79/26.45 | | SIMP: (7) implies:
% 170.79/26.45 | | (8) all_52_2 = e0
% 170.79/26.45 | |
% 170.79/26.45 | | REDUCE: (4), (8) imply:
% 170.79/26.45 | | (9) $false
% 170.79/26.45 | |
% 170.79/26.45 | | CLOSE: (9) is inconsistent.
% 170.79/26.45 | |
% 170.79/26.45 | End of split
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #689 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_8 = all_52_2
% 170.79/26.45 (2) all_54_8 = e1
% 170.79/26.45 (3) ~ (all_52_2 = e1)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.45 | (4) all_52_2 = e1
% 170.79/26.45 |
% 170.79/26.45 | SIMP: (4) implies:
% 170.79/26.45 | (5) all_52_2 = e1
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (3), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #690 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_8 = all_52_2
% 170.79/26.45 (2) all_54_8 = e3
% 170.79/26.45 (3) ~ (all_52_2 = e3)
% 170.79/26.45
% 170.79/26.45 Begin of proof
% 170.79/26.45 |
% 170.79/26.45 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.45 | (4) all_52_2 = e3
% 170.79/26.45 |
% 170.79/26.45 | SIMP: (4) implies:
% 170.79/26.45 | (5) all_52_2 = e3
% 170.79/26.45 |
% 170.79/26.45 | REDUCE: (3), (5) imply:
% 170.79/26.45 | (6) $false
% 170.79/26.45 |
% 170.79/26.45 | CLOSE: (6) is inconsistent.
% 170.79/26.45 |
% 170.79/26.45 End of proof
% 170.79/26.45
% 170.79/26.45 Sub-proof #691 shows that the following formulas are inconsistent:
% 170.79/26.45 ----------------------------------------------------------------
% 170.79/26.45 (1) all_54_4 = all_52_1
% 170.79/26.45 (2) all_54_4 = e2
% 170.79/26.45 (3) ~ (all_52_1 = e2)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.46 | (4) all_52_1 = e2
% 170.79/26.46 |
% 170.79/26.46 | SIMP: (4) implies:
% 170.79/26.46 | (5) all_52_1 = e2
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #692 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) ~ (all_52_1 = e3)
% 170.79/26.46 (2) ~ (all_8_2 = e3)
% 170.79/26.46 (3) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 170.79/26.46 (4) op(e2, e3) = all_52_1
% 170.79/26.46 (5) op(e2, e2) = all_8_2
% 170.79/26.46 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | BETA: splitting (3) gives:
% 170.79/26.46 |
% 170.79/26.46 | Case 1:
% 170.79/26.46 | |
% 170.79/26.46 | | (7) all_58_2 = e3 & op(e2, e3) = e3
% 170.79/26.46 | |
% 170.79/26.46 | | ALPHA: (7) implies:
% 170.79/26.46 | | (8) op(e2, e3) = e3
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #989.
% 170.79/26.46 | |
% 170.79/26.46 | Case 2:
% 170.79/26.46 | |
% 170.79/26.46 | | (9) all_58_3 = e3 & op(e2, e2) = e3
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #973.
% 170.79/26.46 | |
% 170.79/26.46 | End of split
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #693 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_2 = e0 & op(e2, e3) = e0
% 170.79/26.46 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.46 (3) op(e2, e3) = all_52_1
% 170.79/26.46 (4) ~ (all_52_1 = e0)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | ALPHA: (1) implies:
% 170.79/26.46 | (5) op(e2, e3) = e0
% 170.79/26.46 |
% 170.79/26.46 | GROUND_INST: instantiating (2) with all_52_1, e0, e3, e2, simplifying with
% 170.79/26.46 | (3), (5) gives:
% 170.79/26.46 | (6) all_52_1 = e0
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (4), (6) imply:
% 170.79/26.46 | (7) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (7) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #694 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) (all_58_7 = e2 & op(e1, e2) = e2) | (all_58_13 = e2 & op(e0, e2) = e2)
% 170.79/26.46 (2) op(e1, e2) = all_52_6
% 170.79/26.46 (3) ~ (all_52_6 = e2)
% 170.79/26.46 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.46 (5) ~ (all_52_7 = e2)
% 170.79/26.46 (6) op(e0, e2) = all_52_7
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | BETA: splitting (1) gives:
% 170.79/26.46 |
% 170.79/26.46 | Case 1:
% 170.79/26.46 | |
% 170.79/26.46 | | (7) all_58_7 = e2 & op(e1, e2) = e2
% 170.79/26.46 | |
% 170.79/26.46 | | ALPHA: (7) implies:
% 170.79/26.46 | | (8) op(e1, e2) = e2
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #986.
% 170.79/26.46 | |
% 170.79/26.46 | Case 2:
% 170.79/26.46 | |
% 170.79/26.46 | | (9) all_58_13 = e2 & op(e0, e2) = e2
% 170.79/26.46 | |
% 170.79/26.46 | | ALPHA: (9) implies:
% 170.79/26.46 | | (10) op(e0, e2) = e2
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #695.
% 170.79/26.46 | |
% 170.79/26.46 | End of split
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #695 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.46 (2) op(e0, e2) = all_52_7
% 170.79/26.46 (3) op(e0, e2) = e2
% 170.79/26.46 (4) ~ (all_52_7 = e2)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | GROUND_INST: instantiating (1) with all_52_7, e2, e2, e0, simplifying with
% 170.79/26.46 | (2), (3) gives:
% 170.79/26.46 | (5) all_52_7 = e2
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (4), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #696 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) ~ (all_4_2 = e2)
% 170.79/26.46 (2) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 170.79/26.46 (3) ~ (all_56_15 = e3) | (all_56_6 = e0 & op(e0, e3) = e0)
% 170.79/26.46 (4) ~ (all_4_2 = e1)
% 170.79/26.46 (5) ~ (all_56_15 = e0) & ( ~ (all_56_10 = e0) | ( ~ (all_56_9 = e3) & op(e3,
% 170.79/26.46 e0) = all_56_9 & $i(all_56_9))) & ( ~ (all_56_12 = e0) | ( ~
% 170.79/26.46 (all_56_11 = e2) & op(e2, e0) = all_56_11 & $i(all_56_11))) & ( ~
% 170.79/26.46 (all_56_14 = e0) | ( ~ (all_56_13 = e1) & op(e1, e0) = all_56_13 &
% 170.79/26.46 $i(all_56_13))) & ((all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2
% 170.79/26.46 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) = e1))
% 170.79/26.46 (6) ~ (all_52_7 = all_4_2)
% 170.79/26.46 (7) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 170.79/26.46 (8) all_54_15 = all_4_2
% 170.79/26.46 (9) all_56_15 = all_4_2
% 170.79/26.46 (10) ~ (all_52_7 = e0)
% 170.79/26.46 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.46 (12) ~ (all_52_7 = e2)
% 170.79/26.46 (13) op(e0, e1) = e2
% 170.79/26.46 (14) op(e0, e2) = all_52_7
% 170.79/26.46 (15) all_54_13 = all_52_7
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | ALPHA: (5) implies:
% 170.79/26.46 | (16) ~ (all_56_15 = e0)
% 170.79/26.46 | (17) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2)
% 170.79/26.46 | | (all_56_8 = e1 & op(e0, e1) = e1)
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (9), (16) imply:
% 170.79/26.46 | (18) ~ (all_4_2 = e0)
% 170.79/26.46 |
% 170.79/26.46 | BETA: splitting (7) gives:
% 170.79/26.46 |
% 170.79/26.46 | Case 1:
% 170.79/26.46 | |
% 170.79/26.46 | | (19) all_54_15 = e3
% 170.79/26.46 | |
% 170.79/26.46 | | COMBINE_EQS: (8), (19) imply:
% 170.79/26.46 | | (20) all_4_2 = e3
% 170.79/26.46 | |
% 170.79/26.46 | | SIMP: (20) implies:
% 170.79/26.46 | | (21) all_4_2 = e3
% 170.79/26.46 | |
% 170.79/26.46 | | COMBINE_EQS: (9), (21) imply:
% 170.79/26.46 | | (22) all_56_15 = e3
% 170.79/26.46 | |
% 170.79/26.46 | | REDUCE: (6), (21) imply:
% 170.79/26.46 | | (23) ~ (all_52_7 = e3)
% 170.79/26.46 | |
% 170.79/26.46 | | REDUCE: (18), (21) imply:
% 170.79/26.46 | | (24) ~ (e3 = e0)
% 170.79/26.46 | |
% 170.79/26.46 | | BETA: splitting (3) gives:
% 170.79/26.46 | |
% 170.79/26.46 | | Case 1:
% 170.79/26.46 | | |
% 170.79/26.46 | | | (25) ~ (all_56_15 = e3)
% 170.79/26.46 | | |
% 170.79/26.46 | | | REDUCE: (22), (25) imply:
% 170.79/26.46 | | | (26) $false
% 170.79/26.46 | | |
% 170.79/26.46 | | | CLOSE: (26) is inconsistent.
% 170.79/26.46 | | |
% 170.79/26.46 | | Case 2:
% 170.79/26.46 | | |
% 170.79/26.46 | | | (27) all_56_6 = e0 & op(e0, e3) = e0
% 170.79/26.46 | | |
% 170.79/26.46 | | | ALPHA: (27) implies:
% 170.79/26.46 | | | (28) all_56_6 = e0
% 170.79/26.46 | | |
% 170.79/26.46 | | | BETA: splitting (2) gives:
% 170.79/26.46 | | |
% 170.79/26.46 | | | Case 1:
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | (29) all_54_13 = e3
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | REF_CLOSE: (15), (23), (29) are inconsistent by sub-proof #971.
% 170.79/26.46 | | | |
% 170.79/26.46 | | | Case 2:
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | (30) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | BETA: splitting (30) gives:
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | Case 1:
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | (31) all_54_13 = e2
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | REF_CLOSE: (12), (15), (31) are inconsistent by sub-proof #970.
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | Case 2:
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | (32) ~ (all_54_13 = e2)
% 170.79/26.46 | | | | | (33) all_54_13 = e1 | all_54_13 = e0
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | BETA: splitting (33) gives:
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | Case 1:
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | | (34) all_54_13 = e1
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | | COMBINE_EQS: (15), (34) imply:
% 170.79/26.46 | | | | | | (35) all_52_7 = e1
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | | SIMP: (35) implies:
% 170.79/26.46 | | | | | | (36) all_52_7 = e1
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | | REDUCE: (12), (36) imply:
% 170.79/26.46 | | | | | | (37) ~ (e2 = e1)
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | | SIMP: (37) implies:
% 170.79/26.46 | | | | | | (38) ~ (e2 = e1)
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | | REDUCE: (14), (36) imply:
% 170.79/26.46 | | | | | | (39) op(e0, e2) = e1
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | | REF_CLOSE: (11), (13), (17), (24), (28), (38), (39) are inconsistent
% 170.79/26.46 | | | | | | by sub-proof #966.
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | Case 2:
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | | (40) all_54_13 = e0
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | | REF_CLOSE: (10), (15), (40) are inconsistent by sub-proof #963.
% 170.79/26.46 | | | | | |
% 170.79/26.46 | | | | | End of split
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | End of split
% 170.79/26.46 | | | |
% 170.79/26.46 | | | End of split
% 170.79/26.46 | | |
% 170.79/26.46 | | End of split
% 170.79/26.46 | |
% 170.79/26.46 | Case 2:
% 170.79/26.46 | |
% 170.79/26.46 | | (41) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (1), (4), (8), (18), (41) are inconsistent by sub-proof #697.
% 170.79/26.46 | |
% 170.79/26.46 | End of split
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #697 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) ~ (all_4_2 = e2)
% 170.79/26.46 (2) ~ (all_4_2 = e1)
% 170.79/26.46 (3) all_54_15 = all_4_2
% 170.79/26.46 (4) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 170.79/26.46 (5) ~ (all_4_2 = e0)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | BETA: splitting (4) gives:
% 170.79/26.46 |
% 170.79/26.46 | Case 1:
% 170.79/26.46 | |
% 170.79/26.46 | | (6) all_54_15 = e2
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #991.
% 170.79/26.46 | |
% 170.79/26.46 | Case 2:
% 170.79/26.46 | |
% 170.79/26.46 | | (7) all_54_15 = e1 | all_54_15 = e0
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #698.
% 170.79/26.46 | |
% 170.79/26.46 | End of split
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #698 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_54_15 = e1 | all_54_15 = e0
% 170.79/26.46 (2) all_54_15 = all_4_2
% 170.79/26.46 (3) ~ (all_4_2 = e1)
% 170.79/26.46 (4) ~ (all_4_2 = e0)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | BETA: splitting (1) gives:
% 170.79/26.46 |
% 170.79/26.46 | Case 1:
% 170.79/26.46 | |
% 170.79/26.46 | | (5) all_54_15 = e1
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #990.
% 170.79/26.46 | |
% 170.79/26.46 | Case 2:
% 170.79/26.46 | |
% 170.79/26.46 | | (6) all_54_15 = e0
% 170.79/26.46 | |
% 170.79/26.46 | | COMBINE_EQS: (2), (6) imply:
% 170.79/26.46 | | (7) all_4_2 = e0
% 170.79/26.46 | |
% 170.79/26.46 | | SIMP: (7) implies:
% 170.79/26.46 | | (8) all_4_2 = e0
% 170.79/26.46 | |
% 170.79/26.46 | | REDUCE: (4), (8) imply:
% 170.79/26.46 | | (9) $false
% 170.79/26.46 | |
% 170.79/26.46 | | CLOSE: (9) is inconsistent.
% 170.79/26.46 | |
% 170.79/26.46 | End of split
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #699 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.46 (2) op(e3, e0) = e2
% 170.79/26.46 (3) op(e3, e0) = e0
% 170.79/26.46 (4) ~ (e2 = e0)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | GROUND_INST: instantiating (1) with e0, e2, e0, e3, simplifying with (2), (3)
% 170.79/26.46 | gives:
% 170.79/26.46 | (5) e2 = e0
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (4), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #700 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_9 = e2
% 170.79/26.46 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.46 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.46 (3) ~ (e3 = e1)
% 170.79/26.46 (4) ~ (e1 = e0)
% 170.79/26.46 (5) ~ (e3 = e0)
% 170.79/26.46 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.79/26.46 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.79/26.46 (7) all_58_4 = e3
% 170.79/26.46 (8) ~ (e2 = e0)
% 170.79/26.46 (9) all_58_0 = e2
% 170.79/26.46 (10) ~ (e2 = e1)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | BETA: splitting (6) gives:
% 170.79/26.46 |
% 170.79/26.46 | Case 1:
% 170.79/26.46 | |
% 170.79/26.46 | | (11) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 170.79/26.46 | | e1)
% 170.79/26.46 | |
% 170.79/26.46 | | BETA: splitting (11) gives:
% 170.79/26.46 | |
% 170.79/26.46 | | Case 1:
% 170.79/26.46 | | |
% 170.79/26.46 | | | (12) all_58_0 = e1 & op(e3, e3) = e1
% 170.79/26.46 | | |
% 170.79/26.46 | | | REF_CLOSE: (9), (10), (12) are inconsistent by sub-proof #706.
% 170.79/26.46 | | |
% 170.79/26.46 | | Case 2:
% 170.79/26.46 | | |
% 170.79/26.46 | | | (13) all_58_1 = e1 & op(e3, e2) = e1
% 170.79/26.46 | | |
% 170.79/26.46 | | | ALPHA: (13) implies:
% 170.79/26.46 | | | (14) all_58_1 = e1
% 170.79/26.46 | | |
% 170.79/26.46 | | | BETA: splitting (2) gives:
% 170.79/26.46 | | |
% 170.79/26.46 | | | Case 1:
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | (15) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 170.79/26.46 | | | | = e0)
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | BETA: splitting (15) gives:
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | Case 1:
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | (16) all_58_0 = e0 & op(e3, e3) = e0
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | REF_CLOSE: (8), (9), (16) are inconsistent by sub-proof #705.
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | Case 2:
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | (17) all_58_1 = e0 & op(e3, e2) = e0
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | REF_CLOSE: (4), (14), (17) are inconsistent by sub-proof #948.
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | End of split
% 170.79/26.46 | | | |
% 170.79/26.46 | | | Case 2:
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | (18) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 170.79/26.46 | | | | = e0)
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | REF_CLOSE: (1), (5), (7), (8), (18) are inconsistent by sub-proof #703.
% 170.79/26.46 | | | |
% 170.79/26.46 | | | End of split
% 170.79/26.46 | | |
% 170.79/26.46 | | End of split
% 170.79/26.46 | |
% 170.79/26.46 | Case 2:
% 170.79/26.46 | |
% 170.79/26.46 | | (19) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 170.79/26.46 | | e1)
% 170.79/26.46 | |
% 170.79/26.46 | | BETA: splitting (19) gives:
% 170.79/26.46 | |
% 170.79/26.46 | | Case 1:
% 170.79/26.46 | | |
% 170.79/26.46 | | | (20) all_58_4 = e1 & op(e3, e1) = e1
% 170.79/26.46 | | |
% 170.79/26.46 | | | REF_CLOSE: (3), (7), (20) are inconsistent by sub-proof #702.
% 170.79/26.46 | | |
% 170.79/26.46 | | Case 2:
% 170.79/26.46 | | |
% 170.79/26.46 | | | (21) all_58_9 = e1 & op(e3, e0) = e1
% 170.79/26.46 | | |
% 170.79/26.46 | | | REF_CLOSE: (1), (10), (21) are inconsistent by sub-proof #701.
% 170.79/26.46 | | |
% 170.79/26.46 | | End of split
% 170.79/26.46 | |
% 170.79/26.46 | End of split
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #701 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_9 = e1 & op(e3, e0) = e1
% 170.79/26.46 (2) all_58_9 = e2
% 170.79/26.46 (3) ~ (e2 = e1)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | ALPHA: (1) implies:
% 170.79/26.46 | (4) all_58_9 = e1
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.46 | (5) e2 = e1
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #702 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_4 = e1 & op(e3, e1) = e1
% 170.79/26.46 (2) all_58_4 = e3
% 170.79/26.46 (3) ~ (e3 = e1)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | ALPHA: (1) implies:
% 170.79/26.46 | (4) all_58_4 = e1
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.46 | (5) e3 = e1
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #703 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_9 = e2
% 170.79/26.46 (2) ~ (e3 = e0)
% 170.79/26.46 (3) all_58_4 = e3
% 170.79/26.46 (4) ~ (e2 = e0)
% 170.79/26.46 (5) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | BETA: splitting (5) gives:
% 170.79/26.46 |
% 170.79/26.46 | Case 1:
% 170.79/26.46 | |
% 170.79/26.46 | | (6) all_58_4 = e0 & op(e3, e1) = e0
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #704.
% 170.79/26.46 | |
% 170.79/26.46 | Case 2:
% 170.79/26.46 | |
% 170.79/26.46 | | (7) all_58_9 = e0 & op(e3, e0) = e0
% 170.79/26.46 | |
% 170.79/26.46 | | ALPHA: (7) implies:
% 170.79/26.46 | | (8) all_58_9 = e0
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #945.
% 170.79/26.46 | |
% 170.79/26.46 | End of split
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #704 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_4 = e0 & op(e3, e1) = e0
% 170.79/26.46 (2) all_58_4 = e3
% 170.79/26.46 (3) ~ (e3 = e0)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | ALPHA: (1) implies:
% 170.79/26.46 | (4) all_58_4 = e0
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.46 | (5) e3 = e0
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #705 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_0 = e0 & op(e3, e3) = e0
% 170.79/26.46 (2) all_58_0 = e2
% 170.79/26.46 (3) ~ (e2 = e0)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | ALPHA: (1) implies:
% 170.79/26.46 | (4) all_58_0 = e0
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.46 | (5) e2 = e0
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #706 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_0 = e1 & op(e3, e3) = e1
% 170.79/26.46 (2) all_58_0 = e2
% 170.79/26.46 (3) ~ (e2 = e1)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | ALPHA: (1) implies:
% 170.79/26.46 | (4) all_58_0 = e1
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.46 | (5) e2 = e1
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #707 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.46 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.46 (2) ~ (e3 = e1)
% 170.79/26.46 (3) all_58_13 = e3
% 170.79/26.46 (4) ~ (e1 = e0)
% 170.79/26.46 (5) ~ (e3 = e0)
% 170.79/26.46 (6) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.46 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.79/26.46 (7) all_58_1 = e3
% 170.79/26.46 (8) all_58_3 = e2
% 170.79/26.46 (9) ~ (e2 = e0)
% 170.79/26.46 (10) ~ (e2 = e1)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | BETA: splitting (6) gives:
% 170.79/26.46 |
% 170.79/26.46 | Case 1:
% 170.79/26.46 | |
% 170.79/26.46 | | (11) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 170.79/26.46 | | e0)
% 170.79/26.46 | |
% 170.79/26.46 | | BETA: splitting (11) gives:
% 170.79/26.46 | |
% 170.79/26.46 | | Case 1:
% 170.79/26.46 | | |
% 170.79/26.46 | | | (12) all_58_1 = e0 & op(e3, e2) = e0
% 170.79/26.46 | | |
% 170.79/26.46 | | | REF_CLOSE: (5), (7), (12) are inconsistent by sub-proof #794.
% 170.79/26.46 | | |
% 170.79/26.46 | | Case 2:
% 170.79/26.46 | | |
% 170.79/26.46 | | | (13) all_58_3 = e0 & op(e2, e2) = e0
% 170.79/26.46 | | |
% 170.79/26.46 | | | ALPHA: (13) implies:
% 170.79/26.46 | | | (14) all_58_3 = e0
% 170.79/26.46 | | |
% 170.79/26.46 | | | REF_CLOSE: (8), (9), (14) are inconsistent by sub-proof #843.
% 170.79/26.46 | | |
% 170.79/26.46 | | End of split
% 170.79/26.46 | |
% 170.79/26.46 | Case 2:
% 170.79/26.46 | |
% 170.79/26.46 | | (15) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 170.79/26.46 | | e0)
% 170.79/26.46 | |
% 170.79/26.46 | | BETA: splitting (15) gives:
% 170.79/26.46 | |
% 170.79/26.46 | | Case 1:
% 170.79/26.46 | | |
% 170.79/26.46 | | | (16) all_58_7 = e0 & op(e1, e2) = e0
% 170.79/26.46 | | |
% 170.79/26.46 | | | ALPHA: (16) implies:
% 170.79/26.46 | | | (17) all_58_7 = e0
% 170.79/26.46 | | |
% 170.79/26.46 | | | BETA: splitting (1) gives:
% 170.79/26.46 | | |
% 170.79/26.46 | | | Case 1:
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | (18) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 170.79/26.46 | | | | = e1)
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | BETA: splitting (18) gives:
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | Case 1:
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | (19) all_58_1 = e1 & op(e3, e2) = e1
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | REF_CLOSE: (2), (7), (19) are inconsistent by sub-proof #711.
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | Case 2:
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | (20) all_58_3 = e1 & op(e2, e2) = e1
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | REF_CLOSE: (8), (10), (20) are inconsistent by sub-proof #914.
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | End of split
% 170.79/26.46 | | | |
% 170.79/26.46 | | | Case 2:
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | (21) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 170.79/26.46 | | | | = e1)
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | BETA: splitting (21) gives:
% 170.79/26.46 | | | |
% 170.79/26.46 | | | | Case 1:
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | (22) all_58_7 = e1 & op(e1, e2) = e1
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | ALPHA: (22) implies:
% 170.79/26.46 | | | | | (23) all_58_7 = e1
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | REF_CLOSE: (4), (17), (23) are inconsistent by sub-proof #710.
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | Case 2:
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | (24) all_58_13 = e1 & op(e0, e2) = e1
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | | REF_CLOSE: (2), (3), (24) are inconsistent by sub-proof #709.
% 170.79/26.46 | | | | |
% 170.79/26.46 | | | | End of split
% 170.79/26.46 | | | |
% 170.79/26.46 | | | End of split
% 170.79/26.46 | | |
% 170.79/26.46 | | Case 2:
% 170.79/26.46 | | |
% 170.79/26.46 | | | (25) all_58_13 = e0 & op(e0, e2) = e0
% 170.79/26.46 | | |
% 170.79/26.46 | | | ALPHA: (25) implies:
% 170.79/26.46 | | | (26) all_58_13 = e0
% 170.79/26.46 | | |
% 170.79/26.46 | | | REF_CLOSE: (3), (5), (26) are inconsistent by sub-proof #708.
% 170.79/26.46 | | |
% 170.79/26.46 | | End of split
% 170.79/26.46 | |
% 170.79/26.46 | End of split
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #708 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_13 = e3
% 170.79/26.46 (2) all_58_13 = e0
% 170.79/26.46 (3) ~ (e3 = e0)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.46 | (4) e3 = e0
% 170.79/26.46 |
% 170.79/26.46 | SIMP: (4) implies:
% 170.79/26.46 | (5) e3 = e0
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #709 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_13 = e1 & op(e0, e2) = e1
% 170.79/26.46 (2) all_58_13 = e3
% 170.79/26.46 (3) ~ (e3 = e1)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | ALPHA: (1) implies:
% 170.79/26.46 | (4) all_58_13 = e1
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.46 | (5) e3 = e1
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #710 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_7 = e1
% 170.79/26.46 (2) all_58_7 = e0
% 170.79/26.46 (3) ~ (e1 = e0)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.46 | (4) e1 = e0
% 170.79/26.46 |
% 170.79/26.46 | SIMP: (4) implies:
% 170.79/26.46 | (5) e1 = e0
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #711 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_1 = e1 & op(e3, e2) = e1
% 170.79/26.46 (2) all_58_1 = e3
% 170.79/26.46 (3) ~ (e3 = e1)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | ALPHA: (1) implies:
% 170.79/26.46 | (4) all_58_1 = e1
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.46 | (5) e3 = e1
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (5) imply:
% 170.79/26.46 | (6) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (6) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #712 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_6 = e0 & op(e1, e3) = e0
% 170.79/26.46 (2) all_58_6 = e2
% 170.79/26.46 (3) ~ (e2 = e0)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | ALPHA: (1) implies:
% 170.79/26.46 | (4) all_58_6 = e0
% 170.79/26.46 |
% 170.79/26.46 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.46 | (5) e2 = e0
% 170.79/26.46 |
% 170.79/26.46 | SIMP: (5) implies:
% 170.79/26.46 | (6) e2 = e0
% 170.79/26.46 |
% 170.79/26.46 | REDUCE: (3), (6) imply:
% 170.79/26.46 | (7) $false
% 170.79/26.46 |
% 170.79/26.46 | CLOSE: (7) is inconsistent.
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #713 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) all_58_12 = e2
% 170.79/26.46 (2) op(e1, e3) = all_52_2
% 170.79/26.46 (3) ~ (e1 = e0)
% 170.79/26.46 (4) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.79/26.46 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.46 (6) ~ (e2 = e0)
% 170.79/26.46 (7) op(e1, e3) = e1
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | BETA: splitting (4) gives:
% 170.79/26.46 |
% 170.79/26.46 | Case 1:
% 170.79/26.46 | |
% 170.79/26.46 | | (8) all_58_6 = e0 & op(e1, e3) = e0
% 170.79/26.46 | |
% 170.79/26.46 | | ALPHA: (8) implies:
% 170.79/26.46 | | (9) op(e1, e3) = e0
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (2), (3), (5), (7), (9) are inconsistent by sub-proof #749.
% 170.79/26.46 | |
% 170.79/26.46 | Case 2:
% 170.79/26.46 | |
% 170.79/26.46 | | (10) all_58_12 = e0 & op(e0, e3) = e0
% 170.79/26.46 | |
% 170.79/26.46 | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #886.
% 170.79/26.46 | |
% 170.79/26.46 | End of split
% 170.79/26.46 |
% 170.79/26.46 End of proof
% 170.79/26.46
% 170.79/26.46 Sub-proof #714 shows that the following formulas are inconsistent:
% 170.79/26.46 ----------------------------------------------------------------
% 170.79/26.46 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.46 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.46 (2) ~ (all_8_2 = e3)
% 170.79/26.46 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0)
% 170.79/26.46 (4) ~ (e3 = e1)
% 170.79/26.46 (5) op(e3, e3) = e1
% 170.79/26.46 (6) ~ (e1 = e0)
% 170.79/26.46 (7) op(e2, e2) = all_8_2
% 170.79/26.46 (8) ~ (e3 = e0)
% 170.79/26.46 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.46 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.46 (10) all_58_3 = e2
% 170.79/26.46 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.46 (12) ~ (e2 = e0)
% 170.79/26.46 (13) all_58_5 = e2
% 170.79/26.46 (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.46 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.46 (15) ~ (e2 = e1)
% 170.79/26.46 (16) ~ (e3 = e2)
% 170.79/26.46
% 170.79/26.46 Begin of proof
% 170.79/26.46 |
% 170.79/26.46 | BETA: splitting (3) gives:
% 170.79/26.46 |
% 170.79/26.46 | Case 1:
% 170.79/26.46 | |
% 170.79/26.46 | | (17) all_58_0 = e0 & op(e3, e3) = e0
% 170.79/26.47 | |
% 170.79/26.47 | | ALPHA: (17) implies:
% 170.79/26.47 | | (18) op(e3, e3) = e0
% 170.79/26.47 | |
% 170.79/26.47 | | REF_CLOSE: (5), (6), (11), (18) are inconsistent by sub-proof #907.
% 170.79/26.47 | |
% 170.79/26.47 | Case 2:
% 170.79/26.47 | |
% 170.79/26.47 | | (19) all_58_2 = e0 & op(e2, e3) = e0
% 170.79/26.47 | |
% 170.79/26.47 | | ALPHA: (19) implies:
% 170.79/26.47 | | (20) all_58_2 = e0
% 170.79/26.47 | |
% 170.79/26.47 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 170.79/26.47 | | (15), (16), (20) are inconsistent by sub-proof #743.
% 170.79/26.47 | |
% 170.79/26.47 | End of split
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #715 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) all_58_6 = e2 & op(e1, e3) = e2
% 170.79/26.47 (2) all_58_6 = e1
% 170.79/26.47 (3) ~ (e2 = e1)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | ALPHA: (1) implies:
% 170.79/26.47 | (4) all_58_6 = e2
% 170.79/26.47 |
% 170.79/26.47 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.47 | (5) e2 = e1
% 170.79/26.47 |
% 170.79/26.47 | REDUCE: (3), (5) imply:
% 170.79/26.47 | (6) $false
% 170.79/26.47 |
% 170.79/26.47 | CLOSE: (6) is inconsistent.
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #716 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.47 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.47 (2) ~ (e1 = e0)
% 170.79/26.47 (3) op(e2, e3) = all_52_1
% 170.79/26.47 (4) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.47 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.47 (5) all_58_3 = e2
% 170.79/26.47 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.47 (7) ~ (e2 = e0)
% 170.79/26.47 (8) all_58_5 = e2
% 170.79/26.47 (9) op(e3, e3) = e3
% 170.79/26.47 (10) ~ (e2 = e1)
% 170.79/26.47 (11) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 170.79/26.47 (12) ~ (e3 = e2)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | BETA: splitting (11) gives:
% 170.79/26.47 |
% 170.79/26.47 | Case 1:
% 170.79/26.47 | |
% 170.79/26.47 | | (13) all_58_0 = e2 & op(e3, e3) = e2
% 170.79/26.47 | |
% 170.79/26.47 | | ALPHA: (13) implies:
% 170.79/26.47 | | (14) op(e3, e3) = e2
% 170.79/26.47 | |
% 170.79/26.47 | | REF_CLOSE: (6), (9), (12), (14) are inconsistent by sub-proof #838.
% 170.79/26.47 | |
% 170.79/26.47 | Case 2:
% 170.79/26.47 | |
% 170.79/26.47 | | (15) all_58_2 = e2 & op(e2, e3) = e2
% 170.79/26.47 | |
% 170.79/26.47 | | ALPHA: (15) implies:
% 170.79/26.47 | | (16) op(e2, e3) = e2
% 170.79/26.47 | |
% 170.79/26.47 | | BETA: splitting (4) gives:
% 170.79/26.47 | |
% 170.79/26.47 | | Case 1:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 170.79/26.47 | | | e0)
% 170.79/26.47 | | |
% 170.79/26.47 | | | BETA: splitting (17) gives:
% 170.79/26.47 | | |
% 170.79/26.47 | | | Case 1:
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | (18) all_58_2 = e0 & op(e2, e3) = e0
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | REF_CLOSE: (3), (6), (7), (16), (18) are inconsistent by sub-proof #782.
% 170.79/26.47 | | | |
% 170.79/26.47 | | | Case 2:
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | (19) all_58_3 = e0 & op(e2, e2) = e0
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | REF_CLOSE: (5), (7), (19) are inconsistent by sub-proof #934.
% 170.79/26.47 | | | |
% 170.79/26.47 | | | End of split
% 170.79/26.47 | | |
% 170.79/26.47 | | Case 2:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (20) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.79/26.47 | | | e0)
% 170.79/26.47 | | |
% 170.79/26.47 | | | BETA: splitting (20) gives:
% 170.79/26.47 | | |
% 170.79/26.47 | | | Case 1:
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | (21) all_58_5 = e0 & op(e2, e1) = e0
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | REF_CLOSE: (7), (8), (21) are inconsistent by sub-proof #933.
% 170.79/26.47 | | | |
% 170.79/26.47 | | | Case 2:
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | (22) all_58_10 = e0 & op(e2, e0) = e0
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | ALPHA: (22) implies:
% 170.79/26.47 | | | | (23) all_58_10 = e0
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | BETA: splitting (1) gives:
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | Case 1:
% 170.79/26.47 | | | | |
% 170.79/26.47 | | | | | (24) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2,
% 170.79/26.47 | | | | | e2) = e1)
% 170.79/26.47 | | | | |
% 170.79/26.47 | | | | | REF_CLOSE: (3), (5), (6), (10), (16), (24) are inconsistent by
% 170.79/26.47 | | | | | sub-proof #783.
% 170.79/26.47 | | | | |
% 170.79/26.47 | | | | Case 2:
% 170.79/26.47 | | | | |
% 170.79/26.47 | | | | | (25) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2,
% 170.79/26.47 | | | | | e0) = e1)
% 170.79/26.47 | | | | |
% 170.79/26.47 | | | | | BETA: splitting (25) gives:
% 170.79/26.47 | | | | |
% 170.79/26.47 | | | | | Case 1:
% 170.79/26.47 | | | | | |
% 170.79/26.47 | | | | | | (26) all_58_5 = e1 & op(e2, e1) = e1
% 170.79/26.47 | | | | | |
% 170.79/26.47 | | | | | | REF_CLOSE: (8), (10), (26) are inconsistent by sub-proof #852.
% 170.79/26.47 | | | | | |
% 170.79/26.47 | | | | | Case 2:
% 170.79/26.47 | | | | | |
% 170.79/26.47 | | | | | | (27) all_58_10 = e1 & op(e2, e0) = e1
% 170.79/26.47 | | | | | |
% 170.79/26.47 | | | | | | ALPHA: (27) implies:
% 170.79/26.47 | | | | | | (28) all_58_10 = e1
% 170.79/26.47 | | | | | |
% 170.79/26.47 | | | | | | REF_CLOSE: (2), (23), (28) are inconsistent by sub-proof #834.
% 170.79/26.47 | | | | | |
% 170.79/26.47 | | | | | End of split
% 170.79/26.47 | | | | |
% 170.79/26.47 | | | | End of split
% 170.79/26.47 | | | |
% 170.79/26.47 | | | End of split
% 170.79/26.47 | | |
% 170.79/26.47 | | End of split
% 170.79/26.47 | |
% 170.79/26.47 | End of split
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #717 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) all_58_14 = e2
% 170.79/26.47 (2) all_58_8 = e1
% 170.79/26.47 (3) ~ (e1 = e0)
% 170.79/26.47 (4) all_58_5 = e3
% 170.79/26.47 (5) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 170.79/26.47 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.79/26.47 (6) ~ (e3 = e0)
% 170.79/26.47 (7) all_58_4 = e1
% 170.79/26.47 (8) ~ (e2 = e0)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | BETA: splitting (5) gives:
% 170.79/26.47 |
% 170.79/26.47 | Case 1:
% 170.79/26.47 | |
% 170.79/26.47 | | (9) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0)
% 170.79/26.47 | |
% 170.79/26.47 | | BETA: splitting (9) gives:
% 170.79/26.47 | |
% 170.79/26.47 | | Case 1:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (10) all_58_4 = e0 & op(e3, e1) = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (3), (7), (10) are inconsistent by sub-proof #793.
% 170.79/26.47 | | |
% 170.79/26.47 | | Case 2:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (11) all_58_5 = e0 & op(e2, e1) = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #926.
% 170.79/26.47 | | |
% 170.79/26.47 | | End of split
% 170.79/26.47 | |
% 170.79/26.47 | Case 2:
% 170.79/26.47 | |
% 170.79/26.47 | | (12) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 170.79/26.47 | | e0)
% 170.79/26.47 | |
% 170.79/26.47 | | BETA: splitting (12) gives:
% 170.79/26.47 | |
% 170.79/26.47 | | Case 1:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (13) all_58_8 = e0 & op(e1, e1) = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #718.
% 170.79/26.47 | | |
% 170.79/26.47 | | Case 2:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (14) all_58_14 = e0 & op(e0, e1) = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | ALPHA: (14) implies:
% 170.79/26.47 | | | (15) all_58_14 = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #806.
% 170.79/26.47 | | |
% 170.79/26.47 | | End of split
% 170.79/26.47 | |
% 170.79/26.47 | End of split
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #718 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) all_58_8 = e0 & op(e1, e1) = e0
% 170.79/26.47 (2) all_58_8 = e1
% 170.79/26.47 (3) ~ (e1 = e0)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | ALPHA: (1) implies:
% 170.79/26.47 | (4) all_58_8 = e0
% 170.79/26.47 |
% 170.79/26.47 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.47 | (5) e1 = e0
% 170.79/26.47 |
% 170.79/26.47 | REDUCE: (3), (5) imply:
% 170.79/26.47 | (6) $false
% 170.79/26.47 |
% 170.79/26.47 | CLOSE: (6) is inconsistent.
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #719 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.79/26.47 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.79/26.47 (2) all_58_15 = e2
% 170.79/26.47 (3) all_58_9 = e2
% 170.79/26.47 (4) ~ (e3 = e1)
% 170.79/26.47 (5) ~ (e1 = e0)
% 170.79/26.47 (6) ~ (e3 = e0)
% 170.79/26.47 (7) all_58_11 = e3
% 170.79/26.47 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.47 (9) ~ (e2 = e0)
% 170.79/26.47 (10) ~ (e2 = e1)
% 170.79/26.47 (11) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.47 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.79/26.47 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.79/26.47 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | BETA: splitting (1) gives:
% 170.79/26.47 |
% 170.79/26.47 | Case 1:
% 170.79/26.47 | |
% 170.79/26.47 | | (12) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 170.79/26.47 | | e1)
% 170.79/26.47 | |
% 170.79/26.47 | | BETA: splitting (12) gives:
% 170.79/26.47 | |
% 170.79/26.47 | | Case 1:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (13) all_58_9 = e1 & op(e3, e0) = e1
% 170.79/26.47 | | |
% 170.79/26.47 | | | ALPHA: (13) implies:
% 170.79/26.47 | | | (14) all_58_9 = e1
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (3), (10), (14) are inconsistent by sub-proof #942.
% 170.79/26.47 | | |
% 170.79/26.47 | | Case 2:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (15) all_58_10 = e1 & op(e2, e0) = e1
% 170.79/26.47 | | |
% 170.79/26.47 | | | ALPHA: (15) implies:
% 170.79/26.47 | | | (16) op(e2, e0) = e1
% 170.79/26.47 | | |
% 170.79/26.47 | | | BETA: splitting (11) gives:
% 170.79/26.47 | | |
% 170.79/26.47 | | | Case 1:
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | (17) all_58_15 = e0 & op(e0, e0) = e0
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | ALPHA: (17) implies:
% 170.79/26.47 | | | | (18) all_58_15 = e0
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | REF_CLOSE: (2), (9), (18) are inconsistent by sub-proof #725.
% 170.79/26.47 | | | |
% 170.79/26.47 | | | Case 2:
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | (19) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 170.79/26.47 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 170.79/26.47 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 170.79/26.47 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | ALPHA: (19) implies:
% 170.79/26.47 | | | | (20) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 170.79/26.47 | | | | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.79/26.47 | | | |
% 170.79/26.47 | | | | REF_CLOSE: (3), (5), (6), (7), (8), (9), (16), (20) are inconsistent by
% 170.79/26.47 | | | | sub-proof #722.
% 170.79/26.47 | | | |
% 170.79/26.47 | | | End of split
% 170.79/26.47 | | |
% 170.79/26.47 | | End of split
% 170.79/26.47 | |
% 170.79/26.47 | Case 2:
% 170.79/26.47 | |
% 170.79/26.47 | | (21) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.79/26.47 | | e1)
% 170.79/26.47 | |
% 170.79/26.47 | | BETA: splitting (21) gives:
% 170.79/26.47 | |
% 170.79/26.47 | | Case 1:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (22) all_58_11 = e1 & op(e1, e0) = e1
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (4), (7), (22) are inconsistent by sub-proof #721.
% 170.79/26.47 | | |
% 170.79/26.47 | | Case 2:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (23) all_58_15 = e1 & op(e0, e0) = e1
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (2), (10), (23) are inconsistent by sub-proof #720.
% 170.79/26.47 | | |
% 170.79/26.47 | | End of split
% 170.79/26.47 | |
% 170.79/26.47 | End of split
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #720 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) all_58_15 = e1 & op(e0, e0) = e1
% 170.79/26.47 (2) all_58_15 = e2
% 170.79/26.47 (3) ~ (e2 = e1)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | ALPHA: (1) implies:
% 170.79/26.47 | (4) all_58_15 = e1
% 170.79/26.47 |
% 170.79/26.47 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.47 | (5) e2 = e1
% 170.79/26.47 |
% 170.79/26.47 | REDUCE: (3), (5) imply:
% 170.79/26.47 | (6) $false
% 170.79/26.47 |
% 170.79/26.47 | CLOSE: (6) is inconsistent.
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #721 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) all_58_11 = e1 & op(e1, e0) = e1
% 170.79/26.47 (2) all_58_11 = e3
% 170.79/26.47 (3) ~ (e3 = e1)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | ALPHA: (1) implies:
% 170.79/26.47 | (4) all_58_11 = e1
% 170.79/26.47 |
% 170.79/26.47 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.47 | (5) e3 = e1
% 170.79/26.47 |
% 170.79/26.47 | REDUCE: (3), (5) imply:
% 170.79/26.47 | (6) $false
% 170.79/26.47 |
% 170.79/26.47 | CLOSE: (6) is inconsistent.
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #722 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) all_58_9 = e2
% 170.79/26.47 (2) ~ (e1 = e0)
% 170.79/26.47 (3) ~ (e3 = e0)
% 170.79/26.47 (4) all_58_11 = e3
% 170.79/26.47 (5) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 170.79/26.47 (all_58_11 = e0 & op(e1, e0) = e0)
% 170.79/26.47 (6) op(e2, e0) = e1
% 170.79/26.47 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.47 (8) ~ (e2 = e0)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | BETA: splitting (5) gives:
% 170.79/26.47 |
% 170.79/26.47 | Case 1:
% 170.79/26.47 | |
% 170.79/26.47 | | (9) all_58_9 = e0 & op(e3, e0) = e0
% 170.79/26.47 | |
% 170.79/26.47 | | ALPHA: (9) implies:
% 170.79/26.47 | | (10) all_58_9 = e0
% 170.79/26.47 | |
% 170.79/26.47 | | REF_CLOSE: (1), (8), (10) are inconsistent by sub-proof #945.
% 170.79/26.47 | |
% 170.79/26.47 | Case 2:
% 170.79/26.47 | |
% 170.79/26.47 | | (11) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 170.79/26.47 | | e0)
% 170.79/26.47 | |
% 170.79/26.47 | | REF_CLOSE: (2), (3), (4), (6), (7), (11) are inconsistent by sub-proof #723.
% 170.79/26.47 | |
% 170.79/26.47 | End of split
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #723 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) ~ (e1 = e0)
% 170.79/26.47 (2) ~ (e3 = e0)
% 170.79/26.47 (3) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.79/26.47 (4) all_58_11 = e3
% 170.79/26.47 (5) op(e2, e0) = e1
% 170.79/26.47 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | BETA: splitting (3) gives:
% 170.79/26.47 |
% 170.79/26.47 | Case 1:
% 170.79/26.47 | |
% 170.79/26.47 | | (7) all_58_10 = e0 & op(e2, e0) = e0
% 170.79/26.47 | |
% 170.79/26.47 | | ALPHA: (7) implies:
% 170.79/26.47 | | (8) op(e2, e0) = e0
% 170.79/26.47 | |
% 170.79/26.47 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #849.
% 170.79/26.47 | |
% 170.79/26.47 | Case 2:
% 170.79/26.47 | |
% 170.79/26.47 | | (9) all_58_11 = e0 & op(e1, e0) = e0
% 170.79/26.47 | |
% 170.79/26.47 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #724.
% 170.79/26.47 | |
% 170.79/26.47 | End of split
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #724 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) all_58_11 = e0 & op(e1, e0) = e0
% 170.79/26.47 (2) all_58_11 = e3
% 170.79/26.47 (3) ~ (e3 = e0)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | ALPHA: (1) implies:
% 170.79/26.47 | (4) all_58_11 = e0
% 170.79/26.47 |
% 170.79/26.47 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.47 | (5) e3 = e0
% 170.79/26.47 |
% 170.79/26.47 | REDUCE: (3), (5) imply:
% 170.79/26.47 | (6) $false
% 170.79/26.47 |
% 170.79/26.47 | CLOSE: (6) is inconsistent.
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #725 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) all_58_15 = e2
% 170.79/26.47 (2) all_58_15 = e0
% 170.79/26.47 (3) ~ (e2 = e0)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.47 | (4) e2 = e0
% 170.79/26.47 |
% 170.79/26.47 | SIMP: (4) implies:
% 170.79/26.47 | (5) e2 = e0
% 170.79/26.47 |
% 170.79/26.47 | REDUCE: (3), (5) imply:
% 170.79/26.47 | (6) $false
% 170.79/26.47 |
% 170.79/26.47 | CLOSE: (6) is inconsistent.
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #726 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) all_58_7 = e1
% 170.79/26.47 (2) ~ (e3 = e1)
% 170.79/26.47 (3) ~ (e1 = e0)
% 170.79/26.47 (4) all_58_11 = e2
% 170.79/26.47 (5) all_58_6 = e2
% 170.79/26.47 (6) ~ (e3 = e0)
% 170.79/26.47 (7) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.79/26.47 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.79/26.47 (8) ~ (e2 = e0)
% 170.79/26.47 (9) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.79/26.47 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.79/26.47 (10) ~ (e3 = e2)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | BETA: splitting (7) gives:
% 170.79/26.47 |
% 170.79/26.47 | Case 1:
% 170.79/26.47 | |
% 170.79/26.47 | | (11) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 170.79/26.47 | | e0)
% 170.79/26.47 | |
% 170.79/26.47 | | BETA: splitting (11) gives:
% 170.79/26.47 | |
% 170.79/26.47 | | Case 1:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (12) all_58_6 = e0 & op(e1, e3) = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (5), (8), (12) are inconsistent by sub-proof #769.
% 170.79/26.47 | | |
% 170.79/26.47 | | Case 2:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (13) all_58_7 = e0 & op(e1, e2) = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (1), (3), (13) are inconsistent by sub-proof #727.
% 170.79/26.47 | | |
% 170.79/26.47 | | End of split
% 170.79/26.47 | |
% 170.79/26.47 | Case 2:
% 170.79/26.47 | |
% 170.79/26.47 | | (14) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 170.79/26.47 | | e0)
% 170.79/26.47 | |
% 170.79/26.47 | | BETA: splitting (14) gives:
% 170.79/26.47 | |
% 170.79/26.47 | | Case 1:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (15) all_58_8 = e0 & op(e1, e1) = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | ALPHA: (15) implies:
% 170.79/26.47 | | | (16) all_58_8 = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (16) are inconsistent by
% 170.79/26.47 | | | sub-proof #819.
% 170.79/26.47 | | |
% 170.79/26.47 | | Case 2:
% 170.79/26.47 | | |
% 170.79/26.47 | | | (17) all_58_11 = e0 & op(e1, e0) = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | ALPHA: (17) implies:
% 170.79/26.47 | | | (18) all_58_11 = e0
% 170.79/26.47 | | |
% 170.79/26.47 | | | REF_CLOSE: (4), (8), (18) are inconsistent by sub-proof #879.
% 170.79/26.47 | | |
% 170.79/26.47 | | End of split
% 170.79/26.47 | |
% 170.79/26.47 | End of split
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #727 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) all_58_7 = e0 & op(e1, e2) = e0
% 170.79/26.47 (2) all_58_7 = e1
% 170.79/26.47 (3) ~ (e1 = e0)
% 170.79/26.47
% 170.79/26.47 Begin of proof
% 170.79/26.47 |
% 170.79/26.47 | ALPHA: (1) implies:
% 170.79/26.47 | (4) all_58_7 = e0
% 170.79/26.47 |
% 170.79/26.47 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.47 | (5) e1 = e0
% 170.79/26.47 |
% 170.79/26.47 | REDUCE: (3), (5) imply:
% 170.79/26.47 | (6) $false
% 170.79/26.47 |
% 170.79/26.47 | CLOSE: (6) is inconsistent.
% 170.79/26.47 |
% 170.79/26.47 End of proof
% 170.79/26.47
% 170.79/26.47 Sub-proof #728 shows that the following formulas are inconsistent:
% 170.79/26.47 ----------------------------------------------------------------
% 170.79/26.47 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.79/26.47 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.79/26.47 (2) ~ (all_52_6 = all_52_14)
% 170.79/26.47 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.79/26.47 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.79/26.47 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.47 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.47 (5) all_58_14 = e2
% 170.79/26.47 (6) ~ (all_52_14 = all_4_2)
% 170.79/26.47 (7) all_54_14 = all_52_11
% 170.79/26.47 (8) ~ (all_52_1 = all_52_2)
% 170.79/26.47 (9) ~ (all_4_2 = e2)
% 170.79/26.47 (10) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.79/26.47 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.79/26.47 (11) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.47 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.79/26.47 (12) all_58_9 = e2
% 170.79/26.47 (13) all_54_12 = all_52_3
% 170.79/26.47 (14) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 170.79/26.47 (15) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 170.79/26.47 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 170.79/26.47 (16) all_54_6 = all_52_9
% 170.79/26.47 (17) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.47 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.47 (18) ~ (all_52_11 = all_4_2)
% 170.79/26.47 (19) ~ (all_52_1 = all_8_2)
% 170.79/26.47 (20) ~ (all_8_2 = e3)
% 170.79/26.47 (21) all_58_6 = e1
% 170.79/26.47 (22) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.79/26.47 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.79/26.47 (23) ~ (all_6_2 = e3)
% 170.79/26.47 (24) ~ (all_52_13 = all_8_2)
% 170.79/26.47 (25) ~ (all_4_2 = e1)
% 170.79/26.47 (26) ~ (all_52_1 = all_52_13)
% 170.79/26.47 (27) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.47 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.47 (28) ~ (all_52_6 = all_52_7)
% 170.79/26.47 (29) ~ (e3 = e1)
% 170.79/26.47 (30) op(e3, e3) = e1
% 170.79/26.47 (31) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.47 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.79/26.47 e1)
% 170.79/26.47 (32) op(e1, e3) = all_52_2
% 170.79/26.47 (33) op(e3, e1) = all_52_8
% 170.79/26.47 (34) ~ (all_52_9 = all_52_11)
% 170.79/26.47 (35) ~ (all_52_2 = all_52_6)
% 170.79/26.47 (36) ~ (e1 = e0)
% 170.79/26.47 (37) ~ (all_52_6 = all_8_2)
% 170.79/26.47 (38) all_56_10 = e1
% 170.79/26.47 (39) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.79/26.47 | (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 170.79/26.47 e3)
% 170.79/26.47 (40) op(e1, e2) = all_52_6
% 170.79/26.47 (41) ~ (all_52_3 = all_4_2)
% 170.79/26.47 (42) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.79/26.47 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.79/26.47 (43) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 170.79/26.47 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.79/26.47 (44) op(e2, e3) = all_52_1
% 170.79/26.47 (45) ~ (all_52_3 = all_52_7)
% 170.79/26.47 (46) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 170.79/26.47 (47) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 170.79/26.47 (48) all_54_15 = all_4_2
% 170.79/26.47 (49) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 170.79/26.47 (50) op(e2, e2) = all_8_2
% 170.79/26.47 (51) ~ (all_6_2 = e2)
% 170.79/26.47 (52) op(e1, e1) = all_6_2
% 170.79/26.47 (53) ~ (all_52_6 = e2)
% 170.79/26.47 (54) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 170.79/26.47 (55) all_54_4 = all_52_1
% 170.79/26.47 (56) ~ (e3 = e0)
% 170.79/26.47 (57) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.47 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.47 (58) ~ (all_52_13 = all_52_14)
% 170.79/26.47 (59) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.79/26.47 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.79/26.47 (60) ~ (all_52_2 = all_52_14)
% 170.79/26.47 (61) all_58_4 = e1
% 170.79/26.47 (62) op(e0, e0) = all_4_2
% 170.79/26.47 (63) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.79/26.47 (64) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.47 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.79/26.47 (65) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 170.79/26.47 (66) all_54_11 = all_52_14
% 170.79/26.47 (67) ~ (all_52_3 = all_52_11)
% 170.79/26.47 (68) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.79/26.47 (69) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.79/26.47 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.79/26.47 (70) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.47 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.47 (71) all_58_3 = e2
% 170.79/26.47 (72) ~ (all_52_7 = all_52_11)
% 170.79/26.47 (73) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.47 (74) ~ (e2 = e0)
% 170.79/26.47 (75) ~ (all_52_13 = all_4_2)
% 170.79/26.47 (76) ~ (all_52_9 = all_8_2)
% 170.79/26.47 (77) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.79/26.47 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.79/26.47 (78) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.79/26.47 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.79/26.47 (79) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.79/26.47 (80) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.47 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.47 (81) all_54_5 = all_8_2
% 170.79/26.48 (82) ~ (e2 = e1)
% 170.79/26.48 (83) op(e3, e2) = all_52_4
% 170.79/26.48 (84) ~ (all_52_1 = all_52_9)
% 170.79/26.48 (85) ~ (all_8_2 = e1)
% 170.79/26.48 (86) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.79/26.48 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.79/26.48 (87) all_54_9 = all_52_6
% 170.79/26.48 (88) op(e0, e2) = all_52_7
% 170.79/26.48 (89) ~ (all_52_4 = e1)
% 170.79/26.48 (90) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.79/26.48 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.79/26.48 (91) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 170.79/26.48 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 170.79/26.48 (92) op(e1, e3) = e1
% 170.79/26.48 (93) ~ (all_52_9 = all_52_13)
% 170.79/26.48 (94) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.48 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.79/26.48 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.79/26.48 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.79/26.48 (95) ~ (all_52_2 = all_52_3)
% 170.79/26.48 (96) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 170.79/26.48 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 170.79/26.48 (97) op(e2, e0) = all_52_13
% 170.79/26.48 (98) ~ (e3 = e2)
% 170.79/26.48
% 170.79/26.48 Begin of proof
% 170.79/26.48 |
% 170.79/26.48 | BETA: splitting (22) gives:
% 170.79/26.48 |
% 170.79/26.48 | Case 1:
% 170.79/26.48 | |
% 170.79/26.48 | | (99) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 170.79/26.48 | | e2)
% 170.79/26.48 | |
% 170.79/26.48 | | BETA: splitting (99) gives:
% 170.79/26.48 | |
% 170.79/26.48 | | Case 1:
% 170.79/26.48 | | |
% 170.79/26.48 | | | (100) all_58_6 = e2 & op(e1, e3) = e2
% 170.79/26.48 | | |
% 170.79/26.48 | | | ALPHA: (100) implies:
% 170.79/26.48 | | | (101) all_58_6 = e2
% 170.79/26.48 | | |
% 170.79/26.48 | | | COMBINE_EQS: (21), (101) imply:
% 170.79/26.48 | | | (102) e2 = e1
% 170.79/26.48 | | |
% 170.79/26.48 | | | COMBINE_EQS: (12), (102) imply:
% 170.79/26.48 | | | (103) all_58_9 = e1
% 170.79/26.48 | | |
% 170.79/26.48 | | | REF_CLOSE: (1), (3), (4), (9), (11), (15), (17), (20), (22), (23), (27),
% 170.79/26.48 | | | (29), (30), (31), (33), (36), (38), (42), (43), (50), (51),
% 170.79/26.48 | | | (52), (56), (57), (59), (62), (64), (69), (70), (71), (73),
% 170.79/26.48 | | | (74), (77), (78), (79), (80), (82), (83), (86), (88), (89),
% 170.79/26.48 | | | (90), (91), (94), (96), (98), (103) are inconsistent by
% 170.79/26.48 | | | sub-proof #799.
% 170.79/26.48 | | |
% 170.79/26.48 | | Case 2:
% 170.79/26.48 | | |
% 170.79/26.48 | | | (104) all_58_7 = e2 & op(e1, e2) = e2
% 170.79/26.48 | | |
% 170.79/26.48 | | | ALPHA: (104) implies:
% 170.79/26.48 | | | (105) op(e1, e2) = e2
% 170.79/26.48 | | |
% 170.79/26.48 | | | REF_CLOSE: (40), (53), (73), (105) are inconsistent by sub-proof #986.
% 170.79/26.48 | | |
% 170.79/26.48 | | End of split
% 170.79/26.48 | |
% 170.79/26.48 | Case 2:
% 170.79/26.48 | |
% 170.79/26.48 | | (106) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 170.79/26.48 | | e2)
% 170.79/26.48 | |
% 170.79/26.48 | | BETA: splitting (106) gives:
% 170.79/26.48 | |
% 170.79/26.48 | | Case 1:
% 170.79/26.48 | | |
% 170.79/26.48 | | | (107) all_58_8 = e2 & op(e1, e1) = e2
% 170.79/26.48 | | |
% 170.79/26.48 | | | REF_CLOSE: (51), (52), (73), (107) are inconsistent by sub-proof #845.
% 170.79/26.48 | | |
% 170.79/26.48 | | Case 2:
% 170.79/26.48 | | |
% 170.79/26.48 | | | (108) all_58_11 = e2 & op(e1, e0) = e2
% 170.79/26.48 | | |
% 170.79/26.48 | | | ALPHA: (108) implies:
% 170.79/26.48 | | | (109) all_58_11 = e2
% 170.79/26.48 | | |
% 170.79/26.48 | | | BETA: splitting (70) gives:
% 170.79/26.48 | | |
% 170.79/26.48 | | | Case 1:
% 170.79/26.48 | | | |
% 170.79/26.48 | | | | (110) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 170.79/26.48 | | | | = e3)
% 170.79/26.48 | | | |
% 170.79/26.48 | | | | BETA: splitting (110) gives:
% 170.79/26.48 | | | |
% 170.79/26.48 | | | | Case 1:
% 170.79/26.48 | | | | |
% 170.79/26.48 | | | | | (111) all_58_0 = e3 & op(e3, e3) = e3
% 170.79/26.48 | | | | |
% 170.79/26.48 | | | | | ALPHA: (111) implies:
% 170.79/26.48 | | | | | (112) all_58_0 = e3
% 170.79/26.48 | | | | | (113) op(e3, e3) = e3
% 170.79/26.48 | | | | |
% 170.79/26.48 | | | | | BETA: splitting (15) gives:
% 170.79/26.48 | | | | |
% 170.79/26.48 | | | | | Case 1:
% 170.79/26.48 | | | | | |
% 170.79/26.48 | | | | | | (114) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 170.79/26.48 | | | | | | e3) = e2)
% 170.79/26.48 | | | | | |
% 170.79/26.48 | | | | | | REF_CLOSE: (4), (29), (36), (44), (56), (57), (71), (73), (74),
% 170.79/26.48 | | | | | | (80), (82), (98), (113), (114) are inconsistent by
% 170.79/26.48 | | | | | | sub-proof #778.
% 170.79/26.48 | | | | | |
% 170.79/26.48 | | | | | Case 2:
% 170.79/26.48 | | | | | |
% 170.79/26.48 | | | | | | (115) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 &
% 170.79/26.48 | | | | | | op(e0, e3) = e2)
% 170.79/26.48 | | | | | |
% 170.79/26.48 | | | | | | BETA: splitting (115) gives:
% 170.79/26.48 | | | | | |
% 170.79/26.48 | | | | | | Case 1:
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | | (116) all_58_6 = e2 & op(e1, e3) = e2
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | | ALPHA: (116) implies:
% 170.79/26.48 | | | | | | | (117) all_58_6 = e2
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | | COMBINE_EQS: (21), (117) imply:
% 170.79/26.48 | | | | | | | (118) e2 = e1
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | | SIMP: (118) implies:
% 170.79/26.48 | | | | | | | (119) e2 = e1
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | | COMBINE_EQS: (12), (119) imply:
% 170.79/26.48 | | | | | | | (120) all_58_9 = e1
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | | REF_CLOSE: (1), (3), (4), (9), (11), (15), (17), (20), (22), (23),
% 170.79/26.48 | | | | | | | (27), (29), (30), (31), (33), (36), (38), (42), (43),
% 170.79/26.48 | | | | | | | (50), (51), (52), (56), (57), (59), (62), (64), (69),
% 170.79/26.48 | | | | | | | (70), (71), (73), (74), (77), (78), (79), (80), (82),
% 170.79/26.48 | | | | | | | (83), (86), (88), (89), (90), (91), (94), (96), (98),
% 170.79/26.48 | | | | | | | (120) are inconsistent by sub-proof #799.
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | Case 2:
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | | (121) all_58_12 = e2 & op(e0, e3) = e2
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | | ALPHA: (121) implies:
% 170.79/26.48 | | | | | | | (122) all_58_12 = e2
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | | BETA: splitting (10) gives:
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | |
% 170.79/26.48 | | | | | | | | (123) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 170.79/26.48 | | | | | | | | op(e2, e3) = e0)
% 170.79/26.48 | | | | | | | |
% 170.79/26.48 | | | | | | | | BETA: splitting (123) gives:
% 170.79/26.48 | | | | | | | |
% 170.79/26.48 | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | (124) all_58_0 = e0 & op(e3, e3) = e0
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | ALPHA: (124) implies:
% 170.79/26.48 | | | | | | | | | (125) op(e3, e3) = e0
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | REF_CLOSE: (30), (36), (73), (125) are inconsistent by
% 170.79/26.48 | | | | | | | | | sub-proof #907.
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | (126) all_58_2 = e0 & op(e2, e3) = e0
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | ALPHA: (126) implies:
% 170.79/26.48 | | | | | | | | | (127) all_58_2 = e0
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | BETA: splitting (78) gives:
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | (128) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3
% 170.79/26.48 | | | | | | | | | | & op(e1, e2) = e3)
% 170.79/26.48 | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | BETA: splitting (128) gives:
% 170.79/26.48 | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | (129) all_58_6 = e3 & op(e1, e3) = e3
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | ALPHA: (129) implies:
% 170.79/26.48 | | | | | | | | | | | (130) op(e1, e3) = e3
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | REF_CLOSE: (29), (32), (73), (92), (130) are inconsistent by
% 170.79/26.48 | | | | | | | | | | | sub-proof #750.
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | (131) all_58_7 = e3 & op(e1, e2) = e3
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | ALPHA: (131) implies:
% 170.79/26.48 | | | | | | | | | | | (132) all_58_7 = e3
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | BETA: splitting (59) gives:
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | (133) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0
% 170.79/26.48 | | | | | | | | | | | | & op(e1, e2) = e0)
% 170.79/26.48 | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | REF_CLOSE: (32), (36), (56), (73), (92), (132), (133) are
% 170.79/26.48 | | | | | | | | | | | | inconsistent by sub-proof #747.
% 170.79/26.48 | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | (134) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 =
% 170.79/26.48 | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 170.79/26.48 | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | BETA: splitting (134) gives:
% 170.79/26.48 | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | (135) all_58_8 = e0 & op(e1, e1) = e0
% 170.79/26.48 | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | ALPHA: (135) implies:
% 170.79/26.48 | | | | | | | | | | | | | (136) all_58_8 = e0
% 170.79/26.48 | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | BETA: splitting (42) gives:
% 170.79/26.48 | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | (137) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 170.79/26.48 | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 170.79/26.48 | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 170.79/26.48 | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | (138) all_58_4 = e3 & op(e3, e1) = e3
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (29), (30), (36), (56), (61), (70),
% 170.79/26.48 | | | | | | | | | | | | | | | (73), (74), (98), (112), (138) are inconsistent by
% 170.79/26.48 | | | | | | | | | | | | | | | sub-proof #777.
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | (139) all_58_5 = e3 & op(e2, e1) = e3
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | (140) all_58_5 = e3
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | (141) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 =
% 170.79/26.48 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 170.79/26.48 | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | (142) all_58_9 = e1 & op(e3, e0) = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | (143) all_58_9 = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (9), (11), (15), (17), (20), (22),
% 170.79/26.48 | | | | | | | | | | | | | | | | | (23), (27), (29), (30), (31), (33), (36), (38),
% 170.79/26.48 | | | | | | | | | | | | | | | | | (42), (43), (50), (51), (52), (56), (57), (59),
% 170.79/26.48 | | | | | | | | | | | | | | | | | (62), (64), (69), (70), (71), (73), (74), (77),
% 170.79/26.48 | | | | | | | | | | | | | | | | | (78), (79), (80), (82), (83), (86), (88), (89),
% 170.79/26.48 | | | | | | | | | | | | | | | | | (90), (91), (94), (96), (98), (143) are
% 170.79/26.48 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #799.
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | (144) all_58_10 = e1 & op(e2, e0) = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | (145) all_58_10 = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | | (146) op(e2, e0) = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | (147) all_58_15 = e0 & op(e0, e0) = e0
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | (148) all_58_15 = e0
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (149) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (150) all_58_9 = e3 & op(e3, e0) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (151) all_58_9 = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (151) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (152) e3 = e2
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | SIMP: (152) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (153) e3 = e2
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (153) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (154) all_58_5 = e2
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (80) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (155) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | | (156) all_58_2 = e3 & op(e2, e3) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | | (157) all_58_2 = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (56), (57), (71), (73), (74), (146), (154),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | | (157) are inconsistent by sub-proof #797.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | | (158) all_58_3 = e3 & op(e2, e2) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (50), (73), (158) are inconsistent by
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | | sub-proof #973.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (159) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (29), (36), (56), (57), (71), (74), (82),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (98), (154), (159) are inconsistent by sub-proof
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | #746.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (160) all_58_10 = e3 & op(e2, e0) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (161) all_58_10 = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (161) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (162) e3 = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | SIMP: (162) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (163) e3 = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (112), (163) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (164) all_58_0 = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (29), (30), (36), (56), (61), (70),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (73), (74), (98), (164) are inconsistent by
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | sub-proof #788.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (165) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (166) all_58_11 = e3 & op(e1, e0) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (167) all_58_11 = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (29), (36), (51), (52), (73), (77), (82),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (98), (132), (136), (167) are inconsistent by
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | sub-proof #753.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (168) all_58_15 = e3 & op(e0, e0) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (56), (148), (168) are inconsistent by sub-proof
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | #812.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | (169) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 170.79/26.48 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 170.79/26.48 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | (170) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 170.79/26.48 | | | | | | | | | | | | | | | | | | e0) = e0)
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (171) all_58_9 = e0 & op(e3, e0) = e0
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (74), (171) are inconsistent by sub-proof
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | #745.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (172) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (173) all_58_10 = e0 & op(e2, e0) = e0
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (145), (173) are inconsistent by sub-proof
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | #925.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (174) all_58_11 = e0 & op(e1, e0) = e0
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (74), (109), (174) are inconsistent by sub-proof
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | #848.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | (175) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 =
% 170.79/26.48 | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 170.79/26.48 | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | (176) all_58_11 = e1 & op(e1, e0) = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | (177) all_58_11 = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | COMBINE_EQS: (109), (177) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | (178) e2 = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (178) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | (179) all_58_9 = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (9), (11), (15), (17), (20), (22),
% 170.79/26.48 | | | | | | | | | | | | | | | | | (23), (27), (29), (30), (31), (33), (36), (38),
% 170.79/26.48 | | | | | | | | | | | | | | | | | (42), (43), (50), (51), (52), (56), (57), (59),
% 170.79/26.48 | | | | | | | | | | | | | | | | | (62), (64), (69), (70), (71), (73), (74), (77),
% 170.79/26.48 | | | | | | | | | | | | | | | | | (78), (79), (80), (82), (83), (86), (88), (89),
% 170.79/26.48 | | | | | | | | | | | | | | | | | (90), (91), (94), (96), (98), (179) are
% 170.79/26.48 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #799.
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | (180) all_58_15 = e1 & op(e0, e0) = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | (181) all_58_15 = e1
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | (182) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (183) all_58_9 = e3 & op(e3, e0) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (184) all_58_9 = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (12), (184) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (185) e3 = e2
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | SIMP: (185) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (186) e3 = e2
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (186) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (187) all_58_5 = e2
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (29), (36), (50), (56), (57), (71),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (73), (74), (80), (82), (98), (127), (187) are
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (188) all_58_10 = e3 & op(e2, e0) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (189) all_58_10 = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | (190) op(e2, e0) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (191) (all_58_12 = e3 & op(e0, e3) = e3) | (all_58_13 =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (192) all_58_12 = e3 & op(e0, e3) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (193) all_58_12 = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (122), (193) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (194) e3 = e2
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (194) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (195) all_58_5 = e2
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (29), (36), (56), (57), (71), (74), (82),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (189), (195) are inconsistent by sub-proof #850.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (196) all_58_13 = e3 & op(e0, e2) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (197) op(e0, e2) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (8), (9), (13), (14), (16), (18),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (19), (24), (25), (26), (28), (32), (34), (35),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (37), (41), (45), (46), (47), (48), (49), (54),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (55), (58), (60), (63), (65), (66), (67), (68),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (72), (73), (75), (76), (81), (84), (85), (87),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (88), (92), (93), (95), (97), (190), (197) are
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #731.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | (198) (all_58_14 = e3 & op(e0, e1) = e3) | (all_58_15 =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (199) all_58_14 = e3 & op(e0, e1) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (200) all_58_14 = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5), (200) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (201) e3 = e2
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (201) imply:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (202) all_58_5 = e2
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (29), (36), (56), (57), (71), (74), (82),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (189), (202) are inconsistent by sub-proof #850.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (203) all_58_15 = e3 & op(e0, e0) = e3
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (27), (29), (30), (36), (56), (61), (70),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | (73), (74), (98), (112), (181), (203) are
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #752.
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | (204) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 170.79/26.48 | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (22), (27), (29), (30), (36), (51), (52),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | (56), (61), (70), (73), (74), (77), (82), (98),
% 170.79/26.48 | | | | | | | | | | | | | | | | | | (112), (132), (136), (181), (204) are inconsistent
% 170.79/26.48 | | | | | | | | | | | | | | | | | | by sub-proof #751.
% 170.79/26.48 | | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | (205) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 170.79/26.48 | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 170.79/26.48 | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 170.79/26.48 | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | (206) all_58_8 = e3 & op(e1, e1) = e3
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | REF_CLOSE: (23), (52), (73), (206) are inconsistent by
% 170.79/26.48 | | | | | | | | | | | | | | | sub-proof #961.
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | (207) all_58_14 = e3 & op(e0, e1) = e3
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | | REF_CLOSE: (5), (98), (207) are inconsistent by sub-proof
% 170.79/26.48 | | | | | | | | | | | | | | | #809.
% 170.79/26.48 | | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | (208) all_58_11 = e0 & op(e1, e0) = e0
% 170.79/26.48 | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | | REF_CLOSE: (74), (109), (208) are inconsistent by sub-proof
% 170.79/26.48 | | | | | | | | | | | | | #848.
% 170.79/26.48 | | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | (209) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3
% 170.79/26.48 | | | | | | | | | | & op(e1, e0) = e3)
% 170.79/26.48 | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | BETA: splitting (209) gives:
% 170.79/26.48 | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | (210) all_58_8 = e3 & op(e1, e1) = e3
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | REF_CLOSE: (23), (52), (73), (210) are inconsistent by
% 170.79/26.48 | | | | | | | | | | | sub-proof #961.
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | (211) all_58_11 = e3 & op(e1, e0) = e3
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | | REF_CLOSE: (98), (109), (211) are inconsistent by sub-proof
% 170.79/26.48 | | | | | | | | | | | #730.
% 170.79/26.48 | | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | | |
% 170.79/26.48 | | | | | | | | | End of split
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | End of split
% 170.79/26.48 | | | | | | | |
% 170.79/26.48 | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | |
% 170.79/26.48 | | | | | | | | (212) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 170.79/26.48 | | | | | | | | op(e0, e3) = e0)
% 170.79/26.48 | | | | | | | |
% 170.79/26.48 | | | | | | | | BETA: splitting (212) gives:
% 170.79/26.48 | | | | | | | |
% 170.79/26.48 | | | | | | | | Case 1:
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | (213) all_58_6 = e0 & op(e1, e3) = e0
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | ALPHA: (213) implies:
% 170.79/26.48 | | | | | | | | | (214) op(e1, e3) = e0
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | REF_CLOSE: (32), (36), (73), (92), (214) are inconsistent by
% 170.79/26.48 | | | | | | | | | sub-proof #749.
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | Case 2:
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | (215) all_58_12 = e0 & op(e0, e3) = e0
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | ALPHA: (215) implies:
% 170.79/26.48 | | | | | | | | | (216) all_58_12 = e0
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | | REF_CLOSE: (74), (122), (216) are inconsistent by sub-proof
% 170.79/26.48 | | | | | | | | | #729.
% 170.79/26.48 | | | | | | | | |
% 170.79/26.48 | | | | | | | | End of split
% 170.79/26.48 | | | | | | | |
% 170.79/26.48 | | | | | | | End of split
% 170.79/26.48 | | | | | | |
% 170.79/26.48 | | | | | | End of split
% 170.79/26.48 | | | | | |
% 170.79/26.48 | | | | | End of split
% 170.79/26.48 | | | | |
% 170.79/26.48 | | | | Case 2:
% 170.79/26.48 | | | | |
% 170.79/26.48 | | | | | (217) all_58_1 = e3 & op(e3, e2) = e3
% 170.79/26.48 | | | | |
% 170.79/26.48 | | | | | REF_CLOSE: (12), (27), (30), (36), (56), (61), (73), (74), (217) are
% 170.79/26.48 | | | | | inconsistent by sub-proof #791.
% 170.79/26.48 | | | | |
% 170.79/26.48 | | | | End of split
% 170.79/26.48 | | | |
% 170.79/26.48 | | | Case 2:
% 170.79/26.48 | | | |
% 170.79/26.48 | | | | (218) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 170.79/26.48 | | | | = e3)
% 170.79/26.48 | | | |
% 170.79/26.48 | | | | REF_CLOSE: (12), (29), (61), (98), (218) are inconsistent by sub-proof
% 170.79/26.48 | | | | #762.
% 170.79/26.48 | | | |
% 170.79/26.48 | | | End of split
% 170.79/26.48 | | |
% 170.79/26.48 | | End of split
% 170.79/26.48 | |
% 170.79/26.48 | End of split
% 170.79/26.48 |
% 170.79/26.48 End of proof
% 170.79/26.48
% 170.79/26.48 Sub-proof #729 shows that the following formulas are inconsistent:
% 170.79/26.48 ----------------------------------------------------------------
% 170.79/26.48 (1) all_58_12 = e2
% 170.79/26.48 (2) all_58_12 = e0
% 170.79/26.48 (3) ~ (e2 = e0)
% 170.79/26.48
% 170.79/26.48 Begin of proof
% 170.79/26.48 |
% 170.79/26.48 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.48 | (4) e2 = e0
% 170.79/26.48 |
% 170.79/26.48 | SIMP: (4) implies:
% 170.79/26.48 | (5) e2 = e0
% 170.79/26.48 |
% 170.79/26.48 | REDUCE: (3), (5) imply:
% 170.79/26.48 | (6) $false
% 170.79/26.48 |
% 170.79/26.48 | CLOSE: (6) is inconsistent.
% 170.79/26.48 |
% 170.79/26.48 End of proof
% 170.79/26.48
% 170.79/26.48 Sub-proof #730 shows that the following formulas are inconsistent:
% 170.79/26.48 ----------------------------------------------------------------
% 170.79/26.48 (1) all_58_11 = e3 & op(e1, e0) = e3
% 170.79/26.48 (2) all_58_11 = e2
% 170.79/26.48 (3) ~ (e3 = e2)
% 170.79/26.48
% 170.79/26.48 Begin of proof
% 170.79/26.48 |
% 170.79/26.48 | ALPHA: (1) implies:
% 170.79/26.48 | (4) all_58_11 = e3
% 170.79/26.48 |
% 170.79/26.48 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.48 | (5) e3 = e2
% 170.79/26.48 |
% 170.79/26.48 | REDUCE: (3), (5) imply:
% 170.79/26.48 | (6) $false
% 170.79/26.48 |
% 170.79/26.48 | CLOSE: (6) is inconsistent.
% 170.79/26.48 |
% 170.79/26.48 End of proof
% 170.79/26.48
% 170.79/26.48 Sub-proof #731 shows that the following formulas are inconsistent:
% 170.79/26.48 ----------------------------------------------------------------
% 170.79/26.48 (1) ~ (all_52_6 = all_52_14)
% 170.79/26.48 (2) ~ (all_52_14 = all_4_2)
% 170.79/26.48 (3) all_54_14 = all_52_11
% 170.79/26.48 (4) ~ (all_52_1 = all_52_2)
% 170.79/26.48 (5) ~ (all_4_2 = e2)
% 170.79/26.48 (6) all_54_12 = all_52_3
% 170.79/26.48 (7) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 170.79/26.48 (8) all_54_6 = all_52_9
% 170.79/26.48 (9) ~ (all_52_11 = all_4_2)
% 170.79/26.48 (10) op(e2, e0) = e3
% 170.79/26.48 (11) ~ (all_52_1 = all_8_2)
% 170.79/26.48 (12) ~ (all_52_13 = all_8_2)
% 170.79/26.48 (13) ~ (all_4_2 = e1)
% 170.79/26.48 (14) ~ (all_52_1 = all_52_13)
% 170.79/26.48 (15) ~ (all_52_6 = all_52_7)
% 170.79/26.48 (16) op(e1, e3) = all_52_2
% 170.79/26.48 (17) ~ (all_52_9 = all_52_11)
% 170.79/26.48 (18) ~ (all_52_2 = all_52_6)
% 170.79/26.48 (19) ~ (all_52_6 = all_8_2)
% 170.79/26.48 (20) ~ (all_52_3 = all_4_2)
% 170.79/26.48 (21) ~ (all_52_3 = all_52_7)
% 170.79/26.48 (22) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 170.79/26.48 (23) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 170.79/26.48 (24) all_54_15 = all_4_2
% 170.79/26.48 (25) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 170.79/26.48 (26) op(e0, e2) = e3
% 170.79/26.48 (27) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 170.79/26.48 (28) all_54_4 = all_52_1
% 170.79/26.48 (29) ~ (all_52_13 = all_52_14)
% 170.79/26.48 (30) ~ (all_52_2 = all_52_14)
% 170.79/26.48 (31) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.79/26.48 (32) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 170.79/26.49 (33) all_54_11 = all_52_14
% 170.79/26.49 (34) ~ (all_52_3 = all_52_11)
% 170.79/26.49 (35) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.79/26.49 (36) ~ (all_52_7 = all_52_11)
% 170.79/26.49 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.49 (38) ~ (all_52_13 = all_4_2)
% 170.79/26.49 (39) ~ (all_52_9 = all_8_2)
% 170.79/26.49 (40) all_54_5 = all_8_2
% 170.79/26.49 (41) ~ (all_52_1 = all_52_9)
% 170.79/26.49 (42) ~ (all_8_2 = e1)
% 170.79/26.49 (43) all_54_9 = all_52_6
% 170.79/26.49 (44) op(e0, e2) = all_52_7
% 170.79/26.49 (45) op(e1, e3) = e1
% 170.79/26.49 (46) ~ (all_52_9 = all_52_13)
% 170.79/26.49 (47) ~ (all_52_2 = all_52_3)
% 170.79/26.49 (48) op(e2, e0) = all_52_13
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | GROUND_INST: instantiating (37) with all_52_7, e3, e2, e0, simplifying with
% 170.79/26.49 | (26), (44) gives:
% 170.79/26.49 | (49) all_52_7 = e3
% 170.79/26.49 |
% 170.79/26.49 | GROUND_INST: instantiating (37) with all_52_2, e1, e3, e1, simplifying with
% 170.79/26.49 | (16), (45) gives:
% 170.79/26.49 | (50) all_52_2 = e1
% 170.79/26.49 |
% 170.79/26.49 | GROUND_INST: instantiating (37) with all_52_13, e3, e0, e2, simplifying with
% 170.79/26.49 | (10), (48) gives:
% 170.79/26.49 | (51) all_52_13 = e3
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (4), (50) imply:
% 170.79/26.49 | (52) ~ (all_52_1 = e1)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (14), (51) imply:
% 170.79/26.49 | (53) ~ (all_52_1 = e3)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (47), (50) imply:
% 170.79/26.49 | (54) ~ (all_52_3 = e1)
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (54) implies:
% 170.79/26.49 | (55) ~ (all_52_3 = e1)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (18), (50) imply:
% 170.79/26.49 | (56) ~ (all_52_6 = e1)
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (56) implies:
% 170.79/26.49 | (57) ~ (all_52_6 = e1)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (30), (50) imply:
% 170.79/26.49 | (58) ~ (all_52_14 = e1)
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (58) implies:
% 170.79/26.49 | (59) ~ (all_52_14 = e1)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (21), (49) imply:
% 170.79/26.49 | (60) ~ (all_52_3 = e3)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (15), (49) imply:
% 170.79/26.49 | (61) ~ (all_52_6 = e3)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (36), (49) imply:
% 170.79/26.49 | (62) ~ (all_52_11 = e3)
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (62) implies:
% 170.79/26.49 | (63) ~ (all_52_11 = e3)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (46), (51) imply:
% 170.79/26.49 | (64) ~ (all_52_9 = e3)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (29), (51) imply:
% 170.79/26.49 | (65) ~ (all_52_14 = e3)
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (65) implies:
% 170.79/26.49 | (66) ~ (all_52_14 = e3)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (12), (51) imply:
% 170.79/26.49 | (67) ~ (all_8_2 = e3)
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (67) implies:
% 170.79/26.49 | (68) ~ (all_8_2 = e3)
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (38), (51) imply:
% 170.79/26.49 | (69) ~ (all_4_2 = e3)
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (69) implies:
% 170.79/26.49 | (70) ~ (all_4_2 = e3)
% 170.79/26.49 |
% 170.79/26.49 | BETA: splitting (23) gives:
% 170.79/26.49 |
% 170.79/26.49 | Case 1:
% 170.79/26.49 | |
% 170.79/26.49 | | (71) all_54_15 = e3
% 170.79/26.49 | |
% 170.79/26.49 | | REF_CLOSE: (24), (70), (71) are inconsistent by sub-proof #992.
% 170.79/26.49 | |
% 170.79/26.49 | Case 2:
% 170.79/26.49 | |
% 170.79/26.49 | | (72) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 170.79/26.49 | |
% 170.79/26.49 | | BETA: splitting (72) gives:
% 170.79/26.49 | |
% 170.79/26.49 | | Case 1:
% 170.79/26.49 | | |
% 170.79/26.49 | | | (73) all_54_15 = e2
% 170.79/26.49 | | |
% 170.79/26.49 | | | REF_CLOSE: (5), (24), (73) are inconsistent by sub-proof #991.
% 170.79/26.49 | | |
% 170.79/26.49 | | Case 2:
% 170.79/26.49 | | |
% 170.79/26.49 | | | (74) all_54_15 = e1 | all_54_15 = e0
% 170.79/26.49 | | |
% 170.79/26.49 | | | BETA: splitting (74) gives:
% 170.79/26.49 | | |
% 170.79/26.49 | | | Case 1:
% 170.79/26.49 | | | |
% 170.79/26.49 | | | | (75) all_54_15 = e1
% 170.79/26.49 | | | |
% 170.79/26.49 | | | | REF_CLOSE: (13), (24), (75) are inconsistent by sub-proof #990.
% 170.79/26.49 | | | |
% 170.79/26.49 | | | Case 2:
% 170.79/26.49 | | | |
% 170.79/26.49 | | | | (76) all_54_15 = e0
% 170.79/26.49 | | | |
% 170.79/26.49 | | | | COMBINE_EQS: (24), (76) imply:
% 170.79/26.49 | | | | (77) all_4_2 = e0
% 170.79/26.49 | | | |
% 170.79/26.49 | | | | SIMP: (77) implies:
% 170.79/26.49 | | | | (78) all_4_2 = e0
% 170.79/26.49 | | | |
% 170.79/26.49 | | | | REDUCE: (20), (78) imply:
% 170.79/26.49 | | | | (79) ~ (all_52_3 = e0)
% 170.79/26.49 | | | |
% 170.79/26.49 | | | | REDUCE: (9), (78) imply:
% 170.79/26.49 | | | | (80) ~ (all_52_11 = e0)
% 170.79/26.49 | | | |
% 170.79/26.49 | | | | REDUCE: (2), (78) imply:
% 170.79/26.49 | | | | (81) ~ (all_52_14 = e0)
% 170.79/26.49 | | | |
% 170.79/26.49 | | | | BETA: splitting (22) gives:
% 170.79/26.49 | | | |
% 170.79/26.49 | | | | Case 1:
% 170.79/26.49 | | | | |
% 170.79/26.49 | | | | | (82) all_54_11 = e3
% 170.79/26.49 | | | | |
% 170.79/26.49 | | | | | REF_CLOSE: (33), (66), (82) are inconsistent by sub-proof #742.
% 170.79/26.49 | | | | |
% 170.79/26.49 | | | | Case 2:
% 170.79/26.49 | | | | |
% 170.79/26.49 | | | | | (83) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 170.79/26.49 | | | | |
% 170.79/26.49 | | | | | BETA: splitting (83) gives:
% 170.79/26.49 | | | | |
% 170.79/26.49 | | | | | Case 1:
% 170.79/26.49 | | | | | |
% 170.79/26.49 | | | | | | (84) all_54_11 = e2
% 170.79/26.49 | | | | | |
% 170.79/26.49 | | | | | | COMBINE_EQS: (33), (84) imply:
% 170.79/26.49 | | | | | | (85) all_52_14 = e2
% 170.79/26.49 | | | | | |
% 170.79/26.49 | | | | | | SIMP: (85) implies:
% 170.79/26.49 | | | | | | (86) all_52_14 = e2
% 170.79/26.49 | | | | | |
% 170.79/26.49 | | | | | | REDUCE: (1), (86) imply:
% 170.79/26.49 | | | | | | (87) ~ (all_52_6 = e2)
% 170.79/26.49 | | | | | |
% 170.79/26.49 | | | | | | BETA: splitting (27) gives:
% 170.79/26.49 | | | | | |
% 170.79/26.49 | | | | | | Case 1:
% 170.79/26.49 | | | | | | |
% 170.79/26.49 | | | | | | | (88) all_54_9 = e3
% 170.79/26.49 | | | | | | |
% 170.79/26.49 | | | | | | | REF_CLOSE: (43), (61), (88) are inconsistent by sub-proof #741.
% 170.79/26.49 | | | | | | |
% 170.79/26.49 | | | | | | Case 2:
% 170.79/26.49 | | | | | | |
% 170.79/26.49 | | | | | | | (89) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 170.79/26.49 | | | | | | |
% 170.79/26.49 | | | | | | | BETA: splitting (89) gives:
% 170.79/26.49 | | | | | | |
% 170.79/26.49 | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | |
% 170.79/26.49 | | | | | | | | (90) all_54_9 = e2
% 170.79/26.49 | | | | | | | |
% 170.79/26.49 | | | | | | | | REF_CLOSE: (43), (87), (90) are inconsistent by sub-proof #740.
% 170.79/26.49 | | | | | | | |
% 170.79/26.49 | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | |
% 170.79/26.49 | | | | | | | | (91) all_54_9 = e1 | all_54_9 = e0
% 170.79/26.49 | | | | | | | |
% 170.79/26.49 | | | | | | | | BETA: splitting (91) gives:
% 170.79/26.49 | | | | | | | |
% 170.79/26.49 | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | | (92) all_54_9 = e1
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | | REF_CLOSE: (43), (57), (92) are inconsistent by sub-proof
% 170.79/26.49 | | | | | | | | | #739.
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | | (93) all_54_9 = e0
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | | COMBINE_EQS: (43), (93) imply:
% 170.79/26.49 | | | | | | | | | (94) all_52_6 = e0
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | | SIMP: (94) implies:
% 170.79/26.49 | | | | | | | | | (95) all_52_6 = e0
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | | REDUCE: (19), (95) imply:
% 170.79/26.49 | | | | | | | | | (96) ~ (all_8_2 = e0)
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | | SIMP: (96) implies:
% 170.79/26.49 | | | | | | | | | (97) ~ (all_8_2 = e0)
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | | BETA: splitting (7) gives:
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | (98) all_54_5 = e3
% 170.79/26.49 | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | COMBINE_EQS: (40), (98) imply:
% 170.79/26.49 | | | | | | | | | | (99) all_8_2 = e3
% 170.79/26.49 | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | REDUCE: (68), (99) imply:
% 170.79/26.49 | | | | | | | | | | (100) $false
% 170.79/26.49 | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | CLOSE: (100) is inconsistent.
% 170.79/26.49 | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | (101) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 170.79/26.49 | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | BETA: splitting (101) gives:
% 170.79/26.49 | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | (102) all_54_5 = e2
% 170.79/26.49 | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | COMBINE_EQS: (40), (102) imply:
% 170.79/26.49 | | | | | | | | | | | (103) all_8_2 = e2
% 170.79/26.49 | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | REDUCE: (11), (103) imply:
% 170.79/26.49 | | | | | | | | | | | (104) ~ (all_52_1 = e2)
% 170.79/26.49 | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | REDUCE: (39), (103) imply:
% 170.79/26.49 | | | | | | | | | | | (105) ~ (all_52_9 = e2)
% 170.79/26.49 | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | BETA: splitting (32) gives:
% 170.79/26.49 | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | (106) all_54_4 = e3
% 170.79/26.49 | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | COMBINE_EQS: (28), (106) imply:
% 170.79/26.49 | | | | | | | | | | | | (107) all_52_1 = e3
% 170.79/26.49 | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | REDUCE: (53), (107) imply:
% 170.79/26.49 | | | | | | | | | | | | (108) $false
% 170.79/26.49 | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | CLOSE: (108) is inconsistent.
% 170.79/26.49 | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | (109) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 170.79/26.49 | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | BETA: splitting (109) gives:
% 170.79/26.49 | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | (110) all_54_4 = e2
% 170.79/26.49 | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | COMBINE_EQS: (28), (110) imply:
% 170.79/26.49 | | | | | | | | | | | | | (111) all_52_1 = e2
% 170.79/26.49 | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | REDUCE: (104), (111) imply:
% 170.79/26.49 | | | | | | | | | | | | | (112) $false
% 170.79/26.49 | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | CLOSE: (112) is inconsistent.
% 170.79/26.49 | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | (113) all_54_4 = e1 | all_54_4 = e0
% 170.79/26.49 | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | BETA: splitting (31) gives:
% 170.79/26.49 | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | (114) all_54_12 = e3
% 170.79/26.49 | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | REF_CLOSE: (6), (60), (114) are inconsistent by sub-proof
% 170.79/26.49 | | | | | | | | | | | | | | #738.
% 170.79/26.49 | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | (115) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 170.79/26.49 | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 170.79/26.49 | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | (116) all_54_12 = e2
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | COMBINE_EQS: (6), (116) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | (117) all_52_3 = e2
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | SIMP: (117) implies:
% 170.79/26.49 | | | | | | | | | | | | | | | (118) all_52_3 = e2
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | REDUCE: (34), (118) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | (119) ~ (all_52_11 = e2)
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | SIMP: (119) implies:
% 170.79/26.49 | | | | | | | | | | | | | | | (120) ~ (all_52_11 = e2)
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | (121) all_54_14 = e3
% 170.79/26.49 | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (63), (121) are inconsistent by sub-proof
% 170.79/26.49 | | | | | | | | | | | | | | | | #969.
% 170.79/26.49 | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | (122) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 170.79/26.49 | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 170.79/26.49 | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | (123) all_54_14 = e2
% 170.79/26.49 | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (120), (123) are inconsistent by sub-proof
% 170.79/26.49 | | | | | | | | | | | | | | | | | #737.
% 170.79/26.49 | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | (124) all_54_14 = e1 | all_54_14 = e0
% 170.79/26.49 | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 170.79/26.49 | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | (125) all_54_14 = e1
% 170.79/26.49 | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3), (125) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | (126) all_52_11 = e1
% 170.79/26.49 | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | SIMP: (126) implies:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | (127) all_52_11 = e1
% 170.79/26.49 | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | REDUCE: (17), (127) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | (128) ~ (all_52_9 = e1)
% 170.79/26.49 | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 170.79/26.49 | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | (129) all_54_6 = e3
% 170.79/26.49 | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (129) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | (130) all_52_9 = e3
% 170.79/26.49 | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | REDUCE: (64), (130) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | (131) $false
% 170.79/26.49 | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | CLOSE: (131) is inconsistent.
% 170.79/26.49 | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | (132) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 170.79/26.49 | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | (133) all_54_6 = e2
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (133) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | (134) all_52_9 = e2
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | REDUCE: (105), (134) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | (135) $false
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | CLOSE: (135) is inconsistent.
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | (136) all_54_6 = e1 | all_54_6 = e0
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | BETA: splitting (113) gives:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | (137) all_54_4 = e1
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (137) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | (138) all_52_1 = e1
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (138) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | (139) $false
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | CLOSE: (139) is inconsistent.
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | (140) all_54_4 = e0
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (28), (140) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | (141) all_52_1 = e0
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | REDUCE: (41), (141) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | (142) ~ (all_52_9 = e0)
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | SIMP: (142) implies:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | (143) ~ (all_52_9 = e0)
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | (144) all_54_6 = e1
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (144) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | (145) all_52_9 = e1
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (145) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | (146) $false
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | (147) all_54_6 = e0
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8), (147) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | (148) all_52_9 = e0
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (148) imply:
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | (149) $false
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | (150) all_54_14 = e0
% 170.79/26.49 | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (80), (150) are inconsistent by sub-proof
% 170.79/26.49 | | | | | | | | | | | | | | | | | | #965.
% 170.79/26.49 | | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | (151) all_54_12 = e1 | all_54_12 = e0
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | | REF_CLOSE: (6), (55), (79), (151) are inconsistent by
% 170.79/26.49 | | | | | | | | | | | | | | | sub-proof #736.
% 170.79/26.49 | | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | Case 2:
% 170.79/26.49 | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | (152) all_54_5 = e1 | all_54_5 = e0
% 170.79/26.49 | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | | REF_CLOSE: (40), (42), (97), (152) are inconsistent by
% 170.79/26.49 | | | | | | | | | | | sub-proof #735.
% 170.79/26.49 | | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | | |
% 170.79/26.49 | | | | | | | | | End of split
% 170.79/26.49 | | | | | | | | |
% 170.79/26.49 | | | | | | | | End of split
% 170.79/26.49 | | | | | | | |
% 170.79/26.49 | | | | | | | End of split
% 170.79/26.49 | | | | | | |
% 170.79/26.49 | | | | | | End of split
% 170.79/26.49 | | | | | |
% 170.79/26.49 | | | | | Case 2:
% 170.79/26.49 | | | | | |
% 170.79/26.49 | | | | | | (153) all_54_11 = e1 | all_54_11 = e0
% 170.79/26.49 | | | | | |
% 170.79/26.49 | | | | | | REF_CLOSE: (33), (59), (81), (153) are inconsistent by sub-proof
% 170.79/26.49 | | | | | | #732.
% 170.79/26.49 | | | | | |
% 170.79/26.49 | | | | | End of split
% 170.79/26.49 | | | | |
% 170.79/26.49 | | | | End of split
% 170.79/26.49 | | | |
% 170.79/26.49 | | | End of split
% 170.79/26.49 | | |
% 170.79/26.49 | | End of split
% 170.79/26.49 | |
% 170.79/26.49 | End of split
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #732 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_11 = e1 | all_54_11 = e0
% 170.79/26.49 (2) all_54_11 = all_52_14
% 170.79/26.49 (3) ~ (all_52_14 = e1)
% 170.79/26.49 (4) ~ (all_52_14 = e0)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | BETA: splitting (1) gives:
% 170.79/26.49 |
% 170.79/26.49 | Case 1:
% 170.79/26.49 | |
% 170.79/26.49 | | (5) all_54_11 = e1
% 170.79/26.49 | |
% 170.79/26.49 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #734.
% 170.79/26.49 | |
% 170.79/26.49 | Case 2:
% 170.79/26.49 | |
% 170.79/26.49 | | (6) all_54_11 = e0
% 170.79/26.49 | |
% 170.79/26.49 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #733.
% 170.79/26.49 | |
% 170.79/26.49 | End of split
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #733 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_11 = all_52_14
% 170.79/26.49 (2) all_54_11 = e0
% 170.79/26.49 (3) ~ (all_52_14 = e0)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.49 | (4) all_52_14 = e0
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (4) implies:
% 170.79/26.49 | (5) all_52_14 = e0
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.49 |
% 170.79/26.49 | CLOSE: (6) is inconsistent.
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #734 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_11 = all_52_14
% 170.79/26.49 (2) all_54_11 = e1
% 170.79/26.49 (3) ~ (all_52_14 = e1)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.49 | (4) all_52_14 = e1
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (4) implies:
% 170.79/26.49 | (5) all_52_14 = e1
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.49 |
% 170.79/26.49 | CLOSE: (6) is inconsistent.
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #735 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_5 = e1 | all_54_5 = e0
% 170.79/26.49 (2) all_54_5 = all_8_2
% 170.79/26.49 (3) ~ (all_8_2 = e1)
% 170.79/26.49 (4) ~ (all_8_2 = e0)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | BETA: splitting (1) gives:
% 170.79/26.49 |
% 170.79/26.49 | Case 1:
% 170.79/26.49 | |
% 170.79/26.49 | | (5) all_54_5 = e1
% 170.79/26.49 | |
% 170.79/26.49 | | COMBINE_EQS: (2), (5) imply:
% 170.79/26.49 | | (6) all_8_2 = e1
% 170.79/26.49 | |
% 170.79/26.49 | | REDUCE: (3), (6) imply:
% 170.79/26.49 | | (7) $false
% 170.79/26.49 | |
% 170.79/26.49 | | CLOSE: (7) is inconsistent.
% 170.79/26.49 | |
% 170.79/26.49 | Case 2:
% 170.79/26.49 | |
% 170.79/26.49 | | (8) all_54_5 = e0
% 170.79/26.49 | |
% 170.79/26.49 | | COMBINE_EQS: (2), (8) imply:
% 170.79/26.49 | | (9) all_8_2 = e0
% 170.79/26.49 | |
% 170.79/26.49 | | REDUCE: (4), (9) imply:
% 170.79/26.49 | | (10) $false
% 170.79/26.49 | |
% 170.79/26.49 | | CLOSE: (10) is inconsistent.
% 170.79/26.49 | |
% 170.79/26.49 | End of split
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #736 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_12 = e1 | all_54_12 = e0
% 170.79/26.49 (2) all_54_12 = all_52_3
% 170.79/26.49 (3) ~ (all_52_3 = e1)
% 170.79/26.49 (4) ~ (all_52_3 = e0)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | BETA: splitting (1) gives:
% 170.79/26.49 |
% 170.79/26.49 | Case 1:
% 170.79/26.49 | |
% 170.79/26.49 | | (5) all_54_12 = e1
% 170.79/26.49 | |
% 170.79/26.49 | | COMBINE_EQS: (2), (5) imply:
% 170.79/26.49 | | (6) all_52_3 = e1
% 170.79/26.49 | |
% 170.79/26.49 | | REDUCE: (3), (6) imply:
% 170.79/26.49 | | (7) $false
% 170.79/26.49 | |
% 170.79/26.49 | | CLOSE: (7) is inconsistent.
% 170.79/26.49 | |
% 170.79/26.49 | Case 2:
% 170.79/26.49 | |
% 170.79/26.49 | | (8) all_54_12 = e0
% 170.79/26.49 | |
% 170.79/26.49 | | COMBINE_EQS: (2), (8) imply:
% 170.79/26.49 | | (9) all_52_3 = e0
% 170.79/26.49 | |
% 170.79/26.49 | | REDUCE: (4), (9) imply:
% 170.79/26.49 | | (10) $false
% 170.79/26.49 | |
% 170.79/26.49 | | CLOSE: (10) is inconsistent.
% 170.79/26.49 | |
% 170.79/26.49 | End of split
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #737 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_14 = all_52_11
% 170.79/26.49 (2) all_54_14 = e2
% 170.79/26.49 (3) ~ (all_52_11 = e2)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.49 | (4) all_52_11 = e2
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (4) implies:
% 170.79/26.49 | (5) all_52_11 = e2
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.49 |
% 170.79/26.49 | CLOSE: (6) is inconsistent.
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #738 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_12 = all_52_3
% 170.79/26.49 (2) all_54_12 = e3
% 170.79/26.49 (3) ~ (all_52_3 = e3)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.49 | (4) all_52_3 = e3
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (4) implies:
% 170.79/26.49 | (5) all_52_3 = e3
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.49 |
% 170.79/26.49 | CLOSE: (6) is inconsistent.
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #739 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_9 = all_52_6
% 170.79/26.49 (2) all_54_9 = e1
% 170.79/26.49 (3) ~ (all_52_6 = e1)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.49 | (4) all_52_6 = e1
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (4) implies:
% 170.79/26.49 | (5) all_52_6 = e1
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.49 |
% 170.79/26.49 | CLOSE: (6) is inconsistent.
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #740 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_9 = all_52_6
% 170.79/26.49 (2) all_54_9 = e2
% 170.79/26.49 (3) ~ (all_52_6 = e2)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.49 | (4) all_52_6 = e2
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (4) implies:
% 170.79/26.49 | (5) all_52_6 = e2
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.49 |
% 170.79/26.49 | CLOSE: (6) is inconsistent.
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #741 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_9 = all_52_6
% 170.79/26.49 (2) all_54_9 = e3
% 170.79/26.49 (3) ~ (all_52_6 = e3)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.49 | (4) all_52_6 = e3
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (4) implies:
% 170.79/26.49 | (5) all_52_6 = e3
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.49 |
% 170.79/26.49 | CLOSE: (6) is inconsistent.
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #742 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_54_11 = all_52_14
% 170.79/26.49 (2) all_54_11 = e3
% 170.79/26.49 (3) ~ (all_52_14 = e3)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.49 | (4) all_52_14 = e3
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (4) implies:
% 170.79/26.49 | (5) all_52_14 = e3
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.49 |
% 170.79/26.49 | CLOSE: (6) is inconsistent.
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #743 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.49 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.49 (2) ~ (all_8_2 = e3)
% 170.79/26.49 (3) ~ (e3 = e1)
% 170.79/26.49 (4) ~ (e1 = e0)
% 170.79/26.49 (5) op(e2, e2) = all_8_2
% 170.79/26.49 (6) ~ (e3 = e0)
% 170.79/26.49 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.49 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.49 (8) all_58_3 = e2
% 170.79/26.49 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.49 (10) ~ (e2 = e0)
% 170.79/26.49 (11) all_58_5 = e2
% 170.79/26.49 (12) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.49 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.49 (13) ~ (e2 = e1)
% 170.79/26.49 (14) all_58_2 = e0
% 170.79/26.49 (15) ~ (e3 = e2)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | BETA: splitting (12) gives:
% 170.79/26.49 |
% 170.79/26.49 | Case 1:
% 170.79/26.49 | |
% 170.79/26.49 | | (16) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.79/26.49 | | e3)
% 170.79/26.49 | |
% 170.79/26.49 | | BETA: splitting (16) gives:
% 170.79/26.49 | |
% 170.79/26.49 | | Case 1:
% 170.79/26.49 | | |
% 170.79/26.49 | | | (17) all_58_2 = e3 & op(e2, e3) = e3
% 170.79/26.49 | | |
% 170.79/26.49 | | | REF_CLOSE: (6), (14), (17) are inconsistent by sub-proof #744.
% 170.79/26.49 | | |
% 170.79/26.49 | | Case 2:
% 170.79/26.49 | | |
% 170.79/26.49 | | | (18) all_58_3 = e3 & op(e2, e2) = e3
% 170.79/26.49 | | |
% 170.79/26.49 | | | REF_CLOSE: (2), (5), (9), (18) are inconsistent by sub-proof #973.
% 170.79/26.49 | | |
% 170.79/26.49 | | End of split
% 170.79/26.49 | |
% 170.79/26.49 | Case 2:
% 170.79/26.49 | |
% 170.79/26.49 | | (19) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 170.79/26.49 | | e3)
% 170.79/26.49 | |
% 170.79/26.49 | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (11), (13), (15), (19) are
% 170.79/26.49 | | inconsistent by sub-proof #746.
% 170.79/26.49 | |
% 170.79/26.49 | End of split
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #744 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_58_2 = e3 & op(e2, e3) = e3
% 170.79/26.49 (2) all_58_2 = e0
% 170.79/26.49 (3) ~ (e3 = e0)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | ALPHA: (1) implies:
% 170.79/26.49 | (4) all_58_2 = e3
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.49 | (5) e3 = e0
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.49 |
% 170.79/26.49 | CLOSE: (6) is inconsistent.
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #745 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_58_9 = e0 & op(e3, e0) = e0
% 170.79/26.49 (2) all_58_9 = e2
% 170.79/26.49 (3) ~ (e2 = e0)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | ALPHA: (1) implies:
% 170.79/26.49 | (4) all_58_9 = e0
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.49 | (5) e2 = e0
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.49 |
% 170.79/26.49 | CLOSE: (6) is inconsistent.
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #746 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.49 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.49 (2) ~ (e3 = e1)
% 170.79/26.49 (3) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.49 (4) ~ (e1 = e0)
% 170.79/26.49 (5) ~ (e3 = e0)
% 170.79/26.49 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.49 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.49 (7) all_58_3 = e2
% 170.79/26.49 (8) ~ (e2 = e0)
% 170.79/26.49 (9) all_58_5 = e2
% 170.79/26.49 (10) ~ (e2 = e1)
% 170.79/26.49 (11) ~ (e3 = e2)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | BETA: splitting (3) gives:
% 170.79/26.49 |
% 170.79/26.49 | Case 1:
% 170.79/26.49 | |
% 170.79/26.49 | | (12) all_58_5 = e3 & op(e2, e1) = e3
% 170.79/26.49 | |
% 170.79/26.49 | | REF_CLOSE: (9), (11), (12) are inconsistent by sub-proof #936.
% 170.79/26.49 | |
% 170.79/26.49 | Case 2:
% 170.79/26.49 | |
% 170.79/26.49 | | (13) all_58_10 = e3 & op(e2, e0) = e3
% 170.79/26.49 | |
% 170.79/26.49 | | ALPHA: (13) implies:
% 170.79/26.49 | | (14) all_58_10 = e3
% 170.79/26.49 | |
% 170.79/26.49 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (14) are
% 170.79/26.49 | | inconsistent by sub-proof #850.
% 170.79/26.49 | |
% 170.79/26.49 | End of split
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #747 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0)
% 170.79/26.49 (2) op(e1, e3) = all_52_2
% 170.79/26.49 (3) ~ (e1 = e0)
% 170.79/26.49 (4) ~ (e3 = e0)
% 170.79/26.49 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.49 (6) op(e1, e3) = e1
% 170.79/26.49 (7) all_58_7 = e3
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | BETA: splitting (1) gives:
% 170.79/26.49 |
% 170.79/26.49 | Case 1:
% 170.79/26.49 | |
% 170.79/26.49 | | (8) all_58_6 = e0 & op(e1, e3) = e0
% 170.79/26.49 | |
% 170.79/26.49 | | ALPHA: (8) implies:
% 170.79/26.49 | | (9) op(e1, e3) = e0
% 170.79/26.49 | |
% 170.79/26.49 | | REF_CLOSE: (2), (3), (5), (6), (9) are inconsistent by sub-proof #749.
% 170.79/26.49 | |
% 170.79/26.49 | Case 2:
% 170.79/26.49 | |
% 170.79/26.49 | | (10) all_58_7 = e0 & op(e1, e2) = e0
% 170.79/26.49 | |
% 170.79/26.49 | | ALPHA: (10) implies:
% 170.79/26.49 | | (11) all_58_7 = e0
% 170.79/26.49 | |
% 170.79/26.49 | | REF_CLOSE: (4), (7), (11) are inconsistent by sub-proof #748.
% 170.79/26.49 | |
% 170.79/26.49 | End of split
% 170.79/26.49 |
% 170.79/26.49 End of proof
% 170.79/26.49
% 170.79/26.49 Sub-proof #748 shows that the following formulas are inconsistent:
% 170.79/26.49 ----------------------------------------------------------------
% 170.79/26.49 (1) all_58_7 = e3
% 170.79/26.49 (2) all_58_7 = e0
% 170.79/26.49 (3) ~ (e3 = e0)
% 170.79/26.49
% 170.79/26.49 Begin of proof
% 170.79/26.49 |
% 170.79/26.49 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.49 | (4) e3 = e0
% 170.79/26.49 |
% 170.79/26.49 | SIMP: (4) implies:
% 170.79/26.49 | (5) e3 = e0
% 170.79/26.49 |
% 170.79/26.49 | REDUCE: (3), (5) imply:
% 170.79/26.49 | (6) $false
% 170.79/26.50 |
% 170.79/26.50 | CLOSE: (6) is inconsistent.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #749 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) op(e1, e3) = all_52_2
% 170.79/26.50 (2) ~ (e1 = e0)
% 170.79/26.50 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.50 (4) op(e1, e3) = e0
% 170.79/26.50 (5) op(e1, e3) = e1
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | GROUND_INST: instantiating (3) with all_52_2, e0, e3, e1, simplifying with
% 170.79/26.50 | (1), (4) gives:
% 170.79/26.50 | (6) all_52_2 = e0
% 170.79/26.50 |
% 170.79/26.50 | GROUND_INST: instantiating (3) with all_52_2, e1, e3, e1, simplifying with
% 170.79/26.50 | (1), (5) gives:
% 170.79/26.50 | (7) all_52_2 = e1
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (6), (7) imply:
% 170.79/26.50 | (8) e1 = e0
% 170.79/26.50 |
% 170.79/26.50 | SIMP: (8) implies:
% 170.79/26.50 | (9) e1 = e0
% 170.79/26.50 |
% 170.79/26.50 | REDUCE: (2), (9) imply:
% 170.79/26.50 | (10) $false
% 170.79/26.50 |
% 170.79/26.50 | CLOSE: (10) is inconsistent.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #750 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) ~ (e3 = e1)
% 170.79/26.50 (2) op(e1, e3) = all_52_2
% 170.79/26.50 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.50 (4) op(e1, e3) = e3
% 170.79/26.50 (5) op(e1, e3) = e1
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | GROUND_INST: instantiating (3) with all_52_2, e1, e3, e1, simplifying with
% 170.79/26.50 | (2), (5) gives:
% 170.79/26.50 | (6) all_52_2 = e1
% 170.79/26.50 |
% 170.79/26.50 | GROUND_INST: instantiating (3) with all_52_2, e3, e3, e1, simplifying with
% 170.79/26.50 | (2), (4) gives:
% 170.79/26.50 | (7) all_52_2 = e3
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (6), (7) imply:
% 170.79/26.50 | (8) e3 = e1
% 170.79/26.50 |
% 170.79/26.50 | REDUCE: (1), (8) imply:
% 170.79/26.50 | (9) $false
% 170.79/26.50 |
% 170.79/26.50 | CLOSE: (9) is inconsistent.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #751 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_15 = e1
% 170.79/26.50 (2) all_58_9 = e2
% 170.79/26.50 (3) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.79/26.50 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.79/26.50 (4) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.50 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.50 (5) ~ (e3 = e1)
% 170.79/26.50 (6) op(e3, e3) = e1
% 170.79/26.50 (7) ~ (e1 = e0)
% 170.79/26.50 (8) all_58_8 = e0
% 170.79/26.50 (9) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.79/26.50 (10) ~ (all_6_2 = e2)
% 170.79/26.50 (11) op(e1, e1) = all_6_2
% 170.79/26.50 (12) ~ (e3 = e0)
% 170.79/26.50 (13) all_58_4 = e1
% 170.79/26.50 (14) all_58_0 = e3
% 170.79/26.50 (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.50 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.50 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.50 (17) ~ (e2 = e0)
% 170.79/26.50 (18) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.79/26.50 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.79/26.50 (19) ~ (e2 = e1)
% 170.79/26.50 (20) all_58_7 = e3
% 170.79/26.50 (21) ~ (e3 = e2)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | BETA: splitting (9) gives:
% 170.79/26.50 |
% 170.79/26.50 | Case 1:
% 170.79/26.50 | |
% 170.79/26.50 | | (22) all_58_11 = e3 & op(e1, e0) = e3
% 170.79/26.50 | |
% 170.79/26.50 | | ALPHA: (22) implies:
% 170.79/26.50 | | (23) all_58_11 = e3
% 170.79/26.50 | |
% 170.79/26.50 | | REF_CLOSE: (3), (5), (7), (8), (10), (11), (16), (18), (19), (20), (21),
% 170.79/26.50 | | (23) are inconsistent by sub-proof #753.
% 170.79/26.50 | |
% 170.79/26.50 | Case 2:
% 170.79/26.50 | |
% 170.79/26.50 | | (24) all_58_15 = e3 & op(e0, e0) = e3
% 170.79/26.50 | |
% 170.79/26.50 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (12), (13), (14), (15), (16), (17),
% 170.79/26.50 | | (21), (24) are inconsistent by sub-proof #752.
% 170.79/26.50 | |
% 170.79/26.50 | End of split
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #752 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_15 = e1
% 170.79/26.50 (2) all_58_9 = e2
% 170.79/26.50 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.50 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.50 (4) ~ (e3 = e1)
% 170.79/26.50 (5) op(e3, e3) = e1
% 170.79/26.50 (6) ~ (e1 = e0)
% 170.79/26.50 (7) ~ (e3 = e0)
% 170.79/26.50 (8) all_58_4 = e1
% 170.79/26.50 (9) all_58_0 = e3
% 170.79/26.50 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.50 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.50 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.50 (12) ~ (e2 = e0)
% 170.79/26.50 (13) all_58_15 = e3 & op(e0, e0) = e3
% 170.79/26.50 (14) ~ (e3 = e2)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | ALPHA: (13) implies:
% 170.79/26.50 | (15) all_58_15 = e3
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (1), (15) imply:
% 170.79/26.50 | (16) e3 = e1
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (9), (16) imply:
% 170.79/26.50 | (17) all_58_0 = e1
% 170.79/26.50 |
% 170.79/26.50 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14), (17) are
% 170.79/26.50 | inconsistent by sub-proof #788.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #753 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.79/26.50 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.79/26.50 (2) ~ (e3 = e1)
% 170.79/26.50 (3) ~ (e1 = e0)
% 170.79/26.50 (4) all_58_8 = e0
% 170.79/26.50 (5) ~ (all_6_2 = e2)
% 170.79/26.50 (6) op(e1, e1) = all_6_2
% 170.79/26.50 (7) all_58_11 = e3
% 170.79/26.50 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.50 (9) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.79/26.50 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.79/26.50 (10) ~ (e2 = e1)
% 170.79/26.50 (11) all_58_7 = e3
% 170.79/26.50 (12) ~ (e3 = e2)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | BETA: splitting (1) gives:
% 170.79/26.50 |
% 170.79/26.50 | Case 1:
% 170.79/26.50 | |
% 170.79/26.50 | | (13) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 170.79/26.50 | | e2)
% 170.79/26.50 | |
% 170.79/26.50 | | BETA: splitting (13) gives:
% 170.79/26.50 | |
% 170.79/26.50 | | Case 1:
% 170.79/26.50 | | |
% 170.79/26.50 | | | (14) all_58_6 = e2 & op(e1, e3) = e2
% 170.79/26.50 | | |
% 170.79/26.50 | | | ALPHA: (14) implies:
% 170.79/26.50 | | | (15) all_58_6 = e2
% 170.79/26.50 | | |
% 170.79/26.50 | | | BETA: splitting (9) gives:
% 170.79/26.50 | | |
% 170.79/26.50 | | | Case 1:
% 170.79/26.50 | | | |
% 170.79/26.50 | | | | (16) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2)
% 170.79/26.50 | | | | = e1)
% 170.79/26.50 | | | |
% 170.79/26.50 | | | | BETA: splitting (16) gives:
% 170.79/26.50 | | | |
% 170.79/26.50 | | | | Case 1:
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | | (17) all_58_6 = e1 & op(e1, e3) = e1
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | | REF_CLOSE: (10), (15), (17) are inconsistent by sub-proof #774.
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | Case 2:
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | | (18) all_58_7 = e1 & op(e1, e2) = e1
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | | REF_CLOSE: (2), (11), (18) are inconsistent by sub-proof #757.
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | End of split
% 170.79/26.50 | | | |
% 170.79/26.50 | | | Case 2:
% 170.79/26.50 | | | |
% 170.79/26.50 | | | | (19) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0)
% 170.79/26.50 | | | | = e1)
% 170.79/26.50 | | | |
% 170.79/26.50 | | | | BETA: splitting (19) gives:
% 170.79/26.50 | | | |
% 170.79/26.50 | | | | Case 1:
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | | (20) all_58_8 = e1 & op(e1, e1) = e1
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | | REF_CLOSE: (3), (4), (20) are inconsistent by sub-proof #756.
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | Case 2:
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | | (21) all_58_11 = e1 & op(e1, e0) = e1
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | | ALPHA: (21) implies:
% 170.79/26.50 | | | | | (22) all_58_11 = e1
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | | REF_CLOSE: (2), (7), (22) are inconsistent by sub-proof #755.
% 170.79/26.50 | | | | |
% 170.79/26.50 | | | | End of split
% 170.79/26.50 | | | |
% 170.79/26.50 | | | End of split
% 170.79/26.50 | | |
% 170.79/26.50 | | Case 2:
% 170.79/26.50 | | |
% 170.79/26.50 | | | (23) all_58_7 = e2 & op(e1, e2) = e2
% 170.79/26.50 | | |
% 170.79/26.50 | | | REF_CLOSE: (11), (12), (23) are inconsistent by sub-proof #754.
% 170.79/26.50 | | |
% 170.79/26.50 | | End of split
% 170.79/26.50 | |
% 170.79/26.50 | Case 2:
% 170.79/26.50 | |
% 170.79/26.50 | | (24) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 170.79/26.50 | | e2)
% 170.79/26.50 | |
% 170.79/26.50 | | BETA: splitting (24) gives:
% 170.79/26.50 | |
% 170.79/26.50 | | Case 1:
% 170.79/26.50 | | |
% 170.79/26.50 | | | (25) all_58_8 = e2 & op(e1, e1) = e2
% 170.79/26.50 | | |
% 170.79/26.50 | | | REF_CLOSE: (5), (6), (8), (25) are inconsistent by sub-proof #845.
% 170.79/26.50 | | |
% 170.79/26.50 | | Case 2:
% 170.79/26.50 | | |
% 170.79/26.50 | | | (26) all_58_11 = e2 & op(e1, e0) = e2
% 170.79/26.50 | | |
% 170.79/26.50 | | | ALPHA: (26) implies:
% 170.79/26.50 | | | (27) all_58_11 = e2
% 170.79/26.50 | | |
% 170.79/26.50 | | | REF_CLOSE: (7), (12), (27) are inconsistent by sub-proof #892.
% 170.79/26.50 | | |
% 170.79/26.50 | | End of split
% 170.79/26.50 | |
% 170.79/26.50 | End of split
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #754 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_7 = e2 & op(e1, e2) = e2
% 170.79/26.50 (2) all_58_7 = e3
% 170.79/26.50 (3) ~ (e3 = e2)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | ALPHA: (1) implies:
% 170.79/26.50 | (4) all_58_7 = e2
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.50 | (5) e3 = e2
% 170.79/26.50 |
% 170.79/26.50 | REDUCE: (3), (5) imply:
% 170.79/26.50 | (6) $false
% 170.79/26.50 |
% 170.79/26.50 | CLOSE: (6) is inconsistent.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #755 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_11 = e3
% 170.79/26.50 (2) all_58_11 = e1
% 170.79/26.50 (3) ~ (e3 = e1)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.50 | (4) e3 = e1
% 170.79/26.50 |
% 170.79/26.50 | SIMP: (4) implies:
% 170.79/26.50 | (5) e3 = e1
% 170.79/26.50 |
% 170.79/26.50 | REDUCE: (3), (5) imply:
% 170.79/26.50 | (6) $false
% 170.79/26.50 |
% 170.79/26.50 | CLOSE: (6) is inconsistent.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #756 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_8 = e1 & op(e1, e1) = e1
% 170.79/26.50 (2) all_58_8 = e0
% 170.79/26.50 (3) ~ (e1 = e0)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | ALPHA: (1) implies:
% 170.79/26.50 | (4) all_58_8 = e1
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.50 | (5) e1 = e0
% 170.79/26.50 |
% 170.79/26.50 | REDUCE: (3), (5) imply:
% 170.79/26.50 | (6) $false
% 170.79/26.50 |
% 170.79/26.50 | CLOSE: (6) is inconsistent.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #757 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_7 = e1 & op(e1, e2) = e1
% 170.79/26.50 (2) all_58_7 = e3
% 170.79/26.50 (3) ~ (e3 = e1)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | ALPHA: (1) implies:
% 170.79/26.50 | (4) all_58_7 = e1
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.50 | (5) e3 = e1
% 170.79/26.50 |
% 170.79/26.50 | REDUCE: (3), (5) imply:
% 170.79/26.50 | (6) $false
% 170.79/26.50 |
% 170.79/26.50 | CLOSE: (6) is inconsistent.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #758 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_10 = e0
% 170.79/26.50 (2) all_58_9 = e2
% 170.79/26.50 (3) ~ (all_8_2 = e3)
% 170.79/26.50 (4) ~ (e3 = e1)
% 170.79/26.50 (5) ~ (e1 = e0)
% 170.79/26.50 (6) all_58_5 = e3
% 170.79/26.50 (7) op(e2, e2) = all_8_2
% 170.79/26.50 (8) ~ (e3 = e0)
% 170.79/26.50 (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.50 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.50 (10) all_58_4 = e1
% 170.79/26.50 (11) all_58_0 = e3
% 170.79/26.50 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.50 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.50 (13) all_58_3 = e2
% 170.79/26.50 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.50 (15) ~ (e2 = e0)
% 170.79/26.50 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.50 (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.50 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.50 (18) all_58_2 = e1
% 170.79/26.50 (19) all_58_1 = e0
% 170.79/26.50 (20) ~ (e3 = e2)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | BETA: splitting (16) gives:
% 170.79/26.50 |
% 170.79/26.50 | Case 1:
% 170.79/26.50 | |
% 170.79/26.50 | | (21) all_58_9 = e3 & op(e3, e0) = e3
% 170.79/26.50 | |
% 170.79/26.50 | | ALPHA: (21) implies:
% 170.79/26.50 | | (22) all_58_9 = e3
% 170.79/26.50 | |
% 170.79/26.50 | | COMBINE_EQS: (2), (22) imply:
% 170.79/26.50 | | (23) e3 = e2
% 170.79/26.50 | |
% 170.79/26.50 | | SIMP: (23) implies:
% 170.79/26.50 | | (24) e3 = e2
% 170.79/26.50 | |
% 170.79/26.50 | | COMBINE_EQS: (6), (24) imply:
% 170.79/26.50 | | (25) all_58_5 = e2
% 170.79/26.50 | |
% 170.79/26.50 | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (13), (14), (15), (17), (18), (20),
% 170.79/26.50 | | (25) are inconsistent by sub-proof #930.
% 170.79/26.50 | |
% 170.79/26.50 | Case 2:
% 170.79/26.50 | |
% 170.79/26.50 | | (26) all_58_10 = e3 & op(e2, e0) = e3
% 170.79/26.50 | |
% 170.79/26.50 | | ALPHA: (26) implies:
% 170.79/26.50 | | (27) all_58_10 = e3
% 170.79/26.50 | |
% 170.79/26.50 | | COMBINE_EQS: (1), (27) imply:
% 170.79/26.50 | | (28) e3 = e0
% 170.79/26.50 | |
% 170.79/26.50 | | REF_CLOSE: (2), (4), (8), (10), (11), (12), (19), (20), (28) are
% 170.79/26.50 | | inconsistent by sub-proof #761.
% 170.79/26.50 | |
% 170.79/26.50 | End of split
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #759 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_9 = e2
% 170.79/26.50 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.50 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.50 (3) ~ (e3 = e1)
% 170.79/26.50 (4) op(e3, e3) = e1
% 170.79/26.50 (5) op(e3, e1) = all_52_8
% 170.79/26.50 (6) ~ (e1 = e0)
% 170.79/26.50 (7) op(e3, e1) = e3
% 170.79/26.50 (8) ~ (e3 = e0)
% 170.79/26.50 (9) all_52_8 = e1
% 170.79/26.50 (10) all_58_4 = e1
% 170.79/26.50 (11) all_58_0 = e3
% 170.79/26.50 (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.50 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.50 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.50 (14) ~ (e2 = e0)
% 170.79/26.50 (15) ~ (e3 = e2)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | GROUND_INST: instantiating (13) with all_52_8, e3, e1, e3, simplifying with
% 170.79/26.50 | (5), (7) gives:
% 170.79/26.50 | (16) all_52_8 = e3
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (9), (16) imply:
% 170.79/26.50 | (17) e3 = e1
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (11), (17) imply:
% 170.79/26.50 | (18) all_58_0 = e1
% 170.79/26.50 |
% 170.79/26.50 | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (12), (13), (14), (15), (18)
% 170.79/26.50 | are inconsistent by sub-proof #788.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #760 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_10 = e2 & op(e2, e0) = e2
% 170.79/26.50 (2) all_58_10 = e0
% 170.79/26.50 (3) ~ (e2 = e0)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | ALPHA: (1) implies:
% 170.79/26.50 | (4) all_58_10 = e2
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.50 | (5) e2 = e0
% 170.79/26.50 |
% 170.79/26.50 | REDUCE: (3), (5) imply:
% 170.79/26.50 | (6) $false
% 170.79/26.50 |
% 170.79/26.50 | CLOSE: (6) is inconsistent.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #761 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_9 = e2
% 170.79/26.50 (2) ~ (e3 = e1)
% 170.79/26.50 (3) ~ (e3 = e0)
% 170.79/26.50 (4) all_58_4 = e1
% 170.79/26.50 (5) all_58_0 = e3
% 170.79/26.50 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.50 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.50 (7) e3 = e0
% 170.79/26.50 (8) all_58_1 = e0
% 170.79/26.50 (9) ~ (e3 = e2)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | SIMP: (7) implies:
% 170.79/26.50 | (10) e3 = e0
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (5), (10) imply:
% 170.79/26.50 | (11) all_58_0 = e0
% 170.79/26.50 |
% 170.79/26.50 | BETA: splitting (6) gives:
% 170.79/26.50 |
% 170.79/26.50 | Case 1:
% 170.79/26.50 | |
% 170.79/26.50 | | (12) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 170.79/26.50 | | e3)
% 170.79/26.50 | |
% 170.79/26.50 | | BETA: splitting (12) gives:
% 170.79/26.50 | |
% 170.79/26.50 | | Case 1:
% 170.79/26.50 | | |
% 170.79/26.50 | | | (13) all_58_0 = e3 & op(e3, e3) = e3
% 170.79/26.50 | | |
% 170.79/26.50 | | | REDUCE: (3), (10) imply:
% 170.79/26.50 | | | (14) $false
% 170.79/26.50 | | |
% 170.79/26.50 | | | CLOSE: (14) is inconsistent.
% 170.79/26.50 | | |
% 170.79/26.50 | | Case 2:
% 170.79/26.50 | | |
% 170.79/26.50 | | | (15) all_58_1 = e3 & op(e3, e2) = e3
% 170.79/26.50 | | |
% 170.79/26.50 | | | REF_CLOSE: (3), (8), (15) are inconsistent by sub-proof #803.
% 170.79/26.50 | | |
% 170.79/26.50 | | End of split
% 170.79/26.50 | |
% 170.79/26.50 | Case 2:
% 170.79/26.50 | |
% 170.79/26.50 | | (16) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 170.79/26.50 | | e3)
% 170.79/26.50 | |
% 170.79/26.50 | | REF_CLOSE: (1), (2), (4), (9), (16) are inconsistent by sub-proof #762.
% 170.79/26.50 | |
% 170.79/26.50 | End of split
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #762 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_9 = e2
% 170.79/26.50 (2) ~ (e3 = e1)
% 170.79/26.50 (3) all_58_4 = e1
% 170.79/26.50 (4) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.50 (5) ~ (e3 = e2)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | BETA: splitting (4) gives:
% 170.79/26.50 |
% 170.79/26.50 | Case 1:
% 170.79/26.50 | |
% 170.79/26.50 | | (6) all_58_4 = e3 & op(e3, e1) = e3
% 170.79/26.50 | |
% 170.79/26.50 | | ALPHA: (6) implies:
% 170.79/26.50 | | (7) all_58_4 = e3
% 170.79/26.50 | |
% 170.79/26.50 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #767.
% 170.79/26.50 | |
% 170.79/26.50 | Case 2:
% 170.79/26.50 | |
% 170.79/26.50 | | (8) all_58_9 = e3 & op(e3, e0) = e3
% 170.79/26.50 | |
% 170.79/26.50 | | ALPHA: (8) implies:
% 170.79/26.50 | | (9) all_58_9 = e3
% 170.79/26.50 | |
% 170.79/26.50 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #790.
% 170.79/26.50 | |
% 170.79/26.50 | End of split
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #763 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 170.79/26.50 (2) ~ (e1 = e0)
% 170.79/26.50 (3) all_58_3 = e2
% 170.79/26.50 (4) ~ (e2 = e0)
% 170.79/26.50 (5) all_58_2 = e1
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | BETA: splitting (1) gives:
% 170.79/26.50 |
% 170.79/26.50 | Case 1:
% 170.79/26.50 | |
% 170.79/26.50 | | (6) all_58_2 = e0 & op(e2, e3) = e0
% 170.79/26.50 | |
% 170.79/26.50 | | ALPHA: (6) implies:
% 170.79/26.50 | | (7) all_58_2 = e0
% 170.79/26.50 | |
% 170.79/26.50 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #776.
% 170.79/26.50 | |
% 170.79/26.50 | Case 2:
% 170.79/26.50 | |
% 170.79/26.50 | | (8) all_58_3 = e0 & op(e2, e2) = e0
% 170.79/26.50 | |
% 170.79/26.50 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #934.
% 170.79/26.50 | |
% 170.79/26.50 | End of split
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #764 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) all_58_9 = e2
% 170.79/26.50 (2) all_58_4 = e3 & op(e3, e1) = e3
% 170.79/26.50 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.50 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.50 (4) ~ (e3 = e1)
% 170.79/26.50 (5) op(e3, e3) = e1
% 170.79/26.50 (6) ~ (e1 = e0)
% 170.79/26.50 (7) ~ (e3 = e0)
% 170.79/26.50 (8) all_58_4 = e1
% 170.79/26.50 (9) all_58_0 = e3
% 170.79/26.50 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.50 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.50 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.50 (12) ~ (e2 = e0)
% 170.79/26.50 (13) ~ (e3 = e2)
% 170.79/26.50
% 170.79/26.50 Begin of proof
% 170.79/26.50 |
% 170.79/26.50 | ALPHA: (2) implies:
% 170.79/26.50 | (14) all_58_4 = e3
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (8), (14) imply:
% 170.79/26.50 | (15) e3 = e1
% 170.79/26.50 |
% 170.79/26.50 | COMBINE_EQS: (9), (15) imply:
% 170.79/26.50 | (16) all_58_0 = e1
% 170.79/26.50 |
% 170.79/26.50 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (16) are
% 170.79/26.50 | inconsistent by sub-proof #788.
% 170.79/26.50 |
% 170.79/26.50 End of proof
% 170.79/26.50
% 170.79/26.50 Sub-proof #765 shows that the following formulas are inconsistent:
% 170.79/26.50 ----------------------------------------------------------------
% 170.79/26.50 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.79/26.50 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.79/26.50 (2) all_58_12 = e1
% 170.79/26.50 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.79/26.50 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.79/26.50 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.50 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.50 (5) all_58_14 = e2
% 170.79/26.50 (6) ~ (all_4_2 = e2)
% 170.79/26.50 (7) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 & op(e2, e3) = e0) |
% 170.79/26.50 (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 & op(e0, e3) = e0)
% 170.79/26.50 (8) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.50 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.79/26.50 (9) all_58_9 = e2
% 170.79/26.50 (10) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 170.79/26.50 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 170.79/26.50 (11) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.50 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.50 (12) ~ (all_8_2 = e3)
% 170.79/26.50 (13) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.79/26.50 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.79/26.50 (14) ~ (all_6_2 = e3)
% 170.79/26.50 (15) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.50 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.50 (16) ~ (e3 = e1)
% 170.79/26.50 (17) op(e3, e3) = e1
% 170.79/26.50 (18) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.50 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.79/26.50 e1)
% 170.79/26.50 (19) op(e3, e1) = all_52_8
% 170.79/26.50 (20) ~ (e1 = e0)
% 170.79/26.50 (21) all_56_10 = e1
% 170.79/26.50 (22) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.79/26.50 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.79/26.50 (23) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 170.79/26.50 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.79/26.50 (24) op(e2, e3) = all_52_1
% 170.79/26.51 (25) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0 & op(e2, e1) = e0) |
% 170.79/26.51 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 170.79/26.51 (26) op(e2, e2) = all_8_2
% 170.79/26.51 (27) ~ (all_6_2 = e2)
% 170.79/26.51 (28) op(e1, e1) = all_6_2
% 170.79/26.51 (29) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.79/26.51 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.79/26.51 (30) ~ (e3 = e0)
% 170.79/26.51 (31) op(e3, e1) = e1
% 170.79/26.51 (32) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.51 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.51 (33) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.79/26.51 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.79/26.51 (34) all_58_4 = e1
% 170.79/26.51 (35) op(e0, e0) = all_4_2
% 170.79/26.51 (36) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.51 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.79/26.51 (37) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.79/26.51 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.79/26.51 (38) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.51 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.51 (39) all_58_3 = e2
% 170.79/26.51 (40) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.51 (41) ~ (e2 = e0)
% 170.79/26.51 (42) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.79/26.51 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.79/26.51 (43) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.79/26.51 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.79/26.51 (44) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.79/26.51 (45) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.51 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.51 (46) ~ (e2 = e1)
% 170.79/26.51 (47) op(e3, e2) = all_52_4
% 170.79/26.51 (48) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.79/26.51 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.79/26.51 (49) op(e0, e2) = all_52_7
% 170.79/26.51 (50) ~ (all_52_4 = e1)
% 170.79/26.51 (51) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.79/26.51 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.79/26.51 (52) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 170.79/26.51 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 170.79/26.51 (53) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.51 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.79/26.51 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.79/26.51 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.79/26.51 (54) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 170.79/26.51 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 170.79/26.51 (55) ~ (e3 = e2)
% 170.79/26.51
% 170.79/26.51 Begin of proof
% 170.79/26.51 |
% 170.79/26.51 | BETA: splitting (44) gives:
% 170.79/26.51 |
% 170.79/26.51 | Case 1:
% 170.79/26.51 | |
% 170.79/26.51 | | (56) ~ (all_56_10 = e1)
% 170.79/26.51 | |
% 170.79/26.51 | | REDUCE: (21), (56) imply:
% 170.79/26.51 | | (57) $false
% 170.79/26.51 | |
% 170.79/26.51 | | CLOSE: (57) is inconsistent.
% 170.79/26.51 | |
% 170.79/26.51 | Case 2:
% 170.79/26.51 | |
% 170.79/26.51 | | (58) all_56_4 = e3 & op(e3, e1) = e3
% 170.79/26.51 | |
% 170.79/26.51 | | ALPHA: (58) implies:
% 170.79/26.51 | | (59) op(e3, e1) = e3
% 170.79/26.51 | |
% 170.79/26.51 | | BETA: splitting (38) gives:
% 170.79/26.51 | |
% 170.79/26.51 | | Case 1:
% 170.79/26.51 | | |
% 170.79/26.51 | | | (60) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 170.79/26.51 | | | e3)
% 170.79/26.51 | | |
% 170.79/26.51 | | | BETA: splitting (60) gives:
% 170.79/26.51 | | |
% 170.79/26.51 | | | Case 1:
% 170.79/26.51 | | | |
% 170.79/26.51 | | | | (61) all_58_0 = e3 & op(e3, e3) = e3
% 170.79/26.51 | | | |
% 170.79/26.51 | | | | ALPHA: (61) implies:
% 170.79/26.51 | | | | (62) all_58_0 = e3
% 170.79/26.51 | | | | (63) op(e3, e3) = e3
% 170.79/26.51 | | | |
% 170.79/26.51 | | | | BETA: splitting (10) gives:
% 170.79/26.51 | | | |
% 170.79/26.51 | | | | Case 1:
% 170.79/26.51 | | | | |
% 170.79/26.51 | | | | | (64) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2,
% 170.79/26.51 | | | | | e3) = e2)
% 170.79/26.51 | | | | |
% 170.79/26.51 | | | | | REF_CLOSE: (4), (16), (20), (24), (30), (32), (39), (40), (41), (45),
% 170.79/26.51 | | | | | (46), (55), (63), (64) are inconsistent by sub-proof #778.
% 170.79/26.51 | | | | |
% 170.79/26.51 | | | | Case 2:
% 170.79/26.51 | | | | |
% 170.79/26.51 | | | | | (65) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0,
% 170.79/26.51 | | | | | e3) = e2)
% 170.79/26.51 | | | | |
% 170.79/26.51 | | | | | BETA: splitting (65) gives:
% 170.79/26.51 | | | | |
% 170.79/26.51 | | | | | Case 1:
% 170.79/26.51 | | | | | |
% 170.79/26.51 | | | | | | (66) all_58_6 = e2 & op(e1, e3) = e2
% 170.79/26.51 | | | | | |
% 170.79/26.51 | | | | | | ALPHA: (66) implies:
% 170.79/26.51 | | | | | | (67) all_58_6 = e2
% 170.79/26.51 | | | | | |
% 170.79/26.51 | | | | | | BETA: splitting (7) gives:
% 170.79/26.51 | | | | | |
% 170.79/26.51 | | | | | | Case 1:
% 170.79/26.51 | | | | | | |
% 170.79/26.51 | | | | | | | (68) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_2 = e0 &
% 170.79/26.51 | | | | | | | op(e2, e3) = e0)
% 170.79/26.51 | | | | | | |
% 170.79/26.51 | | | | | | | BETA: splitting (68) gives:
% 170.79/26.51 | | | | | | |
% 170.79/26.51 | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | (69) all_58_0 = e0 & op(e3, e3) = e0
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | ALPHA: (69) implies:
% 170.79/26.51 | | | | | | | | (70) op(e3, e3) = e0
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | REF_CLOSE: (17), (20), (40), (70) are inconsistent by sub-proof
% 170.79/26.51 | | | | | | | | #907.
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | (71) all_58_2 = e0 & op(e2, e3) = e0
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | ALPHA: (71) implies:
% 170.79/26.51 | | | | | | | | (72) all_58_2 = e0
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | BETA: splitting (22) gives:
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | |
% 170.79/26.51 | | | | | | | | | (73) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 &
% 170.79/26.51 | | | | | | | | | op(e2, e1) = e3)
% 170.79/26.51 | | | | | | | | |
% 170.79/26.51 | | | | | | | | | BETA: splitting (73) gives:
% 170.79/26.51 | | | | | | | | |
% 170.79/26.51 | | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | (74) all_58_4 = e3 & op(e3, e1) = e3
% 170.79/26.51 | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | REF_CLOSE: (9), (15), (16), (17), (20), (30), (34), (38),
% 170.79/26.51 | | | | | | | | | | (40), (41), (55), (62), (74) are inconsistent by
% 170.79/26.51 | | | | | | | | | | sub-proof #777.
% 170.79/26.51 | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | (75) all_58_5 = e3 & op(e2, e1) = e3
% 170.79/26.51 | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | ALPHA: (75) implies:
% 170.79/26.51 | | | | | | | | | | (76) all_58_5 = e3
% 170.79/26.51 | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | BETA: splitting (25) gives:
% 170.79/26.51 | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | (77) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_5 = e0
% 170.79/26.51 | | | | | | | | | | | & op(e2, e1) = e0)
% 170.79/26.51 | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | BETA: splitting (77) gives:
% 170.79/26.51 | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | (78) all_58_4 = e0 & op(e3, e1) = e0
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | REF_CLOSE: (2), (16), (20), (29), (34), (46), (62), (67),
% 170.79/26.51 | | | | | | | | | | | | (72), (78) are inconsistent by sub-proof #771.
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | (79) all_58_5 = e0 & op(e2, e1) = e0
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | ALPHA: (79) implies:
% 170.79/26.51 | | | | | | | | | | | | (80) all_58_5 = e0
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | REF_CLOSE: (30), (76), (80) are inconsistent by sub-proof
% 170.79/26.51 | | | | | | | | | | | | #919.
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | End of split
% 170.79/26.51 | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | (81) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_14 =
% 170.79/26.51 | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 170.79/26.51 | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | BETA: splitting (81) gives:
% 170.79/26.51 | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | (82) all_58_8 = e0 & op(e1, e1) = e0
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | ALPHA: (82) implies:
% 170.79/26.51 | | | | | | | | | | | | (83) all_58_8 = e0
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | BETA: splitting (15) gives:
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | (84) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0
% 170.79/26.51 | | | | | | | | | | | | | & op(e3, e2) = e0)
% 170.79/26.51 | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | BETA: splitting (84) gives:
% 170.79/26.51 | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | (85) all_58_0 = e0 & op(e3, e3) = e0
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | ALPHA: (85) implies:
% 170.79/26.51 | | | | | | | | | | | | | | (86) op(e3, e3) = e0
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | REF_CLOSE: (17), (20), (40), (86) are inconsistent by
% 170.79/26.51 | | | | | | | | | | | | | | sub-proof #907.
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | GROUND_INST: instantiating (40) with all_52_8, e1, e1, e3,
% 170.79/26.51 | | | | | | | | | | | | | | simplifying with (19), (31) gives:
% 170.79/26.51 | | | | | | | | | | | | | | (87) all_52_8 = e1
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | GROUND_INST: instantiating (40) with all_52_8, e3, e1, e3,
% 170.79/26.51 | | | | | | | | | | | | | | simplifying with (19), (59) gives:
% 170.79/26.51 | | | | | | | | | | | | | | (88) all_52_8 = e3
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | COMBINE_EQS: (87), (88) imply:
% 170.79/26.51 | | | | | | | | | | | | | | (89) e3 = e1
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | SIMP: (89) implies:
% 170.79/26.51 | | | | | | | | | | | | | | (90) e3 = e1
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | COMBINE_EQS: (62), (90) imply:
% 170.79/26.51 | | | | | | | | | | | | | | (91) all_58_0 = e1
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | REF_CLOSE: (9), (15), (16), (17), (20), (30), (34), (38),
% 170.79/26.51 | | | | | | | | | | | | | | (40), (41), (55), (91) are inconsistent by
% 170.79/26.51 | | | | | | | | | | | | | | sub-proof #788.
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | End of split
% 170.79/26.51 | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | (92) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0
% 170.79/26.51 | | | | | | | | | | | | | & op(e3, e0) = e0)
% 170.79/26.51 | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | BETA: splitting (92) gives:
% 170.79/26.51 | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | (93) all_58_4 = e0 & op(e3, e1) = e0
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | REF_CLOSE: (2), (16), (20), (29), (34), (46), (62), (67),
% 170.79/26.51 | | | | | | | | | | | | | | (72), (93) are inconsistent by sub-proof #771.
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | (94) all_58_9 = e0 & op(e3, e0) = e0
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | ALPHA: (94) implies:
% 170.79/26.51 | | | | | | | | | | | | | | (95) all_58_9 = e0
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | (96) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 =
% 170.79/26.51 | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 170.79/26.51 | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 170.79/26.51 | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | (97) all_58_9 = e2 & op(e3, e0) = e2
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (95) imply:
% 170.79/26.51 | | | | | | | | | | | | | | | | (98) e2 = e0
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (10), (16), (20), (30), (32), (39),
% 170.79/26.51 | | | | | | | | | | | | | | | | (40), (41), (46), (55), (63), (67), (76), (98) are
% 170.79/26.51 | | | | | | | | | | | | | | | | inconsistent by sub-proof #770.
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | (99) all_58_10 = e2 & op(e2, e0) = e2
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 170.79/26.51 | | | | | | | | | | | | | | | | (100) all_58_10 = e2
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (20), (30), (32), (39), (41), (46),
% 170.79/26.51 | | | | | | | | | | | | | | | | (48), (55), (76), (100) are inconsistent by
% 170.79/26.51 | | | | | | | | | | | | | | | | sub-proof #917.
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | End of split
% 170.79/26.51 | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | (101) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 =
% 170.79/26.51 | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 170.79/26.51 | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 170.79/26.51 | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | (102) all_58_11 = e2 & op(e1, e0) = e2
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 170.79/26.51 | | | | | | | | | | | | | | | | (103) all_58_11 = e2
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (20), (30), (42), (43), (46), (55), (67),
% 170.79/26.51 | | | | | | | | | | | | | | | | (83), (103) are inconsistent by sub-proof #817.
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | (104) all_58_15 = e2 & op(e0, e0) = e2
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (35), (40), (104) are inconsistent by
% 170.79/26.51 | | | | | | | | | | | | | | | | sub-proof #854.
% 170.79/26.51 | | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | | End of split
% 170.79/26.51 | | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | | End of split
% 170.79/26.51 | | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | | End of split
% 170.79/26.51 | | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | End of split
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | (105) all_58_14 = e0 & op(e0, e1) = e0
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | ALPHA: (105) implies:
% 170.79/26.51 | | | | | | | | | | | | (106) all_58_14 = e0
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | COMBINE_EQS: (5), (106) imply:
% 170.79/26.51 | | | | | | | | | | | | (107) e2 = e0
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | | REF_CLOSE: (2), (4), (10), (16), (20), (30), (32), (39),
% 170.79/26.51 | | | | | | | | | | | | (40), (41), (46), (55), (63), (67), (76), (107)
% 170.79/26.51 | | | | | | | | | | | | are inconsistent by sub-proof #770.
% 170.79/26.51 | | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | | End of split
% 170.79/26.51 | | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | | End of split
% 170.79/26.51 | | | | | | | | | |
% 170.79/26.51 | | | | | | | | | End of split
% 170.79/26.51 | | | | | | | | |
% 170.79/26.51 | | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | | |
% 170.79/26.51 | | | | | | | | | (108) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 &
% 170.79/26.51 | | | | | | | | | op(e0, e1) = e3)
% 170.79/26.51 | | | | | | | | |
% 170.79/26.51 | | | | | | | | | REF_CLOSE: (5), (14), (28), (40), (55), (108) are inconsistent
% 170.79/26.51 | | | | | | | | | by sub-proof #805.
% 170.79/26.51 | | | | | | | | |
% 170.79/26.51 | | | | | | | | End of split
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | End of split
% 170.79/26.51 | | | | | | |
% 170.79/26.51 | | | | | | Case 2:
% 170.79/26.51 | | | | | | |
% 170.79/26.51 | | | | | | | (109) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_12 = e0 &
% 170.79/26.51 | | | | | | | op(e0, e3) = e0)
% 170.79/26.51 | | | | | | |
% 170.79/26.51 | | | | | | | BETA: splitting (109) gives:
% 170.79/26.51 | | | | | | |
% 170.79/26.51 | | | | | | | Case 1:
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | (110) all_58_6 = e0 & op(e1, e3) = e0
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | REF_CLOSE: (41), (67), (110) are inconsistent by sub-proof #769.
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | Case 2:
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | (111) all_58_12 = e0 & op(e0, e3) = e0
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | ALPHA: (111) implies:
% 170.79/26.51 | | | | | | | | (112) all_58_12 = e0
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | | REF_CLOSE: (2), (20), (112) are inconsistent by sub-proof #873.
% 170.79/26.51 | | | | | | | |
% 170.79/26.51 | | | | | | | End of split
% 170.79/26.51 | | | | | | |
% 170.79/26.51 | | | | | | End of split
% 170.79/26.51 | | | | | |
% 170.79/26.51 | | | | | Case 2:
% 170.79/26.51 | | | | | |
% 170.79/26.51 | | | | | | (113) all_58_12 = e2 & op(e0, e3) = e2
% 170.79/26.51 | | | | | |
% 170.79/26.51 | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12),
% 170.79/26.51 | | | | | | (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 170.79/26.51 | | | | | | (22), (23), (26), (27), (28), (30), (32), (33), (35),
% 170.79/26.51 | | | | | | (36), (37), (38), (39), (40), (41), (42), (43), (44),
% 170.79/26.51 | | | | | | (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 170.79/26.51 | | | | | | (54), (55), (113) are inconsistent by sub-proof #768.
% 170.79/26.51 | | | | | |
% 170.79/26.51 | | | | | End of split
% 170.79/26.51 | | | | |
% 170.79/26.51 | | | | End of split
% 170.79/26.51 | | | |
% 170.79/26.51 | | | Case 2:
% 170.79/26.51 | | | |
% 170.79/26.51 | | | | (114) all_58_1 = e3 & op(e3, e2) = e3
% 170.79/26.51 | | | |
% 170.79/26.51 | | | | REF_CLOSE: (9), (15), (17), (20), (30), (34), (40), (41), (114) are
% 170.79/26.51 | | | | inconsistent by sub-proof #791.
% 170.79/26.51 | | | |
% 170.79/26.51 | | | End of split
% 170.79/26.51 | | |
% 170.79/26.51 | | Case 2:
% 170.79/26.51 | | |
% 170.79/26.51 | | | (115) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 170.79/26.51 | | | e3)
% 170.79/26.51 | | |
% 170.79/26.51 | | | REF_CLOSE: (9), (16), (34), (55), (115) are inconsistent by sub-proof
% 170.79/26.51 | | | #766.
% 170.79/26.51 | | |
% 170.79/26.51 | | End of split
% 170.79/26.51 | |
% 170.79/26.51 | End of split
% 170.79/26.51 |
% 170.79/26.51 End of proof
% 170.79/26.51
% 170.79/26.51 Sub-proof #766 shows that the following formulas are inconsistent:
% 170.79/26.51 ----------------------------------------------------------------
% 170.79/26.51 (1) all_58_9 = e2
% 170.79/26.51 (2) ~ (e3 = e1)
% 170.79/26.51 (3) all_58_4 = e1
% 170.79/26.51 (4) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.51 (5) ~ (e3 = e2)
% 170.79/26.51
% 170.79/26.51 Begin of proof
% 170.79/26.51 |
% 170.79/26.51 | BETA: splitting (4) gives:
% 170.79/26.51 |
% 170.79/26.51 | Case 1:
% 170.79/26.51 | |
% 170.79/26.51 | | (6) all_58_4 = e3 & op(e3, e1) = e3
% 170.79/26.51 | |
% 170.79/26.51 | | ALPHA: (6) implies:
% 170.79/26.51 | | (7) all_58_4 = e3
% 170.79/26.51 | |
% 170.79/26.51 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #767.
% 170.79/26.51 | |
% 170.79/26.51 | Case 2:
% 170.79/26.51 | |
% 170.79/26.51 | | (8) all_58_9 = e3 & op(e3, e0) = e3
% 170.79/26.51 | |
% 170.79/26.51 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #940.
% 170.79/26.51 | |
% 170.79/26.51 | End of split
% 170.79/26.51 |
% 170.79/26.51 End of proof
% 170.79/26.51
% 170.79/26.51 Sub-proof #767 shows that the following formulas are inconsistent:
% 170.79/26.51 ----------------------------------------------------------------
% 170.79/26.51 (1) all_58_4 = e3
% 170.79/26.51 (2) all_58_4 = e1
% 170.79/26.51 (3) ~ (e3 = e1)
% 170.79/26.51
% 170.79/26.51 Begin of proof
% 170.79/26.51 |
% 170.79/26.51 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.51 | (4) e3 = e1
% 170.79/26.51 |
% 170.79/26.51 | SIMP: (4) implies:
% 170.79/26.51 | (5) e3 = e1
% 170.79/26.51 |
% 170.79/26.51 | REDUCE: (3), (5) imply:
% 170.79/26.51 | (6) $false
% 170.79/26.51 |
% 170.79/26.51 | CLOSE: (6) is inconsistent.
% 170.79/26.51 |
% 170.79/26.51 End of proof
% 170.79/26.51
% 170.79/26.51 Sub-proof #768 shows that the following formulas are inconsistent:
% 170.79/26.51 ----------------------------------------------------------------
% 170.79/26.51 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.79/26.51 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.79/26.51 (2) all_58_12 = e1
% 170.79/26.51 (3) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.79/26.51 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.79/26.51 (4) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.51 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.51 (5) ~ (all_4_2 = e2)
% 170.79/26.51 (6) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.51 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.79/26.51 (7) all_58_9 = e2
% 170.79/26.51 (8) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 170.79/26.51 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 170.79/26.51 (9) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.51 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.51 (10) ~ (all_8_2 = e3)
% 170.79/26.51 (11) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.79/26.51 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.79/26.51 (12) ~ (all_6_2 = e3)
% 170.79/26.51 (13) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.51 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.51 (14) ~ (e3 = e1)
% 170.79/26.51 (15) op(e3, e3) = e1
% 170.79/26.51 (16) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.51 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.79/26.51 e1)
% 170.79/26.51 (17) op(e3, e1) = all_52_8
% 170.79/26.51 (18) ~ (e1 = e0)
% 170.79/26.51 (19) all_56_10 = e1
% 170.79/26.51 (20) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.79/26.51 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.79/26.51 (21) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 170.79/26.51 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.79/26.51 (22) op(e2, e2) = all_8_2
% 170.79/26.51 (23) ~ (all_6_2 = e2)
% 170.79/26.51 (24) op(e1, e1) = all_6_2
% 170.79/26.51 (25) ~ (e3 = e0)
% 170.79/26.51 (26) all_58_12 = e2 & op(e0, e3) = e2
% 170.79/26.51 (27) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.51 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.51 (28) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.79/26.51 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.79/26.51 (29) op(e0, e0) = all_4_2
% 170.79/26.51 (30) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.51 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 170.79/26.51 (31) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 170.79/26.51 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 170.79/26.51 (32) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.51 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.51 (33) all_58_3 = e2
% 170.79/26.51 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.51 (35) ~ (e2 = e0)
% 170.79/26.51 (36) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 170.79/26.51 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 170.79/26.51 (37) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 170.79/26.51 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 170.79/26.51 (38) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.79/26.51 (39) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.51 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.51 (40) ~ (e2 = e1)
% 170.79/26.51 (41) op(e3, e2) = all_52_4
% 170.79/26.51 (42) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 170.79/26.51 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 170.79/26.51 (43) op(e0, e2) = all_52_7
% 170.79/26.51 (44) ~ (all_52_4 = e1)
% 170.79/26.51 (45) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 170.79/26.51 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 170.79/26.51 (46) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 170.79/26.51 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 170.79/26.51 (47) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.51 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 170.79/26.51 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 170.79/26.51 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 170.79/26.51 (48) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 170.79/26.51 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 170.79/26.51 (49) ~ (e3 = e2)
% 170.79/26.51
% 170.79/26.51 Begin of proof
% 170.79/26.51 |
% 170.79/26.51 | ALPHA: (26) implies:
% 170.79/26.51 | (50) all_58_12 = e2
% 170.79/26.51 |
% 170.79/26.51 | COMBINE_EQS: (2), (50) imply:
% 170.79/26.51 | (51) e2 = e1
% 170.79/26.51 |
% 170.79/26.51 | COMBINE_EQS: (7), (51) imply:
% 170.79/26.51 | (52) all_58_9 = e1
% 170.79/26.51 |
% 170.79/26.51 | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14),
% 170.79/26.51 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 170.79/26.51 | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 170.79/26.51 | (38), (39), (40), (41), (42), (43), (44), (45), (46), (47), (48),
% 170.79/26.51 | (49), (52) are inconsistent by sub-proof #799.
% 170.79/26.51 |
% 170.79/26.51 End of proof
% 170.79/26.51
% 170.79/26.51 Sub-proof #769 shows that the following formulas are inconsistent:
% 170.79/26.51 ----------------------------------------------------------------
% 170.79/26.51 (1) all_58_6 = e0 & op(e1, e3) = e0
% 170.79/26.51 (2) all_58_6 = e2
% 170.79/26.51 (3) ~ (e2 = e0)
% 170.79/26.51
% 170.79/26.51 Begin of proof
% 170.79/26.51 |
% 170.79/26.51 | ALPHA: (1) implies:
% 170.79/26.51 | (4) all_58_6 = e0
% 170.79/26.51 |
% 170.79/26.51 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.51 | (5) e2 = e0
% 170.79/26.51 |
% 170.79/26.51 | REDUCE: (3), (5) imply:
% 170.79/26.51 | (6) $false
% 170.79/26.51 |
% 170.79/26.51 | CLOSE: (6) is inconsistent.
% 170.79/26.51 |
% 170.79/26.51 End of proof
% 170.79/26.51
% 170.79/26.51 Sub-proof #770 shows that the following formulas are inconsistent:
% 170.79/26.51 ----------------------------------------------------------------
% 170.79/26.51 (1) all_58_12 = e1
% 170.79/26.51 (2) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.51 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.51 (3) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 170.79/26.51 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 170.79/26.51 (4) ~ (e3 = e1)
% 170.79/26.51 (5) e2 = e0
% 170.79/26.51 (6) ~ (e1 = e0)
% 170.79/26.51 (7) all_58_5 = e3
% 170.79/26.51 (8) all_58_6 = e2
% 170.79/26.51 (9) ~ (e3 = e0)
% 170.79/26.51 (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.51 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.51 (11) all_58_3 = e2
% 170.79/26.51 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.51 (13) ~ (e2 = e0)
% 170.79/26.51 (14) op(e3, e3) = e3
% 170.79/26.51 (15) ~ (e2 = e1)
% 170.79/26.51 (16) ~ (e3 = e2)
% 170.79/26.51
% 170.79/26.51 Begin of proof
% 170.79/26.51 |
% 170.79/26.51 | SIMP: (5) implies:
% 170.79/26.51 | (17) e2 = e0
% 170.79/26.51 |
% 170.79/26.51 | COMBINE_EQS: (8), (17) imply:
% 170.79/26.51 | (18) all_58_6 = e0
% 170.79/26.51 |
% 170.79/26.51 | BETA: splitting (3) gives:
% 170.79/26.51 |
% 170.79/26.51 | Case 1:
% 170.79/26.51 | |
% 170.79/26.52 | | (19) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) =
% 170.79/26.52 | | e2)
% 170.79/26.52 | |
% 170.79/26.52 | | REF_CLOSE: (2), (4), (6), (7), (9), (10), (11), (12), (13), (14), (15),
% 170.79/26.52 | | (16), (19) are inconsistent by sub-proof #808.
% 170.79/26.52 | |
% 170.79/26.52 | Case 2:
% 170.79/26.52 | |
% 170.79/26.52 | | (20) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) =
% 170.79/26.52 | | e2)
% 170.79/26.52 | |
% 170.79/26.52 | | BETA: splitting (20) gives:
% 170.79/26.52 | |
% 170.79/26.52 | | Case 1:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (21) all_58_6 = e2 & op(e1, e3) = e2
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (13), (18), (21) are inconsistent by sub-proof #826.
% 170.79/26.52 | | |
% 170.79/26.52 | | Case 2:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (22) all_58_12 = e2 & op(e0, e3) = e2
% 170.79/26.52 | | |
% 170.79/26.52 | | | ALPHA: (22) implies:
% 170.79/26.52 | | | (23) all_58_12 = e2
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (1), (15), (23) are inconsistent by sub-proof #862.
% 170.79/26.52 | | |
% 170.79/26.52 | | End of split
% 170.79/26.52 | |
% 170.79/26.52 | End of split
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #771 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_12 = e1
% 170.79/26.52 (2) ~ (e3 = e1)
% 170.79/26.52 (3) ~ (e1 = e0)
% 170.79/26.52 (4) all_58_4 = e0 & op(e3, e1) = e0
% 170.79/26.52 (5) all_58_6 = e2
% 170.79/26.52 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.79/26.52 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.79/26.52 (7) all_58_4 = e1
% 170.79/26.52 (8) all_58_0 = e3
% 170.79/26.52 (9) ~ (e2 = e1)
% 170.79/26.52 (10) all_58_2 = e0
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | ALPHA: (4) implies:
% 170.79/26.52 | (11) all_58_4 = e0
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (7), (11) imply:
% 170.79/26.52 | (12) e1 = e0
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (1), (12) imply:
% 170.79/26.52 | (13) all_58_12 = e0
% 170.79/26.52 |
% 170.79/26.52 | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (13) are inconsistent by
% 170.79/26.52 | sub-proof #772.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #772 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) ~ (e3 = e1)
% 170.79/26.52 (2) ~ (e1 = e0)
% 170.79/26.52 (3) all_58_6 = e2
% 170.79/26.52 (4) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1) |
% 170.79/26.52 (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) = e1)
% 170.79/26.52 (5) all_58_12 = e0
% 170.79/26.52 (6) all_58_0 = e3
% 170.79/26.52 (7) ~ (e2 = e1)
% 170.79/26.52 (8) all_58_2 = e0
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | BETA: splitting (4) gives:
% 170.79/26.52 |
% 170.79/26.52 | Case 1:
% 170.79/26.52 | |
% 170.79/26.52 | | (9) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 170.79/26.52 | |
% 170.79/26.52 | | REF_CLOSE: (1), (2), (6), (8), (9) are inconsistent by sub-proof #775.
% 170.79/26.52 | |
% 170.79/26.52 | Case 2:
% 170.79/26.52 | |
% 170.79/26.52 | | (10) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_12 = e1 & op(e0, e3) =
% 170.79/26.52 | | e1)
% 170.79/26.52 | |
% 170.79/26.52 | | BETA: splitting (10) gives:
% 170.79/26.52 | |
% 170.79/26.52 | | Case 1:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (11) all_58_6 = e1 & op(e1, e3) = e1
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (3), (7), (11) are inconsistent by sub-proof #774.
% 170.79/26.52 | | |
% 170.79/26.52 | | Case 2:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (12) all_58_12 = e1 & op(e0, e3) = e1
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (2), (5), (12) are inconsistent by sub-proof #773.
% 170.79/26.52 | | |
% 170.79/26.52 | | End of split
% 170.79/26.52 | |
% 170.79/26.52 | End of split
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #773 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_12 = e1 & op(e0, e3) = e1
% 170.79/26.52 (2) all_58_12 = e0
% 170.79/26.52 (3) ~ (e1 = e0)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | ALPHA: (1) implies:
% 170.79/26.52 | (4) all_58_12 = e1
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.52 | (5) e1 = e0
% 170.79/26.52 |
% 170.79/26.52 | REDUCE: (3), (5) imply:
% 170.79/26.52 | (6) $false
% 170.79/26.52 |
% 170.79/26.52 | CLOSE: (6) is inconsistent.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #774 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_6 = e1 & op(e1, e3) = e1
% 170.79/26.52 (2) all_58_6 = e2
% 170.79/26.52 (3) ~ (e2 = e1)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | ALPHA: (1) implies:
% 170.79/26.52 | (4) all_58_6 = e1
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.52 | (5) e2 = e1
% 170.79/26.52 |
% 170.79/26.52 | REDUCE: (3), (5) imply:
% 170.79/26.52 | (6) $false
% 170.79/26.52 |
% 170.79/26.52 | CLOSE: (6) is inconsistent.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #775 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) ~ (e3 = e1)
% 170.79/26.52 (2) ~ (e1 = e0)
% 170.79/26.52 (3) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_2 = e1 & op(e2, e3) = e1)
% 170.79/26.52 (4) all_58_0 = e3
% 170.79/26.52 (5) all_58_2 = e0
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | BETA: splitting (3) gives:
% 170.79/26.52 |
% 170.79/26.52 | Case 1:
% 170.79/26.52 | |
% 170.79/26.52 | | (6) all_58_0 = e1 & op(e3, e3) = e1
% 170.79/26.52 | |
% 170.79/26.52 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #950.
% 170.79/26.52 | |
% 170.79/26.52 | Case 2:
% 170.79/26.52 | |
% 170.79/26.52 | | (7) all_58_2 = e1 & op(e2, e3) = e1
% 170.79/26.52 | |
% 170.79/26.52 | | ALPHA: (7) implies:
% 170.79/26.52 | | (8) all_58_2 = e1
% 170.79/26.52 | |
% 170.79/26.52 | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #776.
% 170.79/26.52 | |
% 170.79/26.52 | End of split
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #776 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_2 = e1
% 170.79/26.52 (2) all_58_2 = e0
% 170.79/26.52 (3) ~ (e1 = e0)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.52 | (4) e1 = e0
% 170.79/26.52 |
% 170.79/26.52 | SIMP: (4) implies:
% 170.79/26.52 | (5) e1 = e0
% 170.79/26.52 |
% 170.79/26.52 | REDUCE: (3), (5) imply:
% 170.79/26.52 | (6) $false
% 170.79/26.52 |
% 170.79/26.52 | CLOSE: (6) is inconsistent.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #777 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_9 = e2
% 170.79/26.52 (2) all_58_4 = e3 & op(e3, e1) = e3
% 170.79/26.52 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.52 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.52 (4) ~ (e3 = e1)
% 170.79/26.52 (5) op(e3, e3) = e1
% 170.79/26.52 (6) ~ (e1 = e0)
% 170.79/26.52 (7) ~ (e3 = e0)
% 170.79/26.52 (8) all_58_4 = e1
% 170.79/26.52 (9) all_58_0 = e3
% 170.79/26.52 (10) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.52 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.52 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.52 (12) ~ (e2 = e0)
% 170.79/26.52 (13) ~ (e3 = e2)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | ALPHA: (2) implies:
% 170.79/26.52 | (14) all_58_4 = e3
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (8), (14) imply:
% 170.79/26.52 | (15) e3 = e1
% 170.79/26.52 |
% 170.79/26.52 | SIMP: (15) implies:
% 170.79/26.52 | (16) e3 = e1
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (9), (16) imply:
% 170.79/26.52 | (17) all_58_0 = e1
% 170.79/26.52 |
% 170.79/26.52 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (17) are
% 170.79/26.52 | inconsistent by sub-proof #788.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #778 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.52 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.52 (2) ~ (e3 = e1)
% 170.79/26.52 (3) ~ (e1 = e0)
% 170.79/26.52 (4) op(e2, e3) = all_52_1
% 170.79/26.52 (5) ~ (e3 = e0)
% 170.79/26.52 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.52 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.52 (7) all_58_3 = e2
% 170.79/26.52 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.52 (9) ~ (e2 = e0)
% 170.79/26.52 (10) op(e3, e3) = e3
% 170.79/26.52 (11) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.52 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.52 (12) ~ (e2 = e1)
% 170.79/26.52 (13) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 170.79/26.52 (14) ~ (e3 = e2)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | BETA: splitting (13) gives:
% 170.79/26.52 |
% 170.79/26.52 | Case 1:
% 170.79/26.52 | |
% 170.79/26.52 | | (15) all_58_0 = e2 & op(e3, e3) = e2
% 170.79/26.52 | |
% 170.79/26.52 | | ALPHA: (15) implies:
% 170.79/26.52 | | (16) op(e3, e3) = e2
% 170.79/26.52 | |
% 170.79/26.52 | | REF_CLOSE: (8), (10), (14), (16) are inconsistent by sub-proof #838.
% 170.79/26.52 | |
% 170.79/26.52 | Case 2:
% 170.79/26.52 | |
% 170.79/26.52 | | (17) all_58_2 = e2 & op(e2, e3) = e2
% 170.79/26.52 | |
% 170.79/26.52 | | ALPHA: (17) implies:
% 170.79/26.52 | | (18) all_58_2 = e2
% 170.79/26.52 | | (19) op(e2, e3) = e2
% 170.79/26.52 | |
% 170.79/26.52 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14),
% 170.79/26.52 | | (18), (19) are inconsistent by sub-proof #779.
% 170.79/26.52 | |
% 170.79/26.52 | End of split
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #779 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.52 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.52 (2) all_58_2 = e2
% 170.79/26.52 (3) ~ (e3 = e1)
% 170.79/26.52 (4) ~ (e1 = e0)
% 170.79/26.52 (5) op(e2, e3) = all_52_1
% 170.79/26.52 (6) op(e2, e3) = e2
% 170.79/26.52 (7) ~ (e3 = e0)
% 170.79/26.52 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.52 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.52 (9) all_58_3 = e2
% 170.79/26.52 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.52 (11) ~ (e2 = e0)
% 170.79/26.52 (12) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.52 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 170.79/26.52 (13) ~ (e2 = e1)
% 170.79/26.52 (14) ~ (e3 = e2)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | BETA: splitting (12) gives:
% 170.79/26.52 |
% 170.79/26.52 | Case 1:
% 170.79/26.52 | |
% 170.79/26.52 | | (15) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 170.79/26.52 | | e3)
% 170.79/26.52 | |
% 170.79/26.52 | | BETA: splitting (15) gives:
% 170.79/26.52 | |
% 170.79/26.52 | | Case 1:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (16) all_58_2 = e3 & op(e2, e3) = e3
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (2), (14), (16) are inconsistent by sub-proof #786.
% 170.79/26.52 | | |
% 170.79/26.52 | | Case 2:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (17) all_58_3 = e3 & op(e2, e2) = e3
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (9), (14), (17) are inconsistent by sub-proof #785.
% 170.79/26.52 | | |
% 170.79/26.52 | | End of split
% 170.79/26.52 | |
% 170.79/26.52 | Case 2:
% 170.79/26.52 | |
% 170.79/26.52 | | (18) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 170.79/26.52 | | e3)
% 170.79/26.52 | |
% 170.79/26.52 | | BETA: splitting (18) gives:
% 170.79/26.52 | |
% 170.79/26.52 | | Case 1:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (19) all_58_5 = e3 & op(e2, e1) = e3
% 170.79/26.52 | | |
% 170.79/26.52 | | | ALPHA: (19) implies:
% 170.79/26.52 | | | (20) all_58_5 = e3
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (13), (20) are
% 170.79/26.52 | | | inconsistent by sub-proof #827.
% 170.79/26.52 | | |
% 170.79/26.52 | | Case 2:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (21) all_58_10 = e3 & op(e2, e0) = e3
% 170.79/26.52 | | |
% 170.79/26.52 | | | ALPHA: (21) implies:
% 170.79/26.52 | | | (22) all_58_10 = e3
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (22)
% 170.79/26.52 | | | are inconsistent by sub-proof #780.
% 170.79/26.52 | | |
% 170.79/26.52 | | End of split
% 170.79/26.52 | |
% 170.79/26.52 | End of split
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #780 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.52 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.52 (2) ~ (e3 = e1)
% 170.79/26.52 (3) ~ (e1 = e0)
% 170.79/26.52 (4) all_58_10 = e3
% 170.79/26.52 (5) op(e2, e3) = all_52_1
% 170.79/26.52 (6) op(e2, e3) = e2
% 170.79/26.52 (7) ~ (e3 = e0)
% 170.79/26.52 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.52 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.52 (9) all_58_3 = e2
% 170.79/26.52 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.52 (11) ~ (e2 = e0)
% 170.79/26.52 (12) ~ (e2 = e1)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | BETA: splitting (1) gives:
% 170.79/26.52 |
% 170.79/26.52 | Case 1:
% 170.79/26.52 | |
% 170.79/26.52 | | (13) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 170.79/26.52 | | e1)
% 170.79/26.52 | |
% 170.79/26.52 | | REF_CLOSE: (5), (6), (9), (10), (12), (13) are inconsistent by sub-proof
% 170.79/26.52 | | #783.
% 170.79/26.52 | |
% 170.79/26.52 | Case 2:
% 170.79/26.52 | |
% 170.79/26.52 | | (14) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 170.79/26.52 | | e1)
% 170.79/26.52 | |
% 170.79/26.52 | | BETA: splitting (14) gives:
% 170.79/26.52 | |
% 170.79/26.52 | | Case 1:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (15) all_58_5 = e1 & op(e2, e1) = e1
% 170.79/26.52 | | |
% 170.79/26.52 | | | ALPHA: (15) implies:
% 170.79/26.52 | | | (16) all_58_5 = e1
% 170.79/26.52 | | |
% 170.79/26.52 | | | BETA: splitting (8) gives:
% 170.79/26.52 | | |
% 170.79/26.52 | | | Case 1:
% 170.79/26.52 | | | |
% 170.79/26.52 | | | | (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2)
% 170.79/26.52 | | | | = e0)
% 170.79/26.52 | | | |
% 170.79/26.52 | | | | BETA: splitting (17) gives:
% 170.79/26.52 | | | |
% 170.79/26.52 | | | | Case 1:
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | | (18) all_58_2 = e0 & op(e2, e3) = e0
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | | REF_CLOSE: (5), (6), (10), (11), (18) are inconsistent by sub-proof
% 170.79/26.52 | | | | | #782.
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | Case 2:
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | | (19) all_58_3 = e0 & op(e2, e2) = e0
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | | REF_CLOSE: (9), (11), (19) are inconsistent by sub-proof #934.
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | End of split
% 170.79/26.52 | | | |
% 170.79/26.52 | | | Case 2:
% 170.79/26.52 | | | |
% 170.79/26.52 | | | | (20) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0)
% 170.79/26.52 | | | | = e0)
% 170.79/26.52 | | | |
% 170.79/26.52 | | | | BETA: splitting (20) gives:
% 170.79/26.52 | | | |
% 170.79/26.52 | | | | Case 1:
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | | (21) all_58_5 = e0 & op(e2, e1) = e0
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | | REF_CLOSE: (3), (16), (21) are inconsistent by sub-proof #781.
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | Case 2:
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | | (22) all_58_10 = e0 & op(e2, e0) = e0
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | | ALPHA: (22) implies:
% 170.79/26.52 | | | | | (23) all_58_10 = e0
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | | REF_CLOSE: (4), (7), (23) are inconsistent by sub-proof #841.
% 170.79/26.52 | | | | |
% 170.79/26.52 | | | | End of split
% 170.79/26.52 | | | |
% 170.79/26.52 | | | End of split
% 170.79/26.52 | | |
% 170.79/26.52 | | Case 2:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (24) all_58_10 = e1 & op(e2, e0) = e1
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (2), (4), (24) are inconsistent by sub-proof #851.
% 170.79/26.52 | | |
% 170.79/26.52 | | End of split
% 170.79/26.52 | |
% 170.79/26.52 | End of split
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #781 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_5 = e0 & op(e2, e1) = e0
% 170.79/26.52 (2) all_58_5 = e1
% 170.79/26.52 (3) ~ (e1 = e0)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | ALPHA: (1) implies:
% 170.79/26.52 | (4) all_58_5 = e0
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.52 | (5) e1 = e0
% 170.79/26.52 |
% 170.79/26.52 | REDUCE: (3), (5) imply:
% 170.79/26.52 | (6) $false
% 170.79/26.52 |
% 170.79/26.52 | CLOSE: (6) is inconsistent.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #782 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) op(e2, e3) = all_52_1
% 170.79/26.52 (2) op(e2, e3) = e2
% 170.79/26.52 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.52 (4) ~ (e2 = e0)
% 170.79/26.52 (5) all_58_2 = e0 & op(e2, e3) = e0
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | ALPHA: (5) implies:
% 170.79/26.52 | (6) op(e2, e3) = e0
% 170.79/26.52 |
% 170.79/26.52 | GROUND_INST: instantiating (3) with all_52_1, e0, e3, e2, simplifying with
% 170.79/26.52 | (1), (6) gives:
% 170.79/26.52 | (7) all_52_1 = e0
% 170.79/26.52 |
% 170.79/26.52 | GROUND_INST: instantiating (3) with all_52_1, e2, e3, e2, simplifying with
% 170.79/26.52 | (1), (2) gives:
% 170.79/26.52 | (8) all_52_1 = e2
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (7), (8) imply:
% 170.79/26.52 | (9) e2 = e0
% 170.79/26.52 |
% 170.79/26.52 | SIMP: (9) implies:
% 170.79/26.52 | (10) e2 = e0
% 170.79/26.52 |
% 170.79/26.52 | REDUCE: (4), (10) imply:
% 170.79/26.52 | (11) $false
% 170.79/26.52 |
% 170.79/26.52 | CLOSE: (11) is inconsistent.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #783 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1)
% 170.79/26.52 (2) op(e2, e3) = all_52_1
% 170.79/26.52 (3) op(e2, e3) = e2
% 170.79/26.52 (4) all_58_3 = e2
% 170.79/26.52 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.52 (6) ~ (e2 = e1)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | BETA: splitting (1) gives:
% 170.79/26.52 |
% 170.79/26.52 | Case 1:
% 170.79/26.52 | |
% 170.79/26.52 | | (7) all_58_2 = e1 & op(e2, e3) = e1
% 170.79/26.52 | |
% 170.79/26.52 | | ALPHA: (7) implies:
% 170.79/26.52 | | (8) op(e2, e3) = e1
% 170.79/26.52 | |
% 170.79/26.52 | | REF_CLOSE: (2), (3), (5), (6), (8) are inconsistent by sub-proof #784.
% 170.79/26.52 | |
% 170.79/26.52 | Case 2:
% 170.79/26.52 | |
% 170.79/26.52 | | (9) all_58_3 = e1 & op(e2, e2) = e1
% 170.79/26.52 | |
% 170.79/26.52 | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #914.
% 170.79/26.52 | |
% 170.79/26.52 | End of split
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #784 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) op(e2, e3) = all_52_1
% 170.79/26.52 (2) op(e2, e3) = e2
% 170.79/26.52 (3) op(e2, e3) = e1
% 170.79/26.52 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.52 (5) ~ (e2 = e1)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | GROUND_INST: instantiating (4) with all_52_1, e1, e3, e2, simplifying with
% 170.79/26.52 | (1), (3) gives:
% 170.79/26.52 | (6) all_52_1 = e1
% 170.79/26.52 |
% 170.79/26.52 | GROUND_INST: instantiating (4) with all_52_1, e2, e3, e2, simplifying with
% 170.79/26.52 | (1), (2) gives:
% 170.79/26.52 | (7) all_52_1 = e2
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (6), (7) imply:
% 170.79/26.52 | (8) e2 = e1
% 170.79/26.52 |
% 170.79/26.52 | REDUCE: (5), (8) imply:
% 170.79/26.52 | (9) $false
% 170.79/26.52 |
% 170.79/26.52 | CLOSE: (9) is inconsistent.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #785 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_3 = e3 & op(e2, e2) = e3
% 170.79/26.52 (2) all_58_3 = e2
% 170.79/26.52 (3) ~ (e3 = e2)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | ALPHA: (1) implies:
% 170.79/26.52 | (4) all_58_3 = e3
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.52 | (5) e3 = e2
% 170.79/26.52 |
% 170.79/26.52 | SIMP: (5) implies:
% 170.79/26.52 | (6) e3 = e2
% 170.79/26.52 |
% 170.79/26.52 | REDUCE: (3), (6) imply:
% 170.79/26.52 | (7) $false
% 170.79/26.52 |
% 170.79/26.52 | CLOSE: (7) is inconsistent.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #786 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_2 = e3 & op(e2, e3) = e3
% 170.79/26.52 (2) all_58_2 = e2
% 170.79/26.52 (3) ~ (e3 = e2)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | ALPHA: (1) implies:
% 170.79/26.52 | (4) all_58_2 = e3
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.52 | (5) e3 = e2
% 170.79/26.52 |
% 170.79/26.52 | SIMP: (5) implies:
% 170.79/26.52 | (6) e3 = e2
% 170.79/26.52 |
% 170.79/26.52 | REDUCE: (3), (6) imply:
% 170.79/26.52 | (7) $false
% 170.79/26.52 |
% 170.79/26.52 | CLOSE: (7) is inconsistent.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #787 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_9 = e2
% 170.79/26.52 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.52 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.52 (3) ~ (e3 = e1)
% 170.79/26.52 (4) op(e3, e3) = e1
% 170.79/26.52 (5) op(e3, e1) = all_52_8
% 170.79/26.52 (6) ~ (e1 = e0)
% 170.79/26.52 (7) all_56_10 = e1
% 170.79/26.52 (8) ~ (e3 = e0)
% 170.79/26.52 (9) all_58_4 = e1
% 170.79/26.52 (10) all_58_4 = e2 & op(e3, e1) = e2
% 170.79/26.52 (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.52 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.52 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.52 (13) ~ (e2 = e0)
% 170.79/26.52 (14) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 170.79/26.52 (15) ~ (e2 = e1)
% 170.79/26.52 (16) ~ (e3 = e2)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | ALPHA: (10) implies:
% 170.79/26.52 | (17) all_58_4 = e2
% 170.79/26.52 | (18) op(e3, e1) = e2
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (9), (17) imply:
% 170.79/26.52 | (19) e2 = e1
% 170.79/26.52 |
% 170.79/26.52 | SIMP: (19) implies:
% 170.79/26.52 | (20) e2 = e1
% 170.79/26.52 |
% 170.79/26.52 | COMBINE_EQS: (1), (20) imply:
% 170.79/26.52 | (21) all_58_9 = e1
% 170.79/26.52 |
% 170.79/26.52 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11), (12), (13), (14), (15),
% 170.79/26.52 | (16), (17), (18), (21) are inconsistent by sub-proof #801.
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #788 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_9 = e2
% 170.79/26.52 (2) all_58_0 = e1
% 170.79/26.52 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.52 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.52 (4) ~ (e3 = e1)
% 170.79/26.52 (5) op(e3, e3) = e1
% 170.79/26.52 (6) ~ (e1 = e0)
% 170.79/26.52 (7) ~ (e3 = e0)
% 170.79/26.52 (8) all_58_4 = e1
% 170.79/26.52 (9) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 170.79/26.52 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.52 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.52 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.52 (11) ~ (e2 = e0)
% 170.79/26.52 (12) ~ (e3 = e2)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | BETA: splitting (9) gives:
% 170.79/26.52 |
% 170.79/26.52 | Case 1:
% 170.79/26.52 | |
% 170.79/26.52 | | (13) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 170.79/26.52 | | e3)
% 170.79/26.52 | |
% 170.79/26.52 | | BETA: splitting (13) gives:
% 170.79/26.52 | |
% 170.79/26.52 | | Case 1:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (14) all_58_0 = e3 & op(e3, e3) = e3
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (2), (4), (14) are inconsistent by sub-proof #905.
% 170.79/26.52 | | |
% 170.79/26.52 | | Case 2:
% 170.79/26.52 | | |
% 170.79/26.52 | | | (15) all_58_1 = e3 & op(e3, e2) = e3
% 170.79/26.52 | | |
% 170.79/26.52 | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (10), (11), (15) are inconsistent
% 170.79/26.52 | | | by sub-proof #791.
% 170.79/26.52 | | |
% 170.79/26.52 | | End of split
% 170.79/26.52 | |
% 170.79/26.52 | Case 2:
% 170.79/26.52 | |
% 170.79/26.52 | | (16) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 170.79/26.52 | | e3)
% 170.79/26.52 | |
% 170.79/26.52 | | REF_CLOSE: (1), (4), (8), (12), (16) are inconsistent by sub-proof #789.
% 170.79/26.52 | |
% 170.79/26.52 | End of split
% 170.79/26.52 |
% 170.79/26.52 End of proof
% 170.79/26.52
% 170.79/26.52 Sub-proof #789 shows that the following formulas are inconsistent:
% 170.79/26.52 ----------------------------------------------------------------
% 170.79/26.52 (1) all_58_9 = e2
% 170.79/26.52 (2) ~ (e3 = e1)
% 170.79/26.52 (3) all_58_4 = e1
% 170.79/26.52 (4) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 170.79/26.52 (5) ~ (e3 = e2)
% 170.79/26.52
% 170.79/26.52 Begin of proof
% 170.79/26.52 |
% 170.79/26.52 | BETA: splitting (4) gives:
% 170.79/26.52 |
% 170.79/26.52 | Case 1:
% 170.79/26.52 | |
% 170.79/26.52 | | (6) all_58_4 = e3 & op(e3, e1) = e3
% 170.79/26.52 | |
% 170.79/26.52 | | ALPHA: (6) implies:
% 170.79/26.52 | | (7) all_58_4 = e3
% 170.79/26.52 | |
% 170.79/26.52 | | COMBINE_EQS: (3), (7) imply:
% 170.79/26.52 | | (8) e3 = e1
% 170.79/26.52 | |
% 170.79/26.52 | | REDUCE: (2), (8) imply:
% 170.79/26.52 | | (9) $false
% 170.79/26.52 | |
% 170.79/26.52 | | CLOSE: (9) is inconsistent.
% 170.79/26.52 | |
% 170.79/26.52 | Case 2:
% 170.79/26.52 | |
% 170.79/26.52 | | (10) all_58_9 = e3 & op(e3, e0) = e3
% 170.79/26.52 | |
% 170.79/26.52 | | ALPHA: (10) implies:
% 170.79/26.52 | | (11) all_58_9 = e3
% 170.79/26.52 | |
% 170.79/26.53 | | REF_CLOSE: (1), (5), (11) are inconsistent by sub-proof #790.
% 170.79/26.53 | |
% 170.79/26.53 | End of split
% 170.79/26.53 |
% 170.79/26.53 End of proof
% 170.79/26.53
% 170.79/26.53 Sub-proof #790 shows that the following formulas are inconsistent:
% 170.79/26.53 ----------------------------------------------------------------
% 170.79/26.53 (1) all_58_9 = e3
% 170.79/26.53 (2) all_58_9 = e2
% 170.79/26.53 (3) ~ (e3 = e2)
% 170.79/26.53
% 170.79/26.53 Begin of proof
% 170.79/26.53 |
% 170.79/26.53 | COMBINE_EQS: (1), (2) imply:
% 170.79/26.53 | (4) e3 = e2
% 170.79/26.53 |
% 170.79/26.53 | SIMP: (4) implies:
% 170.79/26.53 | (5) e3 = e2
% 170.79/26.53 |
% 170.79/26.53 | REDUCE: (3), (5) imply:
% 170.79/26.53 | (6) $false
% 170.79/26.53 |
% 170.79/26.53 | CLOSE: (6) is inconsistent.
% 170.79/26.53 |
% 170.79/26.53 End of proof
% 170.79/26.53
% 170.79/26.53 Sub-proof #791 shows that the following formulas are inconsistent:
% 170.79/26.53 ----------------------------------------------------------------
% 170.79/26.53 (1) all_58_9 = e2
% 170.79/26.53 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.53 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.53 (3) op(e3, e3) = e1
% 170.79/26.53 (4) ~ (e1 = e0)
% 170.79/26.53 (5) ~ (e3 = e0)
% 170.79/26.53 (6) all_58_4 = e1
% 170.79/26.53 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.53 (8) ~ (e2 = e0)
% 170.79/26.53 (9) all_58_1 = e3 & op(e3, e2) = e3
% 170.79/26.53
% 170.79/26.53 Begin of proof
% 170.79/26.53 |
% 170.79/26.53 | ALPHA: (9) implies:
% 170.79/26.53 | (10) all_58_1 = e3
% 170.79/26.53 |
% 170.79/26.53 | BETA: splitting (2) gives:
% 170.79/26.53 |
% 170.79/26.53 | Case 1:
% 170.79/26.53 | |
% 170.79/26.53 | | (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 170.79/26.53 | | e0)
% 170.79/26.53 | |
% 170.79/26.53 | | BETA: splitting (11) gives:
% 170.79/26.53 | |
% 170.79/26.53 | | Case 1:
% 170.79/26.53 | | |
% 170.79/26.53 | | | (12) all_58_0 = e0 & op(e3, e3) = e0
% 170.79/26.53 | | |
% 170.79/26.53 | | | ALPHA: (12) implies:
% 170.79/26.53 | | | (13) op(e3, e3) = e0
% 170.79/26.53 | | |
% 170.79/26.53 | | | REF_CLOSE: (3), (4), (7), (13) are inconsistent by sub-proof #907.
% 170.79/26.53 | | |
% 170.79/26.53 | | Case 2:
% 170.79/26.53 | | |
% 170.79/26.53 | | | (14) all_58_1 = e0 & op(e3, e2) = e0
% 170.79/26.53 | | |
% 170.79/26.53 | | | REF_CLOSE: (5), (10), (14) are inconsistent by sub-proof #794.
% 170.79/26.53 | | |
% 170.79/26.53 | | End of split
% 170.79/26.53 | |
% 170.79/26.53 | Case 2:
% 170.79/26.53 | |
% 170.79/26.53 | | (15) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 170.79/26.53 | | e0)
% 170.79/26.53 | |
% 170.79/26.53 | | REF_CLOSE: (1), (4), (6), (8), (15) are inconsistent by sub-proof #792.
% 170.79/26.53 | |
% 170.79/26.53 | End of split
% 170.79/26.53 |
% 170.79/26.53 End of proof
% 170.79/26.53
% 170.79/26.53 Sub-proof #792 shows that the following formulas are inconsistent:
% 170.79/26.53 ----------------------------------------------------------------
% 170.79/26.53 (1) all_58_9 = e2
% 170.79/26.53 (2) ~ (e1 = e0)
% 170.79/26.53 (3) all_58_4 = e1
% 170.79/26.53 (4) ~ (e2 = e0)
% 170.79/26.53 (5) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.53
% 170.79/26.53 Begin of proof
% 170.79/26.53 |
% 170.79/26.53 | BETA: splitting (5) gives:
% 170.79/26.53 |
% 170.79/26.53 | Case 1:
% 170.79/26.53 | |
% 170.79/26.53 | | (6) all_58_4 = e0 & op(e3, e1) = e0
% 170.79/26.53 | |
% 170.79/26.53 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #793.
% 170.79/26.53 | |
% 170.79/26.53 | Case 2:
% 170.79/26.53 | |
% 170.79/26.53 | | (7) all_58_9 = e0 & op(e3, e0) = e0
% 170.79/26.53 | |
% 170.79/26.53 | | ALPHA: (7) implies:
% 170.79/26.53 | | (8) all_58_9 = e0
% 170.79/26.53 | |
% 170.79/26.53 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #945.
% 170.79/26.53 | |
% 170.79/26.53 | End of split
% 170.79/26.53 |
% 170.79/26.53 End of proof
% 170.79/26.53
% 170.79/26.53 Sub-proof #793 shows that the following formulas are inconsistent:
% 170.79/26.53 ----------------------------------------------------------------
% 170.79/26.53 (1) all_58_4 = e0 & op(e3, e1) = e0
% 170.79/26.53 (2) all_58_4 = e1
% 170.79/26.53 (3) ~ (e1 = e0)
% 170.79/26.53
% 170.79/26.53 Begin of proof
% 170.79/26.53 |
% 170.79/26.53 | ALPHA: (1) implies:
% 170.79/26.53 | (4) all_58_4 = e0
% 170.79/26.53 |
% 170.79/26.53 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.53 | (5) e1 = e0
% 170.79/26.53 |
% 170.79/26.53 | REDUCE: (3), (5) imply:
% 170.79/26.53 | (6) $false
% 170.79/26.53 |
% 170.79/26.53 | CLOSE: (6) is inconsistent.
% 170.79/26.53 |
% 170.79/26.53 End of proof
% 170.79/26.53
% 170.79/26.53 Sub-proof #794 shows that the following formulas are inconsistent:
% 170.79/26.53 ----------------------------------------------------------------
% 170.79/26.53 (1) all_58_1 = e0 & op(e3, e2) = e0
% 170.79/26.53 (2) all_58_1 = e3
% 170.79/26.53 (3) ~ (e3 = e0)
% 170.79/26.53
% 170.79/26.53 Begin of proof
% 170.79/26.53 |
% 170.79/26.53 | ALPHA: (1) implies:
% 170.79/26.53 | (4) all_58_1 = e0
% 170.79/26.53 |
% 170.79/26.53 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.53 | (5) e3 = e0
% 170.79/26.53 |
% 170.79/26.53 | REDUCE: (3), (5) imply:
% 170.79/26.53 | (6) $false
% 170.79/26.53 |
% 170.79/26.53 | CLOSE: (6) is inconsistent.
% 170.79/26.53 |
% 170.79/26.53 End of proof
% 170.79/26.53
% 170.79/26.53 Sub-proof #795 shows that the following formulas are inconsistent:
% 170.79/26.53 ----------------------------------------------------------------
% 170.79/26.53 (1) ~ (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 170.79/26.53 $i(all_56_4))
% 170.79/26.53 (2) all_56_10 = e1
% 170.79/26.53 (3) all_56_4 = e3
% 170.79/26.53
% 170.79/26.53 Begin of proof
% 170.79/26.53 |
% 170.79/26.53 | BETA: splitting (1) gives:
% 170.79/26.53 |
% 170.79/26.53 | Case 1:
% 170.79/26.53 | |
% 170.79/26.53 | | (4) ~ (all_56_10 = e1)
% 170.79/26.53 | |
% 170.79/26.53 | | REDUCE: (2), (4) imply:
% 170.79/26.53 | | (5) $false
% 170.79/26.53 | |
% 170.79/26.53 | | CLOSE: (5) is inconsistent.
% 170.79/26.53 | |
% 170.79/26.53 | Case 2:
% 170.79/26.53 | |
% 170.79/26.53 | | (6) ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4)
% 170.79/26.53 | |
% 170.79/26.53 | | ALPHA: (6) implies:
% 170.79/26.53 | | (7) ~ (all_56_4 = e3)
% 170.79/26.53 | |
% 170.79/26.53 | | REDUCE: (3), (7) imply:
% 170.79/26.53 | | (8) $false
% 170.79/26.53 | |
% 170.79/26.53 | | CLOSE: (8) is inconsistent.
% 170.79/26.53 | |
% 170.79/26.53 | End of split
% 170.79/26.53 |
% 170.79/26.53 End of proof
% 170.79/26.53
% 170.79/26.53 Sub-proof #796 shows that the following formulas are inconsistent:
% 170.79/26.53 ----------------------------------------------------------------
% 170.79/26.53 (1) all_56_12 = e2
% 170.79/26.53 (2) op(e3, e2) = e0
% 170.79/26.53 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.53 (4) ~ (e2 = e0)
% 170.79/26.53 (5) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 170.79/26.53 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 170.79/26.53 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 170.79/26.53 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 170.79/26.53 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 170.79/26.53 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 170.79/26.53 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 170.79/26.53 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 170.79/26.53 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 170.79/26.53 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 170.79/26.53
% 170.79/26.53 Begin of proof
% 170.79/26.53 |
% 170.79/26.53 | BETA: splitting (5) gives:
% 170.79/26.53 |
% 170.79/26.53 | Case 1:
% 170.79/26.53 | |
% 170.79/26.53 | | (6) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 170.79/26.53 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 170.79/26.53 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 170.79/26.53 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 170.79/26.53 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 170.79/26.53 | |
% 170.79/26.53 | | ALPHA: (6) implies:
% 170.79/26.53 | | (7) ~ (all_56_12 = e2)
% 170.79/26.53 | |
% 170.79/26.53 | | REDUCE: (1), (7) imply:
% 170.79/26.53 | | (8) $false
% 170.79/26.53 | |
% 170.79/26.53 | | CLOSE: (8) is inconsistent.
% 170.79/26.53 | |
% 170.79/26.53 | Case 2:
% 170.79/26.53 | |
% 170.79/26.53 | | (9) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 170.79/26.53 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 170.79/26.53 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 170.79/26.53 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 170.79/26.53 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 170.79/26.53 | |
% 170.79/26.53 | | ALPHA: (9) implies:
% 170.79/26.53 | | (10) op(e3, e2) = e2
% 170.79/26.53 | |
% 170.79/26.53 | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #953.
% 170.79/26.53 | |
% 170.79/26.53 | End of split
% 170.79/26.53 |
% 170.79/26.53 End of proof
% 170.79/26.53
% 170.79/26.53 Sub-proof #797 shows that the following formulas are inconsistent:
% 170.79/26.53 ----------------------------------------------------------------
% 170.79/26.53 (1) all_58_2 = e3
% 170.79/26.53 (2) ~ (e1 = e0)
% 170.79/26.53 (3) ~ (e3 = e0)
% 170.79/26.53 (4) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.53 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.53 (5) op(e2, e0) = e1
% 170.79/26.53 (6) all_58_3 = e2
% 170.79/26.53 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 170.79/26.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 170.79/26.53 (8) ~ (e2 = e0)
% 170.79/26.53 (9) all_58_5 = e2
% 170.79/26.53
% 170.79/26.53 Begin of proof
% 170.79/26.53 |
% 170.79/26.53 | BETA: splitting (4) gives:
% 170.79/26.53 |
% 170.79/26.53 | Case 1:
% 170.79/26.53 | |
% 170.79/26.53 | | (10) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 170.79/26.53 | | e0)
% 170.79/26.53 | |
% 170.79/26.53 | | REF_CLOSE: (1), (3), (6), (8), (10) are inconsistent by sub-proof #912.
% 170.79/26.53 | |
% 170.79/26.53 | Case 2:
% 170.79/26.53 | |
% 170.79/26.53 | | (11) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 170.79/26.53 | | e0)
% 170.79/26.53 | |
% 170.79/26.53 | | BETA: splitting (11) gives:
% 170.79/26.53 | |
% 170.79/26.53 | | Case 1:
% 170.79/26.53 | | |
% 170.79/26.53 | | | (12) all_58_5 = e0 & op(e2, e1) = e0
% 170.79/26.53 | | |
% 170.79/26.53 | | | REF_CLOSE: (8), (9), (12) are inconsistent by sub-proof #798.
% 170.79/26.53 | | |
% 170.79/26.53 | | Case 2:
% 170.79/26.53 | | |
% 170.79/26.53 | | | (13) all_58_10 = e0 & op(e2, e0) = e0
% 170.79/26.53 | | |
% 170.79/26.53 | | | ALPHA: (13) implies:
% 170.79/26.53 | | | (14) op(e2, e0) = e0
% 170.79/26.53 | | |
% 170.79/26.53 | | | REF_CLOSE: (2), (5), (7), (14) are inconsistent by sub-proof #849.
% 170.79/26.53 | | |
% 170.79/26.53 | | End of split
% 170.79/26.53 | |
% 170.79/26.53 | End of split
% 170.79/26.53 |
% 170.79/26.53 End of proof
% 170.79/26.53
% 170.79/26.53 Sub-proof #798 shows that the following formulas are inconsistent:
% 170.79/26.53 ----------------------------------------------------------------
% 170.79/26.53 (1) all_58_5 = e0 & op(e2, e1) = e0
% 170.79/26.53 (2) all_58_5 = e2
% 170.79/26.53 (3) ~ (e2 = e0)
% 170.79/26.53
% 170.79/26.53 Begin of proof
% 170.79/26.53 |
% 170.79/26.53 | ALPHA: (1) implies:
% 170.79/26.53 | (4) all_58_5 = e0
% 170.79/26.53 |
% 170.79/26.53 | COMBINE_EQS: (2), (4) imply:
% 170.79/26.53 | (5) e2 = e0
% 170.79/26.53 |
% 170.79/26.53 | SIMP: (5) implies:
% 170.79/26.53 | (6) e2 = e0
% 170.79/26.53 |
% 170.79/26.53 | REDUCE: (3), (6) imply:
% 170.79/26.53 | (7) $false
% 170.79/26.53 |
% 170.79/26.53 | CLOSE: (7) is inconsistent.
% 170.79/26.53 |
% 170.79/26.53 End of proof
% 170.79/26.53
% 170.79/26.53 Sub-proof #799 shows that the following formulas are inconsistent:
% 170.79/26.53 ----------------------------------------------------------------
% 170.79/26.53 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 170.79/26.53 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.79/26.53 (2) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 170.79/26.53 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 170.79/26.53 (3) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.53 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 170.79/26.53 (4) ~ (all_4_2 = e2)
% 170.79/26.53 (5) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 170.79/26.53 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 170.79/26.53 (6) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2) |
% 170.79/26.53 (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 = e2 & op(e0, e3) = e2)
% 170.79/26.53 (7) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 170.79/26.53 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.53 (8) ~ (all_8_2 = e3)
% 170.79/26.53 (9) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 170.79/26.53 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 170.79/26.53 (10) ~ (all_6_2 = e3)
% 170.79/26.53 (11) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 170.79/26.53 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 170.79/26.53 (12) ~ (e3 = e1)
% 170.79/26.53 (13) op(e3, e3) = e1
% 170.79/26.53 (14) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 170.79/26.53 | (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 170.79/26.53 e1)
% 170.79/26.53 (15) op(e3, e1) = all_52_8
% 170.79/26.53 (16) ~ (e1 = e0)
% 170.79/26.53 (17) all_56_10 = e1
% 170.79/26.53 (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 170.79/26.53 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 170.79/26.53 (19) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0) = e2) |
% 170.79/26.53 (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 170.79/26.53 (20) op(e2, e2) = all_8_2
% 170.79/26.53 (21) ~ (all_6_2 = e2)
% 170.79/26.53 (22) op(e1, e1) = all_6_2
% 170.79/26.53 (23) ~ (e3 = e0)
% 170.79/26.53 (24) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 170.79/26.53 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 170.79/26.53 (25) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 170.79/26.53 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 170.79/26.53 (26) op(e0, e0) = all_4_2
% 171.17/26.53 (27) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.17/26.53 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 171.17/26.53 (28) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 171.17/26.53 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 171.17/26.53 (29) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 171.17/26.53 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 171.17/26.53 (30) all_58_3 = e2
% 171.17/26.53 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.17/26.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.17/26.53 (32) ~ (e2 = e0)
% 171.17/26.53 (33) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 171.17/26.53 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 171.17/26.53 (34) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 171.17/26.53 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 171.17/26.53 (35) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 171.17/26.53 (36) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 171.17/26.53 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 171.17/26.53 (37) ~ (e2 = e1)
% 171.17/26.53 (38) op(e3, e2) = all_52_4
% 171.17/26.53 (39) all_58_9 = e1
% 171.17/26.53 (40) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 171.17/26.53 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 171.17/26.53 (41) op(e0, e2) = all_52_7
% 171.17/26.53 (42) ~ (all_52_4 = e1)
% 171.17/26.53 (43) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 171.17/26.53 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.17/26.53 (44) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) = e2) |
% 171.17/26.53 (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 171.17/26.53 (45) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.17/26.53 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 171.17/26.53 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.17/26.53 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.17/26.53 (46) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 & op(e2, e1) = e2) |
% 171.17/26.53 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 & op(e0, e1) = e2)
% 171.17/26.53 (47) ~ (e3 = e2)
% 171.17/26.53
% 171.17/26.53 Begin of proof
% 171.17/26.53 |
% 171.17/26.53 | BETA: splitting (44) gives:
% 171.17/26.53 |
% 171.17/26.53 | Case 1:
% 171.17/26.53 | |
% 171.17/26.53 | | (48) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_1 = e2 & op(e3, e2) =
% 171.17/26.53 | | e2)
% 171.17/26.53 | |
% 171.17/26.53 | | BETA: splitting (48) gives:
% 171.17/26.53 | |
% 171.17/26.53 | | Case 1:
% 171.17/26.53 | | |
% 171.17/26.53 | | | (49) all_58_0 = e2 & op(e3, e3) = e2
% 171.17/26.53 | | |
% 171.17/26.53 | | | ALPHA: (49) implies:
% 171.17/26.53 | | | (50) op(e3, e3) = e2
% 171.17/26.53 | | |
% 171.17/26.53 | | | REF_CLOSE: (13), (31), (37), (50) are inconsistent by sub-proof #957.
% 171.17/26.53 | | |
% 171.17/26.53 | | Case 2:
% 171.17/26.53 | | |
% 171.17/26.53 | | | (51) all_58_1 = e2 & op(e3, e2) = e2
% 171.17/26.53 | | |
% 171.17/26.53 | | | ALPHA: (51) implies:
% 171.17/26.53 | | | (52) all_58_1 = e2
% 171.17/26.53 | | |
% 171.17/26.53 | | | BETA: splitting (19) gives:
% 171.17/26.53 | | |
% 171.17/26.53 | | | Case 1:
% 171.17/26.53 | | | |
% 171.17/26.53 | | | | (53) (all_58_9 = e2 & op(e3, e0) = e2) | (all_58_10 = e2 & op(e2, e0)
% 171.17/26.53 | | | | = e2)
% 171.17/26.53 | | | |
% 171.17/26.53 | | | | BETA: splitting (53) gives:
% 171.17/26.53 | | | |
% 171.17/26.53 | | | | Case 1:
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | | (54) all_58_9 = e2 & op(e3, e0) = e2
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | | ALPHA: (54) implies:
% 171.17/26.53 | | | | | (55) all_58_9 = e2
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | | REF_CLOSE: (37), (39), (55) are inconsistent by sub-proof #942.
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | Case 2:
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | | (56) all_58_10 = e2 & op(e2, e0) = e2
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | | ALPHA: (56) implies:
% 171.17/26.53 | | | | | (57) all_58_10 = e2
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | | REF_CLOSE: (3), (8), (12), (16), (20), (23), (24), (30), (31), (32),
% 171.17/26.53 | | | | | (36), (37), (40), (47), (57) are inconsistent by sub-proof
% 171.17/26.53 | | | | | #908.
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | End of split
% 171.17/26.53 | | | |
% 171.17/26.53 | | | Case 2:
% 171.17/26.53 | | | |
% 171.17/26.53 | | | | (58) (all_58_11 = e2 & op(e1, e0) = e2) | (all_58_15 = e2 & op(e0,
% 171.17/26.53 | | | | e0) = e2)
% 171.17/26.53 | | | |
% 171.17/26.53 | | | | BETA: splitting (58) gives:
% 171.17/26.53 | | | |
% 171.17/26.53 | | | | Case 1:
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | | (59) all_58_11 = e2 & op(e1, e0) = e2
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | | ALPHA: (59) implies:
% 171.17/26.53 | | | | | (60) all_58_11 = e2
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | | BETA: splitting (11) gives:
% 171.17/26.53 | | | | |
% 171.17/26.53 | | | | | Case 1:
% 171.17/26.53 | | | | | |
% 171.17/26.53 | | | | | | (61) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 171.17/26.53 | | | | | | e2) = e0)
% 171.17/26.53 | | | | | |
% 171.17/26.53 | | | | | | BETA: splitting (61) gives:
% 171.17/26.53 | | | | | |
% 171.17/26.53 | | | | | | Case 1:
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | | (62) all_58_0 = e0 & op(e3, e3) = e0
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | | ALPHA: (62) implies:
% 171.17/26.53 | | | | | | | (63) op(e3, e3) = e0
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | | REF_CLOSE: (13), (16), (31), (63) are inconsistent by sub-proof
% 171.17/26.53 | | | | | | | #907.
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | Case 2:
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | | (64) all_58_1 = e0 & op(e3, e2) = e0
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | | REF_CLOSE: (32), (52), (64) are inconsistent by sub-proof #906.
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | End of split
% 171.17/26.53 | | | | | |
% 171.17/26.53 | | | | | Case 2:
% 171.17/26.53 | | | | | |
% 171.17/26.53 | | | | | | (65) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 171.17/26.53 | | | | | | e0) = e0)
% 171.17/26.53 | | | | | |
% 171.17/26.53 | | | | | | BETA: splitting (65) gives:
% 171.17/26.53 | | | | | |
% 171.17/26.53 | | | | | | Case 1:
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | | (66) all_58_4 = e0 & op(e3, e1) = e0
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | | ALPHA: (66) implies:
% 171.17/26.53 | | | | | | | (67) all_58_4 = e0
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | | BETA: splitting (46) gives:
% 171.17/26.53 | | | | | | |
% 171.17/26.53 | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | |
% 171.17/26.53 | | | | | | | | (68) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_5 = e2 &
% 171.17/26.53 | | | | | | | | op(e2, e1) = e2)
% 171.17/26.53 | | | | | | | |
% 171.17/26.53 | | | | | | | | BETA: splitting (68) gives:
% 171.17/26.53 | | | | | | | |
% 171.17/26.53 | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | (69) all_58_4 = e2 & op(e3, e1) = e2
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | ALPHA: (69) implies:
% 171.17/26.53 | | | | | | | | | (70) all_58_4 = e2
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | REF_CLOSE: (11), (12), (16), (23), (28), (29), (32), (37),
% 171.17/26.53 | | | | | | | | | (47), (52), (70) are inconsistent by sub-proof
% 171.17/26.53 | | | | | | | | | #895.
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | Case 2:
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | (71) all_58_5 = e2 & op(e2, e1) = e2
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | ALPHA: (71) implies:
% 171.17/26.53 | | | | | | | | | (72) all_58_5 = e2
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | BETA: splitting (3) gives:
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | (73) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 &
% 171.17/26.53 | | | | | | | | | | op(e2, e2) = e1)
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | BETA: splitting (73) gives:
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | (74) all_58_2 = e1 & op(e2, e3) = e1
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | ALPHA: (74) implies:
% 171.17/26.53 | | | | | | | | | | | (75) all_58_2 = e1
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (10), (12), (14), (16),
% 171.17/26.53 | | | | | | | | | | | (18), (20), (22), (23), (24), (26), (27), (30),
% 171.17/26.53 | | | | | | | | | | | (31), (32), (37), (38), (39), (41), (42), (43),
% 171.17/26.53 | | | | | | | | | | | (45), (47), (52), (60), (67), (72), (75) are
% 171.17/26.53 | | | | | | | | | | | inconsistent by sub-proof #853.
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | Case 2:
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | (76) all_58_3 = e1 & op(e2, e2) = e1
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | REF_CLOSE: (30), (37), (76) are inconsistent by sub-proof
% 171.17/26.53 | | | | | | | | | | | #914.
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | End of split
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | Case 2:
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | (77) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1
% 171.17/26.53 | | | | | | | | | | & op(e2, e0) = e1)
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | BETA: splitting (77) gives:
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | (78) all_58_5 = e1 & op(e2, e1) = e1
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | REF_CLOSE: (37), (72), (78) are inconsistent by sub-proof
% 171.17/26.53 | | | | | | | | | | | #852.
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | Case 2:
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | (79) all_58_10 = e1 & op(e2, e0) = e1
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | ALPHA: (79) implies:
% 171.17/26.53 | | | | | | | | | | | (80) op(e2, e0) = e1
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | REF_CLOSE: (3), (12), (16), (23), (24), (30), (31), (32),
% 171.17/26.53 | | | | | | | | | | | (37), (39), (43), (45), (47), (60), (72), (80) are
% 171.17/26.53 | | | | | | | | | | | inconsistent by sub-proof #846.
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | End of split
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | End of split
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | End of split
% 171.17/26.53 | | | | | | | |
% 171.17/26.53 | | | | | | | Case 2:
% 171.17/26.53 | | | | | | | |
% 171.17/26.53 | | | | | | | | (81) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_14 = e2 &
% 171.17/26.53 | | | | | | | | op(e0, e1) = e2)
% 171.17/26.53 | | | | | | | |
% 171.17/26.53 | | | | | | | | BETA: splitting (81) gives:
% 171.17/26.53 | | | | | | | |
% 171.17/26.53 | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | (82) all_58_8 = e2 & op(e1, e1) = e2
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | REF_CLOSE: (21), (22), (31), (82) are inconsistent by
% 171.17/26.53 | | | | | | | | | sub-proof #845.
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | Case 2:
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | (83) all_58_14 = e2 & op(e0, e1) = e2
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | ALPHA: (83) implies:
% 171.17/26.53 | | | | | | | | | (84) all_58_14 = e2
% 171.17/26.53 | | | | | | | | | (85) op(e0, e1) = e2
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | BETA: splitting (14) gives:
% 171.17/26.53 | | | | | | | | |
% 171.17/26.53 | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | (86) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1
% 171.17/26.53 | | | | | | | | | | & op(e0, e2) = e1)
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | BETA: splitting (86) gives:
% 171.17/26.53 | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | (87) all_58_12 = e1 & op(e0, e3) = e1
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | ALPHA: (87) implies:
% 171.17/26.53 | | | | | | | | | | | (88) all_58_12 = e1
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | BETA: splitting (18) gives:
% 171.17/26.53 | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | (89) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 171.17/26.53 | | | | | | | | | | | | & op(e2, e1) = e3)
% 171.17/26.53 | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | BETA: splitting (89) gives:
% 171.17/26.53 | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | (90) all_58_4 = e3 & op(e3, e1) = e3
% 171.17/26.53 | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | REF_CLOSE: (23), (67), (90) are inconsistent by sub-proof
% 171.17/26.53 | | | | | | | | | | | | | #844.
% 171.17/26.53 | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | Case 2:
% 171.17/26.53 | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | (91) all_58_5 = e3 & op(e2, e1) = e3
% 171.17/26.53 | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | ALPHA: (91) implies:
% 171.17/26.53 | | | | | | | | | | | | | (92) all_58_5 = e3
% 171.17/26.53 | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | BETA: splitting (3) gives:
% 171.17/26.53 | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | (93) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 171.17/26.53 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 171.17/26.53 | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 171.17/26.53 | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | (94) all_58_2 = e1 & op(e2, e3) = e1
% 171.17/26.53 | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | ALPHA: (94) implies:
% 171.17/26.53 | | | | | | | | | | | | | | | (95) all_58_2 = e1
% 171.17/26.53 | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 171.17/26.53 | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | (96) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 171.17/26.53 | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 171.17/26.53 | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | REF_CLOSE: (16), (30), (32), (95), (96) are inconsistent by
% 171.17/26.53 | | | | | | | | | | | | | | | | sub-proof #842.
% 171.17/26.53 | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | Case 2:
% 171.17/26.53 | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | (97) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 171.17/26.53 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 171.17/26.53 | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 171.17/26.53 | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | (98) all_58_5 = e0 & op(e2, e1) = e0
% 171.17/26.53 | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 171.17/26.53 | | | | | | | | | | | | | | | | | (99) all_58_5 = e0
% 171.17/26.53 | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (92), (99) are inconsistent by sub-proof
% 171.17/26.53 | | | | | | | | | | | | | | | | | #919.
% 171.17/26.53 | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.53 | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | (100) all_58_10 = e0 & op(e2, e0) = e0
% 171.17/26.53 | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 171.17/26.53 | | | | | | | | | | | | | | | | | (101) all_58_10 = e0
% 171.17/26.53 | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 171.17/26.53 | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | | (102) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 171.17/26.53 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 171.17/26.53 | | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (23), (39), (101), (102) are inconsistent by
% 171.17/26.53 | | | | | | | | | | | | | | | | | | sub-proof #840.
% 171.17/26.53 | | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.53 | | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | | (103) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 171.17/26.53 | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 171.17/26.53 | | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 171.17/26.53 | | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.53 | | | | | | | | | | | | | | | | | | |
% 171.17/26.53 | | | | | | | | | | | | | | | | | | | (104) all_58_11 = e3 & op(e1, e0) = e3
% 171.17/26.53 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (10), (12), (14), (16),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | (18), (20), (22), (23), (24), (26), (27), (30),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | (31), (32), (37), (38), (39), (41), (42), (43),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | (45), (47), (52), (60), (67), (92), (95), (104)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #839.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | (105) all_58_15 = e3 & op(e0, e0) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | (106) all_58_15 = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | (107) all_58_15 = e0 & op(e0, e0) = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | (108) all_58_15 = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (106), (108) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | #860.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | (109) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | (110) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | (111) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (112) all_58_0 = e2 & op(e3, e3) = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (113) op(e3, e3) = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | (114) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (115) all_58_0 = e3 & op(e3, e3) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (116) op(e3, e3) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (31), (47), (113), (116) are inconsistent by
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #838.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (117) all_58_1 = e3 & op(e3, e2) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (10), (12), (14), (16),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (18), (20), (22), (23), (24), (26), (27), (30),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (31), (32), (37), (38), (39), (41), (42), (43),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (45), (47), (52), (60), (67), (92), (95), (117)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #837.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | (118) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (119) all_58_4 = e3 & op(e3, e1) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (120) all_58_4 = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (67), (120) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | #894.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (121) all_58_9 = e3 & op(e3, e0) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (122) all_58_9 = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (12), (16), (23), (32), (37), (60), (106),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (110), (122) are inconsistent by sub-proof #830.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (123) all_58_2 = e2 & op(e2, e3) = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (124) all_58_2 = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (16), (23), (24), (30), (32), (37),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (92), (124) are inconsistent by sub-proof #827.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | (125) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (126) all_58_6 = e2 & op(e1, e3) = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (127) all_58_6 = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (12), (14),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (16), (18), (20), (21), (22), (23), (24), (25),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (26), (27), (30), (31), (32), (33), (34), (37),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (38), (39), (41), (42), (43), (45), (47), (52),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (60), (67), (92), (95), (127) are inconsistent by
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | sub-proof #815.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (128) all_58_12 = e2 & op(e0, e3) = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (88), (128) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | #814.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | (129) all_58_3 = e1 & op(e2, e2) = e1
% 171.17/26.54 | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | (130) all_58_3 = e1
% 171.17/26.54 | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | REF_CLOSE: (30), (37), (130) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | | | #924.
% 171.17/26.54 | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | (131) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 171.17/26.54 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 171.17/26.54 | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (16), (23), (24), (30), (31), (32),
% 171.17/26.54 | | | | | | | | | | | | | | (37), (39), (43), (45), (47), (60), (92), (131)
% 171.17/26.54 | | | | | | | | | | | | | | are inconsistent by sub-proof #810.
% 171.17/26.54 | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | (132) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 171.17/26.54 | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 171.17/26.54 | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | BETA: splitting (132) gives:
% 171.17/26.54 | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | (133) all_58_8 = e3 & op(e1, e1) = e3
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | REF_CLOSE: (10), (22), (31), (133) are inconsistent by
% 171.17/26.54 | | | | | | | | | | | | | sub-proof #961.
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | (134) all_58_14 = e3 & op(e0, e1) = e3
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | REF_CLOSE: (47), (84), (134) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | #809.
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | (135) all_58_13 = e1 & op(e0, e2) = e1
% 171.17/26.54 | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | ALPHA: (135) implies:
% 171.17/26.54 | | | | | | | | | | | (136) op(e0, e2) = e1
% 171.17/26.54 | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | BETA: splitting (18) gives:
% 171.17/26.54 | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | (137) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3
% 171.17/26.54 | | | | | | | | | | | | & op(e2, e1) = e3)
% 171.17/26.54 | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | BETA: splitting (137) gives:
% 171.17/26.54 | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | (138) all_58_4 = e3 & op(e3, e1) = e3
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | ALPHA: (138) implies:
% 171.17/26.54 | | | | | | | | | | | | | (139) all_58_4 = e3
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | REF_CLOSE: (23), (67), (139) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | #894.
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | (140) all_58_5 = e3 & op(e2, e1) = e3
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | ALPHA: (140) implies:
% 171.17/26.54 | | | | | | | | | | | | | (141) all_58_5 = e3
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | BETA: splitting (3) gives:
% 171.17/26.54 | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | (142) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1
% 171.17/26.54 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 171.17/26.54 | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 171.17/26.54 | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | (143) all_58_2 = e1 & op(e2, e3) = e1
% 171.17/26.54 | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | (144) all_58_2 = e1
% 171.17/26.54 | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 171.17/26.54 | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | (145) all_58_4 = e3 & op(e3, e1) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | (146) all_58_4 = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (67), (146) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | | | | | #894.
% 171.17/26.54 | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | (147) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 171.17/26.54 | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (30), (32), (144), (147) are inconsistent by
% 171.17/26.54 | | | | | | | | | | | | | | | | | | sub-proof #842.
% 171.17/26.54 | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | (148) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 171.17/26.54 | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | (149) all_58_5 = e0 & op(e2, e1) = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | (150) all_58_5 = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (141), (150) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | #919.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | (151) all_58_10 = e0 & op(e2, e0) = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | (152) all_58_10 = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | (153) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (23), (39), (152), (153) are inconsistent by
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | sub-proof #840.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | (154) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | (155) all_58_11 = e3 & op(e1, e0) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (10), (12), (14), (16),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | (18), (20), (22), (23), (24), (26), (27), (30),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | (31), (32), (37), (38), (39), (41), (42), (43),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | (45), (47), (52), (60), (67), (141), (144), (155)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #839.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | (156) all_58_15 = e3 & op(e0, e0) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | (157) all_58_15 = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | (158) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | (159) all_58_0 = e3 & op(e3, e3) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | (160) op(e3, e3) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (161) all_58_15 = e0 & op(e0, e0) = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (162) all_58_15 = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (157), (162) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | #860.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (163) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | (164) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | (165) all_58_12 = e0 & op(e0, e3) = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (165) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | (166) all_58_12 = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (167) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (16), (23), (24), (30), (31), (32),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (37), (47), (141), (160), (167) are inconsistent
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #808.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (168) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_12 =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (169) all_58_6 = e2 & op(e1, e3) = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_58_6 = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (10), (12), (14),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (16), (18), (20), (21), (22), (23), (24), (25),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (26), (27), (30), (31), (32), (33), (34), (37),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (38), (39), (41), (42), (43), (45), (47), (52),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (60), (67), (141), (144), (170) are inconsistent
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #815.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (171) all_58_12 = e2 & op(e0, e3) = e2
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (166), (171) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | #807.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | (172) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 =
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_58_13 = e0 & op(e0, e2) = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (174) op(e0, e2) = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (31), (41), (136), (174) are inconsistent by
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #889.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_58_14 = e0 & op(e0, e1) = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_58_14 = e0
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (84), (176) are inconsistent by sub-proof
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | | #806.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | (177) all_58_1 = e3 & op(e3, e2) = e3
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (5), (7), (8), (10), (12), (14), (16),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | (18), (20), (22), (23), (24), (26), (27), (30),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | (31), (32), (37), (38), (39), (41), (42), (43),
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | (45), (47), (52), (60), (67), (141), (144), (177)
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #837.
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.54 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | (178) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | (179) all_58_4 = e3 & op(e3, e1) = e3
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | (180) all_58_4 = e3
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (67), (180) are inconsistent by sub-proof
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | #894.
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | (181) all_58_9 = e3 & op(e3, e0) = e3
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | (182) all_58_9 = e3
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | (183) all_58_15 = e0 & op(e0, e0) = e0
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | (184) all_58_15 = e0
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (157), (184) are inconsistent by sub-proof
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | #860.
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | (185) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | (186) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (12), (16), (23), (32), (37), (60), (157),
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | | (182), (186) are inconsistent by sub-proof #830.
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | Case 2:
% 171.17/26.55 | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | (187) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 171.17/26.55 | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 171.17/26.55 | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | | REF_CLOSE: (10), (22), (31), (47), (84), (187) are
% 171.17/26.55 | | | | | | | | | | | | | | | | inconsistent by sub-proof #805.
% 171.17/26.55 | | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | Case 2:
% 171.17/26.55 | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | (188) all_58_3 = e1 & op(e2, e2) = e1
% 171.17/26.55 | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 171.17/26.55 | | | | | | | | | | | | | | | (189) all_58_3 = e1
% 171.17/26.55 | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | | REF_CLOSE: (30), (37), (189) are inconsistent by sub-proof
% 171.17/26.55 | | | | | | | | | | | | | | | #924.
% 171.17/26.55 | | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | Case 2:
% 171.17/26.55 | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | (190) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 =
% 171.17/26.55 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 171.17/26.55 | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (16), (23), (24), (30), (31), (32),
% 171.17/26.55 | | | | | | | | | | | | | | (37), (39), (43), (45), (47), (60), (141), (190)
% 171.17/26.55 | | | | | | | | | | | | | | are inconsistent by sub-proof #810.
% 171.17/26.55 | | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | Case 2:
% 171.17/26.55 | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | (191) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 =
% 171.17/26.55 | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 171.17/26.55 | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | | REF_CLOSE: (10), (22), (31), (47), (84), (191) are
% 171.17/26.55 | | | | | | | | | | | | inconsistent by sub-proof #805.
% 171.17/26.55 | | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | Case 2:
% 171.17/26.55 | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | (192) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 =
% 171.17/26.55 | | | | | | | | | | e1 & op(e0, e0) = e1)
% 171.17/26.55 | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | BETA: splitting (192) gives:
% 171.17/26.55 | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | Case 1:
% 171.17/26.55 | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | (193) all_58_14 = e1 & op(e0, e1) = e1
% 171.17/26.55 | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | ALPHA: (193) implies:
% 171.17/26.55 | | | | | | | | | | | (194) op(e0, e1) = e1
% 171.17/26.55 | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | REF_CLOSE: (31), (37), (85), (194) are inconsistent by
% 171.17/26.55 | | | | | | | | | | | sub-proof #967.
% 171.17/26.55 | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | Case 2:
% 171.17/26.55 | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | (195) all_58_15 = e1 & op(e0, e0) = e1
% 171.17/26.55 | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | ALPHA: (195) implies:
% 171.17/26.55 | | | | | | | | | | | (196) all_58_15 = e1
% 171.17/26.55 | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | | REF_CLOSE: (12), (16), (23), (32), (39), (43), (45), (47),
% 171.17/26.55 | | | | | | | | | | | (60), (196) are inconsistent by sub-proof #876.
% 171.17/26.55 | | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | | |
% 171.17/26.55 | | | | | | | | | End of split
% 171.17/26.55 | | | | | | | | |
% 171.17/26.55 | | | | | | | | End of split
% 171.17/26.55 | | | | | | | |
% 171.17/26.55 | | | | | | | End of split
% 171.17/26.55 | | | | | | |
% 171.17/26.55 | | | | | | Case 2:
% 171.17/26.55 | | | | | | |
% 171.17/26.55 | | | | | | | (197) all_58_9 = e0 & op(e3, e0) = e0
% 171.17/26.55 | | | | | | |
% 171.17/26.55 | | | | | | | REF_CLOSE: (16), (39), (197) are inconsistent by sub-proof #880.
% 171.17/26.55 | | | | | | |
% 171.17/26.55 | | | | | | End of split
% 171.17/26.55 | | | | | |
% 171.17/26.55 | | | | | End of split
% 171.17/26.55 | | | | |
% 171.17/26.55 | | | | Case 2:
% 171.17/26.55 | | | | |
% 171.17/26.55 | | | | | (198) all_58_15 = e2 & op(e0, e0) = e2
% 171.17/26.55 | | | | |
% 171.17/26.55 | | | | | REF_CLOSE: (4), (26), (31), (198) are inconsistent by sub-proof #854.
% 171.17/26.55 | | | | |
% 171.17/26.55 | | | | End of split
% 171.17/26.55 | | | |
% 171.17/26.55 | | | End of split
% 171.17/26.55 | | |
% 171.17/26.55 | | End of split
% 171.17/26.55 | |
% 171.17/26.55 | Case 2:
% 171.17/26.55 | |
% 171.17/26.55 | | (199) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) =
% 171.17/26.55 | | e2)
% 171.17/26.55 | |
% 171.17/26.55 | | REF_CLOSE: (11), (12), (13), (15), (16), (17), (23), (29), (31), (32), (35),
% 171.17/26.55 | | (37), (39), (47), (199) are inconsistent by sub-proof #800.
% 171.17/26.55 | |
% 171.17/26.55 | End of split
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #800 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 171.17/26.55 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 171.17/26.55 (2) ~ (e3 = e1)
% 171.17/26.55 (3) op(e3, e3) = e1
% 171.17/26.55 (4) op(e3, e1) = all_52_8
% 171.17/26.55 (5) ~ (e1 = e0)
% 171.17/26.55 (6) all_56_10 = e1
% 171.17/26.55 (7) ~ (e3 = e0)
% 171.17/26.55 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 171.17/26.55 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 171.17/26.55 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.17/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.17/26.55 (10) ~ (e2 = e0)
% 171.17/26.55 (11) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 171.17/26.55 (12) ~ (e2 = e1)
% 171.17/26.55 (13) all_58_9 = e1
% 171.17/26.55 (14) (all_58_4 = e2 & op(e3, e1) = e2) | (all_58_9 = e2 & op(e3, e0) = e2)
% 171.17/26.55 (15) ~ (e3 = e2)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | BETA: splitting (14) gives:
% 171.17/26.55 |
% 171.17/26.55 | Case 1:
% 171.17/26.55 | |
% 171.17/26.55 | | (16) all_58_4 = e2 & op(e3, e1) = e2
% 171.17/26.55 | |
% 171.17/26.55 | | ALPHA: (16) implies:
% 171.17/26.55 | | (17) all_58_4 = e2
% 171.17/26.55 | | (18) op(e3, e1) = e2
% 171.17/26.55 | |
% 171.17/26.55 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 171.17/26.55 | | (13), (15), (17), (18) are inconsistent by sub-proof #801.
% 171.17/26.55 | |
% 171.17/26.55 | Case 2:
% 171.17/26.55 | |
% 171.17/26.55 | | (19) all_58_9 = e2 & op(e3, e0) = e2
% 171.17/26.55 | |
% 171.17/26.55 | | ALPHA: (19) implies:
% 171.17/26.55 | | (20) all_58_9 = e2
% 171.17/26.55 | |
% 171.17/26.55 | | REF_CLOSE: (12), (13), (20) are inconsistent by sub-proof #942.
% 171.17/26.55 | |
% 171.17/26.55 | End of split
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #801 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 171.17/26.55 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 171.17/26.55 (2) ~ (e3 = e1)
% 171.17/26.55 (3) op(e3, e3) = e1
% 171.17/26.55 (4) op(e3, e1) = all_52_8
% 171.17/26.55 (5) ~ (e1 = e0)
% 171.17/26.55 (6) all_56_10 = e1
% 171.17/26.55 (7) ~ (e3 = e0)
% 171.17/26.55 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 171.17/26.55 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 171.17/26.55 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.17/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.17/26.55 (10) ~ (e2 = e0)
% 171.17/26.55 (11) ~ (all_56_10 = e1) | (all_56_4 = e3 & op(e3, e1) = e3)
% 171.17/26.55 (12) ~ (e2 = e1)
% 171.17/26.55 (13) all_58_9 = e1
% 171.17/26.55 (14) all_58_4 = e2
% 171.17/26.55 (15) op(e3, e1) = e2
% 171.17/26.55 (16) ~ (e3 = e2)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | BETA: splitting (11) gives:
% 171.17/26.55 |
% 171.17/26.55 | Case 1:
% 171.17/26.55 | |
% 171.17/26.55 | | (17) ~ (all_56_10 = e1)
% 171.17/26.55 | |
% 171.17/26.55 | | REDUCE: (6), (17) imply:
% 171.17/26.55 | | (18) $false
% 171.17/26.55 | |
% 171.17/26.55 | | CLOSE: (18) is inconsistent.
% 171.17/26.55 | |
% 171.17/26.55 | Case 2:
% 171.17/26.55 | |
% 171.17/26.55 | | (19) all_56_4 = e3 & op(e3, e1) = e3
% 171.17/26.55 | |
% 171.17/26.55 | | ALPHA: (19) implies:
% 171.17/26.55 | | (20) op(e3, e1) = e3
% 171.17/26.55 | |
% 171.17/26.55 | | BETA: splitting (1) gives:
% 171.17/26.55 | |
% 171.17/26.55 | | Case 1:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (21) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 171.17/26.55 | | | e0)
% 171.17/26.55 | | |
% 171.17/26.55 | | | BETA: splitting (21) gives:
% 171.17/26.55 | | |
% 171.17/26.55 | | | Case 1:
% 171.17/26.55 | | | |
% 171.17/26.55 | | | | (22) all_58_0 = e0 & op(e3, e3) = e0
% 171.17/26.55 | | | |
% 171.17/26.55 | | | | ALPHA: (22) implies:
% 171.17/26.55 | | | | (23) op(e3, e3) = e0
% 171.17/26.55 | | | |
% 171.17/26.55 | | | | REF_CLOSE: (3), (5), (9), (23) are inconsistent by sub-proof #907.
% 171.17/26.55 | | | |
% 171.17/26.55 | | | Case 2:
% 171.17/26.55 | | | |
% 171.17/26.55 | | | | (24) all_58_1 = e0 & op(e3, e2) = e0
% 171.17/26.55 | | | |
% 171.17/26.55 | | | | ALPHA: (24) implies:
% 171.17/26.55 | | | | (25) all_58_1 = e0
% 171.17/26.55 | | | |
% 171.17/26.55 | | | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (12), (13), (14), (15), (16),
% 171.17/26.55 | | | | (20), (25) are inconsistent by sub-proof #802.
% 171.17/26.55 | | | |
% 171.17/26.55 | | | End of split
% 171.17/26.55 | | |
% 171.17/26.55 | | Case 2:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (26) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 171.17/26.55 | | | e0)
% 171.17/26.55 | | |
% 171.17/26.55 | | | BETA: splitting (26) gives:
% 171.17/26.55 | | |
% 171.17/26.55 | | | Case 1:
% 171.17/26.55 | | | |
% 171.17/26.55 | | | | (27) all_58_4 = e0 & op(e3, e1) = e0
% 171.17/26.55 | | | |
% 171.17/26.55 | | | | REF_CLOSE: (10), (14), (27) are inconsistent by sub-proof #902.
% 171.17/26.55 | | | |
% 171.17/26.55 | | | Case 2:
% 171.17/26.55 | | | |
% 171.17/26.55 | | | | (28) all_58_9 = e0 & op(e3, e0) = e0
% 171.17/26.55 | | | |
% 171.17/26.55 | | | | REF_CLOSE: (5), (13), (28) are inconsistent by sub-proof #880.
% 171.17/26.55 | | | |
% 171.17/26.55 | | | End of split
% 171.17/26.55 | | |
% 171.17/26.55 | | End of split
% 171.17/26.55 | |
% 171.17/26.55 | End of split
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #802 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) ~ (e3 = e1)
% 171.17/26.55 (2) op(e3, e3) = e1
% 171.17/26.55 (3) op(e3, e1) = all_52_8
% 171.17/26.55 (4) op(e3, e1) = e3
% 171.17/26.55 (5) ~ (e3 = e0)
% 171.17/26.55 (6) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 171.17/26.55 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 171.17/26.55 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.17/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.17/26.55 (8) ~ (e2 = e1)
% 171.17/26.55 (9) all_58_9 = e1
% 171.17/26.55 (10) all_58_4 = e2
% 171.17/26.55 (11) all_58_1 = e0
% 171.17/26.55 (12) op(e3, e1) = e2
% 171.17/26.55 (13) ~ (e3 = e2)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | BETA: splitting (6) gives:
% 171.17/26.55 |
% 171.17/26.55 | Case 1:
% 171.17/26.55 | |
% 171.17/26.55 | | (14) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 171.17/26.55 | | e3)
% 171.17/26.55 | |
% 171.17/26.55 | | BETA: splitting (14) gives:
% 171.17/26.55 | |
% 171.17/26.55 | | Case 1:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (15) all_58_0 = e3 & op(e3, e3) = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | ALPHA: (15) implies:
% 171.17/26.55 | | | (16) op(e3, e3) = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | REF_CLOSE: (2), (3), (4), (7), (8), (12), (16) are inconsistent by
% 171.17/26.55 | | | sub-proof #804.
% 171.17/26.55 | | |
% 171.17/26.55 | | Case 2:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (17) all_58_1 = e3 & op(e3, e2) = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | REF_CLOSE: (5), (11), (17) are inconsistent by sub-proof #803.
% 171.17/26.55 | | |
% 171.17/26.55 | | End of split
% 171.17/26.55 | |
% 171.17/26.55 | Case 2:
% 171.17/26.55 | |
% 171.17/26.55 | | (18) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 171.17/26.55 | | e3)
% 171.17/26.55 | |
% 171.17/26.55 | | BETA: splitting (18) gives:
% 171.17/26.55 | |
% 171.17/26.55 | | Case 1:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (19) all_58_4 = e3 & op(e3, e1) = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | REF_CLOSE: (10), (13), (19) are inconsistent by sub-proof #952.
% 171.17/26.55 | | |
% 171.17/26.55 | | Case 2:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (20) all_58_9 = e3 & op(e3, e0) = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | REF_CLOSE: (1), (9), (20) are inconsistent by sub-proof #893.
% 171.17/26.55 | | |
% 171.17/26.55 | | End of split
% 171.17/26.55 | |
% 171.17/26.55 | End of split
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #803 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) all_58_1 = e3 & op(e3, e2) = e3
% 171.17/26.55 (2) all_58_1 = e0
% 171.17/26.55 (3) ~ (e3 = e0)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | ALPHA: (1) implies:
% 171.17/26.55 | (4) all_58_1 = e3
% 171.17/26.55 |
% 171.17/26.55 | COMBINE_EQS: (2), (4) imply:
% 171.17/26.55 | (5) e3 = e0
% 171.17/26.55 |
% 171.17/26.55 | SIMP: (5) implies:
% 171.17/26.55 | (6) e3 = e0
% 171.17/26.55 |
% 171.17/26.55 | REDUCE: (3), (6) imply:
% 171.17/26.55 | (7) $false
% 171.17/26.55 |
% 171.17/26.55 | CLOSE: (7) is inconsistent.
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #804 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) op(e3, e3) = e1
% 171.17/26.55 (2) op(e3, e1) = all_52_8
% 171.17/26.55 (3) op(e3, e1) = e3
% 171.17/26.55 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.17/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.17/26.55 (5) op(e3, e3) = e3
% 171.17/26.55 (6) ~ (e2 = e1)
% 171.17/26.55 (7) op(e3, e1) = e2
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | GROUND_INST: instantiating (4) with all_52_8, e2, e1, e3, simplifying with
% 171.17/26.55 | (2), (7) gives:
% 171.17/26.55 | (8) all_52_8 = e2
% 171.17/26.55 |
% 171.17/26.55 | GROUND_INST: instantiating (4) with all_52_8, e3, e1, e3, simplifying with
% 171.17/26.55 | (2), (3) gives:
% 171.17/26.55 | (9) all_52_8 = e3
% 171.17/26.55 |
% 171.17/26.55 | GROUND_INST: instantiating (4) with e1, e3, e3, e3, simplifying with (1), (5)
% 171.17/26.55 | gives:
% 171.17/26.55 | (10) e3 = e1
% 171.17/26.55 |
% 171.17/26.55 | COMBINE_EQS: (8), (9) imply:
% 171.17/26.55 | (11) e3 = e2
% 171.17/26.55 |
% 171.17/26.55 | COMBINE_EQS: (10), (11) imply:
% 171.17/26.55 | (12) e2 = e1
% 171.17/26.55 |
% 171.17/26.55 | REDUCE: (6), (12) imply:
% 171.17/26.55 | (13) $false
% 171.17/26.55 |
% 171.17/26.55 | CLOSE: (13) is inconsistent.
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #805 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) all_58_14 = e2
% 171.17/26.55 (2) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 171.17/26.55 (3) ~ (all_6_2 = e3)
% 171.17/26.55 (4) op(e1, e1) = all_6_2
% 171.17/26.55 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.17/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.17/26.55 (6) ~ (e3 = e2)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | BETA: splitting (2) gives:
% 171.17/26.55 |
% 171.17/26.55 | Case 1:
% 171.17/26.55 | |
% 171.17/26.55 | | (7) all_58_8 = e3 & op(e1, e1) = e3
% 171.17/26.55 | |
% 171.17/26.55 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #961.
% 171.17/26.55 | |
% 171.17/26.55 | Case 2:
% 171.17/26.55 | |
% 171.17/26.55 | | (8) all_58_14 = e3 & op(e0, e1) = e3
% 171.17/26.55 | |
% 171.17/26.55 | | ALPHA: (8) implies:
% 171.17/26.55 | | (9) all_58_14 = e3
% 171.17/26.55 | |
% 171.17/26.55 | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #855.
% 171.17/26.55 | |
% 171.17/26.55 | End of split
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #806 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) all_58_14 = e2
% 171.17/26.55 (2) all_58_14 = e0
% 171.17/26.55 (3) ~ (e2 = e0)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | COMBINE_EQS: (1), (2) imply:
% 171.17/26.55 | (4) e2 = e0
% 171.17/26.55 |
% 171.17/26.55 | SIMP: (4) implies:
% 171.17/26.55 | (5) e2 = e0
% 171.17/26.55 |
% 171.17/26.55 | REDUCE: (3), (5) imply:
% 171.17/26.55 | (6) $false
% 171.17/26.55 |
% 171.17/26.55 | CLOSE: (6) is inconsistent.
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #807 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) all_58_12 = e2 & op(e0, e3) = e2
% 171.17/26.55 (2) all_58_12 = e0
% 171.17/26.55 (3) ~ (e2 = e0)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | ALPHA: (1) implies:
% 171.17/26.55 | (4) all_58_12 = e2
% 171.17/26.55 |
% 171.17/26.55 | COMBINE_EQS: (2), (4) imply:
% 171.17/26.55 | (5) e2 = e0
% 171.17/26.55 |
% 171.17/26.55 | REDUCE: (3), (5) imply:
% 171.17/26.55 | (6) $false
% 171.17/26.55 |
% 171.17/26.55 | CLOSE: (6) is inconsistent.
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #808 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.17/26.55 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 171.17/26.55 (2) ~ (e3 = e1)
% 171.17/26.55 (3) ~ (e1 = e0)
% 171.17/26.55 (4) all_58_5 = e3
% 171.17/26.55 (5) ~ (e3 = e0)
% 171.17/26.55 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.17/26.55 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.17/26.55 (7) all_58_3 = e2
% 171.17/26.55 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.17/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.17/26.55 (9) ~ (e2 = e0)
% 171.17/26.55 (10) op(e3, e3) = e3
% 171.17/26.55 (11) ~ (e2 = e1)
% 171.17/26.55 (12) (all_58_0 = e2 & op(e3, e3) = e2) | (all_58_2 = e2 & op(e2, e3) = e2)
% 171.17/26.55 (13) ~ (e3 = e2)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | BETA: splitting (12) gives:
% 171.17/26.55 |
% 171.17/26.55 | Case 1:
% 171.17/26.55 | |
% 171.17/26.55 | | (14) all_58_0 = e2 & op(e3, e3) = e2
% 171.17/26.55 | |
% 171.17/26.55 | | ALPHA: (14) implies:
% 171.17/26.55 | | (15) op(e3, e3) = e2
% 171.17/26.55 | |
% 171.17/26.55 | | REF_CLOSE: (8), (10), (13), (15) are inconsistent by sub-proof #838.
% 171.17/26.55 | |
% 171.17/26.55 | Case 2:
% 171.17/26.55 | |
% 171.17/26.55 | | (16) all_58_2 = e2 & op(e2, e3) = e2
% 171.17/26.55 | |
% 171.17/26.55 | | ALPHA: (16) implies:
% 171.17/26.55 | | (17) all_58_2 = e2
% 171.17/26.55 | |
% 171.17/26.55 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (17) are
% 171.17/26.55 | | inconsistent by sub-proof #827.
% 171.17/26.55 | |
% 171.17/26.55 | End of split
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #809 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) all_58_14 = e3 & op(e0, e1) = e3
% 171.17/26.55 (2) all_58_14 = e2
% 171.17/26.55 (3) ~ (e3 = e2)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | ALPHA: (1) implies:
% 171.17/26.55 | (4) all_58_14 = e3
% 171.17/26.55 |
% 171.17/26.55 | COMBINE_EQS: (2), (4) imply:
% 171.17/26.55 | (5) e3 = e2
% 171.17/26.55 |
% 171.17/26.55 | REDUCE: (3), (5) imply:
% 171.17/26.55 | (6) $false
% 171.17/26.55 |
% 171.17/26.55 | CLOSE: (6) is inconsistent.
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #810 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.17/26.55 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 171.17/26.55 (2) ~ (e3 = e1)
% 171.17/26.55 (3) ~ (e1 = e0)
% 171.17/26.55 (4) all_58_11 = e2
% 171.17/26.55 (5) all_58_5 = e3
% 171.17/26.55 (6) ~ (e3 = e0)
% 171.17/26.55 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.17/26.55 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.17/26.55 (8) all_58_3 = e2
% 171.17/26.55 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.17/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.17/26.55 (10) ~ (e2 = e0)
% 171.17/26.55 (11) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 171.17/26.55 (12) ~ (e2 = e1)
% 171.17/26.55 (13) all_58_9 = e1
% 171.17/26.55 (14) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 171.17/26.55 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.17/26.55 (15) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.17/26.55 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 171.17/26.55 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.17/26.55 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.17/26.55 (16) ~ (e3 = e2)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | BETA: splitting (11) gives:
% 171.17/26.55 |
% 171.17/26.55 | Case 1:
% 171.17/26.55 | |
% 171.17/26.55 | | (17) all_58_5 = e1 & op(e2, e1) = e1
% 171.17/26.55 | |
% 171.17/26.55 | | ALPHA: (17) implies:
% 171.17/26.55 | | (18) all_58_5 = e1
% 171.17/26.55 | |
% 171.17/26.55 | | REF_CLOSE: (2), (5), (18) are inconsistent by sub-proof #920.
% 171.17/26.55 | |
% 171.17/26.55 | Case 2:
% 171.17/26.55 | |
% 171.17/26.55 | | (19) all_58_10 = e1 & op(e2, e0) = e1
% 171.17/26.55 | |
% 171.17/26.55 | | ALPHA: (19) implies:
% 171.17/26.55 | | (20) all_58_10 = e1
% 171.17/26.55 | | (21) op(e2, e0) = e1
% 171.17/26.55 | |
% 171.17/26.55 | | BETA: splitting (15) gives:
% 171.17/26.55 | |
% 171.17/26.55 | | Case 1:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (22) all_58_15 = e0 & op(e0, e0) = e0
% 171.17/26.55 | | |
% 171.17/26.55 | | | ALPHA: (22) implies:
% 171.17/26.55 | | | (23) all_58_15 = e0
% 171.17/26.55 | | |
% 171.17/26.55 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 171.17/26.55 | | | (14), (15), (16), (20), (21), (23) are inconsistent by
% 171.17/26.55 | | | sub-proof #811.
% 171.17/26.55 | | |
% 171.17/26.55 | | Case 2:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (24) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 171.17/26.55 | | | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0
% 171.17/26.55 | | | & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 171.17/26.55 | | | (all_58_14 = e0 & op(e0, e1) = e0))
% 171.17/26.55 | | |
% 171.17/26.55 | | | ALPHA: (24) implies:
% 171.17/26.55 | | | (25) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 171.17/26.55 | | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 171.17/26.55 | | |
% 171.17/26.55 | | | REF_CLOSE: (3), (4), (9), (10), (13), (21), (25) are inconsistent by
% 171.17/26.55 | | | sub-proof #847.
% 171.17/26.55 | | |
% 171.17/26.55 | | End of split
% 171.17/26.55 | |
% 171.17/26.55 | End of split
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #811 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.17/26.55 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 171.17/26.55 (2) ~ (e3 = e1)
% 171.17/26.55 (3) ~ (e1 = e0)
% 171.17/26.55 (4) all_58_11 = e2
% 171.17/26.55 (5) all_58_5 = e3
% 171.17/26.55 (6) ~ (e3 = e0)
% 171.17/26.55 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.17/26.55 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.17/26.55 (8) op(e2, e0) = e1
% 171.17/26.55 (9) all_58_3 = e2
% 171.17/26.55 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.17/26.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.17/26.55 (11) ~ (e2 = e0)
% 171.17/26.55 (12) ~ (e2 = e1)
% 171.17/26.55 (13) all_58_15 = e0
% 171.17/26.55 (14) all_58_9 = e1
% 171.17/26.55 (15) all_58_10 = e1
% 171.17/26.55 (16) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 171.17/26.55 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.17/26.55 (17) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.17/26.55 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 171.17/26.55 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.17/26.55 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.17/26.55 (18) ~ (e3 = e2)
% 171.17/26.55
% 171.17/26.55 Begin of proof
% 171.17/26.55 |
% 171.17/26.55 | BETA: splitting (16) gives:
% 171.17/26.55 |
% 171.17/26.55 | Case 1:
% 171.17/26.55 | |
% 171.17/26.55 | | (19) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 171.17/26.55 | | e3)
% 171.17/26.55 | |
% 171.17/26.55 | | BETA: splitting (19) gives:
% 171.17/26.55 | |
% 171.17/26.55 | | Case 1:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (20) all_58_9 = e3 & op(e3, e0) = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | ALPHA: (20) implies:
% 171.17/26.55 | | | (21) all_58_9 = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | REF_CLOSE: (2), (14), (21) are inconsistent by sub-proof #896.
% 171.17/26.55 | | |
% 171.17/26.55 | | Case 2:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (22) all_58_10 = e3 & op(e2, e0) = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | REF_CLOSE: (2), (15), (22) are inconsistent by sub-proof #813.
% 171.17/26.55 | | |
% 171.17/26.55 | | End of split
% 171.17/26.55 | |
% 171.17/26.55 | Case 2:
% 171.17/26.55 | |
% 171.17/26.55 | | (23) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 171.17/26.55 | | e3)
% 171.17/26.55 | |
% 171.17/26.55 | | BETA: splitting (23) gives:
% 171.17/26.55 | |
% 171.17/26.55 | | Case 1:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (24) all_58_11 = e3 & op(e1, e0) = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | ALPHA: (24) implies:
% 171.17/26.55 | | | (25) all_58_11 = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | COMBINE_EQS: (4), (25) imply:
% 171.17/26.55 | | | (26) e3 = e2
% 171.17/26.55 | | |
% 171.17/26.55 | | | COMBINE_EQS: (5), (26) imply:
% 171.17/26.55 | | | (27) all_58_5 = e2
% 171.17/26.55 | | |
% 171.17/26.55 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (14),
% 171.17/26.55 | | | (16), (17), (18), (27) are inconsistent by sub-proof #846.
% 171.17/26.55 | | |
% 171.17/26.55 | | Case 2:
% 171.17/26.55 | | |
% 171.17/26.55 | | | (28) all_58_15 = e3 & op(e0, e0) = e3
% 171.17/26.55 | | |
% 171.17/26.55 | | | REF_CLOSE: (6), (13), (28) are inconsistent by sub-proof #812.
% 171.17/26.55 | | |
% 171.17/26.55 | | End of split
% 171.17/26.55 | |
% 171.17/26.55 | End of split
% 171.17/26.55 |
% 171.17/26.55 End of proof
% 171.17/26.55
% 171.17/26.55 Sub-proof #812 shows that the following formulas are inconsistent:
% 171.17/26.55 ----------------------------------------------------------------
% 171.17/26.55 (1) all_58_15 = e3 & op(e0, e0) = e3
% 171.17/26.55 (2) all_58_15 = e0
% 171.17/26.55 (3) ~ (e3 = e0)
% 171.17/26.56
% 171.17/26.56 Begin of proof
% 171.17/26.56 |
% 171.17/26.56 | ALPHA: (1) implies:
% 171.17/26.56 | (4) all_58_15 = e3
% 171.17/26.56 |
% 171.17/26.56 | COMBINE_EQS: (2), (4) imply:
% 171.17/26.56 | (5) e3 = e0
% 171.17/26.56 |
% 171.17/26.56 | REDUCE: (3), (5) imply:
% 171.17/26.56 | (6) $false
% 171.17/26.56 |
% 171.17/26.56 | CLOSE: (6) is inconsistent.
% 171.17/26.56 |
% 171.17/26.56 End of proof
% 171.17/26.56
% 171.17/26.56 Sub-proof #813 shows that the following formulas are inconsistent:
% 171.17/26.56 ----------------------------------------------------------------
% 171.17/26.56 (1) all_58_10 = e3 & op(e2, e0) = e3
% 171.17/26.56 (2) all_58_10 = e1
% 171.17/26.56 (3) ~ (e3 = e1)
% 171.17/26.56
% 171.17/26.56 Begin of proof
% 171.17/26.56 |
% 171.17/26.56 | ALPHA: (1) implies:
% 171.17/26.56 | (4) all_58_10 = e3
% 171.17/26.56 |
% 171.17/26.56 | COMBINE_EQS: (2), (4) imply:
% 171.17/26.56 | (5) e3 = e1
% 171.17/26.56 |
% 171.17/26.56 | REDUCE: (3), (5) imply:
% 171.17/26.56 | (6) $false
% 171.17/26.56 |
% 171.17/26.56 | CLOSE: (6) is inconsistent.
% 171.17/26.56 |
% 171.17/26.56 End of proof
% 171.17/26.56
% 171.17/26.56 Sub-proof #814 shows that the following formulas are inconsistent:
% 171.17/26.56 ----------------------------------------------------------------
% 171.17/26.56 (1) all_58_12 = e2 & op(e0, e3) = e2
% 171.17/26.56 (2) all_58_12 = e1
% 171.17/26.56 (3) ~ (e2 = e1)
% 171.17/26.56
% 171.17/26.56 Begin of proof
% 171.17/26.56 |
% 171.17/26.56 | ALPHA: (1) implies:
% 171.17/26.56 | (4) all_58_12 = e2
% 171.17/26.56 |
% 171.17/26.56 | COMBINE_EQS: (2), (4) imply:
% 171.17/26.56 | (5) e2 = e1
% 171.17/26.56 |
% 171.17/26.56 | REDUCE: (3), (5) imply:
% 171.17/26.56 | (6) $false
% 171.17/26.56 |
% 171.17/26.56 | CLOSE: (6) is inconsistent.
% 171.17/26.56 |
% 171.17/26.56 End of proof
% 171.17/26.56
% 171.17/26.56 Sub-proof #815 shows that the following formulas are inconsistent:
% 171.17/26.56 ----------------------------------------------------------------
% 171.17/26.56 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 171.17/26.56 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 171.17/26.56 (2) ~ (all_4_2 = e2)
% 171.17/26.56 (3) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 171.17/26.56 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 171.17/26.56 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.17/26.56 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 171.17/26.56 (5) ~ (all_8_2 = e3)
% 171.17/26.56 (6) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 171.17/26.56 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 171.17/26.56 (7) ~ (all_6_2 = e3)
% 171.17/26.56 (8) ~ (e3 = e1)
% 171.17/26.56 (9) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 171.17/26.56 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 171.17/26.56 (10) ~ (e1 = e0)
% 171.17/26.56 (11) all_58_11 = e2
% 171.17/26.56 (12) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 171.17/26.56 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 171.17/26.56 (13) all_58_5 = e3
% 171.17/26.56 (14) all_58_1 = e2
% 171.17/26.56 (15) op(e2, e2) = all_8_2
% 171.17/26.56 (16) ~ (all_6_2 = e2)
% 171.17/26.56 (17) all_58_6 = e2
% 171.17/26.56 (18) op(e1, e1) = all_6_2
% 171.17/26.56 (19) ~ (e3 = e0)
% 171.17/26.56 (20) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.17/26.56 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.17/26.56 (21) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 171.17/26.56 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 171.17/26.56 (22) op(e0, e0) = all_4_2
% 171.17/26.56 (23) all_58_4 = e0
% 171.17/26.56 (24) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.17/26.56 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 171.17/26.56 (25) all_58_3 = e2
% 171.17/26.56 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.17/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.17/26.56 (27) ~ (e2 = e0)
% 171.17/26.56 (28) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 171.17/26.56 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 171.17/26.56 (29) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 171.17/26.56 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 171.17/26.56 (30) ~ (e2 = e1)
% 171.17/26.56 (31) op(e3, e2) = all_52_4
% 171.17/26.56 (32) all_58_9 = e1
% 171.17/26.56 (33) all_58_2 = e1
% 171.17/26.56 (34) op(e0, e2) = all_52_7
% 171.17/26.56 (35) ~ (all_52_4 = e1)
% 171.17/26.56 (36) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 171.17/26.56 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.17/26.56 (37) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.17/26.56 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 171.17/26.56 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.17/26.56 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.17/26.56 (38) ~ (e3 = e2)
% 171.17/26.56
% 171.17/26.56 Begin of proof
% 171.17/26.56 |
% 171.17/26.56 | BETA: splitting (29) gives:
% 171.17/26.56 |
% 171.17/26.56 | Case 1:
% 171.17/26.56 | |
% 171.17/26.56 | | (39) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) =
% 171.17/26.56 | | e3)
% 171.17/26.56 | |
% 171.17/26.56 | | BETA: splitting (39) gives:
% 171.17/26.56 | |
% 171.17/26.56 | | Case 1:
% 171.17/26.56 | | |
% 171.17/26.56 | | | (40) all_58_6 = e3 & op(e1, e3) = e3
% 171.17/26.56 | | |
% 171.17/26.56 | | | ALPHA: (40) implies:
% 171.17/26.56 | | | (41) all_58_6 = e3
% 171.17/26.56 | | |
% 171.17/26.56 | | | COMBINE_EQS: (17), (41) imply:
% 171.17/26.56 | | | (42) e3 = e2
% 171.17/26.56 | | |
% 171.17/26.56 | | | COMBINE_EQS: (13), (42) imply:
% 171.17/26.56 | | | (43) all_58_5 = e2
% 171.17/26.56 | | |
% 171.17/26.56 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14),
% 171.17/26.56 | | | (15), (18), (19), (20), (22), (23), (24), (25), (26), (27),
% 171.17/26.56 | | | (30), (31), (32), (33), (34), (35), (36), (37), (38), (43) are
% 171.17/26.56 | | | inconsistent by sub-proof #853.
% 171.17/26.56 | | |
% 171.17/26.56 | | Case 2:
% 171.17/26.56 | | |
% 171.17/26.56 | | | (44) all_58_7 = e3 & op(e1, e2) = e3
% 171.17/26.56 | | |
% 171.17/26.56 | | | ALPHA: (44) implies:
% 171.17/26.56 | | | (45) all_58_7 = e3
% 171.17/26.56 | | |
% 171.17/26.56 | | | REF_CLOSE: (6), (8), (10), (11), (16), (17), (18), (19), (21), (26), (27),
% 171.17/26.56 | | | (28), (29), (30), (38), (45) are inconsistent by sub-proof
% 171.17/26.56 | | | #816.
% 171.17/26.56 | | |
% 171.17/26.56 | | End of split
% 171.17/26.56 | |
% 171.17/26.56 | Case 2:
% 171.17/26.56 | |
% 171.17/26.56 | | (46) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 171.17/26.56 | | e3)
% 171.17/26.56 | |
% 171.17/26.56 | | BETA: splitting (46) gives:
% 171.17/26.56 | |
% 171.17/26.56 | | Case 1:
% 171.17/26.56 | | |
% 171.17/26.56 | | | (47) all_58_8 = e3 & op(e1, e1) = e3
% 171.17/26.56 | | |
% 171.17/26.56 | | | REF_CLOSE: (7), (18), (26), (47) are inconsistent by sub-proof #961.
% 171.17/26.56 | | |
% 171.17/26.56 | | Case 2:
% 171.17/26.56 | | |
% 171.17/26.56 | | | (48) all_58_11 = e3 & op(e1, e0) = e3
% 171.17/26.56 | | |
% 171.17/26.56 | | | ALPHA: (48) implies:
% 171.17/26.56 | | | (49) all_58_11 = e3
% 171.17/26.56 | | |
% 171.17/26.56 | | | COMBINE_EQS: (11), (49) imply:
% 171.17/26.56 | | | (50) e3 = e2
% 171.17/26.56 | | |
% 171.17/26.56 | | | COMBINE_EQS: (13), (50) imply:
% 171.17/26.56 | | | (51) all_58_5 = e2
% 171.17/26.56 | | |
% 171.17/26.56 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14),
% 171.17/26.56 | | | (15), (18), (19), (20), (22), (23), (24), (25), (26), (27),
% 171.17/26.56 | | | (30), (31), (32), (33), (34), (35), (36), (37), (38), (51) are
% 171.17/26.56 | | | inconsistent by sub-proof #853.
% 171.17/26.56 | | |
% 171.17/26.56 | | End of split
% 171.17/26.56 | |
% 171.17/26.56 | End of split
% 171.17/26.56 |
% 171.17/26.56 End of proof
% 171.17/26.56
% 171.17/26.56 Sub-proof #816 shows that the following formulas are inconsistent:
% 171.17/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 171.23/26.56 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 171.23/26.56 (2) ~ (e3 = e1)
% 171.23/26.56 (3) ~ (e1 = e0)
% 171.23/26.56 (4) all_58_11 = e2
% 171.23/26.56 (5) ~ (all_6_2 = e2)
% 171.23/26.56 (6) all_58_6 = e2
% 171.23/26.56 (7) op(e1, e1) = all_6_2
% 171.23/26.56 (8) ~ (e3 = e0)
% 171.23/26.56 (9) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) = e0) |
% 171.23/26.56 (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 171.23/26.56 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.56 (11) ~ (e2 = e0)
% 171.23/26.56 (12) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 171.23/26.56 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 171.23/26.56 (13) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 171.23/26.56 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 171.23/26.56 (14) ~ (e2 = e1)
% 171.23/26.56 (15) all_58_7 = e3
% 171.23/26.56 (16) ~ (e3 = e2)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | BETA: splitting (9) gives:
% 171.23/26.56 |
% 171.23/26.56 | Case 1:
% 171.23/26.56 | |
% 171.23/26.56 | | (17) (all_58_6 = e0 & op(e1, e3) = e0) | (all_58_7 = e0 & op(e1, e2) =
% 171.23/26.56 | | e0)
% 171.23/26.56 | |
% 171.23/26.56 | | BETA: splitting (17) gives:
% 171.23/26.56 | |
% 171.23/26.56 | | Case 1:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (18) all_58_6 = e0 & op(e1, e3) = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (18) implies:
% 171.23/26.56 | | | (19) all_58_6 = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | COMBINE_EQS: (6), (19) imply:
% 171.23/26.56 | | | (20) e2 = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | SIMP: (20) implies:
% 171.23/26.56 | | | (21) e2 = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | COMBINE_EQS: (4), (21) imply:
% 171.23/26.56 | | | (22) all_58_11 = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (1), (5), (7), (10), (11), (15), (16), (19), (22) are
% 171.23/26.56 | | | inconsistent by sub-proof #824.
% 171.23/26.56 | | |
% 171.23/26.56 | | Case 2:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (23) all_58_7 = e0 & op(e1, e2) = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (8), (15), (23) are inconsistent by sub-proof #890.
% 171.23/26.56 | | |
% 171.23/26.56 | | End of split
% 171.23/26.56 | |
% 171.23/26.56 | Case 2:
% 171.23/26.56 | |
% 171.23/26.56 | | (24) (all_58_8 = e0 & op(e1, e1) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 171.23/26.56 | | e0)
% 171.23/26.56 | |
% 171.23/26.56 | | BETA: splitting (24) gives:
% 171.23/26.56 | |
% 171.23/26.56 | | Case 1:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (25) all_58_8 = e0 & op(e1, e1) = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (25) implies:
% 171.23/26.56 | | | (26) all_58_8 = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (2), (3), (4), (6), (8), (12), (13), (14), (16), (26) are
% 171.23/26.56 | | | inconsistent by sub-proof #817.
% 171.23/26.56 | | |
% 171.23/26.56 | | Case 2:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (27) all_58_11 = e0 & op(e1, e0) = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (27) implies:
% 171.23/26.56 | | | (28) all_58_11 = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | COMBINE_EQS: (4), (28) imply:
% 171.23/26.56 | | | (29) e2 = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | SIMP: (29) implies:
% 171.23/26.56 | | | (30) e2 = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | COMBINE_EQS: (6), (30) imply:
% 171.23/26.56 | | | (31) all_58_6 = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (1), (5), (7), (10), (11), (15), (16), (28), (31) are
% 171.23/26.56 | | | inconsistent by sub-proof #824.
% 171.23/26.56 | | |
% 171.23/26.56 | | End of split
% 171.23/26.56 | |
% 171.23/26.56 | End of split
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #817 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) ~ (e3 = e1)
% 171.23/26.56 (2) ~ (e1 = e0)
% 171.23/26.56 (3) all_58_11 = e2
% 171.23/26.56 (4) all_58_8 = e0
% 171.23/26.56 (5) all_58_6 = e2
% 171.23/26.56 (6) ~ (e3 = e0)
% 171.23/26.56 (7) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) = e1) |
% 171.23/26.56 (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) = e1)
% 171.23/26.56 (8) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 171.23/26.56 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 171.23/26.56 (9) ~ (e2 = e1)
% 171.23/26.56 (10) ~ (e3 = e2)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | BETA: splitting (7) gives:
% 171.23/26.56 |
% 171.23/26.56 | Case 1:
% 171.23/26.56 | |
% 171.23/26.56 | | (11) (all_58_6 = e1 & op(e1, e3) = e1) | (all_58_7 = e1 & op(e1, e2) =
% 171.23/26.56 | | e1)
% 171.23/26.56 | |
% 171.23/26.56 | | BETA: splitting (11) gives:
% 171.23/26.56 | |
% 171.23/26.56 | | Case 1:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (12) all_58_6 = e1 & op(e1, e3) = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (12) implies:
% 171.23/26.56 | | | (13) all_58_6 = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #823.
% 171.23/26.56 | | |
% 171.23/26.56 | | Case 2:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (14) all_58_7 = e1 & op(e1, e2) = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (14) implies:
% 171.23/26.56 | | | (15) all_58_7 = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (10), (15) are inconsistent by
% 171.23/26.56 | | | sub-proof #819.
% 171.23/26.56 | | |
% 171.23/26.56 | | End of split
% 171.23/26.56 | |
% 171.23/26.56 | Case 2:
% 171.23/26.56 | |
% 171.23/26.56 | | (16) (all_58_8 = e1 & op(e1, e1) = e1) | (all_58_11 = e1 & op(e1, e0) =
% 171.23/26.56 | | e1)
% 171.23/26.56 | |
% 171.23/26.56 | | BETA: splitting (16) gives:
% 171.23/26.56 | |
% 171.23/26.56 | | Case 1:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (17) all_58_8 = e1 & op(e1, e1) = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (17) implies:
% 171.23/26.56 | | | (18) all_58_8 = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (2), (4), (18) are inconsistent by sub-proof #818.
% 171.23/26.56 | | |
% 171.23/26.56 | | Case 2:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (19) all_58_11 = e1 & op(e1, e0) = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (19) implies:
% 171.23/26.56 | | | (20) all_58_11 = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (3), (9), (20) are inconsistent by sub-proof #832.
% 171.23/26.56 | | |
% 171.23/26.56 | | End of split
% 171.23/26.56 | |
% 171.23/26.56 | End of split
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #818 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) all_58_8 = e1
% 171.23/26.56 (2) all_58_8 = e0
% 171.23/26.56 (3) ~ (e1 = e0)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.56 | (4) e1 = e0
% 171.23/26.56 |
% 171.23/26.56 | SIMP: (4) implies:
% 171.23/26.56 | (5) e1 = e0
% 171.23/26.56 |
% 171.23/26.56 | REDUCE: (3), (5) imply:
% 171.23/26.56 | (6) $false
% 171.23/26.56 |
% 171.23/26.56 | CLOSE: (6) is inconsistent.
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #819 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) all_58_7 = e1
% 171.23/26.56 (2) ~ (e3 = e1)
% 171.23/26.56 (3) all_58_11 = e2
% 171.23/26.56 (4) all_58_8 = e0
% 171.23/26.56 (5) all_58_6 = e2
% 171.23/26.56 (6) ~ (e3 = e0)
% 171.23/26.56 (7) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3) |
% 171.23/26.56 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) = e3)
% 171.23/26.56 (8) ~ (e3 = e2)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | BETA: splitting (7) gives:
% 171.23/26.56 |
% 171.23/26.56 | Case 1:
% 171.23/26.56 | |
% 171.23/26.56 | | (9) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 171.23/26.56 | |
% 171.23/26.56 | | REF_CLOSE: (1), (2), (5), (8), (9) are inconsistent by sub-proof #820.
% 171.23/26.56 | |
% 171.23/26.56 | Case 2:
% 171.23/26.56 | |
% 171.23/26.56 | | (10) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_11 = e3 & op(e1, e0) =
% 171.23/26.56 | | e3)
% 171.23/26.56 | |
% 171.23/26.56 | | BETA: splitting (10) gives:
% 171.23/26.56 | |
% 171.23/26.56 | | Case 1:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (11) all_58_8 = e3 & op(e1, e1) = e3
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (11) implies:
% 171.23/26.56 | | | (12) all_58_8 = e3
% 171.23/26.56 | | |
% 171.23/26.56 | | | COMBINE_EQS: (4), (12) imply:
% 171.23/26.56 | | | (13) e3 = e0
% 171.23/26.56 | | |
% 171.23/26.56 | | | REDUCE: (6), (13) imply:
% 171.23/26.56 | | | (14) $false
% 171.23/26.56 | | |
% 171.23/26.56 | | | CLOSE: (14) is inconsistent.
% 171.23/26.56 | | |
% 171.23/26.56 | | Case 2:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (15) all_58_11 = e3 & op(e1, e0) = e3
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (15) implies:
% 171.23/26.56 | | | (16) all_58_11 = e3
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (3), (8), (16) are inconsistent by sub-proof #892.
% 171.23/26.56 | | |
% 171.23/26.56 | | End of split
% 171.23/26.56 | |
% 171.23/26.56 | End of split
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #820 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) (all_58_6 = e3 & op(e1, e3) = e3) | (all_58_7 = e3 & op(e1, e2) = e3)
% 171.23/26.56 (2) all_58_7 = e1
% 171.23/26.56 (3) ~ (e3 = e1)
% 171.23/26.56 (4) all_58_6 = e2
% 171.23/26.56 (5) ~ (e3 = e2)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | BETA: splitting (1) gives:
% 171.23/26.56 |
% 171.23/26.56 | Case 1:
% 171.23/26.56 | |
% 171.23/26.56 | | (6) all_58_6 = e3 & op(e1, e3) = e3
% 171.23/26.56 | |
% 171.23/26.56 | | ALPHA: (6) implies:
% 171.23/26.56 | | (7) all_58_6 = e3
% 171.23/26.56 | |
% 171.23/26.56 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #822.
% 171.23/26.56 | |
% 171.23/26.56 | Case 2:
% 171.23/26.56 | |
% 171.23/26.56 | | (8) all_58_7 = e3 & op(e1, e2) = e3
% 171.23/26.56 | |
% 171.23/26.56 | | ALPHA: (8) implies:
% 171.23/26.56 | | (9) all_58_7 = e3
% 171.23/26.56 | |
% 171.23/26.56 | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #821.
% 171.23/26.56 | |
% 171.23/26.56 | End of split
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #821 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) all_58_7 = e3
% 171.23/26.56 (2) all_58_7 = e1
% 171.23/26.56 (3) ~ (e3 = e1)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.56 | (4) e3 = e1
% 171.23/26.56 |
% 171.23/26.56 | SIMP: (4) implies:
% 171.23/26.56 | (5) e3 = e1
% 171.23/26.56 |
% 171.23/26.56 | REDUCE: (3), (5) imply:
% 171.23/26.56 | (6) $false
% 171.23/26.56 |
% 171.23/26.56 | CLOSE: (6) is inconsistent.
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #822 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) all_58_6 = e3
% 171.23/26.56 (2) all_58_6 = e2
% 171.23/26.56 (3) ~ (e3 = e2)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.56 | (4) e3 = e2
% 171.23/26.56 |
% 171.23/26.56 | SIMP: (4) implies:
% 171.23/26.56 | (5) e3 = e2
% 171.23/26.56 |
% 171.23/26.56 | REDUCE: (3), (5) imply:
% 171.23/26.56 | (6) $false
% 171.23/26.56 |
% 171.23/26.56 | CLOSE: (6) is inconsistent.
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #823 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) all_58_6 = e2
% 171.23/26.56 (2) all_58_6 = e1
% 171.23/26.56 (3) ~ (e2 = e1)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.56 | (4) e2 = e1
% 171.23/26.56 |
% 171.23/26.56 | SIMP: (4) implies:
% 171.23/26.56 | (5) e2 = e1
% 171.23/26.56 |
% 171.23/26.56 | REDUCE: (3), (5) imply:
% 171.23/26.56 | (6) $false
% 171.23/26.56 |
% 171.23/26.56 | CLOSE: (6) is inconsistent.
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #824 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) = e2) |
% 171.23/26.56 (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) = e2)
% 171.23/26.56 (2) all_58_11 = e0
% 171.23/26.56 (3) ~ (all_6_2 = e2)
% 171.23/26.56 (4) op(e1, e1) = all_6_2
% 171.23/26.56 (5) all_58_6 = e0
% 171.23/26.56 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.56 (7) ~ (e2 = e0)
% 171.23/26.56 (8) all_58_7 = e3
% 171.23/26.56 (9) ~ (e3 = e2)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | BETA: splitting (1) gives:
% 171.23/26.56 |
% 171.23/26.56 | Case 1:
% 171.23/26.56 | |
% 171.23/26.56 | | (10) (all_58_6 = e2 & op(e1, e3) = e2) | (all_58_7 = e2 & op(e1, e2) =
% 171.23/26.56 | | e2)
% 171.23/26.56 | |
% 171.23/26.56 | | BETA: splitting (10) gives:
% 171.23/26.56 | |
% 171.23/26.56 | | Case 1:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (11) all_58_6 = e2 & op(e1, e3) = e2
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (5), (7), (11) are inconsistent by sub-proof #826.
% 171.23/26.56 | | |
% 171.23/26.56 | | Case 2:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (12) all_58_7 = e2 & op(e1, e2) = e2
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (12) implies:
% 171.23/26.56 | | | (13) all_58_7 = e2
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (8), (9), (13) are inconsistent by sub-proof #825.
% 171.23/26.56 | | |
% 171.23/26.56 | | End of split
% 171.23/26.56 | |
% 171.23/26.56 | Case 2:
% 171.23/26.56 | |
% 171.23/26.56 | | (14) (all_58_8 = e2 & op(e1, e1) = e2) | (all_58_11 = e2 & op(e1, e0) =
% 171.23/26.56 | | e2)
% 171.23/26.56 | |
% 171.23/26.56 | | BETA: splitting (14) gives:
% 171.23/26.56 | |
% 171.23/26.56 | | Case 1:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (15) all_58_8 = e2 & op(e1, e1) = e2
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (3), (4), (6), (15) are inconsistent by sub-proof #845.
% 171.23/26.56 | | |
% 171.23/26.56 | | Case 2:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (16) all_58_11 = e2 & op(e1, e0) = e2
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (16) implies:
% 171.23/26.56 | | | (17) all_58_11 = e2
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (2), (7), (17) are inconsistent by sub-proof #879.
% 171.23/26.56 | | |
% 171.23/26.56 | | End of split
% 171.23/26.56 | |
% 171.23/26.56 | End of split
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #825 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) all_58_7 = e3
% 171.23/26.56 (2) all_58_7 = e2
% 171.23/26.56 (3) ~ (e3 = e2)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.56 | (4) e3 = e2
% 171.23/26.56 |
% 171.23/26.56 | SIMP: (4) implies:
% 171.23/26.56 | (5) e3 = e2
% 171.23/26.56 |
% 171.23/26.56 | REDUCE: (3), (5) imply:
% 171.23/26.56 | (6) $false
% 171.23/26.56 |
% 171.23/26.56 | CLOSE: (6) is inconsistent.
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #826 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) all_58_6 = e2 & op(e1, e3) = e2
% 171.23/26.56 (2) all_58_6 = e0
% 171.23/26.56 (3) ~ (e2 = e0)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | ALPHA: (1) implies:
% 171.23/26.56 | (4) all_58_6 = e2
% 171.23/26.56 |
% 171.23/26.56 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.56 | (5) e2 = e0
% 171.23/26.56 |
% 171.23/26.56 | REDUCE: (3), (5) imply:
% 171.23/26.56 | (6) $false
% 171.23/26.56 |
% 171.23/26.56 | CLOSE: (6) is inconsistent.
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #827 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.23/26.56 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 171.23/26.56 (2) all_58_2 = e2
% 171.23/26.56 (3) ~ (e3 = e1)
% 171.23/26.56 (4) ~ (e1 = e0)
% 171.23/26.56 (5) all_58_5 = e3
% 171.23/26.56 (6) ~ (e3 = e0)
% 171.23/26.56 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.56 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.56 (8) all_58_3 = e2
% 171.23/26.56 (9) ~ (e2 = e0)
% 171.23/26.56 (10) ~ (e2 = e1)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | BETA: splitting (1) gives:
% 171.23/26.56 |
% 171.23/26.56 | Case 1:
% 171.23/26.56 | |
% 171.23/26.56 | | (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 171.23/26.56 | | e1)
% 171.23/26.56 | |
% 171.23/26.56 | | BETA: splitting (11) gives:
% 171.23/26.56 | |
% 171.23/26.56 | | Case 1:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (12) all_58_2 = e1 & op(e2, e3) = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (2), (10), (12) are inconsistent by sub-proof #829.
% 171.23/26.56 | | |
% 171.23/26.56 | | Case 2:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (13) all_58_3 = e1 & op(e2, e2) = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (8), (10), (13) are inconsistent by sub-proof #914.
% 171.23/26.56 | | |
% 171.23/26.56 | | End of split
% 171.23/26.56 | |
% 171.23/26.56 | Case 2:
% 171.23/26.56 | |
% 171.23/26.56 | | (14) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 171.23/26.56 | | e1)
% 171.23/26.56 | |
% 171.23/26.56 | | BETA: splitting (14) gives:
% 171.23/26.56 | |
% 171.23/26.56 | | Case 1:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (15) all_58_5 = e1 & op(e2, e1) = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | REF_CLOSE: (3), (5), (15) are inconsistent by sub-proof #828.
% 171.23/26.56 | | |
% 171.23/26.56 | | Case 2:
% 171.23/26.56 | | |
% 171.23/26.56 | | | (16) all_58_10 = e1 & op(e2, e0) = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | ALPHA: (16) implies:
% 171.23/26.56 | | | (17) all_58_10 = e1
% 171.23/26.56 | | |
% 171.23/26.56 | | | BETA: splitting (7) gives:
% 171.23/26.56 | | |
% 171.23/26.56 | | | Case 1:
% 171.23/26.56 | | | |
% 171.23/26.56 | | | | (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2)
% 171.23/26.56 | | | | = e0)
% 171.23/26.56 | | | |
% 171.23/26.56 | | | | BETA: splitting (18) gives:
% 171.23/26.56 | | | |
% 171.23/26.56 | | | | Case 1:
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | | (19) all_58_2 = e0 & op(e2, e3) = e0
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | | REF_CLOSE: (2), (9), (19) are inconsistent by sub-proof #928.
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | Case 2:
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | | (20) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | | REF_CLOSE: (8), (9), (20) are inconsistent by sub-proof #934.
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | End of split
% 171.23/26.56 | | | |
% 171.23/26.56 | | | Case 2:
% 171.23/26.56 | | | |
% 171.23/26.56 | | | | (21) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0)
% 171.23/26.56 | | | | = e0)
% 171.23/26.56 | | | |
% 171.23/26.56 | | | | BETA: splitting (21) gives:
% 171.23/26.56 | | | |
% 171.23/26.56 | | | | Case 1:
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | | (22) all_58_5 = e0 & op(e2, e1) = e0
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | | REF_CLOSE: (5), (6), (22) are inconsistent by sub-proof #926.
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | Case 2:
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | | (23) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | | ALPHA: (23) implies:
% 171.23/26.56 | | | | | (24) all_58_10 = e0
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | | REF_CLOSE: (4), (17), (24) are inconsistent by sub-proof #834.
% 171.23/26.56 | | | | |
% 171.23/26.56 | | | | End of split
% 171.23/26.56 | | | |
% 171.23/26.56 | | | End of split
% 171.23/26.56 | | |
% 171.23/26.56 | | End of split
% 171.23/26.56 | |
% 171.23/26.56 | End of split
% 171.23/26.56 |
% 171.23/26.56 End of proof
% 171.23/26.56
% 171.23/26.56 Sub-proof #828 shows that the following formulas are inconsistent:
% 171.23/26.56 ----------------------------------------------------------------
% 171.23/26.56 (1) all_58_5 = e1 & op(e2, e1) = e1
% 171.23/26.56 (2) all_58_5 = e3
% 171.23/26.56 (3) ~ (e3 = e1)
% 171.23/26.56
% 171.23/26.56 Begin of proof
% 171.23/26.56 |
% 171.23/26.56 | ALPHA: (1) implies:
% 171.23/26.56 | (4) all_58_5 = e1
% 171.23/26.56 |
% 171.23/26.56 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.56 | (5) e3 = e1
% 171.23/26.56 |
% 171.23/26.56 | REDUCE: (3), (5) imply:
% 171.23/26.56 | (6) $false
% 171.23/26.56 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #829 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_2 = e1 & op(e2, e3) = e1
% 171.23/26.57 (2) all_58_2 = e2
% 171.23/26.57 (3) ~ (e2 = e1)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | ALPHA: (1) implies:
% 171.23/26.57 | (4) all_58_2 = e1
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.57 | (5) e2 = e1
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (3), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #830 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) = e1) |
% 171.23/26.57 (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 171.23/26.57 (2) ~ (e3 = e1)
% 171.23/26.57 (3) ~ (e1 = e0)
% 171.23/26.57 (4) all_58_11 = e2
% 171.23/26.57 (5) ~ (e3 = e0)
% 171.23/26.57 (6) all_58_15 = e3
% 171.23/26.57 (7) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 171.23/26.57 (all_58_11 = e0 & op(e1, e0) = e0)
% 171.23/26.57 (8) ~ (e2 = e0)
% 171.23/26.57 (9) all_58_9 = e3
% 171.23/26.57 (10) ~ (e2 = e1)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | BETA: splitting (1) gives:
% 171.23/26.57 |
% 171.23/26.57 | Case 1:
% 171.23/26.57 | |
% 171.23/26.57 | | (11) (all_58_9 = e1 & op(e3, e0) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 171.23/26.57 | | e1)
% 171.23/26.57 | |
% 171.23/26.57 | | BETA: splitting (11) gives:
% 171.23/26.57 | |
% 171.23/26.57 | | Case 1:
% 171.23/26.57 | | |
% 171.23/26.57 | | | (12) all_58_9 = e1 & op(e3, e0) = e1
% 171.23/26.57 | | |
% 171.23/26.57 | | | REF_CLOSE: (2), (9), (12) are inconsistent by sub-proof #836.
% 171.23/26.57 | | |
% 171.23/26.57 | | Case 2:
% 171.23/26.57 | | |
% 171.23/26.57 | | | (13) all_58_10 = e1 & op(e2, e0) = e1
% 171.23/26.57 | | |
% 171.23/26.57 | | | ALPHA: (13) implies:
% 171.23/26.57 | | | (14) all_58_10 = e1
% 171.23/26.57 | | |
% 171.23/26.57 | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (14) are inconsistent by
% 171.23/26.57 | | | sub-proof #833.
% 171.23/26.57 | | |
% 171.23/26.57 | | End of split
% 171.23/26.57 | |
% 171.23/26.57 | Case 2:
% 171.23/26.57 | |
% 171.23/26.57 | | (15) (all_58_11 = e1 & op(e1, e0) = e1) | (all_58_15 = e1 & op(e0, e0) =
% 171.23/26.57 | | e1)
% 171.23/26.57 | |
% 171.23/26.57 | | BETA: splitting (15) gives:
% 171.23/26.57 | |
% 171.23/26.57 | | Case 1:
% 171.23/26.57 | | |
% 171.23/26.57 | | | (16) all_58_11 = e1 & op(e1, e0) = e1
% 171.23/26.57 | | |
% 171.23/26.57 | | | ALPHA: (16) implies:
% 171.23/26.57 | | | (17) all_58_11 = e1
% 171.23/26.57 | | |
% 171.23/26.57 | | | REF_CLOSE: (4), (10), (17) are inconsistent by sub-proof #832.
% 171.23/26.57 | | |
% 171.23/26.57 | | Case 2:
% 171.23/26.57 | | |
% 171.23/26.57 | | | (18) all_58_15 = e1 & op(e0, e0) = e1
% 171.23/26.57 | | |
% 171.23/26.57 | | | REF_CLOSE: (2), (6), (18) are inconsistent by sub-proof #831.
% 171.23/26.57 | | |
% 171.23/26.57 | | End of split
% 171.23/26.57 | |
% 171.23/26.57 | End of split
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #831 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_15 = e1 & op(e0, e0) = e1
% 171.23/26.57 (2) all_58_15 = e3
% 171.23/26.57 (3) ~ (e3 = e1)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | ALPHA: (1) implies:
% 171.23/26.57 | (4) all_58_15 = e1
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.57 | (5) e3 = e1
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (3), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #832 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_11 = e2
% 171.23/26.57 (2) all_58_11 = e1
% 171.23/26.57 (3) ~ (e2 = e1)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.57 | (4) e2 = e1
% 171.23/26.57 |
% 171.23/26.57 | SIMP: (4) implies:
% 171.23/26.57 | (5) e2 = e1
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (3), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #833 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) ~ (e1 = e0)
% 171.23/26.57 (2) all_58_11 = e2
% 171.23/26.57 (3) ~ (e3 = e0)
% 171.23/26.57 (4) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 171.23/26.57 (all_58_11 = e0 & op(e1, e0) = e0)
% 171.23/26.57 (5) ~ (e2 = e0)
% 171.23/26.57 (6) all_58_9 = e3
% 171.23/26.57 (7) all_58_10 = e1
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | BETA: splitting (4) gives:
% 171.23/26.57 |
% 171.23/26.57 | Case 1:
% 171.23/26.57 | |
% 171.23/26.57 | | (8) all_58_9 = e0 & op(e3, e0) = e0
% 171.23/26.57 | |
% 171.23/26.57 | | ALPHA: (8) implies:
% 171.23/26.57 | | (9) all_58_9 = e0
% 171.23/26.57 | |
% 171.23/26.57 | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #835.
% 171.23/26.57 | |
% 171.23/26.57 | Case 2:
% 171.23/26.57 | |
% 171.23/26.57 | | (10) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 171.23/26.57 | | e0)
% 171.23/26.57 | |
% 171.23/26.57 | | BETA: splitting (10) gives:
% 171.23/26.57 | |
% 171.23/26.57 | | Case 1:
% 171.23/26.57 | | |
% 171.23/26.57 | | | (11) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.57 | | |
% 171.23/26.57 | | | ALPHA: (11) implies:
% 171.23/26.57 | | | (12) all_58_10 = e0
% 171.23/26.57 | | |
% 171.23/26.57 | | | REF_CLOSE: (1), (7), (12) are inconsistent by sub-proof #834.
% 171.23/26.57 | | |
% 171.23/26.57 | | Case 2:
% 171.23/26.57 | | |
% 171.23/26.57 | | | (13) all_58_11 = e0 & op(e1, e0) = e0
% 171.23/26.57 | | |
% 171.23/26.57 | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #848.
% 171.23/26.57 | | |
% 171.23/26.57 | | End of split
% 171.23/26.57 | |
% 171.23/26.57 | End of split
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #834 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_10 = e1
% 171.23/26.57 (2) all_58_10 = e0
% 171.23/26.57 (3) ~ (e1 = e0)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.57 | (4) e1 = e0
% 171.23/26.57 |
% 171.23/26.57 | SIMP: (4) implies:
% 171.23/26.57 | (5) e1 = e0
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (3), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #835 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_9 = e3
% 171.23/26.57 (2) all_58_9 = e0
% 171.23/26.57 (3) ~ (e3 = e0)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.57 | (4) e3 = e0
% 171.23/26.57 |
% 171.23/26.57 | SIMP: (4) implies:
% 171.23/26.57 | (5) e3 = e0
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (3), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #836 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_9 = e1 & op(e3, e0) = e1
% 171.23/26.57 (2) all_58_9 = e3
% 171.23/26.57 (3) ~ (e3 = e1)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | ALPHA: (1) implies:
% 171.23/26.57 | (4) all_58_9 = e1
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.57 | (5) e3 = e1
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (3), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #837 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 171.23/26.57 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 171.23/26.57 (2) ~ (all_4_2 = e2)
% 171.23/26.57 (3) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 171.23/26.57 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 171.23/26.57 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.23/26.57 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 171.23/26.57 (5) ~ (all_8_2 = e3)
% 171.23/26.57 (6) ~ (all_6_2 = e3)
% 171.23/26.57 (7) ~ (e3 = e1)
% 171.23/26.57 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 171.23/26.57 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 171.23/26.57 (9) ~ (e1 = e0)
% 171.23/26.57 (10) all_58_11 = e2
% 171.23/26.57 (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 171.23/26.57 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 171.23/26.57 (12) all_58_5 = e3
% 171.23/26.57 (13) all_58_1 = e2
% 171.23/26.57 (14) op(e2, e2) = all_8_2
% 171.23/26.57 (15) op(e1, e1) = all_6_2
% 171.23/26.57 (16) ~ (e3 = e0)
% 171.23/26.57 (17) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.57 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.57 (18) op(e0, e0) = all_4_2
% 171.23/26.57 (19) all_58_4 = e0
% 171.23/26.57 (20) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.57 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 171.23/26.57 (21) all_58_3 = e2
% 171.23/26.57 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.57 (23) ~ (e2 = e0)
% 171.23/26.57 (24) all_58_1 = e3 & op(e3, e2) = e3
% 171.23/26.57 (25) ~ (e2 = e1)
% 171.23/26.57 (26) op(e3, e2) = all_52_4
% 171.23/26.57 (27) all_58_9 = e1
% 171.23/26.57 (28) all_58_2 = e1
% 171.23/26.57 (29) op(e0, e2) = all_52_7
% 171.23/26.57 (30) ~ (all_52_4 = e1)
% 171.23/26.57 (31) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 171.23/26.57 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.23/26.57 (32) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.57 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 171.23/26.57 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.23/26.57 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.23/26.57 (33) ~ (e3 = e2)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | ALPHA: (24) implies:
% 171.23/26.57 | (34) all_58_1 = e3
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (13), (34) imply:
% 171.23/26.57 | (35) e3 = e2
% 171.23/26.57 |
% 171.23/26.57 | SIMP: (35) implies:
% 171.23/26.57 | (36) e3 = e2
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (12), (36) imply:
% 171.23/26.57 | (37) all_58_5 = e2
% 171.23/26.57 |
% 171.23/26.57 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 171.23/26.57 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (25),
% 171.23/26.57 | (26), (27), (28), (29), (30), (31), (32), (33), (37) are
% 171.23/26.57 | inconsistent by sub-proof #853.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #838 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.57 (2) op(e3, e3) = e3
% 171.23/26.57 (3) op(e3, e3) = e2
% 171.23/26.57 (4) ~ (e3 = e2)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | GROUND_INST: instantiating (1) with e2, e3, e3, e3, simplifying with (2), (3)
% 171.23/26.57 | gives:
% 171.23/26.57 | (5) e3 = e2
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (4), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #839 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 171.23/26.57 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 171.23/26.57 (2) ~ (all_4_2 = e2)
% 171.23/26.57 (3) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 171.23/26.57 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 171.23/26.57 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.23/26.57 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 171.23/26.57 (5) ~ (all_8_2 = e3)
% 171.23/26.57 (6) ~ (all_6_2 = e3)
% 171.23/26.57 (7) ~ (e3 = e1)
% 171.23/26.57 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 171.23/26.57 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 171.23/26.57 (9) ~ (e1 = e0)
% 171.23/26.57 (10) all_58_11 = e2
% 171.23/26.57 (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 171.23/26.57 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 171.23/26.57 (12) all_58_5 = e3
% 171.23/26.57 (13) all_58_1 = e2
% 171.23/26.57 (14) all_58_11 = e3 & op(e1, e0) = e3
% 171.23/26.57 (15) op(e2, e2) = all_8_2
% 171.23/26.57 (16) op(e1, e1) = all_6_2
% 171.23/26.57 (17) ~ (e3 = e0)
% 171.23/26.57 (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.57 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.57 (19) op(e0, e0) = all_4_2
% 171.23/26.57 (20) all_58_4 = e0
% 171.23/26.57 (21) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.57 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 171.23/26.57 (22) all_58_3 = e2
% 171.23/26.57 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.57 (24) ~ (e2 = e0)
% 171.23/26.57 (25) ~ (e2 = e1)
% 171.23/26.57 (26) op(e3, e2) = all_52_4
% 171.23/26.57 (27) all_58_9 = e1
% 171.23/26.57 (28) all_58_2 = e1
% 171.23/26.57 (29) op(e0, e2) = all_52_7
% 171.23/26.57 (30) ~ (all_52_4 = e1)
% 171.23/26.57 (31) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 171.23/26.57 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.23/26.57 (32) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.57 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 171.23/26.57 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.23/26.57 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.23/26.57 (33) ~ (e3 = e2)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | ALPHA: (14) implies:
% 171.23/26.57 | (34) all_58_11 = e3
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (10), (34) imply:
% 171.23/26.57 | (35) e3 = e2
% 171.23/26.57 |
% 171.23/26.57 | SIMP: (35) implies:
% 171.23/26.57 | (36) e3 = e2
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (12), (36) imply:
% 171.23/26.57 | (37) all_58_5 = e2
% 171.23/26.57 |
% 171.23/26.57 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 171.23/26.57 | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 171.23/26.57 | (26), (27), (28), (29), (30), (31), (32), (33), (37) are
% 171.23/26.57 | inconsistent by sub-proof #853.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #840 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_10 = e0
% 171.23/26.57 (2) ~ (e3 = e1)
% 171.23/26.57 (3) ~ (e3 = e0)
% 171.23/26.57 (4) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 171.23/26.57 (5) all_58_9 = e1
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | BETA: splitting (4) gives:
% 171.23/26.57 |
% 171.23/26.57 | Case 1:
% 171.23/26.57 | |
% 171.23/26.57 | | (6) all_58_9 = e3 & op(e3, e0) = e3
% 171.23/26.57 | |
% 171.23/26.57 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #893.
% 171.23/26.57 | |
% 171.23/26.57 | Case 2:
% 171.23/26.57 | |
% 171.23/26.57 | | (7) all_58_10 = e3 & op(e2, e0) = e3
% 171.23/26.57 | |
% 171.23/26.57 | | ALPHA: (7) implies:
% 171.23/26.57 | | (8) all_58_10 = e3
% 171.23/26.57 | |
% 171.23/26.57 | | REF_CLOSE: (1), (3), (8) are inconsistent by sub-proof #841.
% 171.23/26.57 | |
% 171.23/26.57 | End of split
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #841 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_10 = e3
% 171.23/26.57 (2) all_58_10 = e0
% 171.23/26.57 (3) ~ (e3 = e0)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.57 | (4) e3 = e0
% 171.23/26.57 |
% 171.23/26.57 | SIMP: (4) implies:
% 171.23/26.57 | (5) e3 = e0
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (3), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #842 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 171.23/26.57 (2) ~ (e1 = e0)
% 171.23/26.57 (3) all_58_3 = e2
% 171.23/26.57 (4) ~ (e2 = e0)
% 171.23/26.57 (5) all_58_2 = e1
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | BETA: splitting (1) gives:
% 171.23/26.57 |
% 171.23/26.57 | Case 1:
% 171.23/26.57 | |
% 171.23/26.57 | | (6) all_58_2 = e0 & op(e2, e3) = e0
% 171.23/26.57 | |
% 171.23/26.57 | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #935.
% 171.23/26.57 | |
% 171.23/26.57 | Case 2:
% 171.23/26.57 | |
% 171.23/26.57 | | (7) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.57 | |
% 171.23/26.57 | | ALPHA: (7) implies:
% 171.23/26.57 | | (8) all_58_3 = e0
% 171.23/26.57 | |
% 171.23/26.57 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #843.
% 171.23/26.57 | |
% 171.23/26.57 | End of split
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #843 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_3 = e2
% 171.23/26.57 (2) all_58_3 = e0
% 171.23/26.57 (3) ~ (e2 = e0)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.57 | (4) e2 = e0
% 171.23/26.57 |
% 171.23/26.57 | SIMP: (4) implies:
% 171.23/26.57 | (5) e2 = e0
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (3), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #844 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_4 = e3 & op(e3, e1) = e3
% 171.23/26.57 (2) all_58_4 = e0
% 171.23/26.57 (3) ~ (e3 = e0)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | ALPHA: (1) implies:
% 171.23/26.57 | (4) all_58_4 = e3
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.57 | (5) e3 = e0
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (3), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #845 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_8 = e2 & op(e1, e1) = e2
% 171.23/26.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.57 (3) op(e1, e1) = all_6_2
% 171.23/26.57 (4) ~ (all_6_2 = e2)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | ALPHA: (1) implies:
% 171.23/26.57 | (5) op(e1, e1) = e2
% 171.23/26.57 |
% 171.23/26.57 | GROUND_INST: instantiating (2) with all_6_2, e2, e1, e1, simplifying with (3),
% 171.23/26.57 | (5) gives:
% 171.23/26.57 | (6) all_6_2 = e2
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (4), (6) imply:
% 171.23/26.57 | (7) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (7) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #846 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.23/26.57 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 171.23/26.57 (2) ~ (e3 = e1)
% 171.23/26.57 (3) ~ (e1 = e0)
% 171.23/26.57 (4) all_58_11 = e2
% 171.23/26.57 (5) ~ (e3 = e0)
% 171.23/26.57 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.57 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.57 (7) op(e2, e0) = e1
% 171.23/26.57 (8) all_58_3 = e2
% 171.23/26.57 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.57 (10) ~ (e2 = e0)
% 171.23/26.57 (11) all_58_5 = e2
% 171.23/26.57 (12) ~ (e2 = e1)
% 171.23/26.57 (13) all_58_9 = e1
% 171.23/26.57 (14) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 171.23/26.57 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.23/26.57 (15) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.57 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 171.23/26.57 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.23/26.57 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.23/26.57 (16) ~ (e3 = e2)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | BETA: splitting (15) gives:
% 171.23/26.57 |
% 171.23/26.57 | Case 1:
% 171.23/26.57 | |
% 171.23/26.57 | | (17) all_58_15 = e0 & op(e0, e0) = e0
% 171.23/26.57 | |
% 171.23/26.57 | | ALPHA: (17) implies:
% 171.23/26.57 | | (18) all_58_15 = e0
% 171.23/26.57 | |
% 171.23/26.57 | | BETA: splitting (14) gives:
% 171.23/26.57 | |
% 171.23/26.57 | | Case 1:
% 171.23/26.57 | | |
% 171.23/26.57 | | | (19) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 171.23/26.57 | | | e3)
% 171.23/26.57 | | |
% 171.23/26.57 | | | BETA: splitting (19) gives:
% 171.23/26.57 | | |
% 171.23/26.57 | | | Case 1:
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | (20) all_58_9 = e3 & op(e3, e0) = e3
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | REF_CLOSE: (2), (13), (20) are inconsistent by sub-proof #893.
% 171.23/26.57 | | | |
% 171.23/26.57 | | | Case 2:
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | (21) all_58_10 = e3 & op(e2, e0) = e3
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | ALPHA: (21) implies:
% 171.23/26.57 | | | | (22) all_58_10 = e3
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (11), (12), (22) are
% 171.23/26.57 | | | | inconsistent by sub-proof #850.
% 171.23/26.57 | | | |
% 171.23/26.57 | | | End of split
% 171.23/26.57 | | |
% 171.23/26.57 | | Case 2:
% 171.23/26.57 | | |
% 171.23/26.57 | | | (23) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0)
% 171.23/26.57 | | | = e3)
% 171.23/26.57 | | |
% 171.23/26.57 | | | BETA: splitting (23) gives:
% 171.23/26.57 | | |
% 171.23/26.57 | | | Case 1:
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | (24) all_58_11 = e3 & op(e1, e0) = e3
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | ALPHA: (24) implies:
% 171.23/26.57 | | | | (25) all_58_11 = e3
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | REF_CLOSE: (4), (16), (25) are inconsistent by sub-proof #892.
% 171.23/26.57 | | | |
% 171.23/26.57 | | | Case 2:
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | (26) all_58_15 = e3 & op(e0, e0) = e3
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | ALPHA: (26) implies:
% 171.23/26.57 | | | | (27) all_58_15 = e3
% 171.23/26.57 | | | |
% 171.23/26.57 | | | | REF_CLOSE: (5), (18), (27) are inconsistent by sub-proof #860.
% 171.23/26.57 | | | |
% 171.23/26.57 | | | End of split
% 171.23/26.57 | | |
% 171.23/26.57 | | End of split
% 171.23/26.57 | |
% 171.23/26.57 | Case 2:
% 171.23/26.57 | |
% 171.23/26.57 | | (28) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 171.23/26.57 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 171.23/26.57 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 171.23/26.57 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 171.23/26.57 | |
% 171.23/26.57 | | ALPHA: (28) implies:
% 171.23/26.57 | | (29) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 171.23/26.57 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 171.23/26.57 | |
% 171.23/26.57 | | REF_CLOSE: (3), (4), (7), (9), (10), (13), (29) are inconsistent by
% 171.23/26.57 | | sub-proof #847.
% 171.23/26.57 | |
% 171.23/26.57 | End of split
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #847 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) ~ (e1 = e0)
% 171.23/26.57 (2) all_58_11 = e2
% 171.23/26.57 (3) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 171.23/26.57 (all_58_11 = e0 & op(e1, e0) = e0)
% 171.23/26.57 (4) op(e2, e0) = e1
% 171.23/26.57 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.57 (6) ~ (e2 = e0)
% 171.23/26.57 (7) all_58_9 = e1
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | BETA: splitting (3) gives:
% 171.23/26.57 |
% 171.23/26.57 | Case 1:
% 171.23/26.57 | |
% 171.23/26.57 | | (8) all_58_9 = e0 & op(e3, e0) = e0
% 171.23/26.57 | |
% 171.23/26.57 | | REF_CLOSE: (1), (7), (8) are inconsistent by sub-proof #880.
% 171.23/26.57 | |
% 171.23/26.57 | Case 2:
% 171.23/26.57 | |
% 171.23/26.57 | | (9) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 171.23/26.57 | | e0)
% 171.23/26.57 | |
% 171.23/26.57 | | BETA: splitting (9) gives:
% 171.23/26.57 | |
% 171.23/26.57 | | Case 1:
% 171.23/26.57 | | |
% 171.23/26.57 | | | (10) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.57 | | |
% 171.23/26.57 | | | ALPHA: (10) implies:
% 171.23/26.57 | | | (11) op(e2, e0) = e0
% 171.23/26.57 | | |
% 171.23/26.57 | | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #849.
% 171.23/26.57 | | |
% 171.23/26.57 | | Case 2:
% 171.23/26.57 | | |
% 171.23/26.57 | | | (12) all_58_11 = e0 & op(e1, e0) = e0
% 171.23/26.57 | | |
% 171.23/26.57 | | | REF_CLOSE: (2), (6), (12) are inconsistent by sub-proof #848.
% 171.23/26.57 | | |
% 171.23/26.57 | | End of split
% 171.23/26.57 | |
% 171.23/26.57 | End of split
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #848 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.57 (1) all_58_11 = e0 & op(e1, e0) = e0
% 171.23/26.57 (2) all_58_11 = e2
% 171.23/26.57 (3) ~ (e2 = e0)
% 171.23/26.57
% 171.23/26.57 Begin of proof
% 171.23/26.57 |
% 171.23/26.57 | ALPHA: (1) implies:
% 171.23/26.57 | (4) all_58_11 = e0
% 171.23/26.57 |
% 171.23/26.57 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.57 | (5) e2 = e0
% 171.23/26.57 |
% 171.23/26.57 | REDUCE: (3), (5) imply:
% 171.23/26.57 | (6) $false
% 171.23/26.57 |
% 171.23/26.57 | CLOSE: (6) is inconsistent.
% 171.23/26.57 |
% 171.23/26.57 End of proof
% 171.23/26.57
% 171.23/26.57 Sub-proof #849 shows that the following formulas are inconsistent:
% 171.23/26.57 ----------------------------------------------------------------
% 171.23/26.58 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.58 (2) op(e2, e0) = e1
% 171.23/26.58 (3) op(e2, e0) = e0
% 171.23/26.58 (4) ~ (e1 = e0)
% 171.23/26.58
% 171.23/26.58 Begin of proof
% 171.23/26.58 |
% 171.23/26.58 | GROUND_INST: instantiating (1) with e1, e0, e0, e2, simplifying with (2), (3)
% 171.23/26.58 | gives:
% 171.23/26.58 | (5) e1 = e0
% 171.23/26.58 |
% 171.23/26.58 | REDUCE: (4), (5) imply:
% 171.23/26.58 | (6) $false
% 171.23/26.58 |
% 171.23/26.58 | CLOSE: (6) is inconsistent.
% 171.23/26.58 |
% 171.23/26.58 End of proof
% 171.23/26.58
% 171.23/26.58 Sub-proof #850 shows that the following formulas are inconsistent:
% 171.23/26.58 ----------------------------------------------------------------
% 171.23/26.58 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.23/26.58 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 171.23/26.58 (2) ~ (e3 = e1)
% 171.23/26.58 (3) ~ (e1 = e0)
% 171.23/26.58 (4) all_58_10 = e3
% 171.23/26.58 (5) ~ (e3 = e0)
% 171.23/26.58 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.58 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.58 (7) all_58_3 = e2
% 171.23/26.58 (8) ~ (e2 = e0)
% 171.23/26.58 (9) all_58_5 = e2
% 171.23/26.58 (10) ~ (e2 = e1)
% 171.23/26.58
% 171.23/26.58 Begin of proof
% 171.23/26.58 |
% 171.23/26.58 | BETA: splitting (1) gives:
% 171.23/26.58 |
% 171.23/26.58 | Case 1:
% 171.23/26.58 | |
% 171.23/26.58 | | (11) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 171.23/26.58 | | e1)
% 171.23/26.58 | |
% 171.23/26.58 | | BETA: splitting (11) gives:
% 171.23/26.58 | |
% 171.23/26.58 | | Case 1:
% 171.23/26.58 | | |
% 171.23/26.58 | | | (12) all_58_2 = e1 & op(e2, e3) = e1
% 171.23/26.58 | | |
% 171.23/26.58 | | | ALPHA: (12) implies:
% 171.23/26.58 | | | (13) all_58_2 = e1
% 171.23/26.58 | | |
% 171.23/26.58 | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (13) are inconsistent by
% 171.23/26.58 | | | sub-proof #931.
% 171.23/26.58 | | |
% 171.23/26.58 | | Case 2:
% 171.23/26.58 | | |
% 171.23/26.58 | | | (14) all_58_3 = e1 & op(e2, e2) = e1
% 171.23/26.58 | | |
% 171.23/26.58 | | | REF_CLOSE: (7), (10), (14) are inconsistent by sub-proof #914.
% 171.23/26.58 | | |
% 171.23/26.58 | | End of split
% 171.23/26.58 | |
% 171.23/26.58 | Case 2:
% 171.23/26.58 | |
% 171.23/26.58 | | (15) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 171.23/26.58 | | e1)
% 171.23/26.58 | |
% 171.23/26.58 | | BETA: splitting (15) gives:
% 171.23/26.58 | |
% 171.23/26.58 | | Case 1:
% 171.23/26.58 | | |
% 171.23/26.58 | | | (16) all_58_5 = e1 & op(e2, e1) = e1
% 171.23/26.58 | | |
% 171.23/26.58 | | | REF_CLOSE: (9), (10), (16) are inconsistent by sub-proof #852.
% 171.23/26.58 | | |
% 171.23/26.58 | | Case 2:
% 171.23/26.58 | | |
% 171.23/26.58 | | | (17) all_58_10 = e1 & op(e2, e0) = e1
% 171.23/26.58 | | |
% 171.23/26.58 | | | REF_CLOSE: (2), (4), (17) are inconsistent by sub-proof #851.
% 171.23/26.58 | | |
% 171.23/26.58 | | End of split
% 171.23/26.58 | |
% 171.23/26.58 | End of split
% 171.23/26.58 |
% 171.23/26.58 End of proof
% 171.23/26.58
% 171.23/26.58 Sub-proof #851 shows that the following formulas are inconsistent:
% 171.23/26.58 ----------------------------------------------------------------
% 171.23/26.58 (1) all_58_10 = e1 & op(e2, e0) = e1
% 171.23/26.58 (2) all_58_10 = e3
% 171.23/26.58 (3) ~ (e3 = e1)
% 171.23/26.58
% 171.23/26.58 Begin of proof
% 171.23/26.58 |
% 171.23/26.58 | ALPHA: (1) implies:
% 171.23/26.58 | (4) all_58_10 = e1
% 171.23/26.58 |
% 171.23/26.58 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.58 | (5) e3 = e1
% 171.23/26.58 |
% 171.23/26.58 | REDUCE: (3), (5) imply:
% 171.23/26.58 | (6) $false
% 171.23/26.58 |
% 171.23/26.58 | CLOSE: (6) is inconsistent.
% 171.23/26.58 |
% 171.23/26.58 End of proof
% 171.23/26.58
% 171.23/26.58 Sub-proof #852 shows that the following formulas are inconsistent:
% 171.23/26.58 ----------------------------------------------------------------
% 171.23/26.58 (1) all_58_5 = e1 & op(e2, e1) = e1
% 171.23/26.58 (2) all_58_5 = e2
% 171.23/26.58 (3) ~ (e2 = e1)
% 171.23/26.58
% 171.23/26.58 Begin of proof
% 171.23/26.58 |
% 171.23/26.58 | ALPHA: (1) implies:
% 171.23/26.58 | (4) all_58_5 = e1
% 171.23/26.58 |
% 171.23/26.58 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.58 | (5) e2 = e1
% 171.23/26.58 |
% 171.23/26.58 | REDUCE: (3), (5) imply:
% 171.23/26.58 | (6) $false
% 171.23/26.58 |
% 171.23/26.58 | CLOSE: (6) is inconsistent.
% 171.23/26.58 |
% 171.23/26.58 End of proof
% 171.23/26.58
% 171.23/26.58 Sub-proof #853 shows that the following formulas are inconsistent:
% 171.23/26.58 ----------------------------------------------------------------
% 171.23/26.58 (1) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 & op(e0, e2) = e2) |
% 171.23/26.58 (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 & op(e0, e0) = e2)
% 171.23/26.58 (2) ~ (all_4_2 = e2)
% 171.23/26.58 (3) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 171.23/26.58 (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3 & op(e0, e2) = e3)
% 171.23/26.58 (4) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.23/26.58 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 171.23/26.58 (5) ~ (all_8_2 = e3)
% 171.23/26.58 (6) ~ (all_6_2 = e3)
% 171.23/26.58 (7) ~ (e3 = e1)
% 171.23/26.58 (8) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 & op(e0, e2) = e1) |
% 171.23/26.58 (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 171.23/26.58 (9) ~ (e1 = e0)
% 171.23/26.58 (10) all_58_11 = e2
% 171.23/26.58 (11) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) = e3) |
% 171.23/26.58 (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) = e3)
% 171.23/26.58 (12) all_58_1 = e2
% 171.23/26.58 (13) op(e2, e2) = all_8_2
% 171.23/26.58 (14) op(e1, e1) = all_6_2
% 171.23/26.58 (15) ~ (e3 = e0)
% 171.23/26.58 (16) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.58 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.58 (17) op(e0, e0) = all_4_2
% 171.23/26.58 (18) all_58_4 = e0
% 171.23/26.58 (19) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.58 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 171.23/26.58 (20) all_58_3 = e2
% 171.23/26.58 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.58 (22) ~ (e2 = e0)
% 171.23/26.58 (23) all_58_5 = e2
% 171.23/26.58 (24) ~ (e2 = e1)
% 171.23/26.58 (25) op(e3, e2) = all_52_4
% 171.23/26.58 (26) all_58_9 = e1
% 171.23/26.58 (27) all_58_2 = e1
% 171.23/26.58 (28) op(e0, e2) = all_52_7
% 171.23/26.58 (29) ~ (all_52_4 = e1)
% 171.23/26.58 (30) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 171.23/26.58 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.23/26.58 (31) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.58 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 171.23/26.58 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.23/26.58 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.23/26.58 (32) ~ (e3 = e2)
% 171.23/26.58
% 171.23/26.58 Begin of proof
% 171.23/26.58 |
% 171.23/26.58 | BETA: splitting (11) gives:
% 171.23/26.58 |
% 171.23/26.58 | Case 1:
% 171.23/26.58 | |
% 171.23/26.58 | | (33) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_5 = e3 & op(e2, e1) =
% 171.23/26.58 | | e3)
% 171.23/26.58 | |
% 171.23/26.58 | | BETA: splitting (33) gives:
% 171.23/26.58 | |
% 171.23/26.58 | | Case 1:
% 171.23/26.58 | | |
% 171.23/26.58 | | | (34) all_58_4 = e3 & op(e3, e1) = e3
% 171.23/26.58 | | |
% 171.23/26.58 | | | ALPHA: (34) implies:
% 171.23/26.58 | | | (35) all_58_4 = e3
% 171.23/26.58 | | |
% 171.23/26.58 | | | REF_CLOSE: (15), (18), (35) are inconsistent by sub-proof #894.
% 171.23/26.58 | | |
% 171.23/26.58 | | Case 2:
% 171.23/26.58 | | |
% 171.23/26.58 | | | (36) all_58_5 = e3 & op(e2, e1) = e3
% 171.23/26.58 | | |
% 171.23/26.58 | | | REF_CLOSE: (23), (32), (36) are inconsistent by sub-proof #936.
% 171.23/26.58 | | |
% 171.23/26.58 | | End of split
% 171.23/26.58 | |
% 171.23/26.58 | Case 2:
% 171.23/26.58 | |
% 171.23/26.58 | | (37) (all_58_8 = e3 & op(e1, e1) = e3) | (all_58_14 = e3 & op(e0, e1) =
% 171.23/26.58 | | e3)
% 171.23/26.58 | |
% 171.23/26.58 | | BETA: splitting (37) gives:
% 171.23/26.58 | |
% 171.23/26.58 | | Case 1:
% 171.23/26.58 | | |
% 171.23/26.58 | | | (38) all_58_8 = e3 & op(e1, e1) = e3
% 171.23/26.58 | | |
% 171.23/26.58 | | | REF_CLOSE: (6), (14), (21), (38) are inconsistent by sub-proof #961.
% 171.23/26.58 | | |
% 171.23/26.58 | | Case 2:
% 171.23/26.58 | | |
% 171.23/26.58 | | | (39) all_58_14 = e3 & op(e0, e1) = e3
% 171.23/26.58 | | |
% 171.23/26.58 | | | ALPHA: (39) implies:
% 171.23/26.58 | | | (40) all_58_14 = e3
% 171.23/26.58 | | |
% 171.23/26.58 | | | BETA: splitting (30) gives:
% 171.23/26.58 | | |
% 171.23/26.58 | | | Case 1:
% 171.23/26.58 | | | |
% 171.23/26.58 | | | | (41) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0)
% 171.23/26.58 | | | | = e3)
% 171.23/26.58 | | | |
% 171.23/26.58 | | | | BETA: splitting (41) gives:
% 171.23/26.58 | | | |
% 171.23/26.58 | | | | Case 1:
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | (42) all_58_9 = e3 & op(e3, e0) = e3
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | REF_CLOSE: (7), (26), (42) are inconsistent by sub-proof #893.
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | Case 2:
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | (43) all_58_10 = e3 & op(e2, e0) = e3
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | ALPHA: (43) implies:
% 171.23/26.58 | | | | | (44) all_58_10 = e3
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | REF_CLOSE: (9), (15), (16), (20), (22), (23), (27), (44) are
% 171.23/26.58 | | | | | inconsistent by sub-proof #931.
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | End of split
% 171.23/26.58 | | | |
% 171.23/26.58 | | | Case 2:
% 171.23/26.58 | | | |
% 171.23/26.58 | | | | (45) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0,
% 171.23/26.58 | | | | e0) = e3)
% 171.23/26.58 | | | |
% 171.23/26.58 | | | | BETA: splitting (45) gives:
% 171.23/26.58 | | | |
% 171.23/26.58 | | | | Case 1:
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | (46) all_58_11 = e3 & op(e1, e0) = e3
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | ALPHA: (46) implies:
% 171.23/26.58 | | | | | (47) all_58_11 = e3
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | REF_CLOSE: (10), (32), (47) are inconsistent by sub-proof #892.
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | Case 2:
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | (48) all_58_15 = e3 & op(e0, e0) = e3
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | ALPHA: (48) implies:
% 171.23/26.58 | | | | | (49) all_58_15 = e3
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | BETA: splitting (1) gives:
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | | Case 1:
% 171.23/26.58 | | | | | |
% 171.23/26.58 | | | | | | (50) (all_58_12 = e2 & op(e0, e3) = e2) | (all_58_13 = e2 &
% 171.23/26.58 | | | | | | op(e0, e2) = e2)
% 171.23/26.58 | | | | | |
% 171.23/26.58 | | | | | | BETA: splitting (50) gives:
% 171.23/26.58 | | | | | |
% 171.23/26.58 | | | | | | Case 1:
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | (51) all_58_12 = e2 & op(e0, e3) = e2
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | ALPHA: (51) implies:
% 171.23/26.58 | | | | | | | (52) all_58_12 = e2
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | BETA: splitting (8) gives:
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | | (53) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 171.23/26.58 | | | | | | | | op(e0, e2) = e1)
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | | BETA: splitting (53) gives:
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | (54) all_58_12 = e1 & op(e0, e3) = e1
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | REF_CLOSE: (24), (52), (54) are inconsistent by sub-proof
% 171.23/26.58 | | | | | | | | | #891.
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | (55) all_58_13 = e1 & op(e0, e2) = e1
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | ALPHA: (55) implies:
% 171.23/26.58 | | | | | | | | | (56) all_58_13 = e1
% 171.23/26.58 | | | | | | | | | (57) op(e0, e2) = e1
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | BETA: splitting (3) gives:
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | (58) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 &
% 171.23/26.58 | | | | | | | | | | op(e2, e2) = e3)
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | BETA: splitting (58) gives:
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | (59) all_58_1 = e3 & op(e3, e2) = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | REF_CLOSE: (12), (32), (59) are inconsistent by sub-proof
% 171.23/26.58 | | | | | | | | | | | #904.
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | (60) all_58_3 = e3 & op(e2, e2) = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | REF_CLOSE: (5), (13), (21), (60) are inconsistent by
% 171.23/26.58 | | | | | | | | | | | sub-proof #973.
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | (61) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3
% 171.23/26.58 | | | | | | | | | | & op(e0, e2) = e3)
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | BETA: splitting (61) gives:
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | (62) all_58_7 = e3 & op(e1, e2) = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | ALPHA: (62) implies:
% 171.23/26.58 | | | | | | | | | | | (63) all_58_7 = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | REF_CLOSE: (9), (12), (15), (19), (20), (21), (22), (28),
% 171.23/26.58 | | | | | | | | | | | (57), (63) are inconsistent by sub-proof #888.
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | (64) all_58_13 = e3 & op(e0, e2) = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | ALPHA: (64) implies:
% 171.23/26.58 | | | | | | | | | | | (65) all_58_13 = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | COMBINE_EQS: (56), (65) imply:
% 171.23/26.58 | | | | | | | | | | | (66) e3 = e1
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | COMBINE_EQS: (40), (66) imply:
% 171.23/26.58 | | | | | | | | | | | (67) all_58_14 = e1
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | REF_CLOSE: (9), (15), (22), (31), (49), (52), (65), (67) are
% 171.23/26.58 | | | | | | | | | | | inconsistent by sub-proof #882.
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | End of split
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | | (68) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 171.23/26.58 | | | | | | | | op(e0, e0) = e1)
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | | REF_CLOSE: (7), (9), (10), (15), (22), (26), (30), (31), (32),
% 171.23/26.58 | | | | | | | | (40), (49), (68) are inconsistent by sub-proof #875.
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | End of split
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | Case 2:
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | (69) all_58_13 = e2 & op(e0, e2) = e2
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | ALPHA: (69) implies:
% 171.23/26.58 | | | | | | | (70) all_58_13 = e2
% 171.23/26.58 | | | | | | | (71) op(e0, e2) = e2
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | BETA: splitting (8) gives:
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | | (72) (all_58_12 = e1 & op(e0, e3) = e1) | (all_58_13 = e1 &
% 171.23/26.58 | | | | | | | | op(e0, e2) = e1)
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | | BETA: splitting (72) gives:
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | (73) all_58_12 = e1 & op(e0, e3) = e1
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | ALPHA: (73) implies:
% 171.23/26.58 | | | | | | | | | (74) all_58_12 = e1
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | BETA: splitting (3) gives:
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | (75) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 &
% 171.23/26.58 | | | | | | | | | | op(e2, e2) = e3)
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | BETA: splitting (75) gives:
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | (76) all_58_1 = e3 & op(e3, e2) = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | ALPHA: (76) implies:
% 171.23/26.58 | | | | | | | | | | | (77) all_58_1 = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | COMBINE_EQS: (12), (77) imply:
% 171.23/26.58 | | | | | | | | | | | (78) e3 = e2
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | SIMP: (78) implies:
% 171.23/26.58 | | | | | | | | | | | (79) e3 = e2
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | COMBINE_EQS: (49), (79) imply:
% 171.23/26.58 | | | | | | | | | | | (80) all_58_15 = e2
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | BETA: splitting (31) gives:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | (81) all_58_15 = e0 & op(e0, e0) = e0
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | REF_CLOSE: (22), (80), (81) are inconsistent by sub-proof
% 171.23/26.58 | | | | | | | | | | | | #874.
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | (82) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 171.23/26.58 | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 171.23/26.58 | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 171.23/26.58 | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 171.23/26.58 | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | REF_CLOSE: (9), (15), (22), (40), (70), (74), (82) are
% 171.23/26.58 | | | | | | | | | | | | inconsistent by sub-proof #870.
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | (83) all_58_3 = e3 & op(e2, e2) = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | ALPHA: (83) implies:
% 171.23/26.58 | | | | | | | | | | | (84) all_58_3 = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (12), (15), (19), (22), (24), (70),
% 171.23/26.58 | | | | | | | | | | | (84) are inconsistent by sub-proof #864.
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | (85) (all_58_7 = e3 & op(e1, e2) = e3) | (all_58_13 = e3
% 171.23/26.58 | | | | | | | | | | & op(e0, e2) = e3)
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | BETA: splitting (85) gives:
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | (86) all_58_7 = e3 & op(e1, e2) = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | ALPHA: (86) implies:
% 171.23/26.58 | | | | | | | | | | | (87) all_58_7 = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | BETA: splitting (4) gives:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | (88) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1
% 171.23/26.58 | | | | | | | | | | | | & op(e2, e2) = e1)
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | BETA: splitting (88) gives:
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | (89) all_58_1 = e1 & op(e3, e2) = e1
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | REF_CLOSE: (21), (25), (29), (89) are inconsistent by
% 171.23/26.58 | | | | | | | | | | | | | sub-proof #863.
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | (90) all_58_3 = e1 & op(e2, e2) = e1
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | ALPHA: (90) implies:
% 171.23/26.58 | | | | | | | | | | | | | (91) all_58_3 = e1
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | REF_CLOSE: (20), (24), (91) are inconsistent by sub-proof
% 171.23/26.58 | | | | | | | | | | | | | #924.
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | (92) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 =
% 171.23/26.58 | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | BETA: splitting (92) gives:
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | (93) all_58_7 = e1 & op(e1, e2) = e1
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | ALPHA: (93) implies:
% 171.23/26.58 | | | | | | | | | | | | | (94) all_58_7 = e1
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | COMBINE_EQS: (87), (94) imply:
% 171.23/26.58 | | | | | | | | | | | | | (95) e3 = e1
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | SIMP: (95) implies:
% 171.23/26.58 | | | | | | | | | | | | | (96) e3 = e1
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | COMBINE_EQS: (49), (96) imply:
% 171.23/26.58 | | | | | | | | | | | | | (97) all_58_15 = e1
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (15), (22), (26), (30), (31),
% 171.23/26.58 | | | | | | | | | | | | | (32), (97) are inconsistent by sub-proof #876.
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | (98) all_58_13 = e1 & op(e0, e2) = e1
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | ALPHA: (98) implies:
% 171.23/26.58 | | | | | | | | | | | | | (99) op(e0, e2) = e1
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | REF_CLOSE: (9), (12), (15), (19), (20), (21), (22), (28),
% 171.23/26.58 | | | | | | | | | | | | | (87), (99) are inconsistent by sub-proof #888.
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | (100) all_58_13 = e3 & op(e0, e2) = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | ALPHA: (100) implies:
% 171.23/26.58 | | | | | | | | | | | (101) all_58_13 = e3
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | BETA: splitting (1) gives:
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | BETA: splitting (50) gives:
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | (102) all_58_12 = e2 & op(e0, e3) = e2
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | ALPHA: (102) implies:
% 171.23/26.58 | | | | | | | | | | | | | (103) all_58_12 = e2
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | REF_CLOSE: (24), (74), (103) are inconsistent by sub-proof
% 171.23/26.58 | | | | | | | | | | | | | #862.
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | REF_CLOSE: (32), (69), (101) are inconsistent by sub-proof
% 171.23/26.58 | | | | | | | | | | | | | #861.
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | (104) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 =
% 171.23/26.58 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | BETA: splitting (104) gives:
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | (105) all_58_14 = e2 & op(e0, e1) = e2
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | ALPHA: (105) implies:
% 171.23/26.58 | | | | | | | | | | | | | (106) all_58_14 = e2
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | BETA: splitting (31) gives:
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | Case 1:
% 171.23/26.58 | | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | | (107) all_58_15 = e0 & op(e0, e0) = e0
% 171.23/26.58 | | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | | ALPHA: (107) implies:
% 171.23/26.58 | | | | | | | | | | | | | | (108) all_58_15 = e0
% 171.23/26.58 | | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | | REF_CLOSE: (15), (49), (108) are inconsistent by sub-proof
% 171.23/26.58 | | | | | | | | | | | | | | #860.
% 171.23/26.58 | | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | | (109) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 =
% 171.23/26.58 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_58_11 = e0 &
% 171.23/26.58 | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0,
% 171.23/26.58 | | | | | | | | | | | | | | e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 171.23/26.58 | | | | | | | | | | | | | | e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 171.23/26.58 | | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | | REF_CLOSE: (9), (15), (22), (74), (101), (106), (109) are
% 171.23/26.58 | | | | | | | | | | | | | | inconsistent by sub-proof #857.
% 171.23/26.58 | | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | (110) all_58_15 = e2 & op(e0, e0) = e2
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | ALPHA: (110) implies:
% 171.23/26.58 | | | | | | | | | | | | | (111) all_58_15 = e2
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | | REF_CLOSE: (32), (49), (111) are inconsistent by sub-proof
% 171.23/26.58 | | | | | | | | | | | | | #856.
% 171.23/26.58 | | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | | |
% 171.23/26.58 | | | | | | | | | End of split
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | (112) all_58_13 = e1 & op(e0, e2) = e1
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | ALPHA: (112) implies:
% 171.23/26.58 | | | | | | | | | (113) op(e0, e2) = e1
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | | REF_CLOSE: (21), (24), (71), (113) are inconsistent by
% 171.23/26.58 | | | | | | | | | sub-proof #968.
% 171.23/26.58 | | | | | | | | |
% 171.23/26.58 | | | | | | | | End of split
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | Case 2:
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | | (114) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 &
% 171.23/26.58 | | | | | | | | op(e0, e0) = e1)
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | | REF_CLOSE: (7), (9), (10), (15), (22), (26), (30), (31), (32),
% 171.23/26.58 | | | | | | | | (40), (49), (114) are inconsistent by sub-proof #875.
% 171.23/26.58 | | | | | | | |
% 171.23/26.58 | | | | | | | End of split
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | End of split
% 171.23/26.58 | | | | | |
% 171.23/26.58 | | | | | Case 2:
% 171.23/26.58 | | | | | |
% 171.23/26.58 | | | | | | (115) (all_58_14 = e2 & op(e0, e1) = e2) | (all_58_15 = e2 &
% 171.23/26.58 | | | | | | op(e0, e0) = e2)
% 171.23/26.58 | | | | | |
% 171.23/26.58 | | | | | | BETA: splitting (115) gives:
% 171.23/26.58 | | | | | |
% 171.23/26.58 | | | | | | Case 1:
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | (116) all_58_14 = e2 & op(e0, e1) = e2
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | ALPHA: (116) implies:
% 171.23/26.58 | | | | | | | (117) all_58_14 = e2
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | REF_CLOSE: (32), (40), (117) are inconsistent by sub-proof #855.
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | Case 2:
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | (118) all_58_15 = e2 & op(e0, e0) = e2
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | | REF_CLOSE: (2), (17), (21), (118) are inconsistent by sub-proof
% 171.23/26.58 | | | | | | | #854.
% 171.23/26.58 | | | | | | |
% 171.23/26.58 | | | | | | End of split
% 171.23/26.58 | | | | | |
% 171.23/26.58 | | | | | End of split
% 171.23/26.58 | | | | |
% 171.23/26.58 | | | | End of split
% 171.23/26.58 | | | |
% 171.23/26.58 | | | End of split
% 171.23/26.58 | | |
% 171.23/26.58 | | End of split
% 171.23/26.58 | |
% 171.23/26.58 | End of split
% 171.23/26.58 |
% 171.23/26.58 End of proof
% 171.23/26.58
% 171.23/26.58 Sub-proof #854 shows that the following formulas are inconsistent:
% 171.23/26.58 ----------------------------------------------------------------
% 171.23/26.58 (1) all_58_15 = e2 & op(e0, e0) = e2
% 171.23/26.58 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.58 (3) op(e0, e0) = all_4_2
% 171.23/26.58 (4) ~ (all_4_2 = e2)
% 171.23/26.58
% 171.23/26.58 Begin of proof
% 171.23/26.58 |
% 171.23/26.58 | ALPHA: (1) implies:
% 171.23/26.58 | (5) op(e0, e0) = e2
% 171.23/26.58 |
% 171.23/26.58 | GROUND_INST: instantiating (2) with all_4_2, e2, e0, e0, simplifying with (3),
% 171.23/26.58 | (5) gives:
% 171.23/26.58 | (6) all_4_2 = e2
% 171.23/26.58 |
% 171.23/26.58 | REDUCE: (4), (6) imply:
% 171.23/26.58 | (7) $false
% 171.23/26.58 |
% 171.23/26.58 | CLOSE: (7) is inconsistent.
% 171.23/26.58 |
% 171.23/26.58 End of proof
% 171.23/26.58
% 171.23/26.58 Sub-proof #855 shows that the following formulas are inconsistent:
% 171.23/26.58 ----------------------------------------------------------------
% 171.23/26.58 (1) all_58_14 = e3
% 171.23/26.58 (2) all_58_14 = e2
% 171.23/26.58 (3) ~ (e3 = e2)
% 171.23/26.58
% 171.23/26.58 Begin of proof
% 171.23/26.58 |
% 171.23/26.58 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.58 | (4) e3 = e2
% 171.23/26.58 |
% 171.23/26.58 | SIMP: (4) implies:
% 171.23/26.58 | (5) e3 = e2
% 171.23/26.58 |
% 171.23/26.58 | REDUCE: (3), (5) imply:
% 171.23/26.58 | (6) $false
% 171.23/26.58 |
% 171.23/26.58 | CLOSE: (6) is inconsistent.
% 171.23/26.58 |
% 171.23/26.58 End of proof
% 171.23/26.58
% 171.23/26.58 Sub-proof #856 shows that the following formulas are inconsistent:
% 171.23/26.58 ----------------------------------------------------------------
% 171.23/26.58 (1) all_58_15 = e3
% 171.23/26.58 (2) all_58_15 = e2
% 171.23/26.58 (3) ~ (e3 = e2)
% 171.23/26.58
% 171.23/26.58 Begin of proof
% 171.23/26.58 |
% 171.23/26.58 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.58 | (4) e3 = e2
% 171.23/26.58 |
% 171.23/26.58 | SIMP: (4) implies:
% 171.23/26.58 | (5) e3 = e2
% 171.23/26.58 |
% 171.23/26.58 | REDUCE: (3), (5) imply:
% 171.23/26.58 | (6) $false
% 171.23/26.58 |
% 171.23/26.58 | CLOSE: (6) is inconsistent.
% 171.23/26.58 |
% 171.23/26.58 End of proof
% 171.23/26.58
% 171.23/26.58 Sub-proof #857 shows that the following formulas are inconsistent:
% 171.23/26.58 ----------------------------------------------------------------
% 171.23/26.58 (1) all_58_12 = e1
% 171.23/26.58 (2) all_58_14 = e2
% 171.23/26.58 (3) all_58_13 = e3
% 171.23/26.58 (4) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 171.23/26.58 (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) =
% 171.23/26.58 e0) | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 171.23/26.58 e1) = e0))
% 171.23/26.58 (5) ~ (e1 = e0)
% 171.23/26.58 (6) ~ (e3 = e0)
% 171.23/26.58 (7) ~ (e2 = e0)
% 171.23/26.58
% 171.23/26.58 Begin of proof
% 171.23/26.58 |
% 171.23/26.58 | ALPHA: (4) implies:
% 171.23/26.58 | (8) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 171.23/26.58 | | (all_58_14 = e0 & op(e0, e1) = e0)
% 171.23/26.58 |
% 171.23/26.58 | BETA: splitting (8) gives:
% 171.23/26.58 |
% 171.23/26.58 | Case 1:
% 171.23/26.58 | |
% 171.23/26.58 | | (9) all_58_12 = e0 & op(e0, e3) = e0
% 171.23/26.58 | |
% 171.23/26.58 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #859.
% 171.23/26.58 | |
% 171.23/26.58 | Case 2:
% 171.23/26.58 | |
% 171.23/26.58 | | (10) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 171.23/26.58 | | e0)
% 171.23/26.58 | |
% 171.23/26.58 | | BETA: splitting (10) gives:
% 171.23/26.58 | |
% 171.23/26.58 | | Case 1:
% 171.23/26.58 | | |
% 171.23/26.58 | | | (11) all_58_13 = e0 & op(e0, e2) = e0
% 171.23/26.58 | | |
% 171.23/26.58 | | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #885.
% 171.23/26.58 | | |
% 171.23/26.58 | | Case 2:
% 171.23/26.58 | | |
% 171.23/26.58 | | | (12) all_58_14 = e0 & op(e0, e1) = e0
% 171.23/26.58 | | |
% 171.23/26.58 | | | REF_CLOSE: (2), (7), (12) are inconsistent by sub-proof #858.
% 171.23/26.58 | | |
% 171.23/26.58 | | End of split
% 171.23/26.58 | |
% 171.23/26.58 | End of split
% 171.23/26.58 |
% 171.23/26.58 End of proof
% 171.23/26.58
% 171.23/26.58 Sub-proof #858 shows that the following formulas are inconsistent:
% 171.23/26.58 ----------------------------------------------------------------
% 171.23/26.58 (1) all_58_14 = e0 & op(e0, e1) = e0
% 171.23/26.59 (2) all_58_14 = e2
% 171.23/26.59 (3) ~ (e2 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_14 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e2 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #859 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_12 = e0 & op(e0, e3) = e0
% 171.23/26.59 (2) all_58_12 = e1
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_12 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e1 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #860 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_15 = e3
% 171.23/26.59 (2) all_58_15 = e0
% 171.23/26.59 (3) ~ (e3 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.59 | (4) e3 = e0
% 171.23/26.59 |
% 171.23/26.59 | SIMP: (4) implies:
% 171.23/26.59 | (5) e3 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #861 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_13 = e2 & op(e0, e2) = e2
% 171.23/26.59 (2) all_58_13 = e3
% 171.23/26.59 (3) ~ (e3 = e2)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_13 = e2
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e3 = e2
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #862 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_12 = e2
% 171.23/26.59 (2) all_58_12 = e1
% 171.23/26.59 (3) ~ (e2 = e1)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.59 | (4) e2 = e1
% 171.23/26.59 |
% 171.23/26.59 | SIMP: (4) implies:
% 171.23/26.59 | (5) e2 = e1
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #863 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_1 = e1 & op(e3, e2) = e1
% 171.23/26.59 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.59 (3) op(e3, e2) = all_52_4
% 171.23/26.59 (4) ~ (all_52_4 = e1)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (5) op(e3, e2) = e1
% 171.23/26.59 |
% 171.23/26.59 | GROUND_INST: instantiating (2) with all_52_4, e1, e2, e3, simplifying with
% 171.23/26.59 | (3), (5) gives:
% 171.23/26.59 | (6) all_52_4 = e1
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (4), (6) imply:
% 171.23/26.59 | (7) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (7) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #864 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.23/26.59 (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2) = e1)
% 171.23/26.59 (2) ~ (e3 = e1)
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59 (4) all_58_1 = e2
% 171.23/26.59 (5) ~ (e3 = e0)
% 171.23/26.59 (6) all_58_13 = e2
% 171.23/26.59 (7) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.59 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 171.23/26.59 (8) ~ (e2 = e0)
% 171.23/26.59 (9) all_58_3 = e3
% 171.23/26.59 (10) ~ (e2 = e1)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | BETA: splitting (7) gives:
% 171.23/26.59 |
% 171.23/26.59 | Case 1:
% 171.23/26.59 | |
% 171.23/26.59 | | (11) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 171.23/26.59 | | e0)
% 171.23/26.59 | |
% 171.23/26.59 | | BETA: splitting (11) gives:
% 171.23/26.59 | |
% 171.23/26.59 | | Case 1:
% 171.23/26.59 | | |
% 171.23/26.59 | | | (12) all_58_1 = e0 & op(e3, e2) = e0
% 171.23/26.59 | | |
% 171.23/26.59 | | | REF_CLOSE: (4), (8), (12) are inconsistent by sub-proof #906.
% 171.23/26.59 | | |
% 171.23/26.59 | | Case 2:
% 171.23/26.59 | | |
% 171.23/26.59 | | | (13) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.59 | | |
% 171.23/26.59 | | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #869.
% 171.23/26.59 | | |
% 171.23/26.59 | | End of split
% 171.23/26.59 | |
% 171.23/26.59 | Case 2:
% 171.23/26.59 | |
% 171.23/26.59 | | (14) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 171.23/26.59 | | e0)
% 171.23/26.59 | |
% 171.23/26.59 | | BETA: splitting (14) gives:
% 171.23/26.59 | |
% 171.23/26.59 | | Case 1:
% 171.23/26.59 | | |
% 171.23/26.59 | | | (15) all_58_7 = e0 & op(e1, e2) = e0
% 171.23/26.59 | | |
% 171.23/26.59 | | | ALPHA: (15) implies:
% 171.23/26.59 | | | (16) all_58_7 = e0
% 171.23/26.59 | | |
% 171.23/26.59 | | | BETA: splitting (1) gives:
% 171.23/26.59 | | |
% 171.23/26.59 | | | Case 1:
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | (17) (all_58_1 = e1 & op(e3, e2) = e1) | (all_58_3 = e1 & op(e2, e2)
% 171.23/26.59 | | | | = e1)
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | BETA: splitting (17) gives:
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | Case 1:
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | (18) all_58_1 = e1 & op(e3, e2) = e1
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | REF_CLOSE: (4), (10), (18) are inconsistent by sub-proof #899.
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | Case 2:
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | (19) all_58_3 = e1 & op(e2, e2) = e1
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | REF_CLOSE: (2), (9), (19) are inconsistent by sub-proof #868.
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | End of split
% 171.23/26.59 | | | |
% 171.23/26.59 | | | Case 2:
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | (20) (all_58_7 = e1 & op(e1, e2) = e1) | (all_58_13 = e1 & op(e0, e2)
% 171.23/26.59 | | | | = e1)
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | BETA: splitting (20) gives:
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | Case 1:
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | (21) all_58_7 = e1 & op(e1, e2) = e1
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | REF_CLOSE: (3), (16), (21) are inconsistent by sub-proof #867.
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | Case 2:
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | (22) all_58_13 = e1 & op(e0, e2) = e1
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | REF_CLOSE: (6), (10), (22) are inconsistent by sub-proof #866.
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | End of split
% 171.23/26.59 | | | |
% 171.23/26.59 | | | End of split
% 171.23/26.59 | | |
% 171.23/26.59 | | Case 2:
% 171.23/26.59 | | |
% 171.23/26.59 | | | (23) all_58_13 = e0 & op(e0, e2) = e0
% 171.23/26.59 | | |
% 171.23/26.59 | | | ALPHA: (23) implies:
% 171.23/26.59 | | | (24) all_58_13 = e0
% 171.23/26.59 | | |
% 171.23/26.59 | | | REF_CLOSE: (6), (8), (24) are inconsistent by sub-proof #865.
% 171.23/26.59 | | |
% 171.23/26.59 | | End of split
% 171.23/26.59 | |
% 171.23/26.59 | End of split
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #865 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_13 = e2
% 171.23/26.59 (2) all_58_13 = e0
% 171.23/26.59 (3) ~ (e2 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.59 | (4) e2 = e0
% 171.23/26.59 |
% 171.23/26.59 | SIMP: (4) implies:
% 171.23/26.59 | (5) e2 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #866 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_13 = e1 & op(e0, e2) = e1
% 171.23/26.59 (2) all_58_13 = e2
% 171.23/26.59 (3) ~ (e2 = e1)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_13 = e1
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e2 = e1
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #867 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_7 = e1 & op(e1, e2) = e1
% 171.23/26.59 (2) all_58_7 = e0
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_7 = e1
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e1 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #868 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_3 = e1 & op(e2, e2) = e1
% 171.23/26.59 (2) all_58_3 = e3
% 171.23/26.59 (3) ~ (e3 = e1)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_3 = e1
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e3 = e1
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #869 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.59 (2) all_58_3 = e3
% 171.23/26.59 (3) ~ (e3 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_3 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e3 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #870 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_12 = e1
% 171.23/26.59 (2) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) = e0) |
% 171.23/26.59 (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 & op(e0, e3) =
% 171.23/26.59 e0) | (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0,
% 171.23/26.59 e1) = e0))
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59 (4) ~ (e3 = e0)
% 171.23/26.59 (5) all_58_13 = e2
% 171.23/26.59 (6) all_58_14 = e3
% 171.23/26.59 (7) ~ (e2 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (2) implies:
% 171.23/26.59 | (8) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 171.23/26.59 | | (all_58_14 = e0 & op(e0, e1) = e0)
% 171.23/26.59 |
% 171.23/26.59 | BETA: splitting (8) gives:
% 171.23/26.59 |
% 171.23/26.59 | Case 1:
% 171.23/26.59 | |
% 171.23/26.59 | | (9) all_58_12 = e0 & op(e0, e3) = e0
% 171.23/26.59 | |
% 171.23/26.59 | | ALPHA: (9) implies:
% 171.23/26.59 | | (10) all_58_12 = e0
% 171.23/26.59 | |
% 171.23/26.59 | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #873.
% 171.23/26.59 | |
% 171.23/26.59 | Case 2:
% 171.23/26.59 | |
% 171.23/26.59 | | (11) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 171.23/26.59 | | e0)
% 171.23/26.59 | |
% 171.23/26.59 | | BETA: splitting (11) gives:
% 171.23/26.59 | |
% 171.23/26.59 | | Case 1:
% 171.23/26.59 | | |
% 171.23/26.59 | | | (12) all_58_13 = e0 & op(e0, e2) = e0
% 171.23/26.59 | | |
% 171.23/26.59 | | | REF_CLOSE: (5), (7), (12) are inconsistent by sub-proof #872.
% 171.23/26.59 | | |
% 171.23/26.59 | | Case 2:
% 171.23/26.59 | | |
% 171.23/26.59 | | | (13) all_58_14 = e0 & op(e0, e1) = e0
% 171.23/26.59 | | |
% 171.23/26.59 | | | REF_CLOSE: (4), (6), (13) are inconsistent by sub-proof #871.
% 171.23/26.59 | | |
% 171.23/26.59 | | End of split
% 171.23/26.59 | |
% 171.23/26.59 | End of split
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #871 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_14 = e0 & op(e0, e1) = e0
% 171.23/26.59 (2) all_58_14 = e3
% 171.23/26.59 (3) ~ (e3 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_14 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e3 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #872 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_13 = e0 & op(e0, e2) = e0
% 171.23/26.59 (2) all_58_13 = e2
% 171.23/26.59 (3) ~ (e2 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_13 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e2 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #873 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_12 = e1
% 171.23/26.59 (2) all_58_12 = e0
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.59 | (4) e1 = e0
% 171.23/26.59 |
% 171.23/26.59 | SIMP: (4) implies:
% 171.23/26.59 | (5) e1 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #874 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_15 = e0 & op(e0, e0) = e0
% 171.23/26.59 (2) all_58_15 = e2
% 171.23/26.59 (3) ~ (e2 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_15 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e2 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #875 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) ~ (e3 = e1)
% 171.23/26.59 (2) ~ (e1 = e0)
% 171.23/26.59 (3) (all_58_14 = e1 & op(e0, e1) = e1) | (all_58_15 = e1 & op(e0, e0) = e1)
% 171.23/26.59 (4) all_58_11 = e2
% 171.23/26.59 (5) ~ (e3 = e0)
% 171.23/26.59 (6) all_58_14 = e3
% 171.23/26.59 (7) all_58_15 = e3
% 171.23/26.59 (8) ~ (e2 = e0)
% 171.23/26.59 (9) all_58_9 = e1
% 171.23/26.59 (10) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 171.23/26.59 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.23/26.59 (11) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.59 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0)
% 171.23/26.59 = e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.23/26.59 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.23/26.59 (12) ~ (e3 = e2)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | BETA: splitting (3) gives:
% 171.23/26.59 |
% 171.23/26.59 | Case 1:
% 171.23/26.59 | |
% 171.23/26.59 | | (13) all_58_14 = e1 & op(e0, e1) = e1
% 171.23/26.59 | |
% 171.23/26.59 | | ALPHA: (13) implies:
% 171.23/26.59 | | (14) all_58_14 = e1
% 171.23/26.59 | |
% 171.23/26.59 | | COMBINE_EQS: (6), (14) imply:
% 171.23/26.59 | | (15) e3 = e1
% 171.23/26.59 | |
% 171.23/26.59 | | SIMP: (15) implies:
% 171.23/26.59 | | (16) e3 = e1
% 171.23/26.59 | |
% 171.23/26.59 | | COMBINE_EQS: (7), (16) imply:
% 171.23/26.59 | | (17) all_58_15 = e1
% 171.23/26.59 | |
% 171.23/26.59 | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (12), (17) are
% 171.23/26.59 | | inconsistent by sub-proof #876.
% 171.23/26.59 | |
% 171.23/26.59 | Case 2:
% 171.23/26.59 | |
% 171.23/26.59 | | (18) all_58_15 = e1 & op(e0, e0) = e1
% 171.23/26.59 | |
% 171.23/26.59 | | ALPHA: (18) implies:
% 171.23/26.59 | | (19) all_58_15 = e1
% 171.23/26.59 | |
% 171.23/26.59 | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (12), (19) are
% 171.23/26.59 | | inconsistent by sub-proof #876.
% 171.23/26.59 | |
% 171.23/26.59 | End of split
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #876 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_15 = e1
% 171.23/26.59 (2) ~ (e3 = e1)
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59 (4) all_58_11 = e2
% 171.23/26.59 (5) ~ (e3 = e0)
% 171.23/26.59 (6) ~ (e2 = e0)
% 171.23/26.59 (7) all_58_9 = e1
% 171.23/26.59 (8) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) = e3) |
% 171.23/26.59 (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.23/26.59 (9) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.59 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 171.23/26.59 e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.23/26.59 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.23/26.59 (10) ~ (e3 = e2)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | BETA: splitting (8) gives:
% 171.23/26.59 |
% 171.23/26.59 | Case 1:
% 171.23/26.59 | |
% 171.23/26.59 | | (11) (all_58_9 = e3 & op(e3, e0) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 171.23/26.59 | | e3)
% 171.23/26.59 | |
% 171.23/26.59 | | BETA: splitting (11) gives:
% 171.23/26.59 | |
% 171.23/26.59 | | Case 1:
% 171.23/26.59 | | |
% 171.23/26.59 | | | (12) all_58_9 = e3 & op(e3, e0) = e3
% 171.23/26.59 | | |
% 171.23/26.59 | | | REF_CLOSE: (2), (7), (12) are inconsistent by sub-proof #893.
% 171.23/26.59 | | |
% 171.23/26.59 | | Case 2:
% 171.23/26.59 | | |
% 171.23/26.59 | | | (13) all_58_10 = e3 & op(e2, e0) = e3
% 171.23/26.59 | | |
% 171.23/26.59 | | | ALPHA: (13) implies:
% 171.23/26.59 | | | (14) all_58_10 = e3
% 171.23/26.59 | | |
% 171.23/26.59 | | | BETA: splitting (9) gives:
% 171.23/26.59 | | |
% 171.23/26.59 | | | Case 1:
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | (15) all_58_15 = e0 & op(e0, e0) = e0
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | ALPHA: (15) implies:
% 171.23/26.59 | | | | (16) all_58_15 = e0
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #881.
% 171.23/26.59 | | | |
% 171.23/26.59 | | | Case 2:
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | (17) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2,
% 171.23/26.59 | | | | e0) = e0) | (all_58_11 = e0 & op(e1, e0) = e0)) &
% 171.23/26.59 | | | | ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0,
% 171.23/26.59 | | | | e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0))
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | ALPHA: (17) implies:
% 171.23/26.59 | | | | (18) (all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0)
% 171.23/26.59 | | | | = e0) | (all_58_11 = e0 & op(e1, e0) = e0)
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | BETA: splitting (18) gives:
% 171.23/26.59 | | | |
% 171.23/26.59 | | | | Case 1:
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | (19) all_58_9 = e0 & op(e3, e0) = e0
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | REF_CLOSE: (3), (7), (19) are inconsistent by sub-proof #880.
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | Case 2:
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | (20) (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1,
% 171.23/26.59 | | | | | e0) = e0)
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | BETA: splitting (20) gives:
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | | Case 1:
% 171.23/26.59 | | | | | |
% 171.23/26.59 | | | | | | (21) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.59 | | | | | |
% 171.23/26.59 | | | | | | REF_CLOSE: (5), (14), (21) are inconsistent by sub-proof #932.
% 171.23/26.59 | | | | | |
% 171.23/26.59 | | | | | Case 2:
% 171.23/26.59 | | | | | |
% 171.23/26.59 | | | | | | (22) all_58_11 = e0 & op(e1, e0) = e0
% 171.23/26.59 | | | | | |
% 171.23/26.59 | | | | | | ALPHA: (22) implies:
% 171.23/26.59 | | | | | | (23) all_58_11 = e0
% 171.23/26.59 | | | | | |
% 171.23/26.59 | | | | | | REF_CLOSE: (4), (6), (23) are inconsistent by sub-proof #879.
% 171.23/26.59 | | | | | |
% 171.23/26.59 | | | | | End of split
% 171.23/26.59 | | | | |
% 171.23/26.59 | | | | End of split
% 171.23/26.59 | | | |
% 171.23/26.59 | | | End of split
% 171.23/26.59 | | |
% 171.23/26.59 | | End of split
% 171.23/26.59 | |
% 171.23/26.59 | Case 2:
% 171.23/26.59 | |
% 171.23/26.59 | | (24) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) =
% 171.23/26.59 | | e3)
% 171.23/26.59 | |
% 171.23/26.59 | | REF_CLOSE: (1), (2), (4), (10), (24) are inconsistent by sub-proof #877.
% 171.23/26.59 | |
% 171.23/26.59 | End of split
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #877 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_15 = e1
% 171.23/26.59 (2) ~ (e3 = e1)
% 171.23/26.59 (3) all_58_11 = e2
% 171.23/26.59 (4) (all_58_11 = e3 & op(e1, e0) = e3) | (all_58_15 = e3 & op(e0, e0) = e3)
% 171.23/26.59 (5) ~ (e3 = e2)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | BETA: splitting (4) gives:
% 171.23/26.59 |
% 171.23/26.59 | Case 1:
% 171.23/26.59 | |
% 171.23/26.59 | | (6) all_58_11 = e3 & op(e1, e0) = e3
% 171.23/26.59 | |
% 171.23/26.59 | | ALPHA: (6) implies:
% 171.23/26.59 | | (7) all_58_11 = e3
% 171.23/26.59 | |
% 171.23/26.59 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #892.
% 171.23/26.59 | |
% 171.23/26.59 | Case 2:
% 171.23/26.59 | |
% 171.23/26.59 | | (8) all_58_15 = e3 & op(e0, e0) = e3
% 171.23/26.59 | |
% 171.23/26.59 | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #878.
% 171.23/26.59 | |
% 171.23/26.59 | End of split
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #878 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_15 = e3 & op(e0, e0) = e3
% 171.23/26.59 (2) all_58_15 = e1
% 171.23/26.59 (3) ~ (e3 = e1)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_15 = e3
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e3 = e1
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #879 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_11 = e2
% 171.23/26.59 (2) all_58_11 = e0
% 171.23/26.59 (3) ~ (e2 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.59 | (4) e2 = e0
% 171.23/26.59 |
% 171.23/26.59 | SIMP: (4) implies:
% 171.23/26.59 | (5) e2 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #880 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_9 = e0 & op(e3, e0) = e0
% 171.23/26.59 (2) all_58_9 = e1
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_9 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e1 = e0
% 171.23/26.59 |
% 171.23/26.59 | SIMP: (5) implies:
% 171.23/26.59 | (6) e1 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (6) imply:
% 171.23/26.59 | (7) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (7) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #881 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_15 = e1
% 171.23/26.59 (2) all_58_15 = e0
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.59 | (4) e1 = e0
% 171.23/26.59 |
% 171.23/26.59 | SIMP: (4) implies:
% 171.23/26.59 | (5) e1 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #882 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_12 = e2
% 171.23/26.59 (2) all_58_13 = e3
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59 (4) all_58_14 = e1
% 171.23/26.59 (5) ~ (e3 = e0)
% 171.23/26.59 (6) all_58_15 = e3
% 171.23/26.59 (7) ~ (e2 = e0)
% 171.23/26.59 (8) (all_58_15 = e0 & op(e0, e0) = e0) | (((all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.59 | (all_58_10 = e0 & op(e2, e0) = e0) | (all_58_11 = e0 & op(e1, e0) =
% 171.23/26.59 e0)) & ((all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 &
% 171.23/26.59 op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) = e0)))
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | BETA: splitting (8) gives:
% 171.23/26.59 |
% 171.23/26.59 | Case 1:
% 171.23/26.59 | |
% 171.23/26.59 | | (9) all_58_15 = e0 & op(e0, e0) = e0
% 171.23/26.59 | |
% 171.23/26.59 | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #887.
% 171.23/26.59 | |
% 171.23/26.59 | Case 2:
% 171.23/26.59 | |
% 171.23/26.59 | | (10) ((all_58_9 = e0 & op(e3, e0) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 171.23/26.59 | | e0) | (all_58_11 = e0 & op(e1, e0) = e0)) & ((all_58_12 = e0 &
% 171.23/26.59 | | op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 171.23/26.59 | | (all_58_14 = e0 & op(e0, e1) = e0))
% 171.23/26.59 | |
% 171.23/26.59 | | ALPHA: (10) implies:
% 171.23/26.59 | | (11) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 171.23/26.59 | | e0) | (all_58_14 = e0 & op(e0, e1) = e0)
% 171.23/26.59 | |
% 171.23/26.59 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (11) are inconsistent by sub-proof
% 171.23/26.59 | | #883.
% 171.23/26.59 | |
% 171.23/26.59 | End of split
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #883 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_12 = e2
% 171.23/26.59 (2) all_58_13 = e3
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59 (4) all_58_14 = e1
% 171.23/26.59 (5) (all_58_12 = e0 & op(e0, e3) = e0) | (all_58_13 = e0 & op(e0, e2) = e0) |
% 171.23/26.59 (all_58_14 = e0 & op(e0, e1) = e0)
% 171.23/26.59 (6) ~ (e3 = e0)
% 171.23/26.59 (7) ~ (e2 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | BETA: splitting (5) gives:
% 171.23/26.59 |
% 171.23/26.59 | Case 1:
% 171.23/26.59 | |
% 171.23/26.59 | | (8) all_58_12 = e0 & op(e0, e3) = e0
% 171.23/26.59 | |
% 171.23/26.59 | | REF_CLOSE: (1), (7), (8) are inconsistent by sub-proof #886.
% 171.23/26.59 | |
% 171.23/26.59 | Case 2:
% 171.23/26.59 | |
% 171.23/26.59 | | (9) (all_58_13 = e0 & op(e0, e2) = e0) | (all_58_14 = e0 & op(e0, e1) =
% 171.23/26.59 | | e0)
% 171.23/26.59 | |
% 171.23/26.59 | | BETA: splitting (9) gives:
% 171.23/26.59 | |
% 171.23/26.59 | | Case 1:
% 171.23/26.59 | | |
% 171.23/26.59 | | | (10) all_58_13 = e0 & op(e0, e2) = e0
% 171.23/26.59 | | |
% 171.23/26.59 | | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #885.
% 171.23/26.59 | | |
% 171.23/26.59 | | Case 2:
% 171.23/26.59 | | |
% 171.23/26.59 | | | (11) all_58_14 = e0 & op(e0, e1) = e0
% 171.23/26.59 | | |
% 171.23/26.59 | | | REF_CLOSE: (3), (4), (11) are inconsistent by sub-proof #884.
% 171.23/26.59 | | |
% 171.23/26.59 | | End of split
% 171.23/26.59 | |
% 171.23/26.59 | End of split
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #884 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_14 = e0 & op(e0, e1) = e0
% 171.23/26.59 (2) all_58_14 = e1
% 171.23/26.59 (3) ~ (e1 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_14 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e1 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #885 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_13 = e0 & op(e0, e2) = e0
% 171.23/26.59 (2) all_58_13 = e3
% 171.23/26.59 (3) ~ (e3 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_13 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e3 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #886 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_12 = e0 & op(e0, e3) = e0
% 171.23/26.59 (2) all_58_12 = e2
% 171.23/26.59 (3) ~ (e2 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_12 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.59 | (5) e2 = e0
% 171.23/26.59 |
% 171.23/26.59 | REDUCE: (3), (5) imply:
% 171.23/26.59 | (6) $false
% 171.23/26.59 |
% 171.23/26.59 | CLOSE: (6) is inconsistent.
% 171.23/26.59 |
% 171.23/26.59 End of proof
% 171.23/26.59
% 171.23/26.59 Sub-proof #887 shows that the following formulas are inconsistent:
% 171.23/26.59 ----------------------------------------------------------------
% 171.23/26.59 (1) all_58_15 = e0 & op(e0, e0) = e0
% 171.23/26.59 (2) all_58_15 = e3
% 171.23/26.59 (3) ~ (e3 = e0)
% 171.23/26.59
% 171.23/26.59 Begin of proof
% 171.23/26.59 |
% 171.23/26.59 | ALPHA: (1) implies:
% 171.23/26.59 | (4) all_58_15 = e0
% 171.23/26.59 |
% 171.23/26.59 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e3 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #888 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) ~ (e1 = e0)
% 171.23/26.60 (2) op(e0, e2) = e1
% 171.23/26.60 (3) all_58_1 = e2
% 171.23/26.60 (4) ~ (e3 = e0)
% 171.23/26.60 (5) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.60 (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) = e0)
% 171.23/26.60 (6) all_58_3 = e2
% 171.23/26.60 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.60 (8) ~ (e2 = e0)
% 171.23/26.60 (9) op(e0, e2) = all_52_7
% 171.23/26.60 (10) all_58_7 = e3
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | BETA: splitting (5) gives:
% 171.23/26.60 |
% 171.23/26.60 | Case 1:
% 171.23/26.60 | |
% 171.23/26.60 | | (11) (all_58_1 = e0 & op(e3, e2) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 171.23/26.60 | | e0)
% 171.23/26.60 | |
% 171.23/26.60 | | BETA: splitting (11) gives:
% 171.23/26.60 | |
% 171.23/26.60 | | Case 1:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (12) all_58_1 = e0 & op(e3, e2) = e0
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (3), (8), (12) are inconsistent by sub-proof #906.
% 171.23/26.60 | | |
% 171.23/26.60 | | Case 2:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (13) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #934.
% 171.23/26.60 | | |
% 171.23/26.60 | | End of split
% 171.23/26.60 | |
% 171.23/26.60 | Case 2:
% 171.23/26.60 | |
% 171.23/26.60 | | (14) (all_58_7 = e0 & op(e1, e2) = e0) | (all_58_13 = e0 & op(e0, e2) =
% 171.23/26.60 | | e0)
% 171.23/26.60 | |
% 171.23/26.60 | | BETA: splitting (14) gives:
% 171.23/26.60 | |
% 171.23/26.60 | | Case 1:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (15) all_58_7 = e0 & op(e1, e2) = e0
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (4), (10), (15) are inconsistent by sub-proof #890.
% 171.23/26.60 | | |
% 171.23/26.60 | | Case 2:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (16) all_58_13 = e0 & op(e0, e2) = e0
% 171.23/26.60 | | |
% 171.23/26.60 | | | ALPHA: (16) implies:
% 171.23/26.60 | | | (17) op(e0, e2) = e0
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (1), (2), (7), (9), (17) are inconsistent by sub-proof #889.
% 171.23/26.60 | | |
% 171.23/26.60 | | End of split
% 171.23/26.60 | |
% 171.23/26.60 | End of split
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #889 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) ~ (e1 = e0)
% 171.23/26.60 (2) op(e0, e2) = e1
% 171.23/26.60 (3) op(e0, e2) = e0
% 171.23/26.60 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.60 (5) op(e0, e2) = all_52_7
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | GROUND_INST: instantiating (4) with all_52_7, e0, e2, e0, simplifying with
% 171.23/26.60 | (3), (5) gives:
% 171.23/26.60 | (6) all_52_7 = e0
% 171.23/26.60 |
% 171.23/26.60 | GROUND_INST: instantiating (4) with all_52_7, e1, e2, e0, simplifying with
% 171.23/26.60 | (2), (5) gives:
% 171.23/26.60 | (7) all_52_7 = e1
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (6), (7) imply:
% 171.23/26.60 | (8) e1 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (1), (8) imply:
% 171.23/26.60 | (9) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (9) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #890 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_7 = e0 & op(e1, e2) = e0
% 171.23/26.60 (2) all_58_7 = e3
% 171.23/26.60 (3) ~ (e3 = e0)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_7 = e0
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e3 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #891 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_12 = e1 & op(e0, e3) = e1
% 171.23/26.60 (2) all_58_12 = e2
% 171.23/26.60 (3) ~ (e2 = e1)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_12 = e1
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e2 = e1
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #892 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_11 = e3
% 171.23/26.60 (2) all_58_11 = e2
% 171.23/26.60 (3) ~ (e3 = e2)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.60 | (4) e3 = e2
% 171.23/26.60 |
% 171.23/26.60 | SIMP: (4) implies:
% 171.23/26.60 | (5) e3 = e2
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #893 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_9 = e3 & op(e3, e0) = e3
% 171.23/26.60 (2) all_58_9 = e1
% 171.23/26.60 (3) ~ (e3 = e1)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_9 = e3
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e3 = e1
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #894 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_4 = e3
% 171.23/26.60 (2) all_58_4 = e0
% 171.23/26.60 (3) ~ (e3 = e0)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.60 | (4) e3 = e0
% 171.23/26.60 |
% 171.23/26.60 | SIMP: (4) implies:
% 171.23/26.60 | (5) e3 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #895 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 171.23/26.60 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.60 (2) ~ (e3 = e1)
% 171.23/26.60 (3) ~ (e1 = e0)
% 171.23/26.60 (4) all_58_1 = e2
% 171.23/26.60 (5) ~ (e3 = e0)
% 171.23/26.60 (6) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 171.23/26.60 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 171.23/26.60 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 171.23/26.60 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 171.23/26.60 (8) ~ (e2 = e0)
% 171.23/26.60 (9) ~ (e2 = e1)
% 171.23/26.60 (10) all_58_4 = e2
% 171.23/26.60 (11) ~ (e3 = e2)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | BETA: splitting (6) gives:
% 171.23/26.60 |
% 171.23/26.60 | Case 1:
% 171.23/26.60 | |
% 171.23/26.60 | | (12) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 171.23/26.60 | | e1)
% 171.23/26.60 | |
% 171.23/26.60 | | BETA: splitting (12) gives:
% 171.23/26.60 | |
% 171.23/26.60 | | Case 1:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (13) all_58_0 = e1 & op(e3, e3) = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | ALPHA: (13) implies:
% 171.23/26.60 | | | (14) all_58_0 = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (11), (14) are
% 171.23/26.60 | | | inconsistent by sub-proof #900.
% 171.23/26.60 | | |
% 171.23/26.60 | | Case 2:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (15) all_58_1 = e1 & op(e3, e2) = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (4), (9), (15) are inconsistent by sub-proof #899.
% 171.23/26.60 | | |
% 171.23/26.60 | | End of split
% 171.23/26.60 | |
% 171.23/26.60 | Case 2:
% 171.23/26.60 | |
% 171.23/26.60 | | (16) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 171.23/26.60 | | e1)
% 171.23/26.60 | |
% 171.23/26.60 | | BETA: splitting (16) gives:
% 171.23/26.60 | |
% 171.23/26.60 | | Case 1:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (17) all_58_4 = e1 & op(e3, e1) = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (9), (10), (17) are inconsistent by sub-proof #943.
% 171.23/26.60 | | |
% 171.23/26.60 | | Case 2:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (18) all_58_9 = e1 & op(e3, e0) = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | ALPHA: (18) implies:
% 171.23/26.60 | | | (19) all_58_9 = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | BETA: splitting (7) gives:
% 171.23/26.60 | | |
% 171.23/26.60 | | | Case 1:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | (20) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2)
% 171.23/26.60 | | | | = e3)
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | BETA: splitting (20) gives:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | Case 1:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | (21) all_58_0 = e3 & op(e3, e3) = e3
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | ALPHA: (21) implies:
% 171.23/26.60 | | | | | (22) all_58_0 = e3
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | BETA: splitting (1) gives:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | Case 1:
% 171.23/26.60 | | | | | |
% 171.23/26.60 | | | | | | (23) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3,
% 171.23/26.60 | | | | | | e2) = e0)
% 171.23/26.60 | | | | | |
% 171.23/26.60 | | | | | | BETA: splitting (23) gives:
% 171.23/26.60 | | | | | |
% 171.23/26.60 | | | | | | Case 1:
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | | (24) all_58_0 = e0 & op(e3, e3) = e0
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | | REF_CLOSE: (5), (22), (24) are inconsistent by sub-proof #898.
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | Case 2:
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | | (25) all_58_1 = e0 & op(e3, e2) = e0
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | | REF_CLOSE: (4), (8), (25) are inconsistent by sub-proof #906.
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | End of split
% 171.23/26.60 | | | | | |
% 171.23/26.60 | | | | | Case 2:
% 171.23/26.60 | | | | | |
% 171.23/26.60 | | | | | | (26) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3,
% 171.23/26.60 | | | | | | e0) = e0)
% 171.23/26.60 | | | | | |
% 171.23/26.60 | | | | | | BETA: splitting (26) gives:
% 171.23/26.60 | | | | | |
% 171.23/26.60 | | | | | | Case 1:
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | | (27) all_58_4 = e0 & op(e3, e1) = e0
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | | REF_CLOSE: (8), (10), (27) are inconsistent by sub-proof #902.
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | Case 2:
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | | (28) all_58_9 = e0 & op(e3, e0) = e0
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | | REF_CLOSE: (3), (19), (28) are inconsistent by sub-proof #897.
% 171.23/26.60 | | | | | | |
% 171.23/26.60 | | | | | | End of split
% 171.23/26.60 | | | | | |
% 171.23/26.60 | | | | | End of split
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | Case 2:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | (29) all_58_1 = e3 & op(e3, e2) = e3
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | REF_CLOSE: (4), (11), (29) are inconsistent by sub-proof #904.
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | End of split
% 171.23/26.60 | | | |
% 171.23/26.60 | | | Case 2:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | (30) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0)
% 171.23/26.60 | | | | = e3)
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | BETA: splitting (30) gives:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | Case 1:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | (31) all_58_4 = e3 & op(e3, e1) = e3
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | REF_CLOSE: (10), (11), (31) are inconsistent by sub-proof #952.
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | Case 2:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | (32) all_58_9 = e3 & op(e3, e0) = e3
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | ALPHA: (32) implies:
% 171.23/26.60 | | | | | (33) all_58_9 = e3
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | REF_CLOSE: (2), (19), (33) are inconsistent by sub-proof #896.
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | End of split
% 171.23/26.60 | | | |
% 171.23/26.60 | | | End of split
% 171.23/26.60 | | |
% 171.23/26.60 | | End of split
% 171.23/26.60 | |
% 171.23/26.60 | End of split
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #896 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_9 = e3
% 171.23/26.60 (2) all_58_9 = e1
% 171.23/26.60 (3) ~ (e3 = e1)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.60 | (4) e3 = e1
% 171.23/26.60 |
% 171.23/26.60 | SIMP: (4) implies:
% 171.23/26.60 | (5) e3 = e1
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #897 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_9 = e0 & op(e3, e0) = e0
% 171.23/26.60 (2) all_58_9 = e1
% 171.23/26.60 (3) ~ (e1 = e0)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_9 = e0
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e1 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #898 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_0 = e0 & op(e3, e3) = e0
% 171.23/26.60 (2) all_58_0 = e3
% 171.23/26.60 (3) ~ (e3 = e0)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_0 = e0
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e3 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #899 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_1 = e1 & op(e3, e2) = e1
% 171.23/26.60 (2) all_58_1 = e2
% 171.23/26.60 (3) ~ (e2 = e1)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_1 = e1
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e2 = e1
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #900 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_0 = e1
% 171.23/26.60 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 171.23/26.60 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.60 (3) ~ (e3 = e1)
% 171.23/26.60 (4) ~ (e1 = e0)
% 171.23/26.60 (5) all_58_1 = e2
% 171.23/26.60 (6) ~ (e3 = e0)
% 171.23/26.60 (7) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 171.23/26.60 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 171.23/26.60 (8) ~ (e2 = e0)
% 171.23/26.60 (9) all_58_4 = e2
% 171.23/26.60 (10) ~ (e3 = e2)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | BETA: splitting (7) gives:
% 171.23/26.60 |
% 171.23/26.60 | Case 1:
% 171.23/26.60 | |
% 171.23/26.60 | | (11) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 171.23/26.60 | | e3)
% 171.23/26.60 | |
% 171.23/26.60 | | BETA: splitting (11) gives:
% 171.23/26.60 | |
% 171.23/26.60 | | Case 1:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (12) all_58_0 = e3 & op(e3, e3) = e3
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (1), (3), (12) are inconsistent by sub-proof #905.
% 171.23/26.60 | | |
% 171.23/26.60 | | Case 2:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (13) all_58_1 = e3 & op(e3, e2) = e3
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (5), (10), (13) are inconsistent by sub-proof #904.
% 171.23/26.60 | | |
% 171.23/26.60 | | End of split
% 171.23/26.60 | |
% 171.23/26.60 | Case 2:
% 171.23/26.60 | |
% 171.23/26.60 | | (14) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 171.23/26.60 | | e3)
% 171.23/26.60 | |
% 171.23/26.60 | | BETA: splitting (14) gives:
% 171.23/26.60 | |
% 171.23/26.60 | | Case 1:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (15) all_58_4 = e3 & op(e3, e1) = e3
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (9), (10), (15) are inconsistent by sub-proof #952.
% 171.23/26.60 | | |
% 171.23/26.60 | | Case 2:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (16) all_58_9 = e3 & op(e3, e0) = e3
% 171.23/26.60 | | |
% 171.23/26.60 | | | ALPHA: (16) implies:
% 171.23/26.60 | | | (17) all_58_9 = e3
% 171.23/26.60 | | |
% 171.23/26.60 | | | BETA: splitting (2) gives:
% 171.23/26.60 | | |
% 171.23/26.60 | | | Case 1:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | (18) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2)
% 171.23/26.60 | | | | = e0)
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | BETA: splitting (18) gives:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | Case 1:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | (19) all_58_0 = e0 & op(e3, e3) = e0
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | REF_CLOSE: (1), (4), (19) are inconsistent by sub-proof #903.
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | Case 2:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | (20) all_58_1 = e0 & op(e3, e2) = e0
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | REF_CLOSE: (5), (8), (20) are inconsistent by sub-proof #906.
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | End of split
% 171.23/26.60 | | | |
% 171.23/26.60 | | | Case 2:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | (21) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0)
% 171.23/26.60 | | | | = e0)
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | BETA: splitting (21) gives:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | Case 1:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | (22) all_58_4 = e0 & op(e3, e1) = e0
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | REF_CLOSE: (8), (9), (22) are inconsistent by sub-proof #902.
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | Case 2:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | (23) all_58_9 = e0 & op(e3, e0) = e0
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | REF_CLOSE: (6), (17), (23) are inconsistent by sub-proof #901.
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | End of split
% 171.23/26.60 | | | |
% 171.23/26.60 | | | End of split
% 171.23/26.60 | | |
% 171.23/26.60 | | End of split
% 171.23/26.60 | |
% 171.23/26.60 | End of split
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #901 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_9 = e0 & op(e3, e0) = e0
% 171.23/26.60 (2) all_58_9 = e3
% 171.23/26.60 (3) ~ (e3 = e0)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_9 = e0
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e3 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #902 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_4 = e0 & op(e3, e1) = e0
% 171.23/26.60 (2) all_58_4 = e2
% 171.23/26.60 (3) ~ (e2 = e0)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_4 = e0
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e2 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #903 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_0 = e0 & op(e3, e3) = e0
% 171.23/26.60 (2) all_58_0 = e1
% 171.23/26.60 (3) ~ (e1 = e0)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_0 = e0
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e1 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #904 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_1 = e3 & op(e3, e2) = e3
% 171.23/26.60 (2) all_58_1 = e2
% 171.23/26.60 (3) ~ (e3 = e2)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_1 = e3
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e3 = e2
% 171.23/26.60 |
% 171.23/26.60 | SIMP: (5) implies:
% 171.23/26.60 | (6) e3 = e2
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (6) imply:
% 171.23/26.60 | (7) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (7) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #905 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_0 = e3 & op(e3, e3) = e3
% 171.23/26.60 (2) all_58_0 = e1
% 171.23/26.60 (3) ~ (e3 = e1)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_0 = e3
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e3 = e1
% 171.23/26.60 |
% 171.23/26.60 | SIMP: (5) implies:
% 171.23/26.60 | (6) e3 = e1
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (6) imply:
% 171.23/26.60 | (7) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (7) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #906 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_1 = e0 & op(e3, e2) = e0
% 171.23/26.60 (2) all_58_1 = e2
% 171.23/26.60 (3) ~ (e2 = e0)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_1 = e0
% 171.23/26.60 |
% 171.23/26.60 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.60 | (5) e2 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (3), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #907 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.60 (2) op(e3, e3) = e1
% 171.23/26.60 (3) op(e3, e3) = e0
% 171.23/26.60 (4) ~ (e1 = e0)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | GROUND_INST: instantiating (1) with e0, e1, e3, e3, simplifying with (2), (3)
% 171.23/26.60 | gives:
% 171.23/26.60 | (5) e1 = e0
% 171.23/26.60 |
% 171.23/26.60 | REDUCE: (4), (5) imply:
% 171.23/26.60 | (6) $false
% 171.23/26.60 |
% 171.23/26.60 | CLOSE: (6) is inconsistent.
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #908 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.23/26.60 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 171.23/26.60 (2) ~ (all_8_2 = e3)
% 171.23/26.60 (3) ~ (e3 = e1)
% 171.23/26.60 (4) ~ (e1 = e0)
% 171.23/26.60 (5) all_58_10 = e2
% 171.23/26.60 (6) op(e2, e2) = all_8_2
% 171.23/26.60 (7) ~ (e3 = e0)
% 171.23/26.60 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.60 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.60 (9) all_58_3 = e2
% 171.23/26.60 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.60 (11) ~ (e2 = e0)
% 171.23/26.60 (12) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 171.23/26.60 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 171.23/26.60 (13) ~ (e2 = e1)
% 171.23/26.60 (14) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 171.23/26.60 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 171.23/26.60 (15) ~ (e3 = e2)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | BETA: splitting (1) gives:
% 171.23/26.60 |
% 171.23/26.60 | Case 1:
% 171.23/26.60 | |
% 171.23/26.60 | | (16) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) =
% 171.23/26.60 | | e1)
% 171.23/26.60 | |
% 171.23/26.60 | | BETA: splitting (16) gives:
% 171.23/26.60 | |
% 171.23/26.60 | | Case 1:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (17) all_58_2 = e1 & op(e2, e3) = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | ALPHA: (17) implies:
% 171.23/26.60 | | | (18) all_58_2 = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 171.23/26.60 | | | (13), (14), (15), (18) are inconsistent by sub-proof #915.
% 171.23/26.60 | | |
% 171.23/26.60 | | Case 2:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (19) all_58_3 = e1 & op(e2, e2) = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (9), (13), (19) are inconsistent by sub-proof #914.
% 171.23/26.60 | | |
% 171.23/26.60 | | End of split
% 171.23/26.60 | |
% 171.23/26.60 | Case 2:
% 171.23/26.60 | |
% 171.23/26.60 | | (20) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) =
% 171.23/26.60 | | e1)
% 171.23/26.60 | |
% 171.23/26.60 | | BETA: splitting (20) gives:
% 171.23/26.60 | |
% 171.23/26.60 | | Case 1:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (21) all_58_5 = e1 & op(e2, e1) = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | ALPHA: (21) implies:
% 171.23/26.60 | | | (22) all_58_5 = e1
% 171.23/26.60 | | | (23) op(e2, e1) = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (15),
% 171.23/26.60 | | | (22), (23) are inconsistent by sub-proof #909.
% 171.23/26.60 | | |
% 171.23/26.60 | | Case 2:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (24) all_58_10 = e1 & op(e2, e0) = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | ALPHA: (24) implies:
% 171.23/26.60 | | | (25) all_58_10 = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | COMBINE_EQS: (5), (25) imply:
% 171.23/26.60 | | | (26) e2 = e1
% 171.23/26.60 | | |
% 171.23/26.60 | | | REDUCE: (13), (26) imply:
% 171.23/26.60 | | | (27) $false
% 171.23/26.60 | | |
% 171.23/26.60 | | | CLOSE: (27) is inconsistent.
% 171.23/26.60 | | |
% 171.23/26.60 | | End of split
% 171.23/26.60 | |
% 171.23/26.60 | End of split
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #909 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) ~ (all_8_2 = e3)
% 171.23/26.60 (2) ~ (e3 = e1)
% 171.23/26.60 (3) ~ (e1 = e0)
% 171.23/26.60 (4) all_58_10 = e2
% 171.23/26.60 (5) op(e2, e2) = all_8_2
% 171.23/26.60 (6) ~ (e3 = e0)
% 171.23/26.60 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.60 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.60 (8) op(e2, e1) = e1
% 171.23/26.60 (9) all_58_3 = e2
% 171.23/26.60 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.60 (11) ~ (e2 = e0)
% 171.23/26.60 (12) all_58_5 = e1
% 171.23/26.60 (13) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 171.23/26.60 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 171.23/26.60 (14) ~ (e3 = e2)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | BETA: splitting (13) gives:
% 171.23/26.60 |
% 171.23/26.60 | Case 1:
% 171.23/26.60 | |
% 171.23/26.60 | | (15) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 171.23/26.60 | | e3)
% 171.23/26.60 | |
% 171.23/26.60 | | BETA: splitting (15) gives:
% 171.23/26.60 | |
% 171.23/26.60 | | Case 1:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (16) all_58_2 = e3 & op(e2, e3) = e3
% 171.23/26.60 | | |
% 171.23/26.60 | | | ALPHA: (16) implies:
% 171.23/26.60 | | | (17) all_58_2 = e3
% 171.23/26.60 | | |
% 171.23/26.60 | | | BETA: splitting (7) gives:
% 171.23/26.60 | | |
% 171.23/26.60 | | | Case 1:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | (18) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2)
% 171.23/26.60 | | | | = e0)
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | REF_CLOSE: (6), (9), (11), (17), (18) are inconsistent by sub-proof
% 171.23/26.60 | | | | #912.
% 171.23/26.60 | | | |
% 171.23/26.60 | | | Case 2:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | (19) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0)
% 171.23/26.60 | | | | = e0)
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | BETA: splitting (19) gives:
% 171.23/26.60 | | | |
% 171.23/26.60 | | | | Case 1:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | (20) all_58_5 = e0 & op(e2, e1) = e0
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | ALPHA: (20) implies:
% 171.23/26.60 | | | | | (21) op(e2, e1) = e0
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | REF_CLOSE: (3), (8), (10), (21) are inconsistent by sub-proof #911.
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | Case 2:
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | (22) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | | REF_CLOSE: (4), (11), (22) are inconsistent by sub-proof #918.
% 171.23/26.60 | | | | |
% 171.23/26.60 | | | | End of split
% 171.23/26.60 | | | |
% 171.23/26.60 | | | End of split
% 171.23/26.60 | | |
% 171.23/26.60 | | Case 2:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (23) all_58_3 = e3 & op(e2, e2) = e3
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (1), (5), (10), (23) are inconsistent by sub-proof #973.
% 171.23/26.60 | | |
% 171.23/26.60 | | End of split
% 171.23/26.60 | |
% 171.23/26.60 | Case 2:
% 171.23/26.60 | |
% 171.23/26.60 | | (24) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 171.23/26.60 | | e3)
% 171.23/26.60 | |
% 171.23/26.60 | | BETA: splitting (24) gives:
% 171.23/26.60 | |
% 171.23/26.60 | | Case 1:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (25) all_58_5 = e3 & op(e2, e1) = e3
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (2), (12), (25) are inconsistent by sub-proof #910.
% 171.23/26.60 | | |
% 171.23/26.60 | | Case 2:
% 171.23/26.60 | | |
% 171.23/26.60 | | | (26) all_58_10 = e3 & op(e2, e0) = e3
% 171.23/26.60 | | |
% 171.23/26.60 | | | REF_CLOSE: (4), (14), (26) are inconsistent by sub-proof #916.
% 171.23/26.60 | | |
% 171.23/26.60 | | End of split
% 171.23/26.60 | |
% 171.23/26.60 | End of split
% 171.23/26.60 |
% 171.23/26.60 End of proof
% 171.23/26.60
% 171.23/26.60 Sub-proof #910 shows that the following formulas are inconsistent:
% 171.23/26.60 ----------------------------------------------------------------
% 171.23/26.60 (1) all_58_5 = e3 & op(e2, e1) = e3
% 171.23/26.60 (2) all_58_5 = e1
% 171.23/26.60 (3) ~ (e3 = e1)
% 171.23/26.60
% 171.23/26.60 Begin of proof
% 171.23/26.60 |
% 171.23/26.60 | ALPHA: (1) implies:
% 171.23/26.60 | (4) all_58_5 = e3
% 171.23/26.60 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e3 = e1
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #911 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.61 (2) op(e2, e1) = e1
% 171.23/26.61 (3) op(e2, e1) = e0
% 171.23/26.61 (4) ~ (e1 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | GROUND_INST: instantiating (1) with e0, e1, e1, e2, simplifying with (2), (3)
% 171.23/26.61 | gives:
% 171.23/26.61 | (5) e1 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (4), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #912 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_2 = e3
% 171.23/26.61 (2) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 171.23/26.61 (3) ~ (e3 = e0)
% 171.23/26.61 (4) all_58_3 = e2
% 171.23/26.61 (5) ~ (e2 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | BETA: splitting (2) gives:
% 171.23/26.61 |
% 171.23/26.61 | Case 1:
% 171.23/26.61 | |
% 171.23/26.61 | | (6) all_58_2 = e0 & op(e2, e3) = e0
% 171.23/26.61 | |
% 171.23/26.61 | | ALPHA: (6) implies:
% 171.23/26.61 | | (7) all_58_2 = e0
% 171.23/26.61 | |
% 171.23/26.61 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #913.
% 171.23/26.61 | |
% 171.23/26.61 | Case 2:
% 171.23/26.61 | |
% 171.23/26.61 | | (8) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.61 | |
% 171.23/26.61 | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #934.
% 171.23/26.61 | |
% 171.23/26.61 | End of split
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #913 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_2 = e3
% 171.23/26.61 (2) all_58_2 = e0
% 171.23/26.61 (3) ~ (e3 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.61 | (4) e3 = e0
% 171.23/26.61 |
% 171.23/26.61 | SIMP: (4) implies:
% 171.23/26.61 | (5) e3 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #914 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_3 = e1 & op(e2, e2) = e1
% 171.23/26.61 (2) all_58_3 = e2
% 171.23/26.61 (3) ~ (e2 = e1)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_3 = e1
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e2 = e1
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #915 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.23/26.61 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 171.23/26.61 (2) ~ (all_8_2 = e3)
% 171.23/26.61 (3) ~ (e3 = e1)
% 171.23/26.61 (4) ~ (e1 = e0)
% 171.23/26.61 (5) all_58_10 = e2
% 171.23/26.61 (6) op(e2, e2) = all_8_2
% 171.23/26.61 (7) ~ (e3 = e0)
% 171.23/26.61 (8) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.61 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.61 (9) all_58_3 = e2
% 171.23/26.61 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.61 (11) ~ (e2 = e0)
% 171.23/26.61 (12) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 171.23/26.61 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 171.23/26.61 (13) ~ (e2 = e1)
% 171.23/26.61 (14) all_58_2 = e1
% 171.23/26.61 (15) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 171.23/26.61 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 171.23/26.61 (16) ~ (e3 = e2)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | BETA: splitting (12) gives:
% 171.23/26.61 |
% 171.23/26.61 | Case 1:
% 171.23/26.61 | |
% 171.23/26.61 | | (17) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 171.23/26.61 | | e3)
% 171.23/26.61 | |
% 171.23/26.61 | | REF_CLOSE: (2), (3), (6), (10), (14), (17) are inconsistent by sub-proof
% 171.23/26.61 | | #937.
% 171.23/26.61 | |
% 171.23/26.61 | Case 2:
% 171.23/26.61 | |
% 171.23/26.61 | | (18) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 171.23/26.61 | | e3)
% 171.23/26.61 | |
% 171.23/26.61 | | BETA: splitting (18) gives:
% 171.23/26.61 | |
% 171.23/26.61 | | Case 1:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (19) all_58_5 = e3 & op(e2, e1) = e3
% 171.23/26.61 | | |
% 171.23/26.61 | | | ALPHA: (19) implies:
% 171.23/26.61 | | | (20) all_58_5 = e3
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11), (13), (15), (16), (20)
% 171.23/26.61 | | | are inconsistent by sub-proof #917.
% 171.23/26.61 | | |
% 171.23/26.61 | | Case 2:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (21) all_58_10 = e3 & op(e2, e0) = e3
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (5), (16), (21) are inconsistent by sub-proof #916.
% 171.23/26.61 | | |
% 171.23/26.61 | | End of split
% 171.23/26.61 | |
% 171.23/26.61 | End of split
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #916 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_10 = e3 & op(e2, e0) = e3
% 171.23/26.61 (2) all_58_10 = e2
% 171.23/26.61 (3) ~ (e3 = e2)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_10 = e3
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e3 = e2
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #917 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2) = e1) |
% 171.23/26.61 (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0) = e1)
% 171.23/26.61 (2) ~ (e3 = e1)
% 171.23/26.61 (3) ~ (e1 = e0)
% 171.23/26.61 (4) all_58_5 = e3
% 171.23/26.61 (5) all_58_10 = e2
% 171.23/26.61 (6) ~ (e3 = e0)
% 171.23/26.61 (7) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.61 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.61 (8) all_58_3 = e2
% 171.23/26.61 (9) ~ (e2 = e0)
% 171.23/26.61 (10) ~ (e2 = e1)
% 171.23/26.61 (11) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 171.23/26.61 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 171.23/26.61 (12) ~ (e3 = e2)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | BETA: splitting (7) gives:
% 171.23/26.61 |
% 171.23/26.61 | Case 1:
% 171.23/26.61 | |
% 171.23/26.61 | | (13) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) =
% 171.23/26.61 | | e0)
% 171.23/26.61 | |
% 171.23/26.61 | | BETA: splitting (13) gives:
% 171.23/26.61 | |
% 171.23/26.61 | | Case 1:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (14) all_58_2 = e0 & op(e2, e3) = e0
% 171.23/26.61 | | |
% 171.23/26.61 | | | ALPHA: (14) implies:
% 171.23/26.61 | | | (15) all_58_2 = e0
% 171.23/26.61 | | |
% 171.23/26.61 | | | BETA: splitting (1) gives:
% 171.23/26.61 | | |
% 171.23/26.61 | | | Case 1:
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | (16) (all_58_2 = e1 & op(e2, e3) = e1) | (all_58_3 = e1 & op(e2, e2)
% 171.23/26.61 | | | | = e1)
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | BETA: splitting (16) gives:
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | Case 1:
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | (17) all_58_2 = e1 & op(e2, e3) = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | REF_CLOSE: (3), (15), (17) are inconsistent by sub-proof #929.
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | Case 2:
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | (18) all_58_3 = e1 & op(e2, e2) = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | ALPHA: (18) implies:
% 171.23/26.61 | | | | | (19) all_58_3 = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | COMBINE_EQS: (8), (19) imply:
% 171.23/26.61 | | | | | (20) e2 = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | COMBINE_EQS: (5), (20) imply:
% 171.23/26.61 | | | | | (21) all_58_10 = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (19), (21) are
% 171.23/26.61 | | | | | inconsistent by sub-proof #921.
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | End of split
% 171.23/26.61 | | | |
% 171.23/26.61 | | | Case 2:
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | (22) (all_58_5 = e1 & op(e2, e1) = e1) | (all_58_10 = e1 & op(e2, e0)
% 171.23/26.61 | | | | = e1)
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | BETA: splitting (22) gives:
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | Case 1:
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | (23) all_58_5 = e1 & op(e2, e1) = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | ALPHA: (23) implies:
% 171.23/26.61 | | | | | (24) all_58_5 = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | REF_CLOSE: (2), (4), (24) are inconsistent by sub-proof #920.
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | Case 2:
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | (25) all_58_10 = e1 & op(e2, e0) = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | ALPHA: (25) implies:
% 171.23/26.61 | | | | | (26) all_58_10 = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | COMBINE_EQS: (5), (26) imply:
% 171.23/26.61 | | | | | (27) e2 = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | COMBINE_EQS: (8), (27) imply:
% 171.23/26.61 | | | | | (28) all_58_3 = e1
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (26), (28) are
% 171.23/26.61 | | | | | inconsistent by sub-proof #921.
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | End of split
% 171.23/26.61 | | | |
% 171.23/26.61 | | | End of split
% 171.23/26.61 | | |
% 171.23/26.61 | | Case 2:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (29) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (8), (9), (29) are inconsistent by sub-proof #934.
% 171.23/26.61 | | |
% 171.23/26.61 | | End of split
% 171.23/26.61 | |
% 171.23/26.61 | Case 2:
% 171.23/26.61 | |
% 171.23/26.61 | | (30) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 171.23/26.61 | | e0)
% 171.23/26.61 | |
% 171.23/26.61 | | BETA: splitting (30) gives:
% 171.23/26.61 | |
% 171.23/26.61 | | Case 1:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (31) all_58_5 = e0 & op(e2, e1) = e0
% 171.23/26.61 | | |
% 171.23/26.61 | | | ALPHA: (31) implies:
% 171.23/26.61 | | | (32) all_58_5 = e0
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (4), (6), (32) are inconsistent by sub-proof #919.
% 171.23/26.61 | | |
% 171.23/26.61 | | Case 2:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (33) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (5), (9), (33) are inconsistent by sub-proof #918.
% 171.23/26.61 | | |
% 171.23/26.61 | | End of split
% 171.23/26.61 | |
% 171.23/26.61 | End of split
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #918 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.61 (2) all_58_10 = e2
% 171.23/26.61 (3) ~ (e2 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_10 = e0
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e2 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #919 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_5 = e3
% 171.23/26.61 (2) all_58_5 = e0
% 171.23/26.61 (3) ~ (e3 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.61 | (4) e3 = e0
% 171.23/26.61 |
% 171.23/26.61 | SIMP: (4) implies:
% 171.23/26.61 | (5) e3 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #920 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_5 = e3
% 171.23/26.61 (2) all_58_5 = e1
% 171.23/26.61 (3) ~ (e3 = e1)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.61 | (4) e3 = e1
% 171.23/26.61 |
% 171.23/26.61 | SIMP: (4) implies:
% 171.23/26.61 | (5) e3 = e1
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #921 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) ~ (e1 = e0)
% 171.23/26.61 (2) all_58_3 = e1
% 171.23/26.61 (3) all_58_5 = e3
% 171.23/26.61 (4) ~ (e3 = e0)
% 171.23/26.61 (5) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.61 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.61 (6) ~ (e2 = e0)
% 171.23/26.61 (7) ~ (e2 = e1)
% 171.23/26.61 (8) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) = e2) |
% 171.23/26.61 (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) = e2)
% 171.23/26.61 (9) all_58_10 = e1
% 171.23/26.61 (10) ~ (e3 = e2)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | BETA: splitting (8) gives:
% 171.23/26.61 |
% 171.23/26.61 | Case 1:
% 171.23/26.61 | |
% 171.23/26.61 | | (11) (all_58_2 = e2 & op(e2, e3) = e2) | (all_58_3 = e2 & op(e2, e2) =
% 171.23/26.61 | | e2)
% 171.23/26.61 | |
% 171.23/26.61 | | BETA: splitting (11) gives:
% 171.23/26.61 | |
% 171.23/26.61 | | Case 1:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (12) all_58_2 = e2 & op(e2, e3) = e2
% 171.23/26.61 | | |
% 171.23/26.61 | | | ALPHA: (12) implies:
% 171.23/26.61 | | | (13) all_58_2 = e2
% 171.23/26.61 | | |
% 171.23/26.61 | | | BETA: splitting (5) gives:
% 171.23/26.61 | | |
% 171.23/26.61 | | | Case 1:
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | (14) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2)
% 171.23/26.61 | | | | = e0)
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | BETA: splitting (14) gives:
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | Case 1:
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | (15) all_58_2 = e0 & op(e2, e3) = e0
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | REF_CLOSE: (6), (13), (15) are inconsistent by sub-proof #928.
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | Case 2:
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | (16) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | REF_CLOSE: (1), (2), (16) are inconsistent by sub-proof #927.
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | End of split
% 171.23/26.61 | | | |
% 171.23/26.61 | | | Case 2:
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | (17) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0)
% 171.23/26.61 | | | | = e0)
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | BETA: splitting (17) gives:
% 171.23/26.61 | | | |
% 171.23/26.61 | | | | Case 1:
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | (18) all_58_5 = e0 & op(e2, e1) = e0
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | REF_CLOSE: (3), (4), (18) are inconsistent by sub-proof #926.
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | Case 2:
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | (19) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | | REF_CLOSE: (1), (9), (19) are inconsistent by sub-proof #925.
% 171.23/26.61 | | | | |
% 171.23/26.61 | | | | End of split
% 171.23/26.61 | | | |
% 171.23/26.61 | | | End of split
% 171.23/26.61 | | |
% 171.23/26.61 | | Case 2:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (20) all_58_3 = e2 & op(e2, e2) = e2
% 171.23/26.61 | | |
% 171.23/26.61 | | | ALPHA: (20) implies:
% 171.23/26.61 | | | (21) all_58_3 = e2
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (2), (7), (21) are inconsistent by sub-proof #924.
% 171.23/26.61 | | |
% 171.23/26.61 | | End of split
% 171.23/26.61 | |
% 171.23/26.61 | Case 2:
% 171.23/26.61 | |
% 171.23/26.61 | | (22) (all_58_5 = e2 & op(e2, e1) = e2) | (all_58_10 = e2 & op(e2, e0) =
% 171.23/26.61 | | e2)
% 171.23/26.61 | |
% 171.23/26.61 | | BETA: splitting (22) gives:
% 171.23/26.61 | |
% 171.23/26.61 | | Case 1:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (23) all_58_5 = e2 & op(e2, e1) = e2
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (3), (10), (23) are inconsistent by sub-proof #923.
% 171.23/26.61 | | |
% 171.23/26.61 | | Case 2:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (24) all_58_10 = e2 & op(e2, e0) = e2
% 171.23/26.61 | | |
% 171.23/26.61 | | | ALPHA: (24) implies:
% 171.23/26.61 | | | (25) all_58_10 = e2
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (7), (9), (25) are inconsistent by sub-proof #922.
% 171.23/26.61 | | |
% 171.23/26.61 | | End of split
% 171.23/26.61 | |
% 171.23/26.61 | End of split
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #922 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_10 = e2
% 171.23/26.61 (2) all_58_10 = e1
% 171.23/26.61 (3) ~ (e2 = e1)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.61 | (4) e2 = e1
% 171.23/26.61 |
% 171.23/26.61 | SIMP: (4) implies:
% 171.23/26.61 | (5) e2 = e1
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #923 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_5 = e2 & op(e2, e1) = e2
% 171.23/26.61 (2) all_58_5 = e3
% 171.23/26.61 (3) ~ (e3 = e2)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_5 = e2
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e3 = e2
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #924 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_3 = e2
% 171.23/26.61 (2) all_58_3 = e1
% 171.23/26.61 (3) ~ (e2 = e1)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.61 | (4) e2 = e1
% 171.23/26.61 |
% 171.23/26.61 | SIMP: (4) implies:
% 171.23/26.61 | (5) e2 = e1
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #925 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.61 (2) all_58_10 = e1
% 171.23/26.61 (3) ~ (e1 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_10 = e0
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e1 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #926 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_5 = e0 & op(e2, e1) = e0
% 171.23/26.61 (2) all_58_5 = e3
% 171.23/26.61 (3) ~ (e3 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_5 = e0
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e3 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #927 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.61 (2) all_58_3 = e1
% 171.23/26.61 (3) ~ (e1 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_3 = e0
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e1 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #928 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_2 = e0 & op(e2, e3) = e0
% 171.23/26.61 (2) all_58_2 = e2
% 171.23/26.61 (3) ~ (e2 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_2 = e0
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e2 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #929 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_2 = e1 & op(e2, e3) = e1
% 171.23/26.61 (2) all_58_2 = e0
% 171.23/26.61 (3) ~ (e1 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_2 = e1
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e1 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #930 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) ~ (all_8_2 = e3)
% 171.23/26.61 (2) ~ (e3 = e1)
% 171.23/26.61 (3) ~ (e1 = e0)
% 171.23/26.61 (4) op(e2, e2) = all_8_2
% 171.23/26.61 (5) ~ (e3 = e0)
% 171.23/26.61 (6) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.61 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.61 (7) all_58_3 = e2
% 171.23/26.61 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.61 (9) ~ (e2 = e0)
% 171.23/26.61 (10) all_58_5 = e2
% 171.23/26.61 (11) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3) |
% 171.23/26.61 (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) = e3)
% 171.23/26.61 (12) all_58_2 = e1
% 171.23/26.61 (13) ~ (e3 = e2)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | BETA: splitting (11) gives:
% 171.23/26.61 |
% 171.23/26.61 | Case 1:
% 171.23/26.61 | |
% 171.23/26.61 | | (14) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) =
% 171.23/26.61 | | e3)
% 171.23/26.61 | |
% 171.23/26.61 | | REF_CLOSE: (1), (2), (4), (8), (12), (14) are inconsistent by sub-proof
% 171.23/26.61 | | #937.
% 171.23/26.61 | |
% 171.23/26.61 | Case 2:
% 171.23/26.61 | |
% 171.23/26.61 | | (15) (all_58_5 = e3 & op(e2, e1) = e3) | (all_58_10 = e3 & op(e2, e0) =
% 171.23/26.61 | | e3)
% 171.23/26.61 | |
% 171.23/26.61 | | BETA: splitting (15) gives:
% 171.23/26.61 | |
% 171.23/26.61 | | Case 1:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (16) all_58_5 = e3 & op(e2, e1) = e3
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (10), (13), (16) are inconsistent by sub-proof #936.
% 171.23/26.61 | | |
% 171.23/26.61 | | Case 2:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (17) all_58_10 = e3 & op(e2, e0) = e3
% 171.23/26.61 | | |
% 171.23/26.61 | | | ALPHA: (17) implies:
% 171.23/26.61 | | | (18) all_58_10 = e3
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (3), (5), (6), (7), (9), (10), (12), (18) are inconsistent by
% 171.23/26.61 | | | sub-proof #931.
% 171.23/26.61 | | |
% 171.23/26.61 | | End of split
% 171.23/26.61 | |
% 171.23/26.61 | End of split
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #931 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) ~ (e1 = e0)
% 171.23/26.61 (2) all_58_10 = e3
% 171.23/26.61 (3) ~ (e3 = e0)
% 171.23/26.61 (4) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0) |
% 171.23/26.61 (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) = e0)
% 171.23/26.61 (5) all_58_3 = e2
% 171.23/26.61 (6) ~ (e2 = e0)
% 171.23/26.61 (7) all_58_5 = e2
% 171.23/26.61 (8) all_58_2 = e1
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | BETA: splitting (4) gives:
% 171.23/26.61 |
% 171.23/26.61 | Case 1:
% 171.23/26.61 | |
% 171.23/26.61 | | (9) (all_58_2 = e0 & op(e2, e3) = e0) | (all_58_3 = e0 & op(e2, e2) = e0)
% 171.23/26.61 | |
% 171.23/26.61 | | BETA: splitting (9) gives:
% 171.23/26.61 | |
% 171.23/26.61 | | Case 1:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (10) all_58_2 = e0 & op(e2, e3) = e0
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (1), (8), (10) are inconsistent by sub-proof #935.
% 171.23/26.61 | | |
% 171.23/26.61 | | Case 2:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (11) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #934.
% 171.23/26.61 | | |
% 171.23/26.61 | | End of split
% 171.23/26.61 | |
% 171.23/26.61 | Case 2:
% 171.23/26.61 | |
% 171.23/26.61 | | (12) (all_58_5 = e0 & op(e2, e1) = e0) | (all_58_10 = e0 & op(e2, e0) =
% 171.23/26.61 | | e0)
% 171.23/26.61 | |
% 171.23/26.61 | | BETA: splitting (12) gives:
% 171.23/26.61 | |
% 171.23/26.61 | | Case 1:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (13) all_58_5 = e0 & op(e2, e1) = e0
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #933.
% 171.23/26.61 | | |
% 171.23/26.61 | | Case 2:
% 171.23/26.61 | | |
% 171.23/26.61 | | | (14) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.61 | | |
% 171.23/26.61 | | | REF_CLOSE: (2), (3), (14) are inconsistent by sub-proof #932.
% 171.23/26.61 | | |
% 171.23/26.61 | | End of split
% 171.23/26.61 | |
% 171.23/26.61 | End of split
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #932 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_10 = e0 & op(e2, e0) = e0
% 171.23/26.61 (2) all_58_10 = e3
% 171.23/26.61 (3) ~ (e3 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_10 = e0
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e3 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #933 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_5 = e0 & op(e2, e1) = e0
% 171.23/26.61 (2) all_58_5 = e2
% 171.23/26.61 (3) ~ (e2 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_5 = e0
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e2 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #934 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_3 = e0 & op(e2, e2) = e0
% 171.23/26.61 (2) all_58_3 = e2
% 171.23/26.61 (3) ~ (e2 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_3 = e0
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e2 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #935 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_2 = e0 & op(e2, e3) = e0
% 171.23/26.61 (2) all_58_2 = e1
% 171.23/26.61 (3) ~ (e1 = e0)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_2 = e0
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e1 = e0
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #936 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) all_58_5 = e3 & op(e2, e1) = e3
% 171.23/26.61 (2) all_58_5 = e2
% 171.23/26.61 (3) ~ (e3 = e2)
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | ALPHA: (1) implies:
% 171.23/26.61 | (4) all_58_5 = e3
% 171.23/26.61 |
% 171.23/26.61 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.61 | (5) e3 = e2
% 171.23/26.61 |
% 171.23/26.61 | REDUCE: (3), (5) imply:
% 171.23/26.61 | (6) $false
% 171.23/26.61 |
% 171.23/26.61 | CLOSE: (6) is inconsistent.
% 171.23/26.61 |
% 171.23/26.61 End of proof
% 171.23/26.61
% 171.23/26.61 Sub-proof #937 shows that the following formulas are inconsistent:
% 171.23/26.61 ----------------------------------------------------------------
% 171.23/26.61 (1) ~ (all_8_2 = e3)
% 171.23/26.61 (2) ~ (e3 = e1)
% 171.23/26.61 (3) (all_58_2 = e3 & op(e2, e3) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 171.23/26.61 (4) op(e2, e2) = all_8_2
% 171.23/26.61 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.61 (6) all_58_2 = e1
% 171.23/26.61
% 171.23/26.61 Begin of proof
% 171.23/26.61 |
% 171.23/26.61 | BETA: splitting (3) gives:
% 171.23/26.61 |
% 171.23/26.61 | Case 1:
% 171.23/26.61 | |
% 171.23/26.61 | | (7) all_58_2 = e3 & op(e2, e3) = e3
% 171.23/26.61 | |
% 171.23/26.61 | | ALPHA: (7) implies:
% 171.23/26.61 | | (8) all_58_2 = e3
% 171.23/26.61 | |
% 171.23/26.61 | | REF_CLOSE: (2), (6), (8) are inconsistent by sub-proof #938.
% 171.23/26.61 | |
% 171.23/26.61 | Case 2:
% 171.23/26.61 | |
% 171.23/26.61 | | (9) all_58_3 = e3 & op(e2, e2) = e3
% 171.23/26.61 | |
% 171.23/26.62 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #973.
% 171.23/26.62 | |
% 171.23/26.62 | End of split
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #938 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_2 = e3
% 171.23/26.62 (2) all_58_2 = e1
% 171.23/26.62 (3) ~ (e3 = e1)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.62 | (4) e3 = e1
% 171.23/26.62 |
% 171.23/26.62 | SIMP: (4) implies:
% 171.23/26.62 | (5) e3 = e1
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #939 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_9 = e2
% 171.23/26.62 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 171.23/26.62 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.62 (3) ~ (e3 = e1)
% 171.23/26.62 (4) ~ (e1 = e0)
% 171.23/26.62 (5) ~ (e3 = e0)
% 171.23/26.62 (6) ~ (all_52_4 = e3)
% 171.23/26.62 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 171.23/26.62 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 171.23/26.62 (8) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) = e3) |
% 171.23/26.62 (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) = e3)
% 171.23/26.62 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (10) ~ (e2 = e0)
% 171.23/26.62 (11) ~ (e2 = e1)
% 171.23/26.62 (12) op(e3, e2) = all_52_4
% 171.23/26.62 (13) all_58_4 = e2
% 171.23/26.62 (14) ~ (e3 = e2)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | BETA: splitting (8) gives:
% 171.23/26.62 |
% 171.23/26.62 | Case 1:
% 171.23/26.62 | |
% 171.23/26.62 | | (15) (all_58_0 = e3 & op(e3, e3) = e3) | (all_58_1 = e3 & op(e3, e2) =
% 171.23/26.62 | | e3)
% 171.23/26.62 | |
% 171.23/26.62 | | BETA: splitting (15) gives:
% 171.23/26.62 | |
% 171.23/26.62 | | Case 1:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (16) all_58_0 = e3 & op(e3, e3) = e3
% 171.23/26.62 | | |
% 171.23/26.62 | | | ALPHA: (16) implies:
% 171.23/26.62 | | | (17) all_58_0 = e3
% 171.23/26.62 | | | (18) op(e3, e3) = e3
% 171.23/26.62 | | |
% 171.23/26.62 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (13), (17), (18)
% 171.23/26.62 | | | are inconsistent by sub-proof #941.
% 171.23/26.62 | | |
% 171.23/26.62 | | Case 2:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (19) all_58_1 = e3 & op(e3, e2) = e3
% 171.23/26.62 | | |
% 171.23/26.62 | | | ALPHA: (19) implies:
% 171.23/26.62 | | | (20) op(e3, e2) = e3
% 171.23/26.62 | | |
% 171.23/26.62 | | | REF_CLOSE: (6), (9), (12), (20) are inconsistent by sub-proof #974.
% 171.23/26.62 | | |
% 171.23/26.62 | | End of split
% 171.23/26.62 | |
% 171.23/26.62 | Case 2:
% 171.23/26.62 | |
% 171.23/26.62 | | (21) (all_58_4 = e3 & op(e3, e1) = e3) | (all_58_9 = e3 & op(e3, e0) =
% 171.23/26.62 | | e3)
% 171.23/26.62 | |
% 171.23/26.62 | | BETA: splitting (21) gives:
% 171.23/26.62 | |
% 171.23/26.62 | | Case 1:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (22) all_58_4 = e3 & op(e3, e1) = e3
% 171.23/26.62 | | |
% 171.23/26.62 | | | REF_CLOSE: (13), (14), (22) are inconsistent by sub-proof #952.
% 171.23/26.62 | | |
% 171.23/26.62 | | Case 2:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (23) all_58_9 = e3 & op(e3, e0) = e3
% 171.23/26.62 | | |
% 171.23/26.62 | | | REF_CLOSE: (1), (14), (23) are inconsistent by sub-proof #940.
% 171.23/26.62 | | |
% 171.23/26.62 | | End of split
% 171.23/26.62 | |
% 171.23/26.62 | End of split
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #940 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_9 = e3 & op(e3, e0) = e3
% 171.23/26.62 (2) all_58_9 = e2
% 171.23/26.62 (3) ~ (e3 = e2)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | ALPHA: (1) implies:
% 171.23/26.62 | (4) all_58_9 = e3
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.62 | (5) e3 = e2
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #941 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_9 = e2
% 171.23/26.62 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 171.23/26.62 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.62 (3) ~ (e3 = e1)
% 171.23/26.62 (4) ~ (e1 = e0)
% 171.23/26.62 (5) ~ (e3 = e0)
% 171.23/26.62 (6) all_58_0 = e3
% 171.23/26.62 (7) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) = e1) |
% 171.23/26.62 (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) = e1)
% 171.23/26.62 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (9) ~ (e2 = e0)
% 171.23/26.62 (10) op(e3, e3) = e3
% 171.23/26.62 (11) ~ (e2 = e1)
% 171.23/26.62 (12) all_58_4 = e2
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | BETA: splitting (7) gives:
% 171.23/26.62 |
% 171.23/26.62 | Case 1:
% 171.23/26.62 | |
% 171.23/26.62 | | (13) (all_58_0 = e1 & op(e3, e3) = e1) | (all_58_1 = e1 & op(e3, e2) =
% 171.23/26.62 | | e1)
% 171.23/26.62 | |
% 171.23/26.62 | | BETA: splitting (13) gives:
% 171.23/26.62 | |
% 171.23/26.62 | | Case 1:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (14) all_58_0 = e1 & op(e3, e3) = e1
% 171.23/26.62 | | |
% 171.23/26.62 | | | REF_CLOSE: (3), (6), (14) are inconsistent by sub-proof #950.
% 171.23/26.62 | | |
% 171.23/26.62 | | Case 2:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (15) all_58_1 = e1 & op(e3, e2) = e1
% 171.23/26.62 | | |
% 171.23/26.62 | | | ALPHA: (15) implies:
% 171.23/26.62 | | | (16) all_58_1 = e1
% 171.23/26.62 | | |
% 171.23/26.62 | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (12), (16) are inconsistent
% 171.23/26.62 | | | by sub-proof #944.
% 171.23/26.62 | | |
% 171.23/26.62 | | End of split
% 171.23/26.62 | |
% 171.23/26.62 | Case 2:
% 171.23/26.62 | |
% 171.23/26.62 | | (17) (all_58_4 = e1 & op(e3, e1) = e1) | (all_58_9 = e1 & op(e3, e0) =
% 171.23/26.62 | | e1)
% 171.23/26.62 | |
% 171.23/26.62 | | BETA: splitting (17) gives:
% 171.23/26.62 | |
% 171.23/26.62 | | Case 1:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (18) all_58_4 = e1 & op(e3, e1) = e1
% 171.23/26.62 | | |
% 171.23/26.62 | | | REF_CLOSE: (11), (12), (18) are inconsistent by sub-proof #943.
% 171.23/26.62 | | |
% 171.23/26.62 | | Case 2:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (19) all_58_9 = e1 & op(e3, e0) = e1
% 171.23/26.62 | | |
% 171.23/26.62 | | | ALPHA: (19) implies:
% 171.23/26.62 | | | (20) all_58_9 = e1
% 171.23/26.62 | | |
% 171.23/26.62 | | | REF_CLOSE: (1), (11), (20) are inconsistent by sub-proof #942.
% 171.23/26.62 | | |
% 171.23/26.62 | | End of split
% 171.23/26.62 | |
% 171.23/26.62 | End of split
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #942 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_9 = e2
% 171.23/26.62 (2) all_58_9 = e1
% 171.23/26.62 (3) ~ (e2 = e1)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.62 | (4) e2 = e1
% 171.23/26.62 |
% 171.23/26.62 | SIMP: (4) implies:
% 171.23/26.62 | (5) e2 = e1
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #943 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_4 = e1 & op(e3, e1) = e1
% 171.23/26.62 (2) all_58_4 = e2
% 171.23/26.62 (3) ~ (e2 = e1)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | ALPHA: (1) implies:
% 171.23/26.62 | (4) all_58_4 = e1
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.62 | (5) e2 = e1
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #944 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_1 = e1
% 171.23/26.62 (2) all_58_9 = e2
% 171.23/26.62 (3) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0) |
% 171.23/26.62 (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) = e0)
% 171.23/26.62 (4) ~ (e1 = e0)
% 171.23/26.62 (5) ~ (e3 = e0)
% 171.23/26.62 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (7) ~ (e2 = e0)
% 171.23/26.62 (8) op(e3, e3) = e3
% 171.23/26.62 (9) all_58_4 = e2
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | BETA: splitting (3) gives:
% 171.23/26.62 |
% 171.23/26.62 | Case 1:
% 171.23/26.62 | |
% 171.23/26.62 | | (10) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) =
% 171.23/26.62 | | e0)
% 171.23/26.62 | |
% 171.23/26.62 | | REF_CLOSE: (1), (4), (5), (6), (8), (10) are inconsistent by sub-proof #947.
% 171.23/26.62 | |
% 171.23/26.62 | Case 2:
% 171.23/26.62 | |
% 171.23/26.62 | | (11) (all_58_4 = e0 & op(e3, e1) = e0) | (all_58_9 = e0 & op(e3, e0) =
% 171.23/26.62 | | e0)
% 171.23/26.62 | |
% 171.23/26.62 | | BETA: splitting (11) gives:
% 171.23/26.62 | |
% 171.23/26.62 | | Case 1:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (12) all_58_4 = e0 & op(e3, e1) = e0
% 171.23/26.62 | | |
% 171.23/26.62 | | | REF_CLOSE: (7), (9), (12) are inconsistent by sub-proof #946.
% 171.23/26.62 | | |
% 171.23/26.62 | | Case 2:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (13) all_58_9 = e0 & op(e3, e0) = e0
% 171.23/26.62 | | |
% 171.23/26.62 | | | ALPHA: (13) implies:
% 171.23/26.62 | | | (14) all_58_9 = e0
% 171.23/26.62 | | |
% 171.23/26.62 | | | REF_CLOSE: (2), (7), (14) are inconsistent by sub-proof #945.
% 171.23/26.62 | | |
% 171.23/26.62 | | End of split
% 171.23/26.62 | |
% 171.23/26.62 | End of split
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #945 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_9 = e2
% 171.23/26.62 (2) all_58_9 = e0
% 171.23/26.62 (3) ~ (e2 = e0)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.62 | (4) e2 = e0
% 171.23/26.62 |
% 171.23/26.62 | SIMP: (4) implies:
% 171.23/26.62 | (5) e2 = e0
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #946 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_4 = e0 & op(e3, e1) = e0
% 171.23/26.62 (2) all_58_4 = e2
% 171.23/26.62 (3) ~ (e2 = e0)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | ALPHA: (1) implies:
% 171.23/26.62 | (4) all_58_4 = e0
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.62 | (5) e2 = e0
% 171.23/26.62 |
% 171.23/26.62 | SIMP: (5) implies:
% 171.23/26.62 | (6) e2 = e0
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (6) imply:
% 171.23/26.62 | (7) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (7) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #947 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_1 = e1
% 171.23/26.62 (2) (all_58_0 = e0 & op(e3, e3) = e0) | (all_58_1 = e0 & op(e3, e2) = e0)
% 171.23/26.62 (3) ~ (e1 = e0)
% 171.23/26.62 (4) ~ (e3 = e0)
% 171.23/26.62 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (6) op(e3, e3) = e3
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | BETA: splitting (2) gives:
% 171.23/26.62 |
% 171.23/26.62 | Case 1:
% 171.23/26.62 | |
% 171.23/26.62 | | (7) all_58_0 = e0 & op(e3, e3) = e0
% 171.23/26.62 | |
% 171.23/26.62 | | ALPHA: (7) implies:
% 171.23/26.62 | | (8) op(e3, e3) = e0
% 171.23/26.62 | |
% 171.23/26.62 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #949.
% 171.23/26.62 | |
% 171.23/26.62 | Case 2:
% 171.23/26.62 | |
% 171.23/26.62 | | (9) all_58_1 = e0 & op(e3, e2) = e0
% 171.23/26.62 | |
% 171.23/26.62 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #948.
% 171.23/26.62 | |
% 171.23/26.62 | End of split
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #948 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_1 = e0 & op(e3, e2) = e0
% 171.23/26.62 (2) all_58_1 = e1
% 171.23/26.62 (3) ~ (e1 = e0)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | ALPHA: (1) implies:
% 171.23/26.62 | (4) all_58_1 = e0
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.62 | (5) e1 = e0
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #949 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (2) op(e3, e3) = e3
% 171.23/26.62 (3) op(e3, e3) = e0
% 171.23/26.62 (4) ~ (e3 = e0)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | GROUND_INST: instantiating (1) with e0, e3, e3, e3, simplifying with (2), (3)
% 171.23/26.62 | gives:
% 171.23/26.62 | (5) e3 = e0
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (4), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #950 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_0 = e1 & op(e3, e3) = e1
% 171.23/26.62 (2) all_58_0 = e3
% 171.23/26.62 (3) ~ (e3 = e1)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | ALPHA: (1) implies:
% 171.23/26.62 | (4) all_58_0 = e1
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.62 | (5) e3 = e1
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #951 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (2) op(e2, e1) = all_52_9
% 171.23/26.62 (3) op(e2, e1) = e3
% 171.23/26.62 (4) ~ (all_52_9 = e3)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | GROUND_INST: instantiating (1) with all_52_9, e3, e1, e2, simplifying with
% 171.23/26.62 | (2), (3) gives:
% 171.23/26.62 | (5) all_52_9 = e3
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (4), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #952 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_4 = e3 & op(e3, e1) = e3
% 171.23/26.62 (2) all_58_4 = e2
% 171.23/26.62 (3) ~ (e3 = e2)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | ALPHA: (1) implies:
% 171.23/26.62 | (4) all_58_4 = e3
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (2), (4) imply:
% 171.23/26.62 | (5) e3 = e2
% 171.23/26.62 |
% 171.23/26.62 | SIMP: (5) implies:
% 171.23/26.62 | (6) e3 = e2
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (6) imply:
% 171.23/26.62 | (7) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (7) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #953 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (2) op(e3, e2) = e2
% 171.23/26.62 (3) op(e3, e2) = e0
% 171.23/26.62 (4) ~ (e2 = e0)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | GROUND_INST: instantiating (1) with e0, e2, e2, e3, simplifying with (2), (3)
% 171.23/26.62 | gives:
% 171.23/26.62 | (5) e2 = e0
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (4), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #954 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_54_1 = all_52_4
% 171.23/26.62 (2) all_54_1 = e1
% 171.23/26.62 (3) ~ (all_52_4 = e1)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.62 | (4) all_52_4 = e1
% 171.23/26.62 |
% 171.23/26.62 | SIMP: (4) implies:
% 171.23/26.62 | (5) all_52_4 = e1
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #955 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_54_1 = all_52_4
% 171.23/26.62 (2) all_54_1 = e2
% 171.23/26.62 (3) ~ (all_52_4 = e2)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.62 | (4) all_52_4 = e2
% 171.23/26.62 |
% 171.23/26.62 | SIMP: (4) implies:
% 171.23/26.62 | (5) all_52_4 = e2
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #956 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_54_1 = all_52_4
% 171.23/26.62 (2) all_54_1 = e3
% 171.23/26.62 (3) ~ (all_52_4 = e3)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.62 | (4) all_52_4 = e3
% 171.23/26.62 |
% 171.23/26.62 | SIMP: (4) implies:
% 171.23/26.62 | (5) all_52_4 = e3
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #957 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (2) op(e3, e3) = e2
% 171.23/26.62 (3) op(e3, e3) = e1
% 171.23/26.62 (4) ~ (e2 = e1)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | GROUND_INST: instantiating (1) with e1, e2, e3, e3, simplifying with (2), (3)
% 171.23/26.62 | gives:
% 171.23/26.62 | (5) e2 = e1
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (4), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #958 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 171.23/26.62 (2) ~ (all_10_2 = e0)
% 171.23/26.62 (3) ~ (all_10_2 = e1)
% 171.23/26.62 (4) ~ (all_10_2 = e2)
% 171.23/26.62 (5) all_54_0 = all_10_2
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | BETA: splitting (1) gives:
% 171.23/26.62 |
% 171.23/26.62 | Case 1:
% 171.23/26.62 | |
% 171.23/26.62 | | (6) all_54_0 = e2
% 171.23/26.62 | |
% 171.23/26.62 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #959.
% 171.23/26.62 | |
% 171.23/26.62 | Case 2:
% 171.23/26.62 | |
% 171.23/26.62 | | (7) all_54_0 = e1 | all_54_0 = e0
% 171.23/26.62 | |
% 171.23/26.62 | | BETA: splitting (7) gives:
% 171.23/26.62 | |
% 171.23/26.62 | | Case 1:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (8) all_54_0 = e1
% 171.23/26.62 | | |
% 171.23/26.62 | | | COMBINE_EQS: (5), (8) imply:
% 171.23/26.62 | | | (9) all_10_2 = e1
% 171.23/26.62 | | |
% 171.23/26.62 | | | SIMP: (9) implies:
% 171.23/26.62 | | | (10) all_10_2 = e1
% 171.23/26.62 | | |
% 171.23/26.62 | | | REDUCE: (3), (10) imply:
% 171.23/26.62 | | | (11) $false
% 171.23/26.62 | | |
% 171.23/26.62 | | | CLOSE: (11) is inconsistent.
% 171.23/26.62 | | |
% 171.23/26.62 | | Case 2:
% 171.23/26.62 | | |
% 171.23/26.62 | | | (12) all_54_0 = e0
% 171.23/26.62 | | |
% 171.23/26.62 | | | COMBINE_EQS: (5), (12) imply:
% 171.23/26.62 | | | (13) all_10_2 = e0
% 171.23/26.62 | | |
% 171.23/26.62 | | | SIMP: (13) implies:
% 171.23/26.62 | | | (14) all_10_2 = e0
% 171.23/26.62 | | |
% 171.23/26.62 | | | REDUCE: (2), (14) imply:
% 171.23/26.62 | | | (15) $false
% 171.23/26.62 | | |
% 171.23/26.62 | | | CLOSE: (15) is inconsistent.
% 171.23/26.62 | | |
% 171.23/26.62 | | End of split
% 171.23/26.62 | |
% 171.23/26.62 | End of split
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #959 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_54_0 = all_10_2
% 171.23/26.62 (2) all_54_0 = e2
% 171.23/26.62 (3) ~ (all_10_2 = e2)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.62 | (4) all_10_2 = e2
% 171.23/26.62 |
% 171.23/26.62 | SIMP: (4) implies:
% 171.23/26.62 | (5) all_10_2 = e2
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #960 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_14 = e3 & op(e0, e1) = e3
% 171.23/26.62 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (3) op(e0, e1) = all_52_11
% 171.23/26.62 (4) ~ (all_52_11 = e3)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | ALPHA: (1) implies:
% 171.23/26.62 | (5) op(e0, e1) = e3
% 171.23/26.62 |
% 171.23/26.62 | GROUND_INST: instantiating (2) with all_52_11, e3, e1, e0, simplifying with
% 171.23/26.62 | (3), (5) gives:
% 171.23/26.62 | (6) all_52_11 = e3
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (4), (6) imply:
% 171.23/26.62 | (7) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (7) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #961 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_8 = e3 & op(e1, e1) = e3
% 171.23/26.62 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (3) op(e1, e1) = all_6_2
% 171.23/26.62 (4) ~ (all_6_2 = e3)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | ALPHA: (1) implies:
% 171.23/26.62 | (5) op(e1, e1) = e3
% 171.23/26.62 |
% 171.23/26.62 | GROUND_INST: instantiating (2) with all_6_2, e3, e1, e1, simplifying with (3),
% 171.23/26.62 | (5) gives:
% 171.23/26.62 | (6) all_6_2 = e3
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (4), (6) imply:
% 171.23/26.62 | (7) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (7) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #962 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_58_13 = e3 & op(e0, e2) = e3
% 171.23/26.62 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.62 (3) op(e0, e2) = all_52_7
% 171.23/26.62 (4) ~ (all_52_7 = e3)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | ALPHA: (1) implies:
% 171.23/26.62 | (5) op(e0, e2) = e3
% 171.23/26.62 |
% 171.23/26.62 | GROUND_INST: instantiating (2) with all_52_7, e3, e2, e0, simplifying with
% 171.23/26.62 | (3), (5) gives:
% 171.23/26.62 | (6) all_52_7 = e3
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (4), (6) imply:
% 171.23/26.62 | (7) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (7) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #963 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_54_13 = all_52_7
% 171.23/26.62 (2) all_54_13 = e0
% 171.23/26.62 (3) ~ (all_52_7 = e0)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.62 | (4) all_52_7 = e0
% 171.23/26.62 |
% 171.23/26.62 | SIMP: (4) implies:
% 171.23/26.62 | (5) all_52_7 = e0
% 171.23/26.62 |
% 171.23/26.62 | REDUCE: (3), (5) imply:
% 171.23/26.62 | (6) $false
% 171.23/26.62 |
% 171.23/26.62 | CLOSE: (6) is inconsistent.
% 171.23/26.62 |
% 171.23/26.62 End of proof
% 171.23/26.62
% 171.23/26.62 Sub-proof #964 shows that the following formulas are inconsistent:
% 171.23/26.62 ----------------------------------------------------------------
% 171.23/26.62 (1) all_54_14 = e1 | all_54_14 = e0
% 171.23/26.62 (2) all_54_14 = all_52_11
% 171.23/26.62 (3) ~ (all_52_11 = e1)
% 171.23/26.62 (4) ~ (all_52_11 = e0)
% 171.23/26.62
% 171.23/26.62 Begin of proof
% 171.23/26.62 |
% 171.23/26.62 | BETA: splitting (1) gives:
% 171.23/26.62 |
% 171.23/26.62 | Case 1:
% 171.23/26.62 | |
% 171.23/26.62 | | (5) all_54_14 = e1
% 171.23/26.62 | |
% 171.23/26.62 | | COMBINE_EQS: (2), (5) imply:
% 171.23/26.62 | | (6) all_52_11 = e1
% 171.23/26.62 | |
% 171.23/26.62 | | SIMP: (6) implies:
% 171.23/26.62 | | (7) all_52_11 = e1
% 171.23/26.62 | |
% 171.23/26.62 | | REDUCE: (3), (7) imply:
% 171.23/26.63 | | (8) $false
% 171.23/26.63 | |
% 171.23/26.63 | | CLOSE: (8) is inconsistent.
% 171.23/26.63 | |
% 171.23/26.63 | Case 2:
% 171.23/26.63 | |
% 171.23/26.63 | | (9) all_54_14 = e0
% 171.23/26.63 | |
% 171.23/26.63 | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #965.
% 171.23/26.63 | |
% 171.23/26.63 | End of split
% 171.23/26.63 |
% 171.23/26.63 End of proof
% 171.23/26.63
% 171.23/26.63 Sub-proof #965 shows that the following formulas are inconsistent:
% 171.23/26.63 ----------------------------------------------------------------
% 171.23/26.63 (1) all_54_14 = all_52_11
% 171.23/26.63 (2) all_54_14 = e0
% 171.23/26.63 (3) ~ (all_52_11 = e0)
% 171.23/26.63
% 171.23/26.63 Begin of proof
% 171.23/26.63 |
% 171.23/26.63 | COMBINE_EQS: (1), (2) imply:
% 171.23/26.63 | (4) all_52_11 = e0
% 171.23/26.63 |
% 171.23/26.63 | SIMP: (4) implies:
% 171.23/26.63 | (5) all_52_11 = e0
% 171.23/26.63 |
% 171.23/26.63 | REDUCE: (3), (5) imply:
% 171.23/26.63 | (6) $false
% 171.23/26.63 |
% 171.23/26.63 | CLOSE: (6) is inconsistent.
% 171.23/26.63 |
% 171.23/26.63 End of proof
% 171.23/26.63
% 171.23/26.63 Sub-proof #966 shows that the following formulas are inconsistent:
% 171.23/26.63 ----------------------------------------------------------------
% 171.23/26.63 (1) all_56_6 = e0
% 171.23/26.63 (2) (all_56_6 = e3 & op(e0, e3) = e3) | (all_56_7 = e2 & op(e0, e2) = e2) |
% 171.23/26.63 (all_56_8 = e1 & op(e0, e1) = e1)
% 171.23/26.63 (3) op(e0, e2) = e1
% 171.23/26.63 (4) ~ (e3 = e0)
% 171.23/26.63 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.23/26.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.23/26.63 (6) ~ (e2 = e1)
% 171.23/26.63 (7) op(e0, e1) = e2
% 171.23/26.63
% 171.23/26.63 Begin of proof
% 171.23/26.63 |
% 171.23/26.63 | BETA: splitting (2) gives:
% 171.23/26.63 |
% 171.23/26.63 | Case 1:
% 171.23/26.63 | |
% 171.23/26.63 | | (8) all_56_6 = e3 & op(e0, e3) = e3
% 171.23/26.63 | |
% 171.23/26.63 | | ALPHA: (8) implies:
% 171.23/26.63 | | (9) all_56_6 = e3
% 171.23/26.63 | |
% 171.23/26.63 | | COMBINE_EQS: (1), (9) imply:
% 171.23/26.63 | | (10) e3 = e0
% 171.23/26.63 | |
% 171.23/26.63 | | REDUCE: (4), (10) imply:
% 171.23/26.63 | | (11) $false
% 171.23/26.63 | |
% 171.23/26.63 | | CLOSE: (11) is inconsistent.
% 171.23/26.63 | |
% 171.23/26.63 | Case 2:
% 171.23/26.63 | |
% 171.23/26.63 | | (12) (all_56_7 = e2 & op(e0, e2) = e2) | (all_56_8 = e1 & op(e0, e1) =
% 171.23/26.63 | | e1)
% 171.23/26.63 | |
% 171.23/26.63 | | BETA: splitting (12) gives:
% 171.23/26.63 | |
% 171.23/26.63 | | Case 1:
% 171.30/26.63 | | |
% 171.30/26.63 | | | (13) all_56_7 = e2 & op(e0, e2) = e2
% 171.30/26.63 | | |
% 171.30/26.63 | | | ALPHA: (13) implies:
% 171.30/26.63 | | | (14) op(e0, e2) = e2
% 171.30/26.63 | | |
% 171.30/26.63 | | | REF_CLOSE: (3), (5), (6), (14) are inconsistent by sub-proof #968.
% 171.30/26.63 | | |
% 171.30/26.63 | | Case 2:
% 171.30/26.63 | | |
% 171.30/26.63 | | | (15) all_56_8 = e1 & op(e0, e1) = e1
% 171.30/26.63 | | |
% 171.30/26.63 | | | ALPHA: (15) implies:
% 171.30/26.63 | | | (16) op(e0, e1) = e1
% 171.30/26.63 | | |
% 171.30/26.63 | | | REF_CLOSE: (5), (6), (7), (16) are inconsistent by sub-proof #967.
% 171.30/26.63 | | |
% 171.30/26.63 | | End of split
% 171.30/26.63 | |
% 171.30/26.63 | End of split
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #967 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.63 (2) op(e0, e1) = e2
% 171.30/26.63 (3) op(e0, e1) = e1
% 171.30/26.63 (4) ~ (e2 = e1)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | GROUND_INST: instantiating (1) with e2, e1, e1, e0, simplifying with (2), (3)
% 171.30/26.63 | gives:
% 171.30/26.63 | (5) e2 = e1
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (4), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #968 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.63 (2) op(e0, e2) = e2
% 171.30/26.63 (3) op(e0, e2) = e1
% 171.30/26.63 (4) ~ (e2 = e1)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | GROUND_INST: instantiating (1) with e1, e2, e2, e0, simplifying with (2), (3)
% 171.30/26.63 | gives:
% 171.30/26.63 | (5) e2 = e1
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (4), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #969 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) all_54_14 = all_52_11
% 171.30/26.63 (2) all_54_14 = e3
% 171.30/26.63 (3) ~ (all_52_11 = e3)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.63 | (4) all_52_11 = e3
% 171.30/26.63 |
% 171.30/26.63 | SIMP: (4) implies:
% 171.30/26.63 | (5) all_52_11 = e3
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (3), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #970 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) all_54_13 = all_52_7
% 171.30/26.63 (2) all_54_13 = e2
% 171.30/26.63 (3) ~ (all_52_7 = e2)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.63 | (4) all_52_7 = e2
% 171.30/26.63 |
% 171.30/26.63 | SIMP: (4) implies:
% 171.30/26.63 | (5) all_52_7 = e2
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (3), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #971 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) all_54_13 = all_52_7
% 171.30/26.63 (2) all_54_13 = e3
% 171.30/26.63 (3) ~ (all_52_7 = e3)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.63 | (4) all_52_7 = e3
% 171.30/26.63 |
% 171.30/26.63 | SIMP: (4) implies:
% 171.30/26.63 | (5) all_52_7 = e3
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (3), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #972 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) ~ (all_8_2 = e3)
% 171.30/26.63 (2) op(e2, e2) = all_8_2
% 171.30/26.63 (3) ~ (all_52_4 = e3)
% 171.30/26.63 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.63 (5) op(e3, e2) = all_52_4
% 171.30/26.63 (6) (all_58_1 = e3 & op(e3, e2) = e3) | (all_58_3 = e3 & op(e2, e2) = e3)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | BETA: splitting (6) gives:
% 171.30/26.63 |
% 171.30/26.63 | Case 1:
% 171.30/26.63 | |
% 171.30/26.63 | | (7) all_58_1 = e3 & op(e3, e2) = e3
% 171.30/26.63 | |
% 171.30/26.63 | | ALPHA: (7) implies:
% 171.30/26.63 | | (8) op(e3, e2) = e3
% 171.30/26.63 | |
% 171.30/26.63 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #974.
% 171.30/26.63 | |
% 171.30/26.63 | Case 2:
% 171.30/26.63 | |
% 171.30/26.63 | | (9) all_58_3 = e3 & op(e2, e2) = e3
% 171.30/26.63 | |
% 171.30/26.63 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #973.
% 171.30/26.63 | |
% 171.30/26.63 | End of split
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #973 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) all_58_3 = e3 & op(e2, e2) = e3
% 171.30/26.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.63 (3) op(e2, e2) = all_8_2
% 171.30/26.63 (4) ~ (all_8_2 = e3)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | ALPHA: (1) implies:
% 171.30/26.63 | (5) op(e2, e2) = e3
% 171.30/26.63 |
% 171.30/26.63 | GROUND_INST: instantiating (2) with all_8_2, e3, e2, e2, simplifying with (3),
% 171.30/26.63 | (5) gives:
% 171.30/26.63 | (6) all_8_2 = e3
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (4), (6) imply:
% 171.30/26.63 | (7) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (7) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #974 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.63 (2) op(e3, e2) = all_52_4
% 171.30/26.63 (3) op(e3, e2) = e3
% 171.30/26.63 (4) ~ (all_52_4 = e3)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | GROUND_INST: instantiating (1) with all_52_4, e3, e2, e3, simplifying with
% 171.30/26.63 | (2), (3) gives:
% 171.30/26.63 | (5) all_52_4 = e3
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (4), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #975 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.63 (2) op(e3, e1) = all_52_8
% 171.30/26.63 (3) op(e3, e1) = e3
% 171.30/26.63 (4) ~ (all_52_8 = e3)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | GROUND_INST: instantiating (1) with all_52_8, e3, e1, e3, simplifying with
% 171.30/26.63 | (2), (3) gives:
% 171.30/26.63 | (5) all_52_8 = e3
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (4), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #976 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) ~ (all_6_2 = e1)
% 171.30/26.63 (2) ~ (all_56_14 = e0) | (all_56_13 = e1 & op(e1, e0) = e1)
% 171.30/26.63 (3) ~ (all_6_2 = e3)
% 171.30/26.63 (4) all_54_10 = all_6_2
% 171.30/26.63 (5) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 171.30/26.63 (6) all_56_14 = all_6_2
% 171.30/26.63 (7) ~ (e1 = e0)
% 171.30/26.63 (8) ~ (all_6_2 = e2)
% 171.30/26.63 (9) all_56_13 = e0
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | BETA: splitting (2) gives:
% 171.30/26.63 |
% 171.30/26.63 | Case 1:
% 171.30/26.63 | |
% 171.30/26.63 | | (10) ~ (all_56_14 = e0)
% 171.30/26.63 | |
% 171.30/26.63 | | REDUCE: (6), (10) imply:
% 171.30/26.63 | | (11) ~ (all_6_2 = e0)
% 171.30/26.63 | |
% 171.30/26.63 | | REF_CLOSE: (1), (3), (4), (5), (8), (11) are inconsistent by sub-proof #978.
% 171.30/26.63 | |
% 171.30/26.63 | Case 2:
% 171.30/26.63 | |
% 171.30/26.63 | | (12) all_56_13 = e1 & op(e1, e0) = e1
% 171.30/26.63 | |
% 171.30/26.63 | | ALPHA: (12) implies:
% 171.30/26.63 | | (13) all_56_13 = e1
% 171.30/26.63 | |
% 171.30/26.63 | | REF_CLOSE: (7), (9), (13) are inconsistent by sub-proof #977.
% 171.30/26.63 | |
% 171.30/26.63 | End of split
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #977 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) all_56_13 = e1
% 171.30/26.63 (2) all_56_13 = e0
% 171.30/26.63 (3) ~ (e1 = e0)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.63 | (4) e1 = e0
% 171.30/26.63 |
% 171.30/26.63 | SIMP: (4) implies:
% 171.30/26.63 | (5) e1 = e0
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (3), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #978 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) ~ (all_6_2 = e1)
% 171.30/26.63 (2) ~ (all_6_2 = e3)
% 171.30/26.63 (3) all_54_10 = all_6_2
% 171.30/26.63 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 171.30/26.63 (5) ~ (all_6_2 = e2)
% 171.30/26.63 (6) ~ (all_6_2 = e0)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | BETA: splitting (4) gives:
% 171.30/26.63 |
% 171.30/26.63 | Case 1:
% 171.30/26.63 | |
% 171.30/26.63 | | (7) all_54_10 = e3
% 171.30/26.63 | |
% 171.30/26.63 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #982.
% 171.30/26.63 | |
% 171.30/26.63 | Case 2:
% 171.30/26.63 | |
% 171.30/26.63 | | (8) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 171.30/26.63 | |
% 171.30/26.63 | | BETA: splitting (8) gives:
% 171.30/26.63 | |
% 171.30/26.63 | | Case 1:
% 171.30/26.63 | | |
% 171.30/26.63 | | | (9) all_54_10 = e2
% 171.30/26.63 | | |
% 171.30/26.63 | | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #981.
% 171.30/26.63 | | |
% 171.30/26.63 | | Case 2:
% 171.30/26.63 | | |
% 171.30/26.63 | | | (10) all_54_10 = e1 | all_54_10 = e0
% 171.30/26.63 | | |
% 171.30/26.63 | | | BETA: splitting (10) gives:
% 171.30/26.63 | | |
% 171.30/26.63 | | | Case 1:
% 171.30/26.63 | | | |
% 171.30/26.63 | | | | (11) all_54_10 = e1
% 171.30/26.63 | | | |
% 171.30/26.63 | | | | REF_CLOSE: (1), (3), (11) are inconsistent by sub-proof #980.
% 171.30/26.63 | | | |
% 171.30/26.63 | | | Case 2:
% 171.30/26.63 | | | |
% 171.30/26.63 | | | | (12) all_54_10 = e0
% 171.30/26.63 | | | |
% 171.30/26.63 | | | | REF_CLOSE: (3), (6), (12) are inconsistent by sub-proof #979.
% 171.30/26.63 | | | |
% 171.30/26.63 | | | End of split
% 171.30/26.63 | | |
% 171.30/26.63 | | End of split
% 171.30/26.63 | |
% 171.30/26.63 | End of split
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #979 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) all_54_10 = all_6_2
% 171.30/26.63 (2) all_54_10 = e0
% 171.30/26.63 (3) ~ (all_6_2 = e0)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.63 | (4) all_6_2 = e0
% 171.30/26.63 |
% 171.30/26.63 | SIMP: (4) implies:
% 171.30/26.63 | (5) all_6_2 = e0
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (3), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #980 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) all_54_10 = all_6_2
% 171.30/26.63 (2) all_54_10 = e1
% 171.30/26.63 (3) ~ (all_6_2 = e1)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.63 | (4) all_6_2 = e1
% 171.30/26.63 |
% 171.30/26.63 | SIMP: (4) implies:
% 171.30/26.63 | (5) all_6_2 = e1
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (3), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #981 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) all_54_10 = all_6_2
% 171.30/26.63 (2) all_54_10 = e2
% 171.30/26.63 (3) ~ (all_6_2 = e2)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.63 | (4) all_6_2 = e2
% 171.30/26.63 |
% 171.30/26.63 | SIMP: (4) implies:
% 171.30/26.63 | (5) all_6_2 = e2
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (3), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #982 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) all_54_10 = all_6_2
% 171.30/26.63 (2) all_54_10 = e3
% 171.30/26.63 (3) ~ (all_6_2 = e3)
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.63 | (4) all_6_2 = e3
% 171.30/26.63 |
% 171.30/26.63 | SIMP: (4) implies:
% 171.30/26.63 | (5) all_6_2 = e3
% 171.30/26.63 |
% 171.30/26.63 | REDUCE: (3), (5) imply:
% 171.30/26.63 | (6) $false
% 171.30/26.63 |
% 171.30/26.63 | CLOSE: (6) is inconsistent.
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #983 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) (all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~ (all_56_10 =
% 171.30/26.63 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 171.30/26.63 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 171.30/26.63 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 171.30/26.63 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_9 = e0 & ~
% 171.30/26.63 (all_56_10 = e3) & op(e3, e0) = e0 & ( ~ (all_56_12 = e3) | ( ~
% 171.30/26.63 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 171.30/26.63 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 171.30/26.63 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 171.30/26.63 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 171.30/26.63 (2) all_56_12 = e2
% 171.30/26.63 (3) all_56_10 = e3
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | BETA: splitting (1) gives:
% 171.30/26.63 |
% 171.30/26.63 | Case 1:
% 171.30/26.63 | |
% 171.30/26.63 | | (4) all_56_5 = e1 & ~ (all_56_12 = e2) & op(e2, e1) = e1 & ( ~
% 171.30/26.63 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 171.30/26.63 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 171.30/26.63 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 171.30/26.63 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 171.30/26.63 | |
% 171.30/26.63 | | ALPHA: (4) implies:
% 171.30/26.63 | | (5) ~ (all_56_12 = e2)
% 171.30/26.63 | |
% 171.30/26.63 | | REDUCE: (2), (5) imply:
% 171.30/26.63 | | (6) $false
% 171.30/26.63 | |
% 171.30/26.63 | | CLOSE: (6) is inconsistent.
% 171.30/26.63 | |
% 171.30/26.63 | Case 2:
% 171.30/26.63 | |
% 171.30/26.63 | | (7) all_56_9 = e0 & ~ (all_56_10 = e3) & op(e3, e0) = e0 & ( ~
% 171.30/26.63 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 171.30/26.63 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 171.30/26.63 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 171.30/26.63 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 171.30/26.63 | |
% 171.30/26.63 | | ALPHA: (7) implies:
% 171.30/26.63 | | (8) ~ (all_56_10 = e3)
% 171.30/26.63 | |
% 171.30/26.63 | | REDUCE: (3), (8) imply:
% 171.30/26.63 | | (9) $false
% 171.30/26.63 | |
% 171.30/26.63 | | CLOSE: (9) is inconsistent.
% 171.30/26.63 | |
% 171.30/26.63 | End of split
% 171.30/26.63 |
% 171.30/26.63 End of proof
% 171.30/26.63
% 171.30/26.63 Sub-proof #984 shows that the following formulas are inconsistent:
% 171.30/26.63 ----------------------------------------------------------------
% 171.30/26.63 (1) ~ (all_52_1 = e3)
% 171.30/26.63 (2) op(e1, e3) = all_52_2
% 171.30/26.63 (3) op(e1, e2) = all_52_6
% 171.30/26.63 (4) op(e2, e3) = all_52_1
% 171.30/26.63 (5) ~ (all_52_6 = e2)
% 171.30/26.63 (6) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 171.30/26.63 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 171.30/26.63 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 171.30/26.63 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 171.30/26.63 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 171.30/26.63 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 171.30/26.63 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 171.30/26.63 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 171.30/26.63 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 171.30/26.63 op(e0, e3) = all_56_6 & $i(all_56_6)))) | (all_56_2 = e3 & ~
% 171.30/26.63 (all_56_14 = e1) & op(e1, e3) = e3 & ( ~ (all_56_10 = e1) | ( ~
% 171.30/26.63 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 171.30/26.63 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 171.30/26.63 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 171.30/26.63 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_3 = e2 & ~
% 171.30/26.63 (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 = e1) | ( ~
% 171.30/26.63 (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4))) & ( ~
% 171.30/26.63 (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 171.30/26.63 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 171.30/26.63 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 171.30/26.63 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 171.30/26.63 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 171.30/26.63 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 171.30/26.63 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 171.30/26.63 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 171.30/26.63 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.63 (8) ~ (all_52_2 = e3)
% 171.30/26.63 (9) all_56_10 = e3
% 171.30/26.63
% 171.30/26.63 Begin of proof
% 171.30/26.63 |
% 171.30/26.63 | BETA: splitting (6) gives:
% 171.30/26.63 |
% 171.30/26.63 | Case 1:
% 171.30/26.63 | |
% 171.30/26.63 | | (10) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 171.30/26.63 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 171.30/26.63 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 171.30/26.63 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2)
% 171.30/26.63 | | | ( ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7))))
% 171.30/26.63 | | | (all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 171.30/26.63 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 171.30/26.63 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 171.30/26.63 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 171.30/26.63 | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 171.30/26.63 | |
% 171.30/26.63 | | REF_CLOSE: (1), (4), (7), (9), (10) are inconsistent by sub-proof #988.
% 171.30/26.63 | |
% 171.30/26.63 | Case 2:
% 171.30/26.63 | |
% 171.30/26.64 | | (11) (all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 171.30/26.64 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 171.30/26.64 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 171.30/26.64 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 171.30/26.64 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8))))
% 171.30/26.64 | | | (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 171.30/26.64 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 171.30/26.64 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 171.30/26.64 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 171.30/26.64 | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8))))
% 171.30/26.64 | | | (all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 171.30/26.64 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 171.30/26.64 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 171.30/26.64 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3)
% 171.30/26.64 | | | ( ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 171.30/26.64 | |
% 171.30/26.64 | | BETA: splitting (11) gives:
% 171.30/26.64 | |
% 171.30/26.64 | | Case 1:
% 171.30/26.64 | | |
% 171.30/26.64 | | | (12) all_56_2 = e3 & ~ (all_56_14 = e1) & op(e1, e3) = e3 & ( ~
% 171.30/26.64 | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 171.30/26.64 | | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 171.30/26.64 | | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1)
% 171.30/26.64 | | | | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 171.30/26.64 | | |
% 171.30/26.64 | | | ALPHA: (12) implies:
% 171.30/26.64 | | | (13) op(e1, e3) = e3
% 171.30/26.64 | | |
% 171.30/26.64 | | | REF_CLOSE: (2), (7), (8), (13) are inconsistent by sub-proof #987.
% 171.30/26.64 | | |
% 171.30/26.64 | | Case 2:
% 171.30/26.64 | | |
% 171.30/26.64 | | | (14) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 171.30/26.64 | | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4
% 171.30/26.64 | | | & $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 =
% 171.30/26.64 | | | e2) & op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~
% 171.30/26.64 | | | (all_56_15 = e1) | ( ~ (all_56_8 = e0) & op(e0, e1) = all_56_8
% 171.30/26.64 | | | & $i(all_56_8)))) | (all_56_4 = e1 & ~ (all_56_10 = e3) &
% 171.30/26.64 | | | op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~ (all_56_0 = e2) &
% 171.30/26.64 | | | op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~ (all_56_14 =
% 171.30/26.64 | | | e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 171.30/26.64 | | | $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0)
% 171.30/26.64 | | | & op(e0, e3) = all_56_6 & $i(all_56_6))))
% 171.30/26.64 | | |
% 171.30/26.64 | | | REF_CLOSE: (3), (5), (7), (9), (14) are inconsistent by sub-proof #985.
% 171.30/26.64 | | |
% 171.30/26.64 | | End of split
% 171.30/26.64 | |
% 171.30/26.64 | End of split
% 171.30/26.64 |
% 171.30/26.64 End of proof
% 171.30/26.64
% 171.30/26.64 Sub-proof #985 shows that the following formulas are inconsistent:
% 171.30/26.64 ----------------------------------------------------------------
% 171.30/26.64 (1) (all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~ (all_56_10 =
% 171.30/26.64 e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 & $i(all_56_4)))
% 171.30/26.64 & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) & op(e2, e1) = all_56_5 &
% 171.30/26.64 $i(all_56_5))) & ( ~ (all_56_15 = e1) | ( ~ (all_56_8 = e0) &
% 171.30/26.64 op(e0, e1) = all_56_8 & $i(all_56_8)))) | (all_56_4 = e1 & ~
% 171.30/26.64 (all_56_10 = e3) & op(e3, e1) = e1 & ( ~ (all_56_12 = e3) | ( ~
% 171.30/26.64 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 171.30/26.64 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 171.30/26.64 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 171.30/26.64 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 171.30/26.64 (2) op(e1, e2) = all_52_6
% 171.30/26.64 (3) ~ (all_52_6 = e2)
% 171.30/26.64 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.64 (5) all_56_10 = e3
% 171.30/26.64
% 171.30/26.64 Begin of proof
% 171.30/26.64 |
% 171.30/26.64 | BETA: splitting (1) gives:
% 171.30/26.64 |
% 171.30/26.64 | Case 1:
% 171.30/26.64 | |
% 171.30/26.64 | | (6) all_56_3 = e2 & ~ (all_56_14 = e1) & op(e1, e2) = e2 & ( ~
% 171.30/26.64 | | (all_56_10 = e1) | ( ~ (all_56_4 = e3) & op(e3, e1) = all_56_4 &
% 171.30/26.64 | | $i(all_56_4))) & ( ~ (all_56_12 = e1) | ( ~ (all_56_5 = e2) &
% 171.30/26.64 | | op(e2, e1) = all_56_5 & $i(all_56_5))) & ( ~ (all_56_15 = e1) | (
% 171.30/26.64 | | ~ (all_56_8 = e0) & op(e0, e1) = all_56_8 & $i(all_56_8)))
% 171.30/26.64 | |
% 171.30/26.64 | | ALPHA: (6) implies:
% 171.30/26.64 | | (7) op(e1, e2) = e2
% 171.30/26.64 | |
% 171.30/26.64 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #986.
% 171.30/26.64 | |
% 171.30/26.64 | Case 2:
% 171.30/26.64 | |
% 171.30/26.64 | | (8) all_56_4 = e1 & ~ (all_56_10 = e3) & op(e3, e1) = e1 & ( ~
% 171.30/26.64 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 171.30/26.64 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 171.30/26.64 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 171.30/26.64 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 171.30/26.64 | |
% 171.30/26.64 | | ALPHA: (8) implies:
% 171.30/26.64 | | (9) ~ (all_56_10 = e3)
% 171.30/26.64 | |
% 171.30/26.64 | | REDUCE: (5), (9) imply:
% 171.30/26.64 | | (10) $false
% 171.30/26.64 | |
% 171.30/26.64 | | CLOSE: (10) is inconsistent.
% 171.30/26.64 | |
% 171.30/26.64 | End of split
% 171.30/26.64 |
% 171.30/26.64 End of proof
% 171.30/26.64
% 171.30/26.64 Sub-proof #986 shows that the following formulas are inconsistent:
% 171.30/26.64 ----------------------------------------------------------------
% 171.30/26.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.64 (2) op(e1, e2) = all_52_6
% 171.30/26.64 (3) op(e1, e2) = e2
% 171.30/26.64 (4) ~ (all_52_6 = e2)
% 171.30/26.64
% 171.30/26.64 Begin of proof
% 171.30/26.64 |
% 171.30/26.64 | GROUND_INST: instantiating (1) with all_52_6, e2, e2, e1, simplifying with
% 171.30/26.64 | (2), (3) gives:
% 171.30/26.64 | (5) all_52_6 = e2
% 171.30/26.64 |
% 171.30/26.64 | REDUCE: (4), (5) imply:
% 171.30/26.64 | (6) $false
% 171.30/26.64 |
% 171.30/26.64 | CLOSE: (6) is inconsistent.
% 171.30/26.64 |
% 171.30/26.64 End of proof
% 171.30/26.64
% 171.30/26.64 Sub-proof #987 shows that the following formulas are inconsistent:
% 171.30/26.64 ----------------------------------------------------------------
% 171.30/26.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.64 (2) op(e1, e3) = all_52_2
% 171.30/26.64 (3) op(e1, e3) = e3
% 171.30/26.64 (4) ~ (all_52_2 = e3)
% 171.30/26.64
% 171.30/26.64 Begin of proof
% 171.30/26.64 |
% 171.30/26.64 | GROUND_INST: instantiating (1) with all_52_2, e3, e3, e1, simplifying with
% 171.30/26.64 | (2), (3) gives:
% 171.30/26.64 | (5) all_52_2 = e3
% 171.30/26.64 |
% 171.30/26.64 | REDUCE: (4), (5) imply:
% 171.30/26.64 | (6) $false
% 171.30/26.64 |
% 171.30/26.64 | CLOSE: (6) is inconsistent.
% 171.30/26.64 |
% 171.30/26.64 End of proof
% 171.30/26.64
% 171.30/26.64 Sub-proof #988 shows that the following formulas are inconsistent:
% 171.30/26.64 ----------------------------------------------------------------
% 171.30/26.64 (1) ~ (all_52_1 = e3)
% 171.30/26.64 (2) op(e2, e3) = all_52_1
% 171.30/26.64 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.64 (4) (all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~ (all_56_10 =
% 171.30/26.64 e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 & $i(all_56_1)))
% 171.30/26.64 & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) & op(e1, e2) = all_56_3 &
% 171.30/26.64 $i(all_56_3))) & ( ~ (all_56_15 = e2) | ( ~ (all_56_7 = e0) &
% 171.30/26.64 op(e0, e2) = all_56_7 & $i(all_56_7)))) | (all_56_1 = e2 & ~
% 171.30/26.64 (all_56_10 = e3) & op(e3, e2) = e2 & ( ~ (all_56_12 = e3) | ( ~
% 171.30/26.64 (all_56_0 = e2) & op(e2, e3) = all_56_0 & $i(all_56_0))) & ( ~
% 171.30/26.64 (all_56_14 = e3) | ( ~ (all_56_2 = e1) & op(e1, e3) = all_56_2 &
% 171.30/26.64 $i(all_56_2))) & ( ~ (all_56_15 = e3) | ( ~ (all_56_6 = e0) &
% 171.30/26.64 op(e0, e3) = all_56_6 & $i(all_56_6))))
% 171.30/26.64 (5) all_56_10 = e3
% 171.30/26.64
% 171.30/26.64 Begin of proof
% 171.30/26.64 |
% 171.30/26.64 | BETA: splitting (4) gives:
% 171.30/26.64 |
% 171.30/26.64 | Case 1:
% 171.30/26.64 | |
% 171.30/26.64 | | (6) all_56_0 = e3 & ~ (all_56_12 = e2) & op(e2, e3) = e3 & ( ~
% 171.30/26.64 | | (all_56_10 = e2) | ( ~ (all_56_1 = e3) & op(e3, e2) = all_56_1 &
% 171.30/26.64 | | $i(all_56_1))) & ( ~ (all_56_14 = e2) | ( ~ (all_56_3 = e1) &
% 171.30/26.64 | | op(e1, e2) = all_56_3 & $i(all_56_3))) & ( ~ (all_56_15 = e2) | (
% 171.30/26.64 | | ~ (all_56_7 = e0) & op(e0, e2) = all_56_7 & $i(all_56_7)))
% 171.30/26.64 | |
% 171.30/26.64 | | ALPHA: (6) implies:
% 171.30/26.64 | | (7) op(e2, e3) = e3
% 171.30/26.64 | |
% 171.30/26.64 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #989.
% 171.30/26.64 | |
% 171.30/26.64 | Case 2:
% 171.30/26.64 | |
% 171.30/26.64 | | (8) all_56_1 = e2 & ~ (all_56_10 = e3) & op(e3, e2) = e2 & ( ~
% 171.30/26.64 | | (all_56_12 = e3) | ( ~ (all_56_0 = e2) & op(e2, e3) = all_56_0 &
% 171.30/26.64 | | $i(all_56_0))) & ( ~ (all_56_14 = e3) | ( ~ (all_56_2 = e1) &
% 171.30/26.64 | | op(e1, e3) = all_56_2 & $i(all_56_2))) & ( ~ (all_56_15 = e3) | (
% 171.30/26.64 | | ~ (all_56_6 = e0) & op(e0, e3) = all_56_6 & $i(all_56_6)))
% 171.30/26.64 | |
% 171.30/26.64 | | ALPHA: (8) implies:
% 171.30/26.64 | | (9) ~ (all_56_10 = e3)
% 171.30/26.64 | |
% 171.30/26.64 | | REDUCE: (5), (9) imply:
% 171.30/26.64 | | (10) $false
% 171.30/26.64 | |
% 171.30/26.64 | | CLOSE: (10) is inconsistent.
% 171.30/26.64 | |
% 171.30/26.64 | End of split
% 171.30/26.64 |
% 171.30/26.64 End of proof
% 171.30/26.64
% 171.30/26.64 Sub-proof #989 shows that the following formulas are inconsistent:
% 171.30/26.64 ----------------------------------------------------------------
% 171.30/26.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.64 (2) op(e2, e3) = all_52_1
% 171.30/26.64 (3) op(e2, e3) = e3
% 171.30/26.64 (4) ~ (all_52_1 = e3)
% 171.30/26.64
% 171.30/26.64 Begin of proof
% 171.30/26.64 |
% 171.30/26.64 | GROUND_INST: instantiating (1) with all_52_1, e3, e3, e2, simplifying with
% 171.30/26.64 | (2), (3) gives:
% 171.30/26.64 | (5) all_52_1 = e3
% 171.30/26.64 |
% 171.30/26.64 | REDUCE: (4), (5) imply:
% 171.30/26.64 | (6) $false
% 171.30/26.64 |
% 171.30/26.64 | CLOSE: (6) is inconsistent.
% 171.30/26.64 |
% 171.30/26.64 End of proof
% 171.30/26.64
% 171.30/26.64 Sub-proof #990 shows that the following formulas are inconsistent:
% 171.30/26.64 ----------------------------------------------------------------
% 171.30/26.64 (1) all_54_15 = all_4_2
% 171.30/26.64 (2) all_54_15 = e1
% 171.30/26.64 (3) ~ (all_4_2 = e1)
% 171.30/26.64
% 171.30/26.64 Begin of proof
% 171.30/26.64 |
% 171.30/26.64 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.64 | (4) all_4_2 = e1
% 171.30/26.64 |
% 171.30/26.64 | SIMP: (4) implies:
% 171.30/26.64 | (5) all_4_2 = e1
% 171.30/26.64 |
% 171.30/26.64 | REDUCE: (3), (5) imply:
% 171.30/26.64 | (6) $false
% 171.30/26.64 |
% 171.30/26.64 | CLOSE: (6) is inconsistent.
% 171.30/26.64 |
% 171.30/26.64 End of proof
% 171.30/26.64
% 171.30/26.64 Sub-proof #991 shows that the following formulas are inconsistent:
% 171.30/26.64 ----------------------------------------------------------------
% 171.30/26.64 (1) all_54_15 = all_4_2
% 171.30/26.64 (2) all_54_15 = e2
% 171.30/26.64 (3) ~ (all_4_2 = e2)
% 171.30/26.64
% 171.30/26.64 Begin of proof
% 171.30/26.64 |
% 171.30/26.64 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.64 | (4) all_4_2 = e2
% 171.30/26.64 |
% 171.30/26.64 | SIMP: (4) implies:
% 171.30/26.64 | (5) all_4_2 = e2
% 171.30/26.64 |
% 171.30/26.64 | REDUCE: (3), (5) imply:
% 171.30/26.64 | (6) $false
% 171.30/26.64 |
% 171.30/26.64 | CLOSE: (6) is inconsistent.
% 171.30/26.64 |
% 171.30/26.64 End of proof
% 171.30/26.64
% 171.30/26.64 Sub-proof #992 shows that the following formulas are inconsistent:
% 171.30/26.64 ----------------------------------------------------------------
% 171.30/26.64 (1) all_54_15 = all_4_2
% 171.30/26.64 (2) all_54_15 = e3
% 171.30/26.64 (3) ~ (all_4_2 = e3)
% 171.30/26.64
% 171.30/26.64 Begin of proof
% 171.30/26.64 |
% 171.30/26.64 | COMBINE_EQS: (1), (2) imply:
% 171.30/26.64 | (4) all_4_2 = e3
% 171.30/26.64 |
% 171.30/26.64 | SIMP: (4) implies:
% 171.30/26.64 | (5) all_4_2 = e3
% 171.30/26.64 |
% 171.30/26.64 | REDUCE: (3), (5) imply:
% 171.30/26.64 | (6) $false
% 171.30/26.64 |
% 171.30/26.64 | CLOSE: (6) is inconsistent.
% 171.30/26.64 |
% 171.30/26.64 End of proof
% 171.30/26.64
% 171.30/26.64 Sub-proof #993 shows that the following formulas are inconsistent:
% 171.30/26.64 ----------------------------------------------------------------
% 171.30/26.64 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 171.30/26.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 171.30/26.64 (2) op(e3, e2) = all_52_4
% 171.30/26.64 (3) op(e3, e2) = e2
% 171.30/26.64 (4) ~ (all_52_4 = e2)
% 171.30/26.64
% 171.30/26.64 Begin of proof
% 171.30/26.64 |
% 171.30/26.64 | GROUND_INST: instantiating (1) with all_52_4, e2, e2, e3, simplifying with
% 171.30/26.64 | (2), (3) gives:
% 171.30/26.64 | (5) all_52_4 = e2
% 171.30/26.64 |
% 171.30/26.64 | REDUCE: (4), (5) imply:
% 171.30/26.64 | (6) $false
% 171.30/26.64 |
% 171.30/26.64 | CLOSE: (6) is inconsistent.
% 171.30/26.64 |
% 171.30/26.64 End of proof
% 171.30/26.64 % SZS output end Proof for theBenchmark
% 171.30/26.64
% 171.30/26.64 26153ms
%------------------------------------------------------------------------------